Author name code: rempel ADS astronomy entries on 2022-09-14 author:"Rempel, Matthias" ------------------------------------------------------------------------ Title: Chromospheric extension of the MURaM code Authors: Przybylski, D.; Cameron, R.; Solanki, S. K.; Rempel, M.; Leenaarts, J.; Anusha, L. S.; Witzke, V.; Shapiro, A. I. Bibcode: 2022A&A...664A..91P Altcode: 2022arXiv220403126P Context. Detailed numerical models of the chromosphere and corona are required to understand the heating of the solar atmosphere. An accurate treatment of the solar chromosphere is complicated by the effects arising from non-local thermodynamic equilibrium (NLTE) radiative transfer. A small number of strong, highly scattering lines dominate the cooling and heating in the chromosphere. Additionally, the recombination times of ionised hydrogen are longer than the dynamical timescales, requiring a non-equilibrium (NE) treatment of hydrogen ionisation.
Aims: We describe a set of necessary additions to the MURaM code that allow it to handle some of the important NLTE effects. We investigate the impact on solar chromosphere models caused by NLTE and NE effects in radiation magnetohydrodynamic simulations of the solar atmosphere.
Methods: The MURaM code was extended to include the physical process required for an accurate simulation of the solar chromosphere, as implemented in the Bifrost code. This includes a time-dependent treatment of hydrogen ionisation, a scattering multi-group radiation transfer scheme, and approximations for NLTE radiative cooling.
Results: The inclusion of NE and NLTE physics has a large impact on the structure of the chromosphere; the NE treatment of hydrogen ionisation leads to a higher ionisation fraction and enhanced populations in the first excited state throughout cold inter-shock regions of the chromosphere. Additionally, this prevents hydrogen ionisation from buffering energy fluctuations, leading to hotter shocks and cooler inter-shock regions. The hydrogen populations in the ground and first excited state are enhanced by 102-103 in the upper chromosphere and by up to 109 near the transition region.
Conclusions: Including the necessary NLTE physics leads to significant differences in chromospheric structure and dynamics. The thermodynamics and hydrogen populations calculated using the extended version of the MURaM code are consistent with previous non-equilibrium simulations. The electron number and temperature calculated using the non-equilibrium treatment of the chromosphere are required to accurately synthesise chromospheric spectral lines.

Movies associated to Fig. 2 are only available at https://www.aanda.org Title: Rapid Blue- and Red-shifted Excursions in H$\alpha$ line profiles synthesized from realistic 3D MHD simulations Authors: Danilovic, S.; Bjørgen, J. P.; Leenaarts, J.; Rempel, M. Bibcode: 2022arXiv220813749D Altcode: Rapid blue- and red-shifted events (RBEs/RREs) may have an important role in mass-loading and heating the solar corona, but their nature and origin are still debatable. We aim to model these features to learn more about their properties, formation and origin. A realistic three-dimensional (3D) magneto-hydrodynamic (MHD) model of a solar plage region is created. Synthetic H$\alpha$ spectra are generated and the spectral signatures of these features are identified. The magnetic field lines associated with these events are traced and the underlying dynamic is studied. The model reproduces well many properties of RBEs and RREs, such as spatial distribution, lateral movement, length and lifetimes. Synthetic H$\alpha$ line profiles, similarly to observed ones, show strong blue- or red-shift and asymmetries. These line profiles are caused by the vertical component of velocity with magnitudes larger than $30-40$ km/s that appear mostly in the height range of $2-4$ Mm. By tracing magnetic field lines, we show that the vertical velocity that causes the appearance of RBE/RREs to appear is always associated with the component of velocity perpendicular to the magnetic field line. The study confirms the hypothesis that RBEs and RREs are signs of Alfv{é}nic waves with, in some cases, a significant contribution from slow magneto-acoustic mode. Title: Effects of spectral resolution on simple magnetic field diagnostics of the Mg II h & k lines Authors: Centeno, Rebecca; Rempel, Matthias; Casini, Roberto; del Pino Aleman, Tanausu Bibcode: 2022arXiv220807507C Altcode: We study the effects of finite spectral resolution on the magnetic field values retrieved through the weak field approximation (WFA) from the cores of the Mg II h & k lines. The retrieval of the line-of-sight (LOS) component of the magnetic field, $B_{\rm LOS}$, from synthetic spectra generated in a uniformly magnetized FAL-C atmosphere are accurate when restricted to the inner lobes of Stokes V. As we degrade the spectral resolution, partial redistribution (PRD) effects, that more prominently affect the outer lobes of Stokes V, are brought into the line core through spectral smearing, degrading the accuracy of the WFA and resulting in an inference bias, which is more pronounced the poorer the resolution. When applied to a diverse set of spectra emerging from a sunspot simulation, we find a good accuracy in the retrieved $B_{\rm LOS}$ when comparing it to the model value at the height where the optical depth in the line core is unity. The accuracy is preserved up to field strengths of B~1500 G. Limited spectral resolution results in a small bias toward weaker retrieved fields. The WFA for the transverse component of the magnetic field is also evaluated. Reduced spectral resolution degrades the accuracy of the inferences because spectral mixing results in the line effectively probing deeper layers of the atmosphere. Title: Derivation of Boundary Conditions for Data-Driven Simulations of Active Regions and their Emission Authors: Tremblay, Benoit; Malanushenko, Anna; Rempel, Matthias; Kazachenko, Maria Bibcode: 2022cosp...44.2472T Altcode: Coronal heating remains a major area of research in solar physics. In particular, the spatial dimensions and the structuring of heating processes have yet to be fully understood. Whereas observations suggest that plasma is heated in bundles of thin flux tubes, it's been theorized from simulations that emission in active regions can be structured in larger flux tubes with irregular boundaries. In the latter case, the emission can appear like the emission from loop bundles, with variations of the column depth at their boundaries causing an impression of individual loops. These scenarios have distinct implications for coronal heating and the study of coronal loops and thus need to be confirmed observationally. Our objective is to develop insight into the spatial properties of solar coronal heating using a statistical analysis of the emission from observed and simulated active regions. To this end, we perform data-driven MHD simulations of active regions. The MURaM simulation is being modified to work with photospheric inputs as boundary conditions, including observed vector magnetograms, and electric field maps and flow maps inferred from observations. We focus on electric field maps derived using the PDFI\_SS inversion technique and flow maps derived through supervised deep learning. More specifically, we train a convolutional neural network to emulate the MURaM simulation and infer MURaM-like flows from observational data, including large-scale flows in the granulation surrounding active regions. We present derivations of boundary conditions (i.e., electric field maps, flows maps) from SDO/HMI observations of selected active regions, and discuss the limitations and challenges associated with the methods. We detail ongoing efforts in driving the MURaM simulation from derived boundary conditions. Finally, we illustrate how these data-driven simulations will be used to study the structuring of the emission of active regions statistically and identify which scenario of coronal heating best matches observations. Title: Predicted appearance of Magnetic Flux Rope and Sheared Magnetic Arcade Structures before a Coronal Mass Ejection via three-dimensional radiative Magnetohydrodynamic Modeling Authors: Chintzoglou, Georgios; Cheung, Mark; Rempel, Matthias Bibcode: 2022cosp...44.2406C Altcode: Magnetic Flux Ropes (MFRs) are free-energy-carrying, three-dimensional magnetized plasma structures characterized by twisted magnetic field lines and are widely considered the core structure of Coronal Mass Ejections (CMEs) propagating in the interplanetary space. The way MFRs form remains unclear as different theories predict that either MFRs form during the initiation of the CME or pre-exist the onset of the CME. The term "pre-existing structure" is synonymous with "filament channels." On the one hand, the theories predicting on-the-fly MFR formation require Sheared Magnetic Arcades (SMAs; low twist but stressed magnetic structures) for the filament channel/pre-existing magnetic structure of CMEs. On the other hand, a growing number of works using SDO/AIA observations (combined with non-linear force-free extrapolations; NLFFF) suggest that MFRs may be the form of filament channels, therefore pre-existing the CME eruption. However, due to the inability to routinely measure the 3D magnetic field in the solar atmosphere, we cannot unambiguously interpret optical and EUV imaging observations as projected on the plane of the sky. Therefore, a raging debate on the nature of the pre-eruptive structure continues. It is also possible that the filament channel/pre-eruptive structure evolves from SMA to MFR slowly, further complicating the distinction between these two types of structures in the solar observations. This work presents realistic simulated optical and EUV observations synthesized on a time-evolving radiative MURaM MHD model at different times along the slow evolution of an SMA converting to an MFR. We discuss the implications of our results in the context of filament channel formation and CME initiation theory. Title: Acoustic-gravity wave propagation characteristics in 3D radiation hydrodynamic simulations of the solar atmosphere Authors: Fleck, Bernhard; Khomenko, Elena; Carlsson, Mats; Rempel, Matthias; Steiner, Oskar; Riva, Fabio; Vigeesh, Gangadharan Bibcode: 2022cosp...44.2503F Altcode: There has been tremendous progress in the degree of realism of three-dimensional radiation magneto-hydrodynamic simulations of the solar atmosphere in the past decades. Four of the most frequently used numerical codes are Bifrost, CO5BOLD, MANCHA3D, and MURaM. Here we test and compare the wave propagation characteristics in model runs from these four codes by measuring the dispersion relation of acoustic-gravity waves at various heights. We find considerable differences between the various models. Title: A Statistical Approach to Study Fine Structure of EUV Emission in Active Regions Authors: Malanushenko, Anna; Rempel, Matthias; Tremblay, Benoit; Kazachenko, Maria Bibcode: 2022cosp...44.2526M Altcode: Heating of the solar corona is one of the major problems in solar physics, and spatial dimension and structuring of the processes involved in heating are yet to be understood. Observations of the numerous thin coronal loops above active regions (ARs) suggest that coronal heating itself is highly variable on small scales, heating plasma in collections of thin flux tubes. It has recently been theorized, based on simulations, that emitting plasma in ARs can also be structured in larger flux tubes with irregular boundaries. The emission of these large flux tubes can appear like emission of loop bundles, with variations of the column depth at their boundaries causing an impression of individual loops. This "coronal veil" theory was argued to be a more general scenario, which better explains AR emission properties than previous models. If confirmed observationally, it will have a large impact on coronal heating studies, suggesting that existing measurements of temperature and density in coronal loops may need to be reevaluated. The observational validation of this hypothesis is as important as it is difficult. For a given coronal loop, it is difficult to tell whether it is a compact feature or a projection artifact. In this talk, we propose a new statistical approach to address this problem. Instead of trying to analyze each loop individually, we focus on scaling relationship between a number of loops in a given AR and the AR's total brightness in a given wavelength. We argue that these two quantities are related by a power law. We demonstrate in theoretical calculations how the power law coefficients will differ depending on whether the emission is structured into (a) compact features, (b) large features with irregular boundaries, or (c) extended and thin veil-like features. We demonstrate that these power laws exist in observations and discuss numerical experiments which may help us to determine which of these scenarios, if any, best describes observations. We further describe the observational statistics that can, in conjunction with numerical experiments, help us understand which of these scenarios take place in the Sun. We also present the first results from our project to collect these data. Title: Heating of the solar chromosphere through current dissipation Authors: da Silva Santos, J. M.; Danilovic, S.; Leenaarts, J.; de la Cruz Rodríguez, J.; Zhu, X.; White, S. M.; Vissers, G. J. M.; Rempel, M. Bibcode: 2022A&A...661A..59D Altcode: 2022arXiv220203955D Context. The solar chromosphere is heated to temperatures higher than predicted by radiative equilibrium. This excess heating is greater in active regions where the magnetic field is stronger.
Aims: We aim to investigate the magnetic topology associated with an area of enhanced millimeter (mm) brightness temperatures in a solar active region mapped by the Atacama Large Millimeter/submillimeter Array (ALMA) using spectropolarimetric co-observations with the 1-m Swedish Solar Telescope (SST).
Methods: We used Milne-Eddington inversions, nonlocal thermodynamic equilibrium (non-LTE) inversions, and a magnetohydrostatic extrapolation to obtain constraints on the three-dimensional (3D) stratification of temperature, magnetic field, and radiative energy losses. We compared the observations to a snapshot of a magnetohydrodynamics simulation and investigate the formation of the thermal continuum at 3 mm using contribution functions.
Results: We find enhanced heating rates in the upper chromosphere of up to ∼5 kW m−2, where small-scale emerging loops interact with the overlying magnetic canopy leading to current sheets as shown by the magnetic field extrapolation. Our estimates are about a factor of two higher than canonical values, but they are limited by the ALMA spatial resolution (∼1.2″). Band 3 brightness temperatures reach about ∼104 K in the region, and the transverse magnetic field strength inferred from the non-LTE inversions is on the order of ∼500 G in the chromosphere.
Conclusions: We are able to quantitatively reproduce many of the observed features including the integrated radiative losses in our numerical simulation. We conclude that the heating is caused by dissipation in current sheets. However, the simulation shows a complex stratification in the flux emergence region where distinct layers may contribute significantly to the emission in the mm continuum.

The movie is available at https://www.aanda.org Title: The Coronal Veil Authors: Malanushenko, A.; Cheung, M. C. M.; DeForest, C. E.; Klimchuk, J. A.; Rempel, M. Bibcode: 2022ApJ...927....1M Altcode: 2021arXiv210614877M Coronal loops, seen in solar coronal images, are believed to represent emission from magnetic flux tubes with compact cross sections. We examine the 3D structure of plasma above an active region in a radiative magnetohydrodynamic simulation to locate volume counterparts for coronal loops. In many cases, a loop cannot be linked to an individual thin strand in the volume. While many thin loops are present in the synthetic images, the bright structures in the volume are fewer and of complex shape. We demonstrate that this complexity can form impressions of thin bright loops, even in the absence of thin bright plasma strands. We demonstrate the difficulty of discerning from observations whether a particular loop corresponds to a strand in the volume, or a projection artifact. We demonstrate how apparently isolated loops could deceive observers, even when observations from multiple viewing angles are available. While we base our analysis on a simulation, the main findings are independent from a particular simulation setup and illustrate the intrinsic complexity involved in interpreting observations resulting from line-of-sight integration in an optically thin plasma. We propose alternative interpretation for strands seen in Extreme Ultraviolet images of the corona. The "coronal veil" hypothesis is mathematically more generic, and naturally explains properties of loops that are difficult to address otherwise-such as their constant cross section and anomalously high density scale height. We challenge the paradigm of coronal loops as thin magnetic flux tubes, offering new understanding of solar corona, and by extension, of other magnetically confined bright hot plasmas. Title: The effect of small-scale magnetic fields on stellar convection and activity Authors: Rempel, M. Bibcode: 2022fysr.confE..39R Altcode: The Sun is a unique star in the sense that we can observe it at high resolution and study phenomena at a detail that is hidden in stellar observations. This applies specifically to small-scale magnetic fields that are organized on the stellar surface on scale of granulation and smaller. Significant progress over the past 10-20 years in both solar observations and modeling through small-scale dynamo simulations point to a small-scale field of a large enough strength to have a dynamical impact on convection, differential rotation as well as large-scale magnetic activity. In this talk I will highlight lessons learned from the Sun that may have a broader impact on understanding stellar convection and magnetism. Title: Probing the Physics of the Solar Atmosphere with the Multi-slit Solar Explorer (MUSE). II. Flares and Eruptions Authors: Cheung, Mark C. M.; Martínez-Sykora, Juan; Testa, Paola; De Pontieu, Bart; Chintzoglou, Georgios; Rempel, Matthias; Polito, Vanessa; Kerr, Graham S.; Reeves, Katharine K.; Fletcher, Lyndsay; Jin, Meng; Nóbrega-Siverio, Daniel; Danilovic, Sanja; Antolin, Patrick; Allred, Joel; Hansteen, Viggo; Ugarte-Urra, Ignacio; DeLuca, Edward; Longcope, Dana; Takasao, Shinsuke; DeRosa, Marc L.; Boerner, Paul; Jaeggli, Sarah; Nitta, Nariaki V.; Daw, Adrian; Carlsson, Mats; Golub, Leon; The Bibcode: 2022ApJ...926...53C Altcode: 2021arXiv210615591C Current state-of-the-art spectrographs cannot resolve the fundamental spatial (subarcseconds) and temporal (less than a few tens of seconds) scales of the coronal dynamics of solar flares and eruptive phenomena. The highest-resolution coronal data to date are based on imaging, which is blind to many of the processes that drive coronal energetics and dynamics. As shown by the Interface Region Imaging Spectrograph for the low solar atmosphere, we need high-resolution spectroscopic measurements with simultaneous imaging to understand the dominant processes. In this paper: (1) we introduce the Multi-slit Solar Explorer (MUSE), a spaceborne observatory to fill this observational gap by providing high-cadence (<20 s), subarcsecond-resolution spectroscopic rasters over an active region size of the solar transition region and corona; (2) using advanced numerical models, we demonstrate the unique diagnostic capabilities of MUSE for exploring solar coronal dynamics and for constraining and discriminating models of solar flares and eruptions; (3) we discuss the key contributions MUSE would make in addressing the science objectives of the Next Generation Solar Physics Mission (NGSPM), and how MUSE, the high-throughput Extreme Ultraviolet Solar Telescope, and the Daniel K Inouye Solar Telescope (and other ground-based observatories) can operate as a distributed implementation of the NGSPM. This is a companion paper to De Pontieu et al., which focuses on investigating coronal heating with MUSE. Title: Convolutional Neural Networks and Stokes Response Functions Authors: Centeno, Rebecca; Flyer, Natasha; Mukherjee, Lipi; Egeland, Ricky; Casini, Roberto; del Pino Alemán, Tanausú; Rempel, Matthias Bibcode: 2022ApJ...925..176C Altcode: 2021arXiv211203802C In this work, we study the information content learned by a convolutional neural network (CNN) when trained to carry out the inverse mapping between a database of synthetic Ca II intensity spectra and the vertical stratification of the temperature of the atmospheres used to generate such spectra. In particular, we evaluate the ability of the neural network to extract information about the sensitivity of the spectral line to temperature as a function of height. By training the CNN on sufficiently narrow wavelength intervals across the Ca II spectral profiles, we find that the error in the temperature prediction shows an inverse relationship to the response function of the spectral line to temperature, that is, different regions of the spectrum yield a better temperature prediction at their expected regions of formation. This work shows that the function that the CNN learns during the training process contains a physically meaningful mapping between wavelength and atmospheric height. Title: A solar coronal loop in a box: Energy generation and heating Authors: Breu, C.; Peter, H.; Cameron, R.; Solanki, S. K.; Przybylski, D.; Rempel, M.; Chitta, L. P. Bibcode: 2022A&A...658A..45B Altcode: 2021arXiv211211549B Context. Coronal loops are the basic building block of the upper solar atmosphere as seen in the extreme UV and X-rays. Comprehending how these are energized, structured, and evolve is key to understanding stellar coronae.
Aims: Here we investigate how the energy to heat the loop is generated by photospheric magneto-convection, transported into the upper atmosphere, and how the internal structure of a coronal magnetic loop forms.
Methods: In a 3D magnetohydrodynamics model, we study an isolated coronal loop rooted with both footpoints in a shallow layer within the convection zone using the MURaM code. To resolve its internal structure, we limited the computational domain to a rectangular box containing a single coronal loop as a straightened magnetic flux tube. Field-aligned heat conduction, gray radiative transfer in the photosphere and chromosphere, and optically thin radiative losses in the corona were taken into account. The footpoints were allowed to interact self-consistently with the granulation surrounding them.
Results: The loop is heated by a Poynting flux that is self-consistently generated through small-scale motions within individual magnetic concentrations in the photosphere. Turbulence develops in the upper layers of the atmosphere as a response to the footpoint motions. We see little sign of heating by large-scale braiding of magnetic flux tubes from different photospheric concentrations at a given footpoint. The synthesized emission, as it would be observed by the Atmospheric Imaging Assembly or the X-Ray Telescope, reveals transient bright strands that form in response to the heating events. Overall, our model roughly reproduces the properties and evolution of the plasma as observed within (the substructures of) coronal loops.
Conclusions: With this model we can build a coherent picture of how the energy flux to heat the upper atmosphere is generated near the solar surface and how this process drives and governs the heating and dynamics of a coronal loop.

Movie associated to Fig. 2 is available at https://www.aanda.org Title: Probing the Physics of the Solar Atmosphere with the Multi-slit Solar Explorer (MUSE). I. Coronal Heating Authors: De Pontieu, Bart; Testa, Paola; Martínez-Sykora, Juan; Antolin, Patrick; Karampelas, Konstantinos; Hansteen, Viggo; Rempel, Matthias; Cheung, Mark C. M.; Reale, Fabio; Danilovic, Sanja; Pagano, Paolo; Polito, Vanessa; De Moortel, Ineke; Nóbrega-Siverio, Daniel; Van Doorsselaere, Tom; Petralia, Antonino; Asgari-Targhi, Mahboubeh; Boerner, Paul; Carlsson, Mats; Chintzoglou, Georgios; Daw, Adrian; DeLuca, Edward; Golub, Leon; Matsumoto, Takuma; Ugarte-Urra, Ignacio; McIntosh, Scott W.; the MUSE Team Bibcode: 2022ApJ...926...52D Altcode: 2021arXiv210615584D The Multi-slit Solar Explorer (MUSE) is a proposed mission composed of a multislit extreme ultraviolet (EUV) spectrograph (in three spectral bands around 171 Å, 284 Å, and 108 Å) and an EUV context imager (in two passbands around 195 Å and 304 Å). MUSE will provide unprecedented spectral and imaging diagnostics of the solar corona at high spatial (≤0.″5) and temporal resolution (down to ~0.5 s for sit-and-stare observations), thanks to its innovative multislit design. By obtaining spectra in four bright EUV lines (Fe IX 171 Å, Fe XV 284 Å, Fe XIX-Fe XXI 108 Å) covering a wide range of transition regions and coronal temperatures along 37 slits simultaneously, MUSE will, for the first time, "freeze" (at a cadence as short as 10 s) with a spectroscopic raster the evolution of the dynamic coronal plasma over a wide range of scales: from the spatial scales on which energy is released (≤0.″5) to the large-scale (~170″ × 170″) atmospheric response. We use numerical modeling to showcase how MUSE will constrain the properties of the solar atmosphere on spatiotemporal scales (≤0.″5, ≤20 s) and the large field of view on which state-of-the-art models of the physical processes that drive coronal heating, flares, and coronal mass ejections (CMEs) make distinguishing and testable predictions. We describe the synergy between MUSE, the single-slit, high-resolution Solar-C EUVST spectrograph, and ground-based observatories (DKIST and others), and the critical role MUSE plays because of the multiscale nature of the physical processes involved. In this first paper, we focus on coronal heating mechanisms. An accompanying paper focuses on flares and CMEs. Title: Probing the Physics of the Solar Atmosphere with the Multi-slit Solar Explorer (MUSE): II. Flares and Eruptions Authors: Cheung, Chun Ming Mark; Martinez-Sykora, Juan; Testa, Paola; De Pontieu, Bart; Chintzoglou, Georgios; Rempel, Matthias; Polito, Vanessa; Kerr, Graham; Reeves, Katharine; Fletcher, Lyndsay; Jin, Meng; Nobrega, Daniel; Danilovic, Sanja; Antolin, Patrick; Allred, Joel; Hansteen, Viggo; Ugarte-Urra, Ignacio; DeLuca, Edward; Longcope, Dana; Takasao, Shinsuke; DeRosa, Marc; Boerner, Paul; Jaeggli, Sarah; Nitta, Nariaki; Daw, Adrian; Carlsson, Mats; Golub, Leon Bibcode: 2021AGUFMSH51A..08C Altcode: Current state-of-the-art spectrographs cannot resolve the fundamental spatial (sub-arcseconds) and temporal scales (less than a few tens of seconds) of the coronal dynamics of solar flares and eruptive phenomena. The highest resolution coronal data to date are based on imaging, which is blind to many of the processes that drive coronal energetics and dynamics. As shown by IRIS for the low solar atmosphere, we need high-resolution spectroscopic measurements with simultaneous imaging to understand the dominant processes. In this paper: (1) we introduce the Multi-slit Solar Explorer (MUSE), a spaceborne observatory to fill this observational gap by providing high-cadence (<20 s), sub-arcsecond resolution spectroscopic rasters over an active region size of the solar transition region and corona; (2) using advanced numerical models, we demonstrate the unique diagnostic capabilities of MUSE for exploring solar coronal dynamics, and for constraining and discriminating models of solar flares and eruptions; (3) we discuss the key contributions MUSE would make in addressing the science objectives of the Next Generation Solar Physics Mission (NGSPM), and how MUSE, the high-throughput EUV Solar Telescope (EUVST) and the Daniel K Inouye Solar Telescope (and other ground-based observatories) can operate as a distributed implementation of the NGSPM. This is a companion paper to De Pontieu et al. (2021, also submitted to SH-17), which focuses on investigating coronal heating with MUSE. Title: Solar Atmosphere Radiative Transfer Model Comparison based on 3D MHD Simulations Authors: Haberreiter, Margit; Criscuoli, Serena; Rempel, Matthias; Mendes Domingos Pereira, Tiago Bibcode: 2021AGUFMSH43A..06H Altcode: The reconstruction of the solar spectral irradiance (SSI) on various time scales is essential for the understanding of the Earths climate response to the SSI variability. The driver of the SSI variability is understood to be the intensity contrast of magnetic features present on the Sun with respect to the largely non-magnetic quiet Sun. However, different spectral synthesis codes lead to diverging projections of SSI variability. We present a study in which we compare three different radiative transfer codes and carry out a a detailed analysis of their performance. We perform the spectral synthesis at the continuum wavelength of 665 nm with the Code for Solar Irradiance (COSI), and the Rybicki-Hummer (RH), and Max Planck University of Chicago Radiative MHD (MURaM) codes for three 3D MHD simulations snapshots, a non-magnetic case, and MHD simulations with 100 G, and 200 G magnetic field strength. We determine the intensity distributions, the intensity differences and ratios for the spectral synthesis codes. We identify that the largest discrepancies originate in the intergranular lanes where the most field concentration occurs. Overall, the applied radiative transfer codes give consistent intensity distributions. Also, the intensity variation as a function of magnetic field strength for the particular 100 G and 200 G snapshots agree within the 2-3% range. Title: Analyzing the Structure of Coronal Loops in MURaM Radiation MHD Simulations Authors: David, Mia; Rempel, Matthias; Malanushenko, Anna Bibcode: 2021AGUFMSH45B2377D Altcode: Coronal loops are emission features that trace out parts of the solar magnetic field in the corona, and as such they provide important information about the magnetic and plasma structure of the solar corona. Their thermal substructure is still an open question: their thickness is at the limit of resolution of the instruments observing them, and higher resolution instruments tend to find finer strands. This raises the question whether the finest strands are resolved with the currently available highest resolution instruments. In this project, we address this from a modeling perspective and look to answer the following questions. Does the number of strands identified in synthetic observations depend on the resolution of the numerical simulation? How many strands remain hidden in current observations that may otherwise be evident in future higher resolution observations? We look at simulations done with MURaM code of a bipolar active region that are available at three different numerical resolutions. We emulate observables at various resolutions, including one which exceeds that of current instruments. We synthesize data in resolution of Atmospheric Imaging Assembly onboard Solar Dynamics Observatory (SDO/AIA) and High-Resolution Coronal Imager (HiC). We find that the number of strands found in synthetic AIA does not depend on the resolution of the simulation, and that it is a small fraction of the strands found in the native resolution of the simulation. The number of strands seen in synthetic HiC data is a factor of 2-4 higher than that in synthetic AIA, and increases moderately with the resolution of the simulation. We compare the results with observations by studying an active region observed by AIA. We study the dependence of the number of loops counted on the viewing angle in both synthetic and observable data. We also report statistical properties of these strands. Title: Modeling the Solar Atmosphere: From quiet Sun to Flares Authors: Rempel, Matthias Bibcode: 2021AGUFMSH43A..01R Altcode: Comparison of models and observations requires simulations with a sufficient degree of realism, ideally simulations that allow for the computation of synthetic observables. This realism is in general a compromise between the sophistication of implemented physics, numerical resolution, extent of the spatial and temporal domain (including dimensionality and boundary conditions) as well as the initial state simulations are started from. I will review selected simulation results from the past decade that strike the balanced for realism in different ways, discuss their limitations and avenues for future improvement. These simulations will encompass the range from detailed studies of quiet Sun magnetism to active region scale simulations including the lower solar corona and flares. I will end this talk with more general remarks on challenges of simulation-observation comparison and challenges from the evolving compute and data infrastructure. Computing platforms continue to rely more heavily on GPUs and the availability of computing resources outpaces data storage capabilities. This requires in the future more scalable and integrated computation and data analysis pipelines that rely less on the storage of intermediate data products. Title: A Statistical Approach to Study Spatial Characteristics of EUV Emission in Active Regions Authors: Malanushenko, Anna; Egeland, Ricky; Kazachenko, Maria; Rempel, Matthias; Tremblay, Benoit Bibcode: 2021AGUFMSH45B2360M Altcode: Heating of the solar corona is one of the major problems in solar physics, and spatial dimension and structuring of the processes involved in heating are yet to be understood. Observations of the numerous thin coronal loops above active regions (ARs) suggest that coronal heating itself is highly variable on small scales, heating plasma in collections of thin flux tubes. It has recently been theorized, based on simulations, that emitting plasma in ARs can also be structured in larger flux tubes with irregular boundaries. The emission of these large flux tubes can appear like emission of loop bundles, with variations of the column depth at their boundaries causing an impression of individual loops. This "coronal veil" theory was argued to be a more general scenario, which better explains AR emission properties than previous models. If confirmed observationally, it will have a large impact on coronal heating studies, suggesting that existing measurements of temperature and density in coronal loops may need to be reevaluated. The observational validation of this hypothesis is as important as it is difficult. For a given coronal loop, it is difficult to tell whether it is a compact feature or a projection artifact. In this talk, we propose a new statistical approach to address this problem. Instead of trying to analyze each loop individually, we focus on scaling relationship between a number of loops in a given AR and the AR's total brightness in a given wavelength. We argue that these two quantities are related by a power law. We demonstrate in theoretical calculations how the power law coefficients will differ depending on whether the emission is structured into (a) compact features, (b) large features with irregular boundaries, or (c) extended and thin veil-like features. We demonstrate that these power laws exist in observations and discuss numerical experiments which may help us to determine which of these scenarios, if any, best describes observations. Title: Visualizing the Solar Corona in Virtual Reality Authors: Wolff, Milana; Dima, Gabriel; Rempel, Matthias; Lacatus, Daniela; Paraschiv, Alin; Lecinski, Alice; Malanushenko, Anna Bibcode: 2021AGUFMSH45B2365W Altcode: This work presents novel visualizations of the optically thin solar corona in a virtual reality environment created using the Unity development platform. Unity enables fast rendering and interaction with three dimensional datasets in an immersive setting. We depict data derived from coronal simulations generated by radiative magnetohydrodynamic MURaM. These visualizations represent synthetic emissivity values computed for a variety of coronal emission lines using high-resolution, time-dependent thermodynamic and magnetic datasets. Users can enter the virtual environment, accessible on desktop and mobile devices or with a virtual reality head-mounted display (such as Oculus or Vive headsets) and observe and interact with both static and dynamic structures in the solar corona from arbitrary vantage points. These types of direct interaction techniques with simulated large-scale structures enhance intuitive understanding of solar dynamics. We welcome ideas from the community on how to further leverage this technology. Title: Efficient Numerical Treatment of Ambipolar and Hall Drift as Hyperbolic System Authors: Rempel, M.; Przybylski, D. Bibcode: 2021ApJ...923...79R Altcode: 2021arXiv211113811R Partially ionized plasmas, such as the solar chromosphere, require a generalized Ohm's law including the effects of ambipolar and Hall drift. While both describe transport processes that arise from the multifluid equations and are therefore of hyperbolic nature, they are often incorporated in models as a diffusive, i.e., parabolic process. While the formulation as such is easy to include in standard MHD models, the resulting diffusive time-step constraints do require often a computationally more expensive implicit treatment or super-time-stepping approaches. In this paper we discuss an implementation that retains the hyperbolic nature and allows for an explicit integration with small computational overhead. In the case of ambipolar drift, this formulation arises naturally by simply retaining a time derivative of the drift velocity that is typically omitted. This alone leads to time-step constraints that are comparable to the native MHD time-step constraint for a solar setup including the region from photosphere to lower solar corona. We discuss an accelerated treatment that can further reduce time-step constraints if necessary. In the case of Hall drift we propose a hyperbolic formulation that is numerically similar to that for the ambipolar drift and we show that the combination of both can be applied to simulations of the solar chromosphere at minimal computational expense. Title: Characterization of magneto-convection in sunspots. The Gough-Tayler stability criterion in MURaM sunspot simulations Authors: Schmassmann, M.; Rempel, M.; Bello González, N.; Schlichenmaier, R.; Jurčák, J. Bibcode: 2021A&A...656A..92S Altcode: Context. Observations have shown that in stable sunspots, the umbral boundary is outlined by a critical value of the vertical magnetic field component. However, the nature of the distinct magnetoconvection regimes in the umbra and penumbra is still unclear.
Aims: We analyse a sunspot simulation in an effort to understand the origin of the convective instabilities giving rise to the penumbral and umbral distinct regimes.
Methods: We applied the criterion from Gough & Tayler (1966, MNRAS, 133, 85), accounting for the stabilising effect of the vertical magnetic field, to investigate the convective instabilities in a MURaM sunspot simulation.
Results: We find: (1) a highly unstable shallow layer right beneath the surface extending all over the simulation box in which convection is triggered by radiative cooling in the photosphere; (2) a deep umbral core (beneath −5 Mm) stabilised against overturning convection that underlies a region with stable background values permeated by slender instabilities coupled to umbral dots; (3) filamentary instabilities below the penumbra nearly parallel to the surface and undulating instabilities coupled to the penumbra which originate in the deep layers. These deep-rooted instabilities result in the vigorous magneto-convection regime characteristic of the penumbra; (4) convective downdrafts in the granulation, penumbra, and umbra develop at about 2 km s−1, 1 km s−1, and 0.1 km s−1, respectively, indicating that the granular regime of convection is more vigorous than the penumbra convection regime, which, in turn, is more vigorous than the close-to-steady umbra; (5) the GT criterion outlines both the sunspot magnetopause and peripatopause, highlighting the tripartite nature of the sub-photospheric layers of magnetohydrodynamic (MHD) sunspot models; and, finally, (6) the Jurčák criterion is the photospheric counterpart of the GT criterion in deep layers.
Conclusions: The GT criterion as a diagnostic tool reveals the tripartite nature of sunspot structure with distinct regimes of magneto-convection in the umbra, penumbra, and granulation operating in realistic MHD simulations.

Movies associated with Figs. 2 and 3 are available at https://www.aanda.org Title: Solar atmosphere radiative transfer model comparison based on 3D MHD simulations Authors: Haberreiter, M.; Criscuoli, S.; Rempel, M.; Pereira, T. M. D. Bibcode: 2021A&A...653A.161H Altcode: 2021arXiv210902681H Context. The reconstruction of the solar spectral irradiance (SSI) on various time scales is essential for the understanding of the Earth's climate response to the SSI variability.
Aims: The driver of the SSI variability is understood to be the intensity contrast of magnetic features present on the Sun with respect to the largely non-magnetic quiet Sun. However, different spectral synthesis codes lead to diverging projections of SSI variability. In this study we compare three different radiative transfer codes and carry out a detailed analysis of their performance.
Methods: We perform the spectral synthesis at the continuum wavelength of 665 nm with the Code for Solar Irradiance, and the Rybicki-Hummer, and Max Planck University of Chicago Radiative MHD codes for three 3D MHD simulations snapshots, a non-magnetic case, and MHD simulations with 100 G, and 200 G magnetic field strength.
Results: We determine the intensity distributions, the intensity differences and ratios for the spectral synthesis codes. We identify that the largest discrepancies originate in the intergranular lanes where the most field concentration occurs.
Conclusions: Overall, the applied radiative transfer codes give consistent intensity distributions. Also, the intensity variation as a function of magnetic field strength for the particular 100 G and 200 G snapshots agree within the 2-3% range. Title: Measuring the Magnetic Origins of Solar Flares, Coronal Mass Ejections, and Space Weather Authors: Judge, Philip; Rempel, Matthias; Ezzeddine, Rana; Kleint, Lucia; Egeland, Ricky; Berdyugina, Svetlana V.; Berger, Thomas; Bryans, Paul; Burkepile, Joan; Centeno, Rebecca; de Toma, Giuliana; Dikpati, Mausumi; Fan, Yuhong; Gilbert, Holly; Lacatus, Daniela A. Bibcode: 2021ApJ...917...27J Altcode: 2021arXiv210607786J We take a broad look at the problem of identifying the magnetic solar causes of space weather. With the lackluster performance of extrapolations based upon magnetic field measurements in the photosphere, we identify a region in the near-UV (NUV) part of the spectrum as optimal for studying the development of magnetic free energy over active regions. Using data from SORCE, the Hubble Space Telescope, and SKYLAB, along with 1D computations of the NUV spectrum and numerical experiments based on the MURaM radiation-magnetohydrodynamic and HanleRT radiative transfer codes, we address multiple challenges. These challenges are best met through a combination of NUV lines of bright Mg II, and lines of Fe II and Fe I (mostly within the 4s-4p transition array) which form in the chromosphere up to 2 × 104 K. Both Hanle and Zeeman effects can in principle be used to derive vector magnetic fields. However, for any given spectral line the τ = 1 surfaces are generally geometrically corrugated owing to fine structure such as fibrils and spicules. By using multiple spectral lines spanning different optical depths, magnetic fields across nearly horizontal surfaces can be inferred in regions of low plasma β, from which free energies, magnetic topology, and other quantities can be derived. Based upon the recently reported successful sub-orbital space measurements of magnetic fields with the CLASP2 instrument, we argue that a modest space-borne telescope will be able to make significant advances in the attempts to predict solar eruptions. Difficulties associated with blended lines are shown to be minor in an Appendix. Title: First Results of the Chromospheric MURaM code Authors: Przybylski, D. F.; Cameron, R.; Solanki, S.; Rempel, M. Bibcode: 2021AAS...23810605P Altcode: The solar chromosphere, spanning the region between the photosphere and the transition to the corona, remains one of the least understood parts of the Sun. This is partly because observing the chromosphere and interpreting these observations is full of pitfalls. Also, the simulation of the chromosphere is complex, as the particle densities and collisional rates are too low to maintain local thermodynamic equilibrium (LTE). Additionally, the recombination rates of hydrogen are larger than the dynamical timescales and the populations must be solved in non-equilibrium (NE). Realistic simulations of the chromosphere must treat the magneto-hydrodynamics, time-dependant atomic and molecular chemistry, and radiation transfer simultaneously.

The MURaM radiation-MHD code has previously been used for investigation of the connection between the solar photosphere and corona, ranging from small-scale dynamo generated 'quiet' sun fields to sunspots and complex active regions. Until now these simulations have been performed in LTE, greatly limiting their realism in the solar chromosphere. We have extended MURaM to include NLTE effects following the prescriptions used in the Bifrost code. The low viscocity and resistivity of the MURaM code leads to turbulent convection in the photosphere with kilo-Gauss mixed-polarity magnetic fields. This results in a dynamic chromosphere with strong shocks and a finely structured magnetic field. We discuss the implications of this new model towards observations of chromospheric spectral lines. Title: A Comprehensive Radiative Magnetohydrodynamics Simulation of Active Region Scale Flux Emergence from the Convection Zone to the Corona Authors: Chen, Feng; Rempel, Matthias; Fan, Yuhong Bibcode: 2021arXiv210614055C Altcode: We present a comprehensive radiative magnetohydrodynamic simulation of the quiet Sun and large solar active regions. The 197 Mm wide simulation domain spans from 18 (10) Mm beneath the photosphere to 113 Mm in the solar corona. Radiative transfer assuming local thermal equilibrium, optically-thin radiative losses, and anisotropic conduction transport provide the necessary realism for synthesizing observables to compare with remote sensing observations of the photosphere and corona. This model self-consistently reproduces observed features of the quiet Sun, emerging and developed active regions, and solar flares up to M class. Here, we report an overview of the first results. The surface magnetoconvection yields an upward Poynting flux that is dissipated in the corona and heats the plasma to over one million K. The quiescent corona also presents ubiquitous propagating waves, jets, and bright points with sizes down to 2 Mm. Magnetic flux bundles emerge into the photosphere and give rise to strong and complex active regions with over $10^{23}$ Mx magnetic flux. The coronal free magnetic energy, which is approximately 18\% of the total magnetic energy, accumulates to approximately $10^{33}$ erg. The coronal magnetic field is clearly non-force-free, as the Lorentz force needs to balance the pressure force and viscous stress as well as drive magnetic field evolution. The emission measure from $\log_{10}T{=}4.5$ to $\log_{10}T{>}7$ provides a comprehensive view of the active region corona, such as coronal loops of various lengths and temperatures, mass circulation by evaporation and condensation, and eruptions from jets to large-scale mass ejections. Title: On the (in)stability of sunspots Authors: Strecker, H.; Schmidt, W.; Schlichenmaier, R.; Rempel, M. Bibcode: 2021A&A...649A.123S Altcode: 2021arXiv210311487S Context. The stability of sunspots is one of the long-standing unsolved puzzles in the field of solar magnetism and the solar cycle. The thermal and magnetic structure of the sunspot beneath the solar surface is not accessible through observations, thus processes in these regions that contribute to the decay of sunspots can only be studied through theoretical and numerical studies.
Aims: We study the effects that destabilise and stabilise the flux tube of a simulated sunspot in the upper convection zone. The depth-varying effects of fluting instability, buoyancy forces, and timescales on the flux tube are analysed.
Methods: We analysed a numerical simulation of a sunspot calculated with the MURaM code. The simulation domain has a lateral extension of more than 98 Mm × 98 Mm and extends almost 18 Mm below the solar surface. The analysed data set of 30 hours shows a stable sunspot at the solar surface. We studied the evolution of the flux tube at defined horizontal layers (1) by means of the relative change in perimeter and area, that is, its compactness; and (2) with a linear stability analysis.
Results: The simulation shows a corrugation along the perimeter of the flux tube (sunspot) that proceeds fastest at a depth of about 8 Mm below the solar surface. Towards the surface and towards deeper layers, the decrease in compactness is damped. From the stability analysis, we find that above a depth of 2 Mm, the sunspot is stabilised by buoyancy forces. The spot is least stable at a depth of about 3 Mm because of the fluting instability. In deeper layers, the flux tube is marginally unstable. The stability of the sunspot at the surface affects the behaviour of the field lines in deeper layers by magnetic tension. Therefore the fluting instability is damped at depths of about 3 Mm, and the decrease in compactness is strongest at a depth of about 8 Mm. The more vertical orientation of the magnetic field and the longer convective timescale lead to slower evolution of the corrugation process in layers deeper than 10 Mm.
Conclusions: The formation of large intrusions of field-free plasma below the surface destabilises the flux tube of the sunspot. This process is not visible at the surface, where the sunspot is stabilised by buoyancy forces. The onset of sunspot decay occurs in deeper layers, while the sunspot still appears stable in the photosphere. The intrusions eventually lead to the disruption and decay of the sunspot.

The animation is available at https://www.aanda.org

This paper is mainly based on Part I of the Ph.D. thesis "On the decay of sunspots", https://freidok.uni-freiburg.de/data/165760 Title: Critical Science Plan for the Daniel K. Inouye Solar Telescope (DKIST) Authors: Rast, Mark P.; Bello González, Nazaret; Bellot Rubio, Luis; Cao, Wenda; Cauzzi, Gianna; Deluca, Edward; de Pontieu, Bart; Fletcher, Lyndsay; Gibson, Sarah E.; Judge, Philip G.; Katsukawa, Yukio; Kazachenko, Maria D.; Khomenko, Elena; Landi, Enrico; Martínez Pillet, Valentín; Petrie, Gordon J. D.; Qiu, Jiong; Rachmeler, Laurel A.; Rempel, Matthias; Schmidt, Wolfgang; Scullion, Eamon; Sun, Xudong; Welsch, Brian T.; Andretta, Vincenzo; Antolin, Patrick; Ayres, Thomas R.; Balasubramaniam, K. S.; Ballai, Istvan; Berger, Thomas E.; Bradshaw, Stephen J.; Campbell, Ryan J.; Carlsson, Mats; Casini, Roberto; Centeno, Rebecca; Cranmer, Steven R.; Criscuoli, Serena; Deforest, Craig; Deng, Yuanyong; Erdélyi, Robertus; Fedun, Viktor; Fischer, Catherine E.; González Manrique, Sergio J.; Hahn, Michael; Harra, Louise; Henriques, Vasco M. J.; Hurlburt, Neal E.; Jaeggli, Sarah; Jafarzadeh, Shahin; Jain, Rekha; Jefferies, Stuart M.; Keys, Peter H.; Kowalski, Adam F.; Kuckein, Christoph; Kuhn, Jeffrey R.; Kuridze, David; Liu, Jiajia; Liu, Wei; Longcope, Dana; Mathioudakis, Mihalis; McAteer, R. T. James; McIntosh, Scott W.; McKenzie, David E.; Miralles, Mari Paz; Morton, Richard J.; Muglach, Karin; Nelson, Chris J.; Panesar, Navdeep K.; Parenti, Susanna; Parnell, Clare E.; Poduval, Bala; Reardon, Kevin P.; Reep, Jeffrey W.; Schad, Thomas A.; Schmit, Donald; Sharma, Rahul; Socas-Navarro, Hector; Srivastava, Abhishek K.; Sterling, Alphonse C.; Suematsu, Yoshinori; Tarr, Lucas A.; Tiwari, Sanjiv; Tritschler, Alexandra; Verth, Gary; Vourlidas, Angelos; Wang, Haimin; Wang, Yi-Ming; NSO and DKIST Project; DKIST Instrument Scientists; DKIST Science Working Group; DKIST Critical Science Plan Community Bibcode: 2021SoPh..296...70R Altcode: 2020arXiv200808203R The National Science Foundation's Daniel K. Inouye Solar Telescope (DKIST) will revolutionize our ability to measure, understand, and model the basic physical processes that control the structure and dynamics of the Sun and its atmosphere. The first-light DKIST images, released publicly on 29 January 2020, only hint at the extraordinary capabilities that will accompany full commissioning of the five facility instruments. With this Critical Science Plan (CSP) we attempt to anticipate some of what those capabilities will enable, providing a snapshot of some of the scientific pursuits that the DKIST hopes to engage as start-of-operations nears. The work builds on the combined contributions of the DKIST Science Working Group (SWG) and CSP Community members, who generously shared their experiences, plans, knowledge, and dreams. Discussion is primarily focused on those issues to which DKIST will uniquely contribute. Title: Acoustic-gravity wave propagation characteristics in three-dimensional radiation hydrodynamic simulations of the solar atmosphere Authors: Fleck, B.; Carlsson, M.; Khomenko, E.; Rempel, M.; Steiner, O.; Vigeesh, G. Bibcode: 2021RSPTA.37900170F Altcode: 2020arXiv200705847F There has been tremendous progress in the degree of realism of three-dimensional radiation magneto-hydrodynamic simulations of the solar atmosphere in the past decades. Four of the most frequently used numerical codes are Bifrost, CO5BOLD, MANCHA3D and MURaM. Here we test and compare the wave propagation characteristics in model runs from these four codes by measuring the dispersion relation of acoustic-gravity waves at various heights. We find considerable differences between the various models. The height dependence of wave power, in particular of high-frequency waves, varies by up to two orders of magnitude between the models, and the phase difference spectra of several models show unexpected features, including ±180° phase jumps.

This article is part of the Theo Murphy meeting issue `High-resolution wave dynamics in the lower solar atmosphere'. Title: Atmosphere and Ocean Responses to Extreme Low Solar Activity and Their Hemispheric Differences Authors: Liu, Hanli; Solomon, Stanley; Rempel, Matthias; McInerney, Joseph; Danabasoglu, Gokhan Bibcode: 2021cosp...43E.724L Altcode: The total solar irradiance (TSI) changes by ~0.1% during solar cycles. The impact of the change on tropospheric climate is small in comparison with the climate variability and it is thus challenging to clearly quantify the solar signal. The rather weak signal also makes it difficult to investigate the processes involved in sun-climate connection. As a result the climate sensitivity to solar forcing is poorly quantified and understood. In this study, we seek to overcome this difficulty by driving a coupled whole atmosphere-ocean model--the NCAR CESM Whole Atmosphere Community Climate Model (WACCM) with the interactive ocean model (POP2)--with an extreme low solar forcing. The TSI and solar spectral irradiance (SSI) are obtained from MHD simulations using the MURaM code, and the TSI/SSI values obtained can be regarded as a lower theoretical limit as allowed by known solar physics principles. With this hypothetical low solar forcing, significant and complex changes are seen throughout the atmosphere and also in the ocean circulation. While the surface generally cools during the 200-year simulation, the evolution path of the cooling and the cooling rates are very different between the two hemispheres. Our analysis suggests that the interplay between the radiative forcing and dynamical feedback determines the response, and the dynamical feedback from atmosphere and ocean coupling, in particular in the form of atmospheric waves, differ between the two hemispheres. Additional simulations with extreme low SSI forcing in the ultraviolet (UV) only and in the visible/infrared (VIR) only show that they can cause troposphere/ocean responses similar to the full forcing case, albeit with different magnitudes. This unambiguously demonstrates the importance of middle atmosphere/lower atmosphere/ocean coupling in sun-climate connection and in studying the climate sensitivity to solar forcing. Title: Flare simulations with the MURaM radiative MHD code Authors: Rempel, Matthias; Cheung, Mark; Chintzoglou, Georgios Bibcode: 2021cosp...43E1772R Altcode: Over the past few years the MURaM radiative MHD code was expanded for its capability to simulate the coupled solar atmosphere from the upper convection zone into the lower solar corona. The code includes the essential physics to synthesize thermal emission ranging from the visible spectrum in the photosphere to EUV and soft X-ray from transition region and corona. A more sophisticated treatment of the chromosphere is currently under development. After a brief review of the code's capabilities and limitations we present a new setup that allows to create collisional polarity inversion lines (cPILs) and study the coronal response including flares. In the setup we start with a bipolar sunspot configuration and set the spots on collision course by imposing the appropriate velocity field at the footpoints in the subphotospheric boundary. We vary parameters such as the initial spot separation, collision speed and collision distance. While all setups lead to the formation of a sigmoid structure, only the cases with a close passing of the spots cause flares and mass eruptions. The energy release is in the $1-2\times 10^{31}$ erg range, putting the simulated flares into the upper C to lower M-class range. While the case with the more distant passing of the spots does not lead to a flare, the corona is nonetheless substantially heated, suggesting non-eruptive energy release mechanisms. We discuss the applicability/implications of our setups for investigating the way cPILs form and produce eruptions and present preliminary results. Title: Flare Simulations with the MURaM Radiative MHD Code Authors: Rempel, M.; Chintzoglou, G.; Cheung, C. M. M. Bibcode: 2020AGUFMSH0500004R Altcode: No abstract at ADS Title: The Dimmest State of the Sun Authors: Yeo, K. L.; Solanki, S. K.; Krivova, N. A.; Rempel, M.; Anusha, L. S.; Shapiro, A. I.; Tagirov, R. V.; Witzke, V. Bibcode: 2020GeoRL..4790243Y Altcode: 2021arXiv210209487Y How the solar electromagnetic energy entering the Earth's atmosphere varied since preindustrial times is an important consideration in the climate change debate. Detrimental to this debate, estimates of the change in total solar irradiance (TSI) since the Maunder minimum, an extended period of weak solar activity preceding the industrial revolution, differ markedly, ranging from a drop of 0.75 W m-2 to a rise of 6.3 W m-2. Consequently, the exact contribution by solar forcing to the rise in global temperatures over the past centuries remains inconclusive. Adopting a novel approach based on state-of-the-art solar imagery and numerical simulations, we establish the TSI level of the Sun when it is in its least-active state to be 2.0 ± 0.7 W m-2 below the 2019 level. This means TSI could not have risen since the Maunder minimum by more than this amount, thus restricting the possible role of solar forcing in global warming. Title: Major Scientific Challenges and Opportunities in Understanding Magnetic Reconnection and Related Explosive Phenomena in Solar and Heliospheric Plasmas Authors: Ji, H.; Karpen, J.; Alt, A.; Antiochos, S.; Baalrud, S.; Bale, S.; Bellan, P. M.; Begelman, M.; Beresnyak, A.; Bhattacharjee, A.; Blackman, E. G.; Brennan, D.; Brown, M.; Buechner, J.; Burch, J.; Cassak, P.; Chen, B.; Chen, L. -J.; Chen, Y.; Chien, A.; Comisso, L.; Craig, D.; Dahlin, J.; Daughton, W.; DeLuca, E.; Dong, C. F.; Dorfman, S.; Drake, J.; Ebrahimi, F.; Egedal, J.; Ergun, R.; Eyink, G.; Fan, Y.; Fiksel, G.; Forest, C.; Fox, W.; Froula, D.; Fujimoto, K.; Gao, L.; Genestreti, K.; Gibson, S.; Goldstein, M.; Guo, F.; Hare, J.; Hesse, M.; Hoshino, M.; Hu, Q.; Huang, Y. -M.; Jara-Almonte, J.; Karimabadi, H.; Klimchuk, J.; Kunz, M.; Kusano, K.; Lazarian, A.; Le, A.; Lebedev, S.; Li, H.; Li, X.; Lin, Y.; Linton, M.; Liu, Y. -H.; Liu, W.; Longcope, D.; Loureiro, N.; Lu, Q. -M.; Ma, Z-W.; Matthaeus, W. H.; Meyerhofer, D.; Mozer, F.; Munsat, T.; Murphy, N. A.; Nilson, P.; Ono, Y.; Opher, M.; Park, H.; Parker, S.; Petropoulou, M.; Phan, T.; Prager, S.; Rempel, M.; Ren, C.; Ren, Y.; Rosner, R.; Roytershteyn, V.; Sarff, J.; Savcheva, A.; Schaffner, D.; Schoeffier, K.; Scime, E.; Shay, M.; Sironi, L.; Sitnov, M.; Stanier, A.; Swisdak, M.; TenBarge, J.; Tharp, T.; Uzdensky, D.; Vaivads, A.; Velli, M.; Vishniac, E.; Wang, H.; Werner, G.; Xiao, C.; Yamada, M.; Yokoyama, T.; Yoo, J.; Zenitani, S.; Zweibel, E. Bibcode: 2020arXiv200908779J Altcode: Magnetic reconnection underlies many explosive phenomena in the heliosphere and in laboratory plasmas. The new research capabilities in theory/simulations, observations, and laboratory experiments provide the opportunity to solve the grand scientific challenges summarized in this whitepaper. Success will require enhanced and sustained investments from relevant funding agencies, increased interagency/international partnerships, and close collaborations of the solar, heliospheric, and laboratory plasma communities. These investments will deliver transformative progress in understanding magnetic reconnection and related explosive phenomena including space weather events. Title: A distinct magnetic property of the inner penumbral boundary. III. Analysis of simulated sunspots Authors: Jurčák, Jan; Schmassmann, Markus; Rempel, Matthias; Bello González, Nazaret; Schlichenmaier, Rolf Bibcode: 2020A&A...638A..28J Altcode: 2020arXiv200403940J Context. Analyses of sunspot observations revealed a fundamental magnetic property of the umbral boundary: the invariance of the vertical component of the magnetic field.
Aims: We analyse the magnetic properties of the umbra-penumbra boundary in simulated sunspots and thus assess their similarity to observed sunspots. We also aim to investigate the role of the plasma β and the ratio of kinetic to magnetic energy in simulated sunspots in the convective motions because these quantities cannot be reliably determined from observations.
Methods: We used a set of non-gray simulation runs of sunspots with the MURaM code. The setups differed in terms of subsurface magnetic field structure and magnetic field boundary imposed at the top of the simulation domain. These data were used to synthesize the Stokes profiles, which were then degraded to the Hinode spectropolarimeter-like observations. Then, the data were treated like real Hinode observations of a sunspot, and magnetic properties at the umbral boundaries were determined.
Results: Simulations with potential field extrapolation produce a realistic magnetic field configuration on the umbral boundaries of the sunspots. Two simulations with a potential field upper boundary, but different subsurface magnetic field structures, differ significantly in the extent of their penumbrae. Increasing the penumbra width by forcing more horizontal magnetic fields at the upper boundary results in magnetic properties that are not consistent with observations. This implies that the size of the penumbra is given by the subsurface structure of the magnetic field, that is, by the depth and inclination of the magnetopause, which is shaped by the expansion of the sunspot flux rope with height. None of the sunspot simulations is consistent with the observed properties of the magnetic field and the direction of the Evershed flow at the same time. Strong outward-directed Evershed flows are only found in setups with an artificially enhanced horizontal component of the magnetic field at the top boundary that are not consistent with the observed magnetic field properties at the umbra-penumbra boundary. We stress that the photospheric boundary of simulated sunspots is defined by a magnetic field strength of equipartition field value. Title: On the Contribution of Quiet-Sun Magnetism to Solar Irradiance Variations: Constraints on Quiet-Sun Variability and Grand-minimum Scenarios Authors: Rempel, M. Bibcode: 2020ApJ...894..140R Altcode: 2020arXiv200401795R While the quiet-Sun magnetic field shows only little variation with the solar cycle, long-term variations cannot be completely ruled out from first principles. We investigate the potential effect of quiet-Sun magnetism on spectral solar irradiance through a series of small-scale dynamo simulations with zero vertical flux imbalance ( $\langle {B}_{z}\rangle =0$) and varying levels of small-scale magnetic field strength, and one weak network case with an additional flux imbalance corresponding to a flux density of $\langle {B}_{z}\rangle =100$ G. From these setups, we compute the dependence of the outgoing radiative energy flux on the mean vertical magnetic field strength in the photosphere at a continuum optical depth τ = 1 ( $\langle | {B}_{z}| {\rangle }_{\tau =1}$). We find that a quiet-Sun setup with a mean vertical field strength of $\langle | {B}_{z}| {\rangle }_{\tau =1}=69$ G is about 0.6% brighter than a non-magnetic reference case. We find a linear dependence of the outgoing radiative energy flux on the mean field strength $\langle | {B}_{z}| {\rangle }_{\tau =1}$ with a relative slope of 1.4 × 10-4 G-1. With this sensitivity, only a moderate change of the quiet-Sun field strength by 10% would lead to a total solar irradiance variation comparable to the observed solar cycle variation. While this does provide strong indirect constraints on possible quiet-Sun variations during a regular solar cycle, it also emphasizes that potential variability over longer timescales could make a significant contribution to longer-term solar irradiance variations. Title: Comparing Radiative Transfer Codes and Opacity Samplings for Solar Irradiance Reconstructions Authors: Criscuoli, Serena; Rempel, Matthias; Haberreiter, Margit; Pereira, Tiago M. D.; Uitenbroek, Han; Fabbian, Damian Bibcode: 2020SoPh..295...50C Altcode: Some techniques developed to reproduce solar irradiance variations make use of synthetic radiative fluxes of quiet and magnetic features. The synthesis of radiative fluxes of astronomical objects is likely to be affected by uncertainties resulting from approximations and specific input employed for the synthesis. In this work we compare spectra obtained with three radiative transfer codes with the purpose of investigating differences in reproducing solar irradiance variations. Specifically, we compare spectral synthesis produced in non-local thermodynamic equilibrium obtained with COSI and RH using 1-D atmosphere models. We also compare local thermodynamic equilibrium syntheses emerging from 3-D MURaM simulations of the solar atmosphere obtained with two sets of opacity tables generated with the ATLAS9 package and with the RH code, and test the effects of opacity sampling on the emergent spectra. We find that, although the different codes and methodologies employed to synthesize the spectrum reproduce overall the observed solar spectrum with a similar degree of accuracy, subtle differences in quiet Sun spectra may translate into larger differences in the computation of the contrasts of magnetic features, which, in turn, critically affect the estimates of solar variability. Title: Major Scientific Challenges and Opportunities in Understanding Magnetic Reconnection and Related Explosive Phenomena throughout the Universe Authors: Ji, H.; Alt, A.; Antiochos, S.; Baalrud, S.; Bale, S.; Bellan, P. M.; Begelman, M.; Beresnyak, A.; Blackman, E. G.; Brennan, D.; Brown, M.; Buechner, J.; Burch, J.; Cassak, P.; Chen, L. -J.; Chen, Y.; Chien, A.; Craig, D.; Dahlin, J.; Daughton, W.; DeLuca, E.; Dong, C. F.; Dorfman, S.; Drake, J.; Ebrahimi, F.; Egedal, J.; Ergun, R.; Eyink, G.; Fan, Y.; Fiksel, G.; Forest, C.; Fox, W.; Froula, D.; Fujimoto, K.; Gao, L.; Genestreti, K.; Gibson, S.; Goldstein, M.; Guo, F.; Hesse, M.; Hoshino, M.; Hu, Q.; Huang, Y. -M.; Jara-Almonte, J.; Karimabadi, H.; Klimchuk, J.; Kunz, M.; Kusano, K.; Lazarian, A.; Le, A.; Li, H.; Li, X.; Lin, Y.; Linton, M.; Liu, Y. -H.; Liu, W.; Longcope, D.; Loureiro, N.; Lu, Q. -M.; Ma, Z-W.; Matthaeus, W. H.; Meyerhofer, D.; Mozer, F.; Munsat, T.; Murphy, N. A.; Nilson, P.; Ono, Y.; Opher, M.; Park, H.; Parker, S.; Petropoulou, M.; Phan, T.; Prager, S.; Rempel, M.; Ren, C.; Ren, Y.; Rosner, R.; Roytershteyn, V.; Sarff, J.; Savcheva, A.; Schaffner, D.; Schoeffier, K.; Scime, E.; Shay, M.; Sitnov, M.; Stanier, A.; TenBarge, J.; Tharp, T.; Uzdensky, D.; Vaivads, A.; Velli, M.; Vishniac, E.; Wang, H.; Werner, G.; Xiao, C.; Yamada, M.; Yokoyama, T.; Yoo, J.; Zenitani, S.; Zweibel, E. Bibcode: 2020arXiv200400079J Altcode: This white paper summarizes major scientific challenges and opportunities in understanding magnetic reconnection and related explosive phenomena as a fundamental plasma process. Title: Using the Butterfly Effect to Probe How the Sun Generates Acoustic Noise Authors: Lindsey, Charles; Rempel, Matthias Bibcode: 2020SoPh..295...26L Altcode: A major encumbrance to recognition of individual episodes of noise emission is the accumulation over hours of other noise emitted long before. This is true in simulations just as it is in the solar environment itself. The composite seismic signature of acoustic radiation accumulated over preceding hours drowns out the signature of newly emitted "acoustic pings." This problem could be alleviated in simulations by periodically damping the accumulated acoustic radiation - if this can be done benignly, i.e. in such a way that the onset transient of the damping (and its subsequent termination) does not emit its own acoustic noise. We introduce a way of doing this based upon a study of the butterfly effect in compressible radiative MHD simulations of convection that excites p-modes. This gives us an encouraging preview of what further development of this utility offers for an understanding of the character of p-mode generation in convective atmospheres. Title: Testing Data-driven Simulations of Solar Eruptive Flares Using Synthetic Magnetograms from Flux Emergence Simulations Authors: Fan, Y.; Rempel, M. Bibcode: 2019AGUFMSH33B3393F Altcode: To understand the feasibility of data-driven simulations of solar eruptive events using the electric field inferred from the observed time sequences of vector magnetograms, we have performed synthetic data driven simulations using synthetic magnetograms and electric fields extracted from interior-to-corona flux emergence simulations. We have carried out coronal simulations of eruptive flares with the MFE MHD code driven by the boundary data at the base of the corona extracted from the flux emergence simulations with the MURaM MHD code. We performed simulations driven with only the horizontal v×B electric field and the vector B field extracted from the MURaM simulation at the transition region height, but with the thermodynamics self-determined from the MFE coronal simulation, which includes the coronal heating due to numerical dissipation, radiative cooling, and field aligned thermal conduction. The coronal heating is due to dissipation of the Poynting flux from the lower boundary electric field due to magneto-convection. We find that the driven coronal simulations produce coronal emissions in AIA channels that are qualitatively similar to those produced by MURaM, and most importantly re-produce the main eruptive flares with sigmoid brightening during the evolution. These experiments suggest that with only the VxB electric field and the B field at the lower boundary (which would be the situation using the observed vector magnetograms), it is possible for coronal MHD simulations to reproduce the coronal magnetic field evolution and onset of eruptions. Title: Combining magnetohydrostatic constraints with Stokes profiles inversions. I. Role of boundary conditions Authors: Borrero, J. M.; Pastor Yabar, A.; Rempel, M.; Ruiz Cobo, B. Bibcode: 2019A&A...632A.111B Altcode: Context. Inversion codes for the polarized radiative transfer equation, when applied to spectropolarimetric observations (i.e., Stokes vector) in spectral lines, can be used to infer the temperature T, line-of-sight velocity vlos, and magnetic field B as a function of the continuum optical-depth τc. However, they do not directly provide the gas pressure Pg or density ρ. In order to obtain these latter parameters, inversion codes rely instead on the assumption of hydrostatic equilibrium (HE) in addition to the equation of state (EOS). Unfortunately, the assumption of HE is rather unrealistic across magnetic field lines, causing estimations of Pg and ρ to be unreliable. This is because the role of the Lorentz force, among other factors, is neglected. Unreliable gas pressure and density also translate into an inaccurate conversion from optical depth τc to geometrical height z.
Aims: We aim at improving the determination of the gas pressure and density via the application of magnetohydrostatic (MHS) equilibrium instead of HE.
Methods: We develop a method to solve the momentum equation under MHS equilibrium (i.e., taking the Lorentz force into account) in three dimensions. The method is based on the iterative solution of a Poisson-like equation. Considering the gas pressure Pg and density ρ from three-dimensional magnetohydrodynamic (MHD) simulations of sunspots as a benchmark, we compare the results from the application of HE and MHS equilibrium using boundary conditions with different degrees of realism. Employing boundary conditions that can be applied to actual observations, we find that HE retrieves the gas pressure and density with an error smaller than one order of magnitude (compared to the MHD values) in only about 47% of the grid points in the three-dimensional domain. Moreover, the inferred values are within a factor of two of the MHD values in only about 23% of the domain. This translates into an error of about 160 - 200 km in the determination of the z - τc conversion (i.e., Wilson depression). On the other hand, the application of MHS equilibrium with similar boundary conditions allows determination of Pg and ρ with an error smaller than an order of magnitude in 84% of the domain. The inferred values are within a factor of two in more than 55% of the domain. In this latter case, the z - τc conversion is obtained with an accuracy of 30 - 70 km. Inaccuracies are due in equal part to deviations from MHS equilibrium and to inaccuracies in the boundary conditions.
Results: Compared to HE, our new method, based on MHS equilibrium, significantly improves the reliability in the determination of the density, gas pressure, and conversion between geometrical height z and continuum optical depth τc. This method could be used in conjunction with the inversion of the radiative transfer equation for polarized light in order to determine the thermodynamic, kinematic, and magnetic parameters of the solar atmosphere. Title: Superstrong photospheric magnetic fields in sunspot penumbrae Authors: Siu-Tapia, A.; Lagg, A.; van Noort, M.; Rempel, M.; Solanki, S. K. Bibcode: 2019A&A...631A..99S Altcode: 2019arXiv190913619S Context. Recently, there have been some reports of unusually strong photospheric magnetic fields (which can reach values of over 7 kG) inferred from Hinode SOT/SP sunspot observations within penumbral regions. These superstrong penumbral fields are even larger than the strongest umbral fields on record and appear to be associated with supersonic downflows. The finding of such fields has been controversial since they seem to show up only when spatially coupled inversions are performed.
Aims: Here, we investigate and discuss the reliability of those findings by studying in detail observed spectra associated with particularly strong magnetic fields at the inner edge of the penumbra of active region 10930.
Methods: We applied classical diagnostic methods and various inversions with different model atmospheres to the observed Stokes profiles in two selected pixels with superstrong magnetic fields, and compared the results with a magnetohydrodynamic simulation of a sunspot whose penumbra contains localized regions with strong fields (nearly 5 kG at τ = 1) associated with supersonic downflows.
Results: The different inversions provide different results: while the SPINOR 2D inversions consider a height-dependent single-component model and return B > 7 kG and supersonic positive vLOS (corresponding to a counter-Evershed flow), height-dependent two-component inversions suggest the presence of an umbral component (almost at rest) with field strengths ∼4 - 4.2 kG and a penumbral component with vLOS ∼ 16 - 18 km s-1 and field strengths up to ∼5.8 kG. Likewise, height-independent two-component inversions find a solution for an umbral component and a strongly redshifted (vLOS ∼ 15 - 17 km s-1) penumbral component with B ∼ 4 kG. According to a Bayesian information criterion, the inversions providing a better balance between the quality of the fits and the number of free parameters considered by the models are the height-independent two-component inversions, but they lie only slightly above the SPINOR 2D inversions. Since it is expected that the physical parameters all display considerable gradients with height, as supported by magnetohydrodynamic (MHD) sunspot simulations, the SPINOR 2D inversions are the preferred ones.
Conclusions: According to the MHD sunspot simulation analyzed here, the presence of counter-Evershed flows in the photospheric penumbra can lead to the necessary conditions for the observation of ∼5 kG fields at the inner penumbra. Although a definite conclusion about the potential existence of fields in excess of 7 kG cannot be given, their nature could be explained (based on the simulation results) as the consequence of the extreme dynamical effects introduced by highly supersonic counter-Evershed flows (vLOS > 10 km s-1 and up to ∼30 km s-1 according to SPINOR 2D). The latter are much faster and more compressive downflows than those found in the MHD simulations and therefore could lead to field intensification up to considerably stronger fields. Also, a lower gas density would lead to a deeper depression of the τ = 1 surface, making possible the observation of deeper-lying stronger fields. The superstrong magnetic fields are expected to be nearly force-free, meaning that they can attain much larger strengths than expected when considering only balance between magnetic pressure and the local gas pressure. Title: Three-dimensional modeling of chromospheric spectral lines in a simulated active region Authors: Bjørgen, Johan P.; Leenaarts, Jorrit; Rempel, Matthias; Cheung, Mark C. M.; Danilovic, Sanja; de la Cruz Rodríguez, Jaime; Sukhorukov, Andrii V. Bibcode: 2019A&A...631A..33B Altcode: 2019arXiv190601098B Context. Because of the complex physics that governs the formation of chromospheric lines, interpretation of solar chromospheric observations is difficult. The origin and characteristics of many chromospheric features are, because of this, unresolved.
Aims: We focus on studying two prominent features: long fibrils and flare ribbons. To model these features, we use a 3D magnetohydrodynamic simulation of an active region, which self-consistently reproduces both of these features.
Methods: We modeled the Hα, Mg II k, Ca II K, and Ca II 8542 Å lines using the 3D non-LTE radiative transfer code Multi3D. To obtain non-LTE electron densities, we solved the statistical equilibrium equations for hydrogen simultaneously with the charge conservation equation. We treated the Ca II K and Mg II k lines with partially coherent scattering.
Results: This simulation reproduces long fibrils that span between the opposite-polarity sunspots and go up to 4 Mm in height. They can be traced in all lines owing to density corrugation. In contrast to previous studies, Hα, Mg II h&k, and Ca II H&K are formed at similar height in this model. Although some of the high fibrils are also visible in the Ca II 8542 Å line, this line tends to sample loops and shocks lower in the chromosphere. Magnetic field lines are aligned with the Hα fibrils, but the latter holds to a lesser extent for the Ca II 8542 Å line. The simulation shows structures in the Hα line core that look like flare ribbons. The emission in the ribbons is caused by a dense chromosphere and a transition region at high column mass. The ribbons are visible in all chromospheric lines, but least prominent in Ca II 8542 Å line. In some pixels, broad asymmetric profiles with a single emission peak are produced similar to the profiles observed in flare ribbons. They are caused by a deep onset of the chromospheric temperature rise and large velocity gradients.
Conclusions: The simulation produces long fibrils similar to what is seen in observations. It also produces structures similar to flare ribbons despite the lack of nonthermal electrons in the simulation. The latter suggests that thermal conduction might be a significant agent in transporting flare energy to the chromosphere in addition to nonthermal electrons. Title: A comprehensive three-dimensional radiative magnetohydrodynamic simulation of a solar flare Authors: Cheung, M. C. M.; Rempel, M.; Chintzoglou, G.; Chen, F.; Testa, P.; Martínez-Sykora, J.; Sainz Dalda, A.; DeRosa, M. L.; Malanushenko, A.; Hansteen, V.; De Pontieu, B.; Carlsson, M.; Gudiksen, B.; McIntosh, S. W. Bibcode: 2019NatAs...3..160C Altcode: 2018NatAs...3..160C Solar and stellar flares are the most intense emitters of X-rays and extreme ultraviolet radiation in planetary systems1,2. On the Sun, strong flares are usually found in newly emerging sunspot regions3. The emergence of these magnetic sunspot groups leads to the accumulation of magnetic energy in the corona. When the magnetic field undergoes abrupt relaxation, the energy released powers coronal mass ejections as well as heating plasma to temperatures beyond tens of millions of kelvins. While recent work has shed light on how magnetic energy and twist accumulate in the corona4 and on how three-dimensional magnetic reconnection allows for rapid energy release5,6, a self-consistent model capturing how such magnetic changes translate into observable diagnostics has remained elusive. Here, we present a comprehensive radiative magnetohydrodynamics simulation of a solar flare capturing the process from emergence to eruption. The simulation has sufficient realism for the synthesis of remote sensing measurements to compare with observations at visible, ultraviolet and X-ray wavelengths. This unifying model allows us to explain a number of well-known features of solar flares7, including the time profile of the X-ray flux during flares, origin and temporal evolution of chromospheric evaporation and condensation, and sweeping of flare ribbons in the lower atmosphere. Furthermore, the model reproduces the apparent non-thermal shape of coronal X-ray spectra, which is the result of the superposition of multi-component super-hot plasmas8 up to and beyond 100 million K. Title: Combining magneto-hydrostatic constraints with Stokes profiles inversions Authors: Borrero, J. M.; Pastor Yabar, A.; Rempel, M.; Ruiz Cobo, B. Bibcode: 2019arXiv191014131B Altcode: Inversion codes for the polarized radiative transfer equation can be used to infer the temperature $T$, line-of-sight velocity $v_{\rm los}$, and magnetic field $\rm{\bf B}$ as a function of the continuum optical-depth $\tau_{\rm c}$. However, they do not directly provide the gas pressure $P_{\rm g}$ or density $\rho$. In order to obtain these latter parameters, inversion codes rely instead on the assumption of hydrostatic equilibrium (HE) in addition to the equation of state (EOS). Unfortunately, the assumption of HE is rather unrealistic across magnetic field lines. This is because the role of the Lorentz force, among other factors, is neglected. This translates into an inaccurate conversion from optical depth $\tau_{\rm c}$ to geometrical height $z$. We aim at improving this conversion via the application of magneto-hydrostatic (MHS) equilibrium instead of HE. We develop a method to solve the momentum equation under MHS equilibrium (i.e., taking the Lorentz force into account) in three dimensions. The method is based on the solution of a Poisson-like equation. Considering the gas pressure $P_{\rm g}$ and density $\rho$ from three-dimensional magneto-hydrodynamic (MHD) simulations of sunspots as a benchmark, we compare the results from the application of HE and MHS equilibrium. We find that HE retrieves the gas pressure and density within an order of magnitude of the MHD values in only about 47 \% of the domain. This translates into an error of about $160-200$ km in the determination of the $z-\tau_{\rm c}$ conversion. On the other hand, the application of MHS equilibrium allows determination of $P_{\rm g}$ and $\rho$ within an order of magnitude in 84 \% of the domain. In this latter case, the $z-\tau_{\rm c}$ conversion is obtained with an accuracy of $30-70$ km. Title: Principles Of Heliophysics: a textbook on the universal processes behind planetary habitability Authors: Schrijver, Karel; Bagenal, Fran; Bastian, Tim; Beer, Juerg; Bisi, Mario; Bogdan, Tom; Bougher, Steve; Boteler, David; Brain, Dave; Brasseur, Guy; Brownlee, Don; Charbonneau, Paul; Cohen, Ofer; Christensen, Uli; Crowley, Tom; Fischer, Debrah; Forbes, Terry; Fuller-Rowell, Tim; Galand, Marina; Giacalone, Joe; Gloeckler, George; Gosling, Jack; Green, Janet; Guetersloh, Steve; Hansteen, Viggo; Hartmann, Lee; Horanyi, Mihaly; Hudson, Hugh; Jakowski, Norbert; Jokipii, Randy; Kivelson, Margaret; Krauss-Varban, Dietmar; Krupp, Norbert; Lean, Judith; Linsky, Jeff; Longcope, Dana; Marsh, Daniel; Miesch, Mark; Moldwin, Mark; Moore, Luke; Odenwald, Sten; Opher, Merav; Osten, Rachel; Rempel, Matthias; Schmidt, Hauke; Siscoe, George; Siskind, Dave; Smith, Chuck; Solomon, Stan; Stallard, Tom; Stanley, Sabine; Sojka, Jan; Tobiska, Kent; Toffoletto, Frank; Tribble, Alan; Vasyliunas, Vytenis; Walterscheid, Richard; Wang, Ji; Wood, Brian; Woods, Tom; Zapp, Neal Bibcode: 2019arXiv191014022S Altcode: This textbook gives a perspective of heliophysics in a way that emphasizes universal processes from a perspective that draws attention to what provides Earth (and similar (exo-)planets) with a relatively stable setting in which life as we know it can thrive. The book is intended for students in physical sciences in later years of their university training and for beginning graduate students in fields of solar, stellar, (exo-)planetary, and planetary-system sciences. Title: Opposite Polarity Magnetic Fields and Convective Downflows in a Simulated Sunspot Penumbra Authors: Bharti, Lokesh; Rempel, Matthias Bibcode: 2019ApJ...884...94B Altcode: 2019arXiv190806439B Recent numerical simulations and observations of sunspots show a significant amount of opposite polarity magnetic fields within the sunspot penumbra. Most of the opposite polarity fields are associated with convective downflows. We present an analysis of 3D MHD simulations through forward modeling of synthetic Stokes profiles of the Fe I 6301.5 Å and Fe I 6302.5 Å lines. The synthetic Stokes profiles are spatially and spectrally degraded considering typical instrument properties. Line bisector shifts of the Fe I 6301.5 Å line are used to determine line-of-sight velocities. Far wing magnetograms are constructed from the Stokes V profiles of the Fe I 6302.5 Å line. While we find an overall good agreement between observations and simulations, the fraction of opposite polarity magnetic fields, the downflow filling factor, and the opposite polarity-downflow association are strongly affected by spatial smearing and presence of strong gradients in the line-of-sight magnetic fields and velocity. A significant fraction of opposite polarity magnetic fields and downflows is hidden in the observations due to typical instrumental noise. Comparing simulations that differ by more than a factor of two in grid spacing, we find that these quantities are robust within the simulations. Title: What the Sudden Death of Solar Cycles Can Tell Us About the Nature of the Solar Interior Authors: McIntosh, Scott W.; Leamon, Robert J.; Egeland, Ricky; Dikpati, Mausumi; Fan, Yuhong; Rempel, Matthias Bibcode: 2019SoPh..294...88M Altcode: 2019arXiv190109083M We observe the abrupt end of solar-activity cycles at the Sun's Equator by combining almost 140 years of observations from ground and space. These "terminator" events appear to be very closely related to the onset of magnetic activity belonging to the next solar cycle at mid-latitudes and the polar-reversal process at high latitudes. Using multi-scale tracers of solar activity we examine the timing of these events in relation to the excitation of new activity and find that the time taken for the solar plasma to communicate this transition is of the order of one solar rotation - but it could be shorter. Utilizing uniquely comprehensive solar observations from the Solar Terrestrial Relations Observatory (STEREO) and Solar Dynamics Observatory (SDO) we see that this transitional event is strongly longitudinal in nature. Combined, these characteristics suggest that information is communicated through the solar interior rapidly. A range of possibilities exist to explain such behavior: for example gravity waves on the solar tachocline, or that the magnetic fields present in the Sun's convection zone could be very large, with a poloidal field strengths reaching 50 kG - considerably larger than conventional explorations of solar and stellar dynamos estimate. Regardless of the mechanism responsible, the rapid timescales demonstrated by the Sun's global magnetic-field reconfiguration present strong constraints on first-principles numerical simulations of the solar interior and, by extension, other stars. Title: Reversed Dynamo at Small Scales and Large Magnetic Prandtl Number Authors: Brandenburg, Axel; Rempel, Matthias Bibcode: 2019ApJ...879...57B Altcode: 2019arXiv190311869B We show that at large magnetic Prandtl numbers, the Lorentz force does work on the flow at small scales and drives fluid motions, whose energy is dissipated viscously. This situation is the opposite of that in a normal dynamo, where the flow does work against the Lorentz force. We compute the spectral conversion rates between kinetic and magnetic energies for several magnetic Prandtl numbers and show that normal (forward) dynamo action occurs on large scales over a progressively narrower range of wavenumbers as the magnetic Prandtl number is increased. At higher wavenumbers, reversed dynamo action occurs, i.e., magnetic energy is converted back into kinetic energy at small scales. We demonstrate this in both direct numerical simulations forced by volume stirring and in large eddy simulations (LESs) of solar convectively driven small-scale dynamos. Low-density plasmas such as stellar coronae tend to have large magnetic Prandtl numbers, i.e., the viscosity is large compared with the magnetic diffusivity. The regime in which viscous dissipation dominates over resistive dissipation for large magnetic Prandtl numbers was also previously found in LESs of the solar corona, i.e., our findings are a more fundamental property of MHD that is not just restricted to dynamos. Viscous energy dissipation is a consequence of positive Lorentz force work, which may partly correspond to particle acceleration in close-to-collisionless plasmas. This is, however, not modeled in the MHD approximation employed. By contrast, resistive energy dissipation on current sheets is expected to be unimportant in stellar coronae. Title: Radiative MHD Simulation of a Solar Flare Authors: Cheung, Mark; Rempel, Matthias D.; Chintzoglou, Georgios; Chen, Feng; Testa, Paola; Martinez-Sykora, Juan; Sainz Dalda, Alberto; DeRosa, Marc L.; Malanushenko, Anna; Hansteen, Viggo; Carlsson, Mats; De Pontieu, Bart; Gudiksen, Boris; McIntosh, Scott W. Bibcode: 2019AAS...23431005C Altcode: We present a radiative MHD simulation of a solar flare. The computational domain captures the near-surface layers of the convection zone and overlying atmosphere. Inspired by the observed evolution of NOAA Active Region (AR) 12017, a parasitic bipolar region is imposed to emerge in the vicinity of a pre-existing sunspot. The emergence of twisted magnetic flux generates shear flows that create a pre-existing flux rope underneath the canopy field of the sunspot. Following erosion of the overlying bootstrapping field, the flux rope erupts. Rapid release of magnetic energy results in multi-wavelength synthetic observables (including X-ray spectra, narrowband EUV images, Doppler shifts of EUV lines) that are consistent with flare observations. This works suggests the super-position of multi-thermal, superhot (up to 100 MK) plasma may be partially responsible for the apparent non-thermal shape of coronal X-ray sources in flares. Implications for remote sensing observations of other astrophysical objects is also discussed. This work is an important stepping stone toward high-fidelity data-driven MHD models. Title: On the Challenges of synthetizing solar and stellar spectra for Irradiance reconstructions Authors: Criscuoli, Serena; Rempel, Matthias D.; Haberreiter, Margit; Pereira, Tiago; Uitenbroek, Han; Fabbian, Damian Bibcode: 2019AAS...23421702C Altcode: Syntheses of solar and stellar spectra strongly depend on the adopted approximations and atomic and molecular databases. We compare LTE and NLTE syntheses of solar spectra obtained with widely used radiative transfer codes, utilizing both 3D-MHD simulations and 1D-static atmosphere models. We show that although different codes reproduce reasonably well the observed spectrum, subtle differences may translate into discrepancies of several tens of percents in the estimate of solar and stellar spectral irradiance variability. Title: Constraining non-linear dynamo models using quasi-biennial oscillations from sunspot area data Authors: Inceoglu, F.; Simoniello, R.; Arlt, R.; Rempel, M. Bibcode: 2019A&A...625A.117I Altcode: 2019arXiv190403724I Context. Solar magnetic activity exhibits variations with periods between 1.5 and 4 years, the so-called quasi-biennial oscillations (QBOs), in addition to the well-known 11-year Schwabe cycles. Solar dynamo is thought to be the mechanism responsible for the generation of QBOs.
Aims: In this work, we analyse sunspot areas to investigate the spatial and temporal behaviour of the QBO signal and study the physical mechanisms responsible using simulations from fully non-linear mean-field flux-transport dynamos.
Methods: We investigated the behaviour of the QBOs in the sunspot area data for the full disk, and the northern and southern hemispheres, using wavelet and Fourier analyses. We also ran solar dynamos with two different approaches to generating a poloidal field from an existing toroidal field, namely Babcock-Leighton and turbulent α mechanisms. We then studied the simulated magnetic field strengths as well as meridional circulation and differential rotation rates using the same methods.
Results: The results from the sunspot areas show that the QBOs are present in the full disk and hemispheric sunspot areas. These QBOs show slightly different spatial and temporal behaviours, indicating slightly decoupled solar hemispheres. The QBO signal is generally intermittent and in-phase with the sunspot area data, surfacing when the solar activity is at its maximum. The results from the BL-dynamos show that they are neither capable of generating the slightly decoupled behaviour of solar hemispheres nor can they generate QBO-like signals. The turbulent α-dynamos on the other hand generated decoupled hemispheres and some QBO-like shorter cycles.
Conclusions: In conclusion, our simulations show that the turbulent α-dynamos with the Lorentz force seem more efficient in generating the observed temporal and spatial behaviour of the QBO signal compared with the BL-dynamos. Title: Major Scientific Challenges and Opportunities in Understanding Magnetic Reconnection and Related Explosive Phenomena throughout the Universe Authors: Ji, Hantao; Alt, A.; Antiochos, S.; Baalrud, S.; Bale, S.; Bellan, P. M.; Begelman, M.; Beresnyak, A.; Blackman, E. G.; Brennan, D.; Brown, M.; Buechner, J.; Burch, J.; Cassak, P.; Chen, L. -J.; Chen, Y.; Chien, A.; Craig, D.; Dahlin, J.; Daughton, W.; DeLuca, E.; Dong, C. F.; Dorfman, S.; Drake, J.; Ebrahimi, F.; Egedal, J.; Ergun, R.; Eyink, G.; Fan, Y.; Fiksel, G.; Forest, C.; Fox, W.; Froula, D.; Fujimoto, K.; Gao, L.; Genestreti, K.; Gibson, S.; Goldstein, M.; Guo, F.; Hesse, M.; Hoshino, M.; Hu, Q.; Huang, Y. -M.; Jara-Almonte, J.; Karimabadi, H.; Klimchuk, J.; Kunz, M.; Kusano, K.; Lazarian, A.; Le, A.; Li, H.; Li, X.; Lin, Y.; Linton, M.; Liu, Y. -H.; Liu, W.; Longcope, D.; Louriero, N.; Lu, Q. -M.; Ma, Z. -W.; Matthaeus, W. H.; Meyerhofer, D.; Mozer, F.; Munsat, T.; Murphy, N. A.; Nilson, P.; Ono, Y.; Opher, M.; Park, H.; Parker, S.; Petropoulou, M.; Phan, T.; Prager, S.; Rempel, M.; Ren, C.; Ren, Y.; Rosner, R.; Roytershteyn, V.; Sarff, J.; Savcheva, A.; Schaffner, D.; Schoeffier, K.; Scime, E.; Shay, M.; Sitnov, M.; Stanier, A.; TenBarge, J.; Tharp, T.; Uzdensky, D.; Vaivads, A.; Velli, M.; Vishniac, E.; Wang, H.; Werner, G.; Xiao, C.; Yamada, M.; Yokoyama, T.; Yoo, J.; Zenitani, S.; Zweibel, E. Bibcode: 2019BAAS...51c...5J Altcode: 2019astro2020T...5J This is a group white paper of 100 authors (each with explicit permission via email) from 51 institutions on the topic of magnetic reconnection which is relevant to 6 thematic areas. Grand challenges and research opportunities are described in observations, numerical modeling and laboratory experiments in the upcoming decade. Title: The Solar Photospheric Continuum Brightness as a Function of Mean Magnetic Flux Density. I. The Role of the Magnetic Structure Size Distribution Authors: Peck, C. L.; Rast, M. P.; Criscuoli, S.; Rempel, M. Bibcode: 2019ApJ...870...89P Altcode: Solar irradiance models indicate that irradiance variations are dominated by changes in the disk-coverage of magnetic structures, whose brightness is thought to be determined by their size and average magnetic flux density. Recent results suggest that the brightness of small-scale magnetic structures also depends on the mean magnetic flux of the extended region surrounding them due to reduced convective vigor. Low spatial resolution, however, may limit the ability to distinguish the role of magnetic structure size distributions from that of the mean magnetic flux. Using high-resolution 3D MHD simulations, we investigate the brightness of magnetic structures embedded in regions characterized by different mean magnetic flux. In agreement with previous results, we find reduced brightness with increasing mean magnetic flux when comparing the pixel-by-pixel continuum brightness versus magnetic field strength. Evaluating equivalently sized magnetic structures, however, we find no significant dependence of the magnetic structure brightness on the mean magnetic flux of the region in which they are embedded. Rather, we find that simulations with larger mean magnetic flux generate larger, and therefore darker, magnetic structures whose contributions result in an overall darkening of the region. The differences in magnetic structure size distributions alone can explain the reduced brightness of regions with larger mean magnetic flux. This implies that, for the range of mean magnetic flux of the simulations, convective suppression plays at most a secondary role in determining radiative output of magnetized regions. Quantifying the role of convective transport over a wider range of mean magnetic flux is the subject of the second paper in this series. Title: Solar Eruptions during Magnetic Flux Emergence from the Convection Zone to the Corona Authors: Chen, Feng; Fan, Yuhong; Rempel, Matthias; Nimmo, Kenzie Bibcode: 2018cosp...42E.599C Altcode: We present a realistic numerical model of magnetic flux emergence from the convection zone to the corona. The magnetic and velocity fields from a solar convective dynamo simulation are used as a time-dependent bottom boundary to drive the radiation magnetohydrodynamic simulations. The sophisticated treatments on the radiation and thermal conduction in the simulation allow a direct comparison between model synthesized observables and real observations. The main results are: (1) The quiet Sun corona is heated to over 1 MK by the energy flux provided by the small-scale magnetic field that is maintained by a local dynamo. (2) Emerging flux bundles create several active regions in a 200 Mm wide domain. The coronal temperature is significantly increased as active regions are forming at the photosphere. (3) Synthetic EUV images show coronal loops with various lengths and temperature. (4) More than 100 flares, with 1/3 reaching C class and above, occur in the simulation. The magnetic energy is mostly release through the work done by the Lorentz force, which is quickly thermalized by the viscosity. Moreover, the energy released during the flares and soft X-ray flux, i.e., the flare class nicely reproduce the relationship derived from observations. (5) The biggest flare reaches M2.5 and releases about 5e31 ergs magnetic energy. Plasma in cusp-shaped post-flare loops is heated to several tens MK. The flare is accompanied by the ejection of a giant flux rope that originates from highly sheared magnetic field at the polarity inversion line of a sunspot pair. Title: Small-scale Dynamo Simulations: Magnetic Field Amplification in Exploding Granules and the Role of Deep and Shallow Recirculation Authors: Rempel, M. Bibcode: 2018ApJ...859..161R Altcode: 2018arXiv180508390R We analyze recent high-resolution photospheric small-scale dynamo simulations that were computed with the MURaM radiative MHD code. We focus our analysis on newly forming downflow lanes in exploding granules, as they show how weakly magnetized regions in the photosphere (the center of granules) evolve into strongly magnetized regions (downflow lanes). We find that newly formed downflow lanes initially exhibit mostly a laminar converging flow that amplifies the vertical magnetic field embedded in the granule from a few 10 G to field strengths exceeding 800 G. This results in extended magnetic sheets that have a length comparable to granular scales. Field amplification by turbulent shear first happens a few 100 km beneath the visible layers of the photosphere. Shallow recirculation transports the resulting turbulent field into the photosphere within minutes, after which the newly formed downflow lane shows a mix of strong magnetic sheets and turbulent field components. We stress in particular the role of shallow and deep recirculation for the organization and strength of magnetic field in the photosphere and discuss the photospheric and sub-photospheric energy conversion associated with the small-scale dynamo process. While the energy conversion through the Lorentz force depends only weakly on the saturation field strength (and therefore deep or shallow recirculation), it is strongly dependent on the magnetic Prandtl number. We discuss the potential of these findings for further constraining small-scale dynamo models through high-resolution observations. Title: Vector Magnetograms - From Photosphere to the Base of the Solar Corona Authors: Malanushenko, Anna V.; Rempel, Matthias; Cheung, Chun Ming Mark Bibcode: 2018tess.conf20234M Altcode: The magnetic field in solar active regions is currently a major topic of research in solar physics. While hard to measure directly, it is commonly modeled with the use of photospheric magnetograms. An assumption that is often made in such modeling is that the plasma beta is small in the rarefied corona and therefore an equilibrium configuration requires that the Lorentz force vanishes through the volume. While this assumption greatly simplifies the modeling, it also complicates the use of the photospheric magnetic field as a boundary condition, as the photosphere is not in general a low-beta environment. While vector magnetograms at the base of the low-beta corona are not routinely available, the photospheric magnetograms continue to be widely used for coronal modeling. Additional steps, such as pre-processing, can be taken during the modeling to make these data as consistent with the low-beta equilibria as possible. In this work, we attempt to analyze how much do magnetograms of the coronal base differ from those of the photosphere, analyze their morphology, magnitude and how they change with height. For this, we analyze some of the most realistic full-MHD simulations of active regions made with MURaM code. They simulation volume includes upper convection zone, photosphere, transition region, and the corona. While they are not simulations of a specific active region, they appear extremely realistic in wide range of diagnostics, from the magnetic field in the photosphere, to the coronal morphology, to evolution typically observed in active regions. We study these simulations and the synthetic data they produce, focusing on the applicability of vector magnetograms to low-beta coronal magnetic modeling. We also describe some alternative methods of gathering vector magnetograms of the chromosphere from the coronal morphology, and compare them to the actual structures of the simulations. Title: Statistical study of the release of magnetic energy during flares in a large-scale MHD simulation Authors: Chen, Feng; Nimmo, Kenzie; Rempel, Matthias; Fan, Yuhong Bibcode: 2018tess.conf10421C Altcode: We analyze how the magnetic energy is release and converted into other forms of energy in (the impulsive phase of) flares that occur in a large scale realistic MHD simulation of magnetic flux emergence from the convection zone to the corona. The magnetic and velocity fields from a solar convective dynamo simulation are used as a time-dependent bottom boundary to drive the radiation magnetohydrodynamic simulations. "Realistic" referred to that the sophisticated treatments on the radiation and thermal conduction in the simulation allow a direct and quantitative comparison between model synthesized observables and real observations. The main results are: (1) The quiet Sun corona is heated to over 1 MK by the energy flux provided by the small-scale magnetic field that is maintained by a local dynamo. Emerging flux bundles bring more than 1023 Mx flux to the photosphere in a period of about 50 hours and give rise to several active regions. The coronal temperature is significantly increased as active regions are forming at the photosphere. (2) More than 100 flares, which are identified by peaks in the magnetic energy releasing rate, occur in the simulation. Synthesized GOES soft X-ray flux shows that about 1/3 of them reaching C class and above. The largest one reaches M2.5 and releases about 5e31 ergs of magnetic energy, and is associated with a flux rope ejection. (3) The magnetic energy is mostly release through the work done by the Lorentz force, which is quickly thermalized by the viscosity, i.e. converted to the internal energy of the plasma. Then above half of the energy released is taken away by the radiative loss during the impulsive phase. (4) The synthesized GOES soft X-ray flux, i.e., the flare class is well correlated with the magnetic energy released during the flares. The relation shows that an M (X) class flare corresponds to 1031 (1032 ) ergs of magnetic energy released. Title: Transport of Internetwork Magnetic Flux Elements in the Solar Photosphere : Signatures of Large-Scale Flows and their Effect on Transport Statistics Authors: Agrawal, Piyush; Rast, Mark; Gosic, Milan; Rempel, Matthias; Bellot Rubio, Luis Bibcode: 2018tess.conf21704A Altcode: The motions of small-scale magnetic <span class="s1" flux elements in the solar photosphere can provide some measure of the Lagrangian properties of the convective <span class="s1" flow. Measurements of these motions have been critical in estimating the turbulent diffusion coef<span class="s1" ficient in <span class="s1" flux-transport dynamo models and in determining the Alfvén wave excitation spectrum for coronal heating models. We examine the motions of internetwork <span class="s1" flux elements in Hinode<span class="s1" /Narrowband Filter Imager magnetograms and study the scaling of their mean squared displacement and the shape of their displacement probability distribution as a function of time. We <span class="s1" find that the mean squared displacement scales super-diffusively with a slope of about 1.48. Super-diffusive scaling has been observed in other studies for temporal increments as small as 5 s, increments over which ballistic scaling would be expected. Using high-cadence MURaM simulations, we show that the observed super-diffusive scaling at short increments is a consequence of random changes in barycenter positions due to <span class="s1" flux evolution. We also <span class="s1" find that for long temporal increments, beyond granular lifetimes, the observed displacement distribution deviates from that expected for a diffusive process, evolving from Rayleigh to Gaussian. This change in distribution can be modeled analytically by accounting for supergranular advection along with granular motions. These results complicate the interpretation of magnetic element motions as strictly advective or diffusive on short and long timescales and suggest that measurements of magnetic element motions must be used with caution in turbulent diffusion or wave excitation models. We propose that passive tracer motions in measured photospheric <span class="s1" flows may yield more robust transport statistics. Title: Measuring the Spatio-temporal Statistics of Magnetic Flux Emergence Authors: Lamb, Derek A.; Glueck, Deborah; Rempel, Matthias Bibcode: 2018tess.conf21163L Altcode: The large-scale solar magnetic field, in the form of sunspots and the associated active regions, exhibits more-or-less predictable patterns of flux emergence associated with the solar cycle: cycle periods fall in a small range of 9-13 years, and sunspot emergence in each cycle starts at latitudes of approximately 30 degrees and progresses towards the equators. The small-scale magnetic field is observed at all phases of the solar cycle and at all latitudes. Do the properties of flux emergence change at different scales, or are there smooth transitions between small- and large-scale flux emergence? We describe our first steps toward addressing this question, by algorithmically and manually identifying flux emergence in sequences of SDO/HMI magnetograms. We measure several properties of the individual flux emergence events, such as the flux emergence rate, the bipole orientation and separation speed, and compare the statistical distributions of these properties as a function of the total emerged flux. We make some preliminary comparisons to flux emergence events identified in small-scale dynamo simulations. Title: Simulations of quiet Sun magnetism: On the role of deep and shallow recirculation in small-scale dynamo simulations Authors: Rempel, Matthias Bibcode: 2018tess.conf11505R Altcode: Observations suggest that small-scale magnetic field in the solar photosphere is mostly independent from the strength of nearby network field as well as independent of the solar cycle. This supports the view that the origin of small-scale magnetism is due to a small-scale dynamo that operates independently from the large-scale dynamo responsible for the solar cycle. The saturation field strength and structure of the resulting magnetic field in the photosphere depends critically on the contributions from deep and shallow recirculation within the strongly stratified convection zone. We analyze recent high resolution photospheric small-scale dynamo simulations that were computed with the MURaM radiative MHD code. We focus the analysis on newly forming downflow lanes in exploding granules since they show how weakly magnetized regions in the photosphere (center of granules) evolve into the most strongly magnetized regions (downflow lanes). We find that newly formed downflow lanes exhibit initially mostly a laminar converging flow that amplifies the vertical magnetic field embedded in the granule from initially a few 10 G to field strengths of up to 1 kG on a time scale of about 2 minutes. This results in extended magnetic sheets that have a length comparable to granular scales. These sheets are a consequence of deep recirculation. Field amplification by turbulent shear happens first a few 100 km beneath the visible layers of the photosphere. Shallow recirculation transports the resulting turbulent field into the photosphere within minutes, after which the newly formed downflow lane shows a mix of strong magnetic sheets and turbulent field components. Furthermore, deep recirculation leads to a magnetic flux imbalance on larger scales that can maintain a quiet Sun (mixed polarity) magnetic network solely through small-scale dynamo action. We discuss the potential of these findings for further constraining small-scale dynamo models through high resolution observations. Title: Transport of Internetwork Magnetic Flux Elements in the Solar Photosphere Authors: Agrawal, Piyush; Rast, Mark P.; Gošić, Milan; Bellot Rubio, Luis R.; Rempel, Matthias Bibcode: 2018ApJ...854..118A Altcode: 2017arXiv171101290A The motions of small-scale magnetic flux elements in the solar photosphere can provide some measure of the Lagrangian properties of the convective flow. Measurements of these motions have been critical in estimating the turbulent diffusion coefficient in flux-transport dynamo models and in determining the Alfvén wave excitation spectrum for coronal heating models. We examine the motions of internetwork flux elements in Hinode/Narrowband Filter Imager magnetograms and study the scaling of their mean squared displacement and the shape of their displacement probability distribution as a function of time. We find that the mean squared displacement scales super-diffusively with a slope of about 1.48. Super-diffusive scaling has been observed in other studies for temporal increments as small as 5 s, increments over which ballistic scaling would be expected. Using high-cadence MURaM simulations, we show that the observed super-diffusive scaling at short increments is a consequence of random changes in barycenter positions due to flux evolution. We also find that for long temporal increments, beyond granular lifetimes, the observed displacement distribution deviates from that expected for a diffusive process, evolving from Rayleigh to Gaussian. This change in distribution can be modeled analytically by accounting for supergranular advection along with granular motions. These results complicate the interpretation of magnetic element motions as strictly advective or diffusive on short and long timescales and suggest that measurements of magnetic element motions must be used with caution in turbulent diffusion or wave excitation models. We propose that passive tracer motions in measured photospheric flows may yield more robust transport statistics. Title: Evershed and Counter-Evershed Flows in Sunspot MHD Simulations Authors: Siu-Tapia, A. L.; Rempel, M.; Lagg, A.; Solanki, S. K. Bibcode: 2018ApJ...852...66S Altcode: 2017arXiv171201202S There have been a few reports in the literature of counter-Evershed flows observed in well-developed sunspot penumbrae, i.e., flows directed toward the umbra along penumbral filaments. Here, we investigate the driving forces of such counter-Evershed flows in a radiative magnetohydrodynamic simulation of a sunspot, and compare them to the forces acting on the normal Evershed flow. The simulation covers a timespan of 100 solar hours and generates an Evershed outflow exceeding 8 km s-1 in the penumbra along radially aligned filaments where the magnetic field is almost horizontal. Additionally, the simulation produces a fast counter-Evershed flow (i.e., an inflow near τ =1) in some regions within the penumbra, reaching peak flow speeds of ∼12 km s-1. The counter-Evershed flows are transient and typically last a few hours before they turn into outflows again. By using the kinetic energy equation and evaluating its various terms in the simulation box, we found that the Evershed flow occurs due to overturning convection in a strongly inclined magnetic field, while the counter-Evershed flows can be well-described as siphon flows. Title: Terminator 2020: Get Ready for the "Event" of The Next Decade Authors: McIntosh, S. W.; Leamon, R. J.; Fan, Y.; Rempel, M.; Dikpati, M. Bibcode: 2017AGUFMSH22B..06M Altcode: The abrupt end of solar activity cycles 22 and 23 at the Sun's equator are observed with instruments from the Solar and Heliospheric Observatory (SOHO), Solar Terrestrial Relations Observatory (STEREO), and Solar Dynamics Observatory (SDO). These events are remarkable in that they rapidly trigger the onset of magnetic activity belonging to the next solar cycle at mid-latitudes. The triggered onset of new cycle flux emergence leads to blossoming of the new cycle shortly thereafter. Using small-scale tracers of magnetic solar activity we examine the timing of the cycle ``termination points'' in relation to the excitation of new activity and find that the time taken for the solar plasma to communicate this transition is less than one solar rotation, and possibly as little as a eight days. This very short transition time implies that the mean magnetic field present in the Sun's convection zone is approximately 80 kG. This value may be considerably larger than conventional explorations estimate and therefore, have a significant dynamical impact on the physical appearance of solar activity, and considerably impacting our ability to perform first-principles numerical simulations of the same. Should solar cycle 24 [and 25] continue in their progression we anticipate that a termination event of this type should occur in the 2020 timeframe. PSP will have a front row seat to observe this systemic flip in solar magnetism and the induced changes in our star's radiative and partiuculate output. Such observations may prove to be critical in assessing the Sun's ability to force short term evolution in the Earth's atmosphere. Title: Numerical MHD Coronal Simulations: Energy Statistics and FORWARD Analysis. Authors: Nimmo, K.; Rempel, M.; Chen, F.; Gibson, S. E.; Fan, Y. Bibcode: 2017AGUFMSH43A2800N Altcode: We analyse a recent realistic radiative MHD simulation of the solar corona that was computed with the extended version of the MURaM code. The simulation covers the uppermost 8Mm of the solar convection zone and reaches 115Mm into the solar corona. The simulation covers 48 hours of solar time and simulates the evolution of a complex active region. The energy release in the corona is highly intermittent and we identify a total of 118 individual events including flares and a coronal mass ejection, which we analyse in further detail. From the simulation we compute an X-ray flux mimicking observations by the GOES (Geostationary Operational Environmental Satellite) satellite in the wavelength range 1-8 Å. The power law index for the GOES X-ray flux for flares of class C and above in this simulation is found to be 1.33452. We analyze the correlation between synthetic coronal emission during flares and the magnetic energy release in the corona. The latter is a quantity that cannot be directly determined in observations.The FORWARD code is a tool used for the purpose of coronal magnetometry. It can be used to compute synthetic observables from coronal models. We focus on the interpretation of the High Altitude Observatory's CoMP observations. The CoMP (COronal Multi-channel Polarimeter) instrument measures the intensity and the linear and circular polarisation of FeXIII at 1074.7nm.We discuss some important limitations of coronal emission line polarimetry when simulating an extremely active solar region, with emphasis on the influence of high velocities, temperatures and densities on the FORWARD output. Title: The Nature of Grand Minima and Maxima from Fully Nonlinear Flux Transport Dynamos Authors: Inceoglu, Fadil; Arlt, Rainer; Rempel, Matthias Bibcode: 2017ApJ...848...93I Altcode: 2017arXiv171008644I We aim to investigate the nature and occurrence characteristics of grand solar minimum and maximum periods, which are observed in the solar proxy records such as 10Be and 14C, using a fully nonlinear Babcock-Leighton type flux transport dynamo including momentum and entropy equations. The differential rotation and meridional circulation are generated from the effect of turbulent Reynolds stress and are subjected to back-reaction from the magnetic field. To generate grand minimum- and maximum-like periods in our simulations, we used random fluctuations in the angular momentum transport process, namely the Λ-mechanism, and in the Babcock-Leighton mechanism. To characterize the nature and occurrences of the identified grand minima and maxima in our simulations, we used the waiting time distribution analyses, which reflect whether the underlying distribution arises from a random or a memory-bearing process. The results show that, in the majority of the cases, the distributions of grand minima and maxima reveal that the nature of these events originates from memoryless processes. We also found that in our simulations the meridional circulation speed tends to be smaller during grand maximum, while it is faster during grand minimum periods. The radial differential rotation tends to be larger during grand maxima, while it is smaller during grand minima. The latitudinal differential rotation, on the other hand, is found to be larger during grand minima. Title: Emergence of Magnetic Flux Generated in a Solar Convective Dynamo. I. The Formation of Sunspots and Active Regions, and The Origin of Their Asymmetries Authors: Chen, Feng; Rempel, Matthias; Fan, Yuhong Bibcode: 2017ApJ...846..149C Altcode: 2017arXiv170405999C We present a realistic numerical model of sunspot and active region formation based on the emergence of flux bundles generated in a solar convective dynamo. To this end, we use the magnetic and velocity fields in a horizontal layer near the top boundary of the solar convective dynamo simulation to drive realistic radiative-magnetohydrodynamic simulations of the uppermost layers of the convection zone. The main results are as follows. (1) The emerging flux bundles rise with the mean speed of convective upflows and fragment into small-scale magnetic elements that further rise to the photosphere, where bipolar sunspot pairs are formed through the coalescence of the small-scale magnetic elements. (2) Filamentary penumbral structures form when the sunspot is still growing through ongoing flux emergence. In contrast to the classical Evershed effect, the inflow seems to prevail over the outflow in a large part of the penumbra. (3) A well-formed sunspot is a mostly monolithic magnetic structure that is anchored in a persistent deep-seated downdraft lane. The flow field outside the spot shows a giant vortex ring that comprises an inflow below 15 Mm depth and an outflow above 15 Mm depth. (4) The sunspots successfully reproduce the fundamental properties of the observed solar active regions, including the more coherent leading spots with a stronger field strength, and the correct tilts of bipolar sunspot pairs. These asymmetries can be linked to the intrinsic asymmetries in the magnetic and flow fields adapted from the convective dynamo simulation. Title: Realistic radiative MHD simulation of a solar flare Authors: Rempel, Matthias D.; Cheung, Mark; Chintzoglou, Georgios; Chen, Feng; Testa, Paola; Martinez-Sykora, Juan; Sainz Dalda, Alberto; DeRosa, Marc L.; Viktorovna Malanushenko, Anna; Hansteen, Viggo H.; De Pontieu, Bart; Carlsson, Mats; Gudiksen, Boris; McIntosh, Scott W. Bibcode: 2017SPD....4840001R Altcode: We present a recently developed version of the MURaM radiative MHD code that includes coronal physics in terms of optically thin radiative loss and field aligned heat conduction. The code employs the "Boris correction" (semi-relativistic MHD with a reduced speed of light) and a hyperbolic treatment of heat conduction, which allow for efficient simulations of the photosphere/corona system by avoiding the severe time-step constraints arising from Alfven wave propagation and heat conduction. We demonstrate that this approach can be used even in dynamic phases such as a flare. We consider a setup in which a flare is triggered by flux emergence into a pre-existing bipolar active region. After the coronal energy release, efficient transport of energy along field lines leads to the formation of flare ribbons within seconds. In the flare ribbons we find downflows for temperatures lower than ~5 MK and upflows at higher temperatures. The resulting soft X-ray emission shows a fast rise and slow decay, reaching a peak corresponding to a mid C-class flare. The post reconnection energy release in the corona leads to average particle energies reaching 50 keV (500 MK under the assumption of a thermal plasma). We show that hard X-ray emission from the corona computed under the assumption of thermal bremsstrahlung can produce a power-law spectrum due to the multi-thermal nature of the plasma. The electron energy flux into the flare ribbons (classic heat conduction with free streaming limit) is highly inhomogeneous and reaches peak values of about 3x1011 erg/cm2/s in a small fraction of the ribbons, indicating regions that could potentially produce hard X-ray footpoint sources. We demonstrate that these findings are robust by comparing simulations computed with different values of the saturation heat flux as well as the "reduced speed of light". Title: 3D Collision of Active Region-Sized Emerging Flux Tubes in the Solar Convection Zone and its Manifestation in the Photospheric Surface Authors: Chintzoglou, Georgios; Cheung, Mark; Rempel, Matthias D. Bibcode: 2017SPD....4830004C Altcode: We present observations obtained with the Solar Dynamics Observatory’s Helioseismic Magnetic Imager (SDO/HMI) of target NOAA Active Regions (AR) 12017 and 12644, which initially were comprised of a simple bipole and later on became quadrupolar via parasitic bipole emergence right next to their leading polarities. Once these ARs became quadrupolar, they spewed multiple Coronal Mass Ejections (CMEs) and a multitude of highly energetic flares (a large number of M class flares). The proximity of the parasitic bipole to one of the two pre-existing sunspots forms a compact polarity inversion line (PIL). This type of quadrupolar ARs are known to be very flare- and CME-productive due to the continuous interaction of newly emerging non-potential flux with pre-existing flux in the photosphere. We show that well before the emergence of the parasitic bipole, the pre-existing polarity (typically a well-developed sunspot) undergoes interesting precursor dynamic evolution, namely (a) displacement of pre-existing sunspot’s position, (b) progressive and significant oblateness of its initially nearly-circular shape, and (c) opposite polarity enhancement in the divergent moat flow around the sunspot. We employ high-resolution radiative-convective 3D MHD simulations of an emerging parasitic bipole to show that all these activity aspects seen in the photosphere are associated with the collision of a parasitic bipole with the nearby pre-existing polarity below the photospheric surface. Given the rich flare and CME productivity of this class of ARs and the precursor-like dynamic evolution of the pre-existing polarity, this work presents the potential for predicting inclement space weather. Title: Realistic simulation of the emergence of magnetic field generated in a solar convective dynamo from the convection zone into the corona Authors: Chen, Feng; Rempel, Matthias D.; Fan, Yuhong Bibcode: 2017SPD....4840501C Altcode: We present a comprehensive realistic numerical model of emergence of magnetic flux generated in a solar convective dynamo from the convection zone to the corona. The magnetic and velocity fields in a horizontal layer near the top boundary of the solar convective dynamo simulation are used as a time-dependent bottom boundary to drive the radiation magnetohydrodynamic simulations of the emergence of the flux bundles through the upper most convection zone to more than 100 Mm above the surface of the Sun. The simualtion allows a direct comparison bewtween model synthesized observable and real obervations of flux emergence processes through different layers of the solar atmopshere.Emerging flux bundles bring more than 1e23 Mx flux to the photosphere in a period of about 50 hours and give rise to several active regions in a horizontal domain of 200 Mm. The mean corona temperature is about 1 MK for the quiet Sun and is significantly increased after active regions form at the photosphere. The flux emergence process produces a lot of dynamical features, such as coronal bright points, jets, waves and propagating disturbances, as well as flares and mass ejections. The biggest flare reaches M2.5 as indicated by synthetic GOES-15 soft X-ray flux. The total magnetic energy released during the eruption is about 5e31 ergs. The flare leads to a significant corona heating. The mean temperature in the coronal reaches more than 5 MK. And plasma in cusp-shaped post-flare loops is heated to several tens MK. The flare is accompanied by the ejection of a giant flux rope that carries cool and dense plasma. The flux rope is formed during the eruption by the reconnection between a sheared arcade that rises up from the low atmosphere above a bipolar sunspot pair and overlying fieldlines that are mostly perpendicular to the axis of the sheared arcade. Title: Characterizing the Motion of Photospheric Magnetic Bright Points at High Resolution Authors: Van Kooten, Samuel Jay; Cranmer, Steven R.; Rempel, Matthias Bibcode: 2017shin.confE..68V Altcode: Magnetic bright points on the solar photosphere, visible in both continuum and G-band images, indicate footpoints of kilogauss magnetic flux tubes extending to the corona. The power spectrum of transverse bright point motion is thus also the power spectrum of Alfven wave excitation, with these waves transporting energy up flux tubes into the corona. This spectrum is a key input in coronal and heliospheric models. After briefly reviewing observations of bright point motion, we present a power spectrum of bright point motion derived from radiative MHD simulations, exploiting spatial resolution higher than can be obtained in observations while using automated tracking to produce large data quantities. We find slightly higher amounts of power at all frequencies compared to observational spectra while confirming the spectrum shape of recent observations. This provides a prediction for DKIST observations of bright points, which will achieve similar resolution. We also present results from tracing test particles in the horizontal plasma flow, finding similar power spectra but differing motion paths. Finally, we introduce a simplified, laminar model of granulation, with which we explore the roles of turbulence and of the properties of the granulation pattern in determining bright point motion. Title: Are Internetwork Magnetic Fields in the Solar Photosphere Horizontal or Vertical? Authors: Lites, B. W.; Rempel, M.; Borrero, J. M.; Danilovic, S. Bibcode: 2017ApJ...835...14L Altcode: Using many observations obtained during 2007 with the Spectro-Polarimeter of the Hinode Solar Optical Telescope, we explore the angular distribution of magnetic fields in the quiet internetwork regions of the solar photosphere. Our work follows from the insight of Stenflo, who examined only linear polarization signals in photospheric lines, thereby avoiding complications of the analysis arising from the differing responses to linear and circular polarization. We identify and isolate regions of a strong polarization signal that occupy only a few percent of the observed quiet Sun area yet contribute most to the net linear polarization signal. The center-to-limb variation of the orientation of linear polarization in these strong signal regions indicates that the associated magnetic fields have a dominant vertical orientation. In contrast, the great majority of the solar disk is occupied by much weaker linear polarization signals. The orientation of the linear polarization in these regions demonstrates that the field orientation is dominantly horizontal throughout the photosphere. We also apply our analysis to Stokes profiles synthesized from the numerical MHD simulations of Rempel as viewed at various oblique angles. The analysis of the synthetic data closely follows that of the observations, lending confidence to using the simulations as a guide for understanding the physical origins of the center-to-limb variation of linear polarization in the quiet Sun area. Title: Extension of the MURaM Radiative MHD Code for Coronal Simulations Authors: Rempel, M. Bibcode: 2017ApJ...834...10R Altcode: 2016arXiv160909818R We present a new version of the MURaM radiative magnetohydrodynamics (MHD) code that allows for simulations spanning from the upper convection zone into the solar corona. We implement the relevant coronal physics in terms of optically thin radiative loss, field aligned heat conduction, and an equilibrium ionization equation of state. We artificially limit the coronal Alfvén and heat conduction speeds to computationally manageable values using an approximation to semi-relativistic MHD with an artificially reduced speed of light (Boris correction). We present example solutions ranging from quiet to active Sun in order to verify the validity of our approach. We quantify the role of numerical diffusivity for the effective coronal heating. We find that the (numerical) magnetic Prandtl number determines the ratio of resistive to viscous heating and that owing to the very large magnetic Prandtl number of the solar corona, heating is expected to happen predominantly through viscous dissipation. We find that reasonable solutions can be obtained with values of the reduced speed of light just marginally larger than the maximum sound speed. Overall this leads to a fully explicit code that can compute the time evolution of the solar corona in response to photospheric driving using numerical time steps not much smaller than 0.1 s. Numerical simulations of the coronal response to flux emergence covering a time span of a few days are well within reach using this approach. Title: Lower solar atmosphere and magnetism at ultra-high spatial resolution Authors: Collet, Remo; Criscuoli, Serena; Ermolli, Ilaria; Fabbian, Damian; Guerreiro, Nuno; Haberreiter, Margit; Peck, Courtney; Pereira, Tiago M. D.; Rempel, Matthias; Solanki, Sami K.; Wedemeyer-Boehm, Sven Bibcode: 2016arXiv161202348C Altcode: We present the scientific case for a future space-based telescope aimed at very high spatial and temporal resolution imaging of the solar photosphere and chromosphere. Previous missions (e.g., HINODE, SUNRISE) have demonstrated the power of observing the solar photosphere and chromosphere at high spatial resolution without contamination from Earth's atmosphere. We argue here that increased spatial resolution (from currently 70 km to 25 km in the future) and high temporal cadence of the observations will vastly improve our understanding of the physical processes controlling solar magnetism and its characteristic scales. This is particularly important as the Sun's magnetic field drives solar activity and can significantly influence the Sun-Earth system. At the same time a better knowledge of solar magnetism can greatly improve our understanding of other astrophysical objects. Title: 3D MHD simulation of a Solar Flare Authors: Rempel, M.; Cheung, M. C. M.; HGCR Team Bibcode: 2016usc..confE...4R Altcode: We present results from a numerical 3D simulation of a solar flare triggered by flux emergence into a pre-existing bipolar active region. The simulation is performed with a recently developed version of the MURaM radiative MHD code and includes coronal physics in terms of optically thin radiative loss and field-aligned heat conduction. Severe time-step constraints arising from Alfven wave propagation and heat conduction are avoided through the use of the Boris correction and a hyperbolic treatment of heat conduction. In the simulation we find a flare releasing about 5x10^30 erg over a time of about 1-2 minutes. The efficient transport of energy along field lines leads to the formation of flare ribbons within seconds and at later times to chromospheric evaporation filling coronal flare loops. Since the efficiency of energy transport by electrons (classic heat conduction vs. non-thermal electrons) is one of the main uncertainties, we compare simulations with different values for the saturation of the heat flux. We present synthetic observables in the form of UV, EUV and soft and hard Xray emission. Title: Observed and simulated power spectra of kinetic and magnetic energy retrieved with 2D inversions Authors: Danilovic, S.; Rempel, M.; van Noort, M.; Cameron, R. Bibcode: 2016A&A...594A.103D Altcode: 2016arXiv160706242D Context. Information on the origin of internetwork magnetic field is hidden at the smallest spatial scales.
Aims: We try to retrieve the power spectra with certainty to the highest spatial frequencies allowed by current instrumentation.
Methods: To accomplish this, we use a 2D inversion code that is able to recover information up to the instrumental diffraction limit.
Results: The retrieved power spectra have shallow slopes that extend further down to much smaller scales than has been found before. They do not seem to show any power law. The observed slopes at subgranular scales agree with those obtained from recent local dynamo simulations. Small differences are found for the vertical component of kinetic energy that suggest that observations suffer from an instrumental effect that is not taken into account.
Conclusions: Local dynamo simulations quantitatively reproduce the observed magnetic energy power spectra on the scales of granulation down to the resolution limit of Hinode/SP, within the error bars inflicted by the method used and the instrumental effects replicated. Title: Internetwork magnetic field as revealed by two-dimensional inversions Authors: Danilovic, S.; van Noort, M.; Rempel, M. Bibcode: 2016A&A...593A..93D Altcode: 2016arXiv160700772D Context. Properties of magnetic field in the internetwork regions are still fairly unknown because of rather weak spectropolarimetric signals.
Aims: We address the matter by using the two-dimensional (2D) inversion code, which is able to retrieve the information on smallest spatial scales up to the diffraction limit, while being less susceptible to noise than most of the previous methods used.
Methods: Performance of the code and the impact of various effects on the retrieved field distribution is tested first on the realistic magneto-hydrodynamic (MHD) simulations. The best inversion scenario is then applied to the real data obtained by Spectropolarimeter (SP) on board Hinode.
Results: Tests on simulations show that: (1) the best choice of node position ensures a decent retrieval of all parameters; (2) the code performs well for different configurations of magnetic field; (3) slightly different noise levels or slightly different defocus included in the spatial point spread function (PSF) produces no significant effect on the results; and (4) temporal integration shifts the field distribution to a stronger, more horizontally inclined field.
Conclusions: Although the contribution of the weak field is slightly overestimated owing to noise, 2D inversions are able to recover well the overall distribution of the magnetic field strength. Application of the 2D inversion code on the Hinode SP internetwork observations reveals a monotonic field strength distribution. The mean field strength at optical depth unity is ~ 130 G. At higher layers, field strength drops as the field becomes more horizontal. Regarding the distribution of the field inclination, tests show that we cannot directly retrieve it with the observations and tools at hand, however, the obtained distributions are consistent with those expected from simulations with a quasi-isotropic field inclination after accounting for observational effects. Title: A low upper limit on the subsurface rise speed of solar active regions Authors: Birch, A. C.; Schunker, H.; Braun, D. C.; Cameron, R.; Gizon, L.; Lo ptien, B.; Rempel, M. Bibcode: 2016SciA....2E0557B Altcode: 2016arXiv160705250B Magnetic field emerges at the surface of the Sun as sunspots and active regions. This process generates a poloidal magnetic field from a rising toroidal flux tube, it is a crucial but poorly understood aspect of the solar dynamo. The emergence of magnetic field is also important because it is a key driver of solar activity. We show that measurements of horizontal flows at the solar surface around emerging active regions, in combination with numerical simulations of solar magnetoconvection, can constrain the subsurface rise speed of emerging magnetic flux. The observed flows imply that the rise speed of the magnetic field is no larger than 150 m/s at a depth of 20 Mm, that is, well below the prediction of the (standard) thin flux tube model but in the range expected for convective velocities at this depth. We conclude that convective flows control the dynamics of rising flux tubes in the upper layers of the Sun and cannot be neglected in models of flux emergence. Title: Turbulent transport of Small-scale magnetic flux elements on Solar Photosphere Authors: Agrawal, Piyush; Rempel, Matthias; Bellot Rubio, Luis; Rast, Mark Bibcode: 2016SPD....47.1201A Altcode: We study the transport of small-scale magnetic elements on the solar photosphere using both observations and simulations. Observational data was obtained from Hinode - Solar Optical Telescope (SOT/SP) instrument and simulations from MURaM code. The magnetic flux elements were tracked in both data sets and statistics were obtained. We compute the probability density of the Eulerian distances traveled by the flux elements along Lagrangian trajectories. For a two-dimensional random walk process this distribution should be Rayleigh. Preliminary results show that the measured probability distribution in both the observed and simulated data approximates a random walk, on time scale close to the lifetime of granules, but deviates from it for longer times. This implies that diffusion may not be an appropriate framework for transport in the solar photosphere. We explore the roles of flux cancelation and element trapping in producing this result. Work is ongoing. Title: Forward and Inverse Modeling of Helioseismic Holography Measurements of MHD Simulations of Convection and Sunspot Flows Authors: DeGrave, Kyle; Braun, Douglas; Birch, Aaron; Crouch, Ashley D.; Javornik, Brenda; Rempel, Matthias D. Bibcode: 2016SPD....4720303D Altcode: We test and validate newly-developed, empirically-derived sensitivity kernels for use in helioseismic analysis. These kernels are based on the Born approximation and derived from applying direct measurements to artificial realizations of incoming and scattered wavefields. These kernels are employed in a series of forward and inverse modeling of flows from the near-surface layers of two publicly available magnetohydrodynamic (MURaM-based) solar simulations - a quiet-Sun simulation, and one containing a sunspot. Forward travel times computed using the kernels generally compare favorably in non-magnetic regions. One finding of note is the presence of flow-like artifacts in the sunspot measurements which appear when the spot umbra or penumbra falls within the measurement pupils. Inversions for the horizontal flow components are able to reproduce the large-scale supergranule-sized flows in the upper 3Mm of both domains, but are compromised by noise at greater depths. In spite of the magnetic artifact, the moat flow surrounding the spot is at least qualitatively recovered. This work is supported by the NASA Heliophysics Division through NNH12CF68C, NNH12CF23C, and NNX16AG88G, and by the NSF Solar-Terrestrial Program through grant AGS-1127327. Title: Formation of sunspots and active regions through the emergence of magnetic flux generated in a solar convective dynamo Authors: Chen, Feng; Rempel, Matthias D.; Fan, Yuhong Bibcode: 2016SPD....4730306C Altcode: We present a realistic numerical model of sunspot and active region formation through the emergence of flux tubes generated in a solar convective dynamo. The magnetic and velocity fields in a horizontal layer near the top boundary of the solar convective dynamo simulation are used as a time-dependent bottom boundary to drive the near surface layer radiation MHD simulations of magneto-convection and flux emergence with the MURaM code. The latter code simulates the emergence of the flux tubes through the upper most layer of the convection zone to the photosphere.The emerging flux tubes interact with the convection and break into small scale magnetic elements that further rise to the photosphere. At the photosphere, several bipolar pairs of sunspots are formed through the coalescence of the small scale magnetic elements. The sunspot pairs in the simulation successfully reproduce the fundamental observed properties of solar active regions, including the more coherent leading spots with a stronger field strength, and the correct tilts of the bipolar pairs. These asymmetries come most probably from the intrinsic asymmetries in the emerging fields imposed at the bottom boundary, where the horizontal fields are already tilted and the leading sides of the emerging flux tubes are usually up against the downdraft lanes of the giant cells. It is also found that penumbrae with numerous filamentary structures form in regions of strong horizontal magnetic fields that naturally comes from the ongoing flux emergence. In contrast to previous models, the penumbrae and umbrae are divided by very sharp boarders, which is highly consistent with observations. Title: Coronal extension of the MURaM radiative MHD code: From quiet sun to flare simulations Authors: Rempel, Matthias D.; Cheung, Mark Bibcode: 2016SPD....4720803R Altcode: We present a new version of the MURaM radiative MHD code, which includes a treatment of the solar corona in terms of MHD, optically thin radiative loss and field-aligned heat conduction. In order to relax the severe time-step constraints imposed by large Alfven velocities and heat conduction we use a combination of semi-relativistic MHD with reduced speed of light ("Boris correction") and a hyperbolic formulation of heat conduction. We apply the numerical setup to 4 different setups including a mixed polarity quiet sun, an open flux region, an arcade solution and an active region setup and find all cases an amount of coronal heating sufficient to maintain a corona with temperatures from 1 MK (quiet sun) to 2 MK (active region, arcade). In all our setups the Poynting flux is self-consistently created by photospheric and sub-photospheric magneto-convection in the lower part of our simulation domain. Varying the maximum allowed Alfven velocity ("reduced speed of light") leads to only minor changes in the coronal structure as long as the limited Alfven velocity remains larger than the speed of sound and about 1.5-3 times larger than the peak advection velocity. We also found that varying details of the numerical diffusivities that govern the resistive and viscous energy dissipation do not strongly affect the overall coronal heating, but the ratio of resistive and viscous energy dependence is strongly dependent on the effective numerical magnetic Prandtl number. We use our active region setup in order to simulate a flare triggered by the emergence of a twisted flux rope into a pre-existing bipolar active region. Our simulation yields a series of flares, with the strongest one reaching GOES M1 class. The simulation reproduces many observed properties of eruptions such as flare ribbons, post flare loops and a sunquake. Title: Distortions of Magnetic Flux Tubes in the Presence of Electric Currents Authors: Malanushenko, Anna; Rempel, Matthias; Cheung, Mark Bibcode: 2016SPD....47.0322M Altcode: Solar coronal loops possess several peculiar properties, which have been a subject of intensive research for a long time. These in particular include the lack of apparent expansion of coronal loops and the increased pressure scale height in loops compared to the diffuse background. Previously, Malanushenko & Schrijver (2013) proposed that these could be explained by the fact that magnetic flux tubes expand with height in a highly anisotropic manner. They used potential field models to demonstrate that flux tubes that have circular cross section at the photosphere, in the corona turn into a highly elongates structures, more resembling thick ribbons. Such ribbons, viewed along the expanding edge, would appear as thin, crisp structures of a constant cross-section with an increased pressure scale height, and when viewed along the non-expanding side, would appear as faint, wide and underdense features. This may also introduce a selection bias,when a set of loops is collected for a further study, towards those viewed along the expanding edge.However, some of the past studies have indicated that strong electric currents flowing in a given flux tube may result in the tube maintaining a relatively constant cross-sectional shape along its length. Given that Malanushenko & Schrijver (2013) focused on a potential, or current-free, field model of an active region, the extend to which their analysis could be applied to the real solar fields, was unclear.In the present study, we use a magnetic field created by MURaM, a highly realistic state-of-the-art radiative MHD code (Vogler et al, 2005; Rempel et al, 2009b). MURaM was shown to reproduce a wide variety of observed features of the solar corona (e.g., Hansteen et al, 2010; Cheung et al. 2007, 2008; Rempel 2009a,b). We analyze the distortions of magnetic flux tubes in a MURaM simulation of an active region corona. We quantify such distortions and correlate them with a number of relevant parameters of flux tubes, with a particular emphasis on the electric currents in the simulated corona. Title: Physics & Diagnostics of the Drivers of Solar Eruptions Authors: Cheung, Mark; Rempel, Matthias D.; Martinez-Sykora, Juan; Testa, Paola; Hansteen, Viggo H.; Viktorovna Malanushenko, Anna; Sainz Dalda, Alberto; DeRosa, Marc L.; De Pontieu, Bart; Carlsson, Mats; Chen, Feng; McIntosh, Scott W.; Gudiksen, Boris Bibcode: 2016SPD....47.0607C Altcode: We provide an update on our NASA Heliophysics Grand Challenges Research (HGCR) project on the ‘Physics & Diagnostics of the Drivers of Solar Eruptions’. This presentation will focus on results from a data-inspired, 3D radiative MHD model of a solar flare. The model flare results from the interaction of newly emerging flux with a pre-existing active region. Synthetic observables from the model reproduce observational features compatible with actual flares. These include signatures of coronal magnetic reconnection, chromospheric evaporation, EUV flare arcades, sweeping motion of flare ribbons and sunquakes. Title: Interpreting Irradiance Distributions Using High-Resolution 3D MHD Simulations Authors: Peck, Courtney; Rast, Mark; Criscuoli, Serena; Uitenbroek, Han; Rempel, Matthias D. Bibcode: 2016SPD....4730302P Altcode: We present initial results of studies aimed at understanding the impact of the unresolved magnetic field distribution on solar spectral irradiance. Using high-resolution 3D MHD simulations (from MURaM code) and spectral synthesis (with the RH code), we examine the emergent spectra of two atmospheres with similar mean field strengths but differing imposed-field conditions at wavelengths spanning from visible to infrared. Comparing the contrast against the magnetic field strength for the two magnetic simulations, we find differences in the distributions of contrasts versus field strength. We repeat the analysis after convolving the images with the PSF of a typical solar telescope (1-meter) and discuss the potential implications for irradiance modeling and future steps. Title: Large-scale magnetic fields at high Reynolds numbers in magnetohydrodynamic simulations Authors: Hotta, H.; Rempel, M.; Yokoyama, T. Bibcode: 2016Sci...351.1427H Altcode: The 11-year solar magnetic cycle shows a high degree of coherence in spite of the turbulent nature of the solar convection zone. It has been found in recent high-resolution magnetohydrodynamics simulations that the maintenance of a large-scale coherent magnetic field is difficult with small viscosity and magnetic diffusivity (≲1012square centimenters per second). We reproduced previous findings that indicate a reduction of the energy in the large-scale magnetic field for lower diffusivities and demonstrate the recovery of the global-scale magnetic field using unprecedentedly high resolution. We found an efficient small-scale dynamo that suppresses small-scale flows, which mimics the properties of large diffusivity. As a result, the global-scale magnetic field is maintained even in the regime of small diffusivities—that is, large Reynolds numbers. Title: The Effects of Magnetic Field Morphology on the Determination of Oxygen and Iron Abundances in the Solar Photosphere Authors: Moore, Christopher S.; Uitenbroek, Han; Rempel, Matthias; Criscuoli, Serena; Rast, Mark Bibcode: 2016AAS...22712501M Altcode: The solar chemical abundance (or a scaled version of it) is implemented in numerous astrophysical analyses. Thus, an accurate and precise estimation of the solar elemental abundance is crucial in astrophysics.We have explored the impact of magnetic fields on the determination of the solar photospheric oxygen andiron abundances using 3D radiation-magnetohydrodynamic (MHD) simulations of convection. Specifically, weexamined differences in abundance deduced from three classes of atmospheres simulated with the MURaM code: apure hydrodynamic (HD) simulation, an MHD simulation with a local dynamo magnetic field that has saturated withan unsigned vertical field strength of 80 G at the optical depth unity surface, and an MHD simulation with an initially imposed vertical mean field of 80 G. We use differential equivalent width analysis for diagnosing abundances derived from five oxygen and four iron spectral lines of differing wavelength, oscillator strength, excitation potential, and Lande g-factor, and find that the morphology of the magnetic field is important to the outcome of abundance determinations. The largest deduced abundance differences are found in the vertical mean field simulations and small scale unresolved field resulting from the local dynamo has a smaller impact on abundance determinations. Title: Evolution of Fine-scale Penumbral Magnetic Structure and Formation of Penumbral Jets Authors: Tiwari, S. K.; Moore, R. L.; Rempel, M.; Winebarger, A. R. Bibcode: 2015AGUFMSH13D2461T Altcode: Sunspot penumbra consists of spines (more vertical field) and penumbral filaments (interspines). Spines are outward extension of umbra. Penumbral filaments are recently found, both in observations and magnetohydrodynamic (MHD) simulations, to be magnetized stretched granule-like convective cells, with strong upflows near the head that continues along the central axis with weakening strength of the flow. Strong downflows are found at the tails of filaments and weak downflows along the sides of it. These lateral downflows often contain opposite polarity magnetic field to that of spines; most strongly near the heads of filaments. In spite of this advancement in understanding of small-scale structure of sunspot penumbra, how the filaments and spines evolve and interact remains uncertain.

Penumbral jets, bright, transient features, seen in the chromosphere, are one of several dynamic events in sunspot penumbra. It has been proposed that these penumbral microjets result from component (acute angle) reconnection of the magnetic field in spines with that in interspines and could contribute to transition-region and coronal heating above sunspots. In a recent investigation, it was proposed that the jets form as a result of reconnection between the opposite polarity field at edges of filaments with spine field, and it was found that these jets do not significantly directly heat the corona above sunspots. We discuss how the proposed formation of penumbral jets is integral to the formation mechanism of penumbral filaments and spines, and may explain why penumbral jets are few and far between. We also point out that the generation of the penumbral jets could indirectly drive coronal heating via generation of MHD waves or braiding of the magnetic field. Title: Numerical Simulations of Sunspot Decay: On the Penumbra-Evershed Flow-Moat Flow Connection Authors: Rempel, M. Bibcode: 2015ApJ...814..125R Altcode: 2015arXiv151101410R We present a series of high-resolution sunspot simulations that cover a timespan of up to 100 hr. The simulation domain extends about 18 Mm in depth beneath the photosphere and 98 Mm horizontally. We use open boundary conditions that do not maintain the initial field structure against decay driven by convective motions. We consider two setups: a sunspot simulation with penumbra, and a “naked-spot” simulation in which we removed the penumbra after 20 hr through a change in the magnetic top boundary condition. While the sunspot has an Evershed outflow of 3-4 km s-1, the naked spot is surrounded by an inflow of 1-2 km s-1 in close proximity. However, both spots are surrounded by an outflow on larger scales with a few 100 m s-1 flow speed in the photosphere. While the sunspot has an almost constant magnetic flux content for the simulated timespan of three to four days, the naked spot decays steadily at a rate of 1021 Mx day-1. A region with reduced downflow filling factor, which is more extended for the sunspot, surrounds both spots. The absence of downflows perturbs the upflow/downflow mass flux balance and leads to a large-scale radially overturning flow system; the photospheric component of this flow is the observable moat flow. The reduction of the downflow filling factor also inhibits the submergence of magnetic field in the proximity of the spots, which stabilizes them against decay. While this effect is present for both spots, it is more pronounced for the sunspot and explains the almost stationary magnetic flux content. Title: Towards a Data-Optimized Coronal Magnetic Field Model (DOC-FM): Synthetic Test Beds and Multiwavelength Forward Modeling Authors: Gibson, S. E.; Dalmasse, K.; Fan, Y.; Fineschi, S.; MacKay, D.; Rempel, M.; White, S. M. Bibcode: 2015AGUFMSH54B..04G Altcode: Understanding the physical state of the solar corona is key to deciphering the origins of space weather as well as to realistically representing the environment to be navigated by missions such as Solar Orbiter and Solar Probe Plus. However, inverting solar coronal observations to reconstruct this physical state -- and in particular the three-dimensional coronal magnetic field - is complicated by limited lines of sight and by projection effects. On the other hand, the sensitivity of multiwavelength observations to different physical mechanisms implies a potential for simultaneous probing of different parts of the coronal plasma. In order to study this complementarity, and to ultimately establish an optimal set of observations for constraining the three-dimensional coronal magnetic field, we are developing a suite of representative simulations to act as diagnostic test beds. We will present three such test beds: a coronal active region, a quiescent prominence, and a global corona. Each fully define the physical state of density, temperature, and vector magnetic field in three dimensions throughout the simulation domain. From these test beds, and using the FORWARD SolarSoft IDL codes, we will create a broad range of synthetic data. Radio observables will include intensity and circular polarization (including gyroresonance effects) and Faraday rotation for a range of frequencies. Infrared and visible forbidden line diagnostics of Zeeman and saturated Hanle effects will yield full Stokes vector (I, Q, U, V) synthetic data, and UV permitted line Hanle diagnostics will yield intensity and linear polarization. In addition, we will synthesize UV and SXR imager data, UV/EUV spectrometric data, and white light brightness and polarized brightness. All of these synthetic data, along with the "ground truth" physical state of the simulations from which they are derived, will be made available to the community for the purpose of testing coronal inversion techniques. Title: Solar Differential rotation Maintained by Small- and Large-scale Convection Authors: Hotta, H.; Rempel, M.; Yokoyama, T. Bibcode: 2015ASPC..498..154H Altcode: We investigate the solar differential rotation with special interest for the near surface shear layer (NSSL) in a high-resolution hydrodynamic numerical calculation. The sun is rotating differentially. Helioseismology has revealed the detailed structure of the solar differential rotation. One of the most important features is the NSSL. It is thought that the solar differential rotation is maintained by the turbulent thermal convection. In the NSSL convection time scales are short, leading to a regime with weak influence of rotation on convection. In order to reproduce the NSSL by the numerical calculations, we must use a large number of grids and integrate a large number of time steps for covering the broad spatial and temporal scales. This requirements for the NSSL is achieved using our recent efficient numerical method. In the calculation, the global scale and the 10 Mm-scale convection is established simultaneously. Then the solar like NSSL is partially reproduced. Around the NSSL, the convection transports the angular momentum radially inward and generates the poleward meridional flow. The small scale convection acts as the turbulent viscosity on the meridional flow. The turbulent viscous stress balances with the Coriolis force in the NSSL. Title: Efficient Small-scale Dynamo in the Solar Convection Zone Authors: Hotta, H.; Rempel, M.; Yokoyama, T. Bibcode: 2015ApJ...803...42H Altcode: 2015arXiv150203846H We investigate small-scale dynamo action in the solar convection zone through a series of high-resolution MHD simulations in a local Cartesian domain with 1 {{R}⊙ } (solar radius) of horizontal extent and a radial extent from 0.715 to 0.96 {{R}⊙ }. The dependence of the solution on resolution and diffusivity is studied. For a grid spacing of less than 350 km, the rms magnetic field strength near the base of the convection zone reaches 95% of the equipartition field strength (i.e., magnetic and kinetic energy are comparable). For these solutions the Lorentz force feedback on the convection velocity is found to be significant. The velocity near the base of the convection zone is reduced to 50% of the hydrodynamic one. In spite of the significant decrease of the convection velocity, the reduction in the enthalpy flux is relatively small, since the magnetic field also suppresses the horizontal mixing of the entropy between up- and downflow regions. This effect increases the amplitude of the entropy perturbation and makes convective energy transport more efficient. We discuss potential implications of these results for solar global convection and dynamo simulations. Title: Photon Mean Free Paths, Scattering, and Ever-Increasing Telescope Resolution Authors: Judge, P. G.; Kleint, L.; Uitenbroek, H.; Rempel, M.; Suematsu, Y.; Tsuneta, S. Bibcode: 2015SoPh..290..979J Altcode: 2014arXiv1409.7866J; 2015SoPh..tmp....3J We revisit an old question: what are the effects of observing stratified atmospheres on scales below a photon mean free path λ? The mean free path of photons emerging from the solar photosphere and chromosphere is ≈ 102 km. Using current 1 m-class telescopes, λ is on the order of the angular resolution. But the Daniel K. Inoue Solar Telescope will have a diffraction limit of 0.020″ near the atmospheric cutoff at 310 nm, corresponding to 14 km at the solar surface. Even a small amount of scattering in the source function leads to physical smearing due to this solar "fog", with effects similar to a degradation of the telescope point spread function. We discuss a unified picture that depends simply on the nature and amount of scattering in the source function. Scalings are derived from which the scattering in the solar atmosphere can be transcribed into an effective Strehl ratio, a quantity useful to observers. Observations in both permitted (e.g., Fe I 630.2 nm) and forbidden (Fe I 525.0 nm) lines will shed light on both instrumental performance as well as on small-scale structures in the solar atmosphere. Title: The Effects of Magnetic Field Morphology on the Determination of Oxygen and Iron Abundances in the Solar Photosphere Authors: Moore, Christopher S.; Uitenbroek, Han; Rempel, Matthias; Criscuoli, Serena; Rast, Mark P. Bibcode: 2015ApJ...799..150M Altcode: We have explored the impact of magnetic fields on the determination of the solar photospheric oxygen and iron abundances using three-dimensional radiation-magnetohydrodynamic (MHD) simulations of convection. Specifically, we examined differences in abundance deduced from three classes of atmospheres simulated with the MURaM code: a pure hydrodynamic (HD) simulation, an MHD simulation with a local dynamo magnetic field that has saturated with an unsigned vertical field strength of 80 G at τ = 1, and an MHD simulation with an initially imposed vertical mean field of 80 G. We use differential equivalent width analysis for diagnosing abundances derived from five oxygen and four iron lines of differing wavelength, oscillator strength, excitation potential, and Landé g-factor, and find that the morphology of the magnetic field is important to the outcome of abundance determinations. The largest deduced abundance differences are found in the vertical mean field simulations, where the O I and Fe I abundance corrections compared to the pure HD case are ~+0.011 dex and +0.065 dex respectively. Small scale unresolved field resulting from the local dynamo has a smaller impact on abundance determinations, with corrections of -0.0001 dex and +0.0044 dex in the magnetized compared to the pure HD simulations. While the overall influence of magnetic field on abundance estimates is found to be small, we stress that such estimates are sensitive not only to the magnitude of magnetic field but also to its morphology. Title: High-resolution Calculation of the Solar Global Convection with the Reduced Speed of Sound Technique. II. Near Surface Shear Layer with the Rotation Authors: Hotta, H.; Rempel, M.; Yokoyama, T. Bibcode: 2015ApJ...798...51H Altcode: 2014arXiv1410.7093H We present a high-resolution, highly stratified numerical simulation of rotating thermal convection in a spherical shell. Our aim is to study in detail the processes that can maintain a near surface shear layer (NSSL) as inferred from helioseismology. Using the reduced speed of sound technique, we can extend our global convection simulation to 0.99 R ⊙ and include, near the top of our domain, small-scale convection with short timescales that is only weakly influenced by rotation. We find the formation of an NSSL preferentially in high latitudes in the depth range of r = 0.95-0.975 R ⊙. The maintenance mechanisms are summarized as follows. Convection under the weak influence of rotation leads to Reynolds stresses that transport angular momentum radially inward in all latitudes. This leads to the formation of a strong poleward-directed meridional flow and an NSSL, which is balanced in the meridional plane by forces resulting from the < v\prime r v\prime _θ > correlation of turbulent velocities. The origin of the required correlations depends to some degree on latitude. In high latitudes, a positive correlation < v\prime _rv\prime _θ > is induced in the NSSL by the poleward meridional flow whose amplitude increases with the radius, while a negative correlation is generated by the Coriolis force in bulk of the convection zone. In low latitudes, a positive correlation < v\prime _rv\prime _θ > results from rotationally aligned convection cells ("banana cells"). The force caused by these Reynolds stresses is in balance with the Coriolis force in the NSSL. Title: Comparison of inversion codes for polarized line formation in MHD simulations. I. Milne-Eddington codes Authors: Borrero, J. M.; Lites, B. W.; Lagg, A.; Rezaei, R.; Rempel, M. Bibcode: 2014A&A...572A..54B Altcode: 2014arXiv1409.3376B Milne-Eddington (M-E) inversion codes for the radiative transfer equation are the most widely used tools to infer the magnetic field from observations of the polarization signals in photospheric and chromospheric spectral lines. Unfortunately, a comprehensive comparison between the different M-E codes available to the solar physics community is still missing, and so is a physical interpretation of their inferences. In this contribution we offer a comparison between three of those codes (VFISV, ASP/HAO, and HeLIx+). These codes are used to invert synthetic Stokes profiles that were previously obtained from realistic non-grey three-dimensional magnetohydrodynamical (3D MHD) simulations. The results of the inversion are compared with each other and with those from the MHD simulations. In the first case, the M-E codes retrieve values for the magnetic field strength, inclination and line-of-sight velocity that agree with each other within σB ≤ 35 (Gauss), σγ ≤ 1.2°, and σv ≤ 10 m s-1, respectively. Additionally, M-E inversion codes agree with the numerical simulations, when compared at a fixed optical depth, within σB ≤ 130 (Gauss), σγ ≤ 5°, and σv ≤ 320 m s-1. Finally, we show that employing generalized response functions to determine the height at which M-E codes measure physical parameters is more meaningful than comparing at a fixed geometrical height or optical depth. In this case the differences between M-E inferences and the 3D MHD simulations decrease to σB ≤ 90 (Gauss), σγ ≤ 3°, and σv ≤ 90 m s-1. Title: Time-distance Helioseismology of Two Realistic Sunspot Simulations Authors: DeGrave, K.; Jackiewicz, J.; Rempel, M. Bibcode: 2014ApJ...794...18D Altcode: 2014arXiv1408.2262D Linear time-distance helioseismic inversions are carried out using several filtering schemes to determine vector flow velocities within two ~1002 Mm2 × 20 Mm realistic magnetohydrodynamic sunspot simulations of 25 hr. One simulation domain contains a model of a full sunspot (i.e., one with both an umbra and penumbra), while the other contains a pore (i.e., a spot without a penumbra). The goal is to test current helioseismic methods using these state-of-the-art simulations of magnetic structures. We find that horizontal flow correlations between inversion and simulation flow maps are reasonably high (~0.5-0.8) in the upper 3 Mm at distances exceeding 25-30 Mm from spot center, but are substantially lower at smaller distances and larger depths. Inversions of forward-modeled travel times consistently outperform those of our measured travel times in terms of horizontal flow correlations, suggesting that our inability to recover flow structure near these active regions is largely due to the fact that we are unable to accurately measure travel times near strong magnetic features. In many cases the velocity amplitudes from the inversions underestimate those of the simulations by up to 50%, possibly indicating nonlinearity of the forward problem. In every case, we find that our inversions are unable to recover the vertical flow structure of the simulations at any depth. Title: The Role of Subsurface Flows in Solar Surface Convection: Modeling the Spectrum of Supergranular and Larger Scale Flows Authors: Lord, J. W.; Cameron, R. H.; Rast, M. P.; Rempel, M.; Roudier, T. Bibcode: 2014ApJ...793...24L Altcode: 2014arXiv1407.2209L We model the solar horizontal velocity power spectrum at scales larger than granulation using a two-component approximation to the mass continuity equation. The model takes four times the density scale height as the integral (driving) scale of the vertical motions at each depth. Scales larger than this decay with height from the deeper layers. Those smaller are assumed to follow a Kolmogorov turbulent cascade, with the total power in the vertical convective motions matching that required to transport the solar luminosity in a mixing length formulation. These model components are validated using large-scale radiative hydrodynamic simulations. We reach two primary conclusions. (1) The model predicts significantly more power at low wavenumbers than is observed in the solar photospheric horizontal velocity spectrum. (2) Ionization plays a minor role in shaping the observed solar velocity spectrum by reducing convective amplitudes in the regions of partial helium ionization. The excess low wavenumber power is also seen in the fully nonlinear three-dimensional radiative hydrodynamic simulations employing a realistic equation of state. This adds to other recent evidence suggesting that the amplitudes of large-scale convective motions in the Sun are significantly lower than expected. Employing the same feature tracking algorithm used with observational data on the simulation output, we show that the observed low wavenumber power can be reproduced in hydrodynamic models if the amplitudes of large-scale modes in the deep layers are artificially reduced. Since the large-scale modes have reduced amplitudes, modes on the scale of supergranulation and smaller remain important to convective heat flux even in the deep layers, suggesting that small-scale convective correlations are maintained through the bulk of the solar convection zone. Title: Numerical Simulations of Quiet Sun Magnetism: On the Contribution from a Small-scale Dynamo Authors: Rempel, M. Bibcode: 2014ApJ...789..132R Altcode: 2014arXiv1405.6814R We present a series of radiative MHD simulations addressing the origin and distribution of the mixed polarity magnetic field in the solar photosphere. To this end, we consider numerical simulations that cover the uppermost 2-6 Mm of the solar convection zone and we explore scales ranging from 2 km to 25 Mm. We study how the strength and distribution of the magnetic field in the photosphere and subsurface layers depend on resolution, domain size, and boundary conditions. We find that 50% of the magnetic energy at the τ = 1 level comes from fields with the less than 500 G strength and that 50% of the energy resides on scales smaller than about 100 km. While the probability distribution functions are essentially independent of resolution, properly describing the spectral energy distribution requires grid spacings of 8 km or smaller. The formation of flux concentrations in the photosphere exceeding 1 kG requires a mean vertical field strength greater than 30-40 G at τ = 1. The filling factor of kG flux concentrations increases with overall domain size as the magnetic field becomes organized by larger, longer-lived flow structures. A solution with a mean vertical field strength of around 85 G at τ = 1 requires a subsurface rms field strength increasing with depth at the same rate as the equipartition field strength. We consider this an upper limit for the quiet Sun field strength, which implies that most of the convection zone is magnetized close to the equipartition. We discuss these findings in view of recent high-resolution spectropolarimetric observations of quiet Sun magnetism. Title: Validating Time-Distance Helioseismology With Realistic Quiet Sun Simulations Authors: DeGrave, Kyle; Jackiewicz, Jason; Rempel, Matthias Bibcode: 2014AAS...22421803D Altcode: Linear time-distance helioseismic inversions are carried out for vector flow velocities using travel times measured from two ~100^2 Mm^2 x 20 Mm realistic magnetohydrodynamic quiet-Sun simulations of about 20 hr. The goal is to test current seismic methods on these state-of-the-art simulations. We find that horizontal flow maps correlate well with the simulations in the upper ~3 Mm of the domains for several filtering schemes, including phase-speed, ridge, and combined phase-speed and ridge measurements. In several cases, however, the velocity amplitudes from the inversions severely underestimate those of the simulations, possibly indicating nonlinearity of the forward problem. We also find that results of the inversions for the vertical velocity component depend significantly on the type of data filtering. In particular, phase-speed filters show better results than the other methods. In many cases, the vertical flows are irretrievable due to high levels of noise, suggesting a need for statistical averaging. Title: Numerical simulations of sunspot decay: On the role of a penumbra and subsurface field structure Authors: Rempel, Matthias D. Bibcode: 2014AAS...22420204R Altcode: We present high-resolution simulations of decaying sunspots that cover a time span of up to 100 hours. The simulations reach 18Mm deep into the convection zone and use open boundaries that do not maintain the initial field structure against decay driven by convective motions. We discuss three experiments: A sunspot simulation with penumbra, a "naked-spot" simulation in which we removed the penumbra after 20 hours, and a sunspot simulation with penumbra, but a less coherent subsurface field structure. In all three simulations we study the decay process and large-scale flows in proximity of the spots. Over the time span covered by the simulation the spot with penumbra is almost stationary with regard to the total flux content, but shows a steady decay of the flux present in the umbra area at a rate comparable to the "naked-spot" experiment. A less coherent sub-surface magnetic field structure leads within 12-24 hours to a less coherent surface appearance, i.e. details of the subsurface structure do not remain hidden from the photosphere. In all three experiments the dominant subsurface flow patterns are outflows. Title: Using Synthetic Data From Convection Simulations To Test Helioseismic Holography Inversions For Three-Dimensional Vector Flows Authors: Crouch, Ashley D.; Birch, Aaron; Braun, Douglas; Javornik, Brenda; Rempel, Matthias D. Bibcode: 2014AAS...22421807C Altcode: We investigate the efficacy of helioseismic holography for inferring the three-dimensional vector flows in the near-surface layers of the solar interior. Synthetic helioseismic data are taken from compressible convection simulations. Travel times are measured from the synthetic data using helioseismic holography. Kernels for the sensitivity of travel times to subsurface flows are calculated using the Born approximation. Inversions for subsurface flows are then performed using subtractive optimally localized averaging. This provides an opportunity to evaluate the accuracy of the inversion technique. We compare the actual flows present in the convection simulations to the flows retrieved by the inversion. We discuss the influence of the regularization used by the inversion, and the effects of noise and spatial resolution. This work is supported by the NASA SDO Science Center program (NNH09CE41C), the NASA Heliophysics Guest Investigator program (NNH12CF68C), and the NASA LWS TR&T tools and methods program (NNH09CF68C). The National Center for Atmospheric Research is sponsored by the National Science Foundation. Title: Validating Time-Distance Helioseismology with Realistic Quiet-Sun Simulations Authors: DeGrave, K.; Jackiewicz, J.; Rempel, M. Bibcode: 2014ApJ...788..127D Altcode: 2014arXiv1404.4645D Linear time-distance helioseismic inversions are carried out for vector flow velocities using travel times measured from two ~1002 Mm2 × 20 Mm realistic magnetohydrodynamic quiet-Sun simulations of about 20 hr. The goal is to test current seismic methods on these state-of-the-art simulations. Using recent three-dimensional inversion schemes, we find that inverted horizontal flow maps correlate well with the simulations in the upper ~3 Mm of the domains for several filtering schemes, including phase-speed, ridge, and combined phase-speed and ridge measurements. In several cases, however, the velocity amplitudes from the inversions severely underestimate those of the simulations, possibly indicating nonlinearity of the forward problem. We also find that, while near-surface inversions of the vertical velocities are best using phase-speed filters, in almost all other example cases these flows are irretrievable due to noise, suggesting a need for statistical averaging to obtain better inferences. Title: High-resolution Calculations of the Solar Global Convection with the Reduced Speed of Sound Technique. I. The Structure of the Convection and the Magnetic Field without the Rotation Authors: Hotta, H.; Rempel, M.; Yokoyama, T. Bibcode: 2014ApJ...786...24H Altcode: 2014arXiv1402.5008H We carry out non-rotating high-resolution calculations of the solar global convection, which resolve convective scales of less than 10 Mm. To cope with the low Mach number conditions in the lower convection zone, we use the reduced speed of sound technique (RSST), which is simple to implement and requires only local communication in the parallel computation. In addition, the RSST allows us to expand the computational domain upward to about 0.99 R ⊙, as it can also handle compressible flows. Using this approach, we study the solar convection zone on the global scale, including small-scale near-surface convection. In particular, we investigate the influence of the top boundary condition on the convective structure throughout the convection zone as well as on small-scale dynamo action. Our main conclusions are as follows. (1) The small-scale downflows generated in the near-surface layer penetrate into deeper layers to some extent and excite small-scale turbulence in the region >0.9 R ⊙, where R ⊙ is the solar radius. (2) In the deeper convection zone (<0.9 R ⊙), the convection is not influenced by the location of the upper boundary. (3) Using a large eddy simulation approach, we can achieve small-scale dynamo action and maintain a field of about 0.15B eq-0.25B eq throughout the convection zone, where B eq is the equipartition magnetic field to the kinetic energy. (4) The overall dynamo efficiency varies significantly in the convection zone as a consequence of the downward directed Poynting flux and the depth variation of the intrinsic convective scales. Title: Numerical Simulations of Active Region Scale Flux Emergence: From Spot Formation to Decay Authors: Rempel, M.; Cheung, M. C. M. Bibcode: 2014ApJ...785...90R Altcode: 2014arXiv1402.4703R We present numerical simulations of active region scale flux emergence covering a time span of up to 6 days. Flux emergence is driven by a bottom boundary condition that advects a semi-torus of magnetic field with 1.7 × 1022 Mx flux into the computational domain. The simulations show that, even in the absence of twist, the magnetic flux is able the rise through the upper 15.5 Mm of the convection zone and emerge into the photosphere to form spots. We find that spot formation is sensitive to the persistence of upflows at the bottom boundary footpoints, i.e., a continuing upflow would prevent spot formation. In addition, the presence of a torus-aligned flow (such flow into the retrograde direction is expected from angular momentum conservation during the rise of flux ropes through the convection zone) leads to a significant asymmetry between the pair of spots, with the spot corresponding to the leading spot on the Sun being more axisymmetric and coherent, but also forming with a delay relative to the following spot. The spot formation phase transitions directly into a decay phase. Subsurface flows fragment the magnetic field and lead to intrusions of almost field free plasma underneath the photosphere. When such intrusions reach photospheric layers, the spot fragments. The timescale for spot decay is comparable to the longest convective timescales present in the simulation domain. We find that the dispersal of flux from a simulated spot in the first two days of the decay phase is consistent with self-similar decay by turbulent diffusion. Title: Magnetoconvection models and what we need the ATST to tell us Authors: Rempel, Matthias D. Bibcode: 2013SPD....4440103R Altcode: So called "realistic" magnetoconvection simulations of the solar photosphere include all relevant physical ingredients in terms of equation of state and 3 dimensional radiative transfer in addition to MHD. In that sense they do not have any explicit free parameters, however, implicit degrees of freedom are present since simulations are limited to a finite volume, have a finite resolution and can be only run for a finite time. This results in dependencies on boundary conditions, on the numerical treatment of unresolved scales and on the chosen initial state. A successful numerical model of the solar photosphere and underlying convection zone is only possible if these implicit degrees of freedom are sufficiently constrained through observations. In this talk I will discuss two examples of recent high resolution simulations: the quiet sun photosphere and sunspot fine structure. Numerical simulations of quiet sun magnetism can explain most of the observed unsigned magnetic flux density as a consequence of a small scale dynamo process. These simulations make however unrealistic assumptions about the small scale dissipation and depend to some degree on the assumed bottom boundary condition several Mm beneath the photosphere. Observations are needed to verify the validity of this modeling approach. Sunspot simulations have successfully linked convective energy transport in the penumbra with penumbral fine structure. Current observations provide several indirect hints on convective flows, but higher resolution is needed to settle this aspect. So far sunspot simulations cannot explain from first principles the existence and extent of a penumbra, since this aspect depends strongly on the magnetic top boundary condition. Observations of the detailed magnetic field structure in the upper photosphere, chromosphere and lower corona above sunspots are needed to guide modeling. The National Center for Atmospheric Research is sponsored by the National Science Foundation. Title: Formation of Magnetic Structures during Emergence of Untwisted Flux Rope Authors: Fang, Fang; Fan, Y.; Rempel, M. Bibcode: 2013SPD....44..102F Altcode: Ideal MHD simulations have shown that the twist of the magnetic flux rope before emergence plays an important role in the coherency of the emerged magnetic structures. Recently, with more realistic simulations with turbulent convection, it is found that magnetic structures can form at the photosphere from emergence of uniform magnetic fields. The discrepancy therefore leads to a controversial question that whether the twist exists before the emergence or is formed afterwards by surface flows. In light of this, we carry out simulations on the emergence of untwisted flux rope from the convection zone into the corona, using more realistic treatment of the thermodynamic processes in the solar interior and the outer atmosphere. In our coupled simulations, we study the interaction between the convective motion and the magnetic fields and also the formation of coronal structures in comparison with observations. Title: The High-latitude Branch of the Solar Torsional Oscillation in the Rising Phase of Cycle 24 Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R.; Larson, T. P.; Rempel, M.; Schou, J.; Thompson, M. J. Bibcode: 2013ApJ...767L..20H Altcode: We use global heliseismic data from the Global Oscillation Network Group, the Michelson Doppler Imager on board the Solar and Heliospheric Observatory, and the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, to examine the behavior, during the rising phase of Solar Cycle 24, of the migrating zonal flow pattern known as the torsional oscillation. Although the high-latitude part of the pattern appears to be absent in the new cycle when the flows are derived by subtracting a mean across a full solar cycle, it can be seen if we subtract the mean over a shorter period in the rising phase of each cycle, and these two mean rotation profiles differ significantly at high latitudes. This indicates that the underlying high-latitude rotation has changed; we speculate that this is in response to weaker polar fields, as suggested by a recent model. Title: The solar dynamo - where do we stand, where do we go? Authors: Rempel, Matthias Bibcode: 2013enss.confE.117R Altcode: Understanding the origin of the large scale solar magnetic field and its temporal evolution is one of the still unsolved key questions in solar physics. While large scale dynamos are understood on a fundamental level for more than 5 decades, the details of how the solar dynamo operates are still heavily debated. In this talk I will review the various approaches taken in the past (mean field models vs. 3D numerical simulations) and discuss their intrinsic strengths and weaknesses. I will present a collection of recent modeling results including cyclic behavior in 3D numerical simulations, the connection between dynamo action and torsional oscillations, the role of flux transport and near surface field evolution (Babcock-Leighton alpha-effects) as well as flux emergence and sunspot formation. I will close the talk with an outlook on future developments. Title: The Sunspot Penumbra in the Photosphere: Results from Forward Synthesized Spectroscopy Authors: Tritschler, A.; Uitenbroek, H.; Rempel, M. Bibcode: 2012ASPC..463...89T Altcode: We present first results from a spectral synthesis of the Zeeman-insensitive Fe 1 557.6 nm line for two different viewing angles (0° and 30°) using numerical simulations of a sunspot as an input model. We performed a bisector analysis to calculate two-dimensional maps of line-of-sight Doppler velocities and the line width. We analyze azimuthal cuts of the LOS velocity at different penumbral radii and calculate the radial behavior of azimuthal averages of line width and intensity. Both are compared with observational results. The properties of dark cores in penumbral filaments are discussed briefly. Within the limitations of this study, we find that the results from the forward synthesized spectroscopy are in good agreement with the observations, corroborating that the photospheric structure and dynamics of the penumbra is a signature of overturning anisotropic magneto-convection. Title: Magnetic Field Intensification by the Three-dimensional "Explosion" Process Authors: Hotta, H.; Rempel, M.; Yokoyama, T. Bibcode: 2012ApJ...759L..24H Altcode: 2012arXiv1210.0949H We investigate an intensification mechanism for the magnetic field near the base of the solar convection zone that does not rely on differential rotation. Such mechanism in addition to differential rotation has been suggested by studies of flux emergence, which typically require field strength in excess of those provided by differential rotation alone. We study here a process in which potential energy of the superadiabatically stratified convection zone is converted into magnetic energy. This mechanism, known as the "explosion of magnetic flux tubes," has been previously studied in thin flux tube approximation as well as two-dimensional magnetohydrodynamic (MHD) simulations; here we expand the investigation to three-dimensional MHD simulations. Our main result is that enough intensification can be achieved in a three-dimensional magnetic flux sheet as long as the spatial scale of the imposed perturbation normal to the magnetic field is sufficiently large. When this spatial scale is small, the flux sheet tends to rise toward the surface, resulting in a significant decrease of the magnetic field amplification. Title: On the Amplitude of Convective Velocities in the Deep Solar Interior Authors: Miesch, Mark S.; Featherstone, Nicholas A.; Rempel, Matthias; Trampedach, Regner Bibcode: 2012ApJ...757..128M Altcode: 2012arXiv1205.1530M We obtain lower limits on the amplitude of convective velocities in the deep solar convection zone (CZ) based only on the observed properties of the differential rotation and meridional circulation together with simple and robust dynamical balances obtained from the fundamental magnetohydrodynamics equations. The linchpin of the approach is the concept of gyroscopic pumping whereby the meridional circulation across isosurfaces of specific angular momentum is linked to the angular momentum transport by the convective Reynolds stress. We find that the amplitude of the convective velocity must be at least 30 m s-1 in the upper CZ (r ~ 0.95R) and at least 8 m s-1 in the lower CZ (r ~ 0.75R) in order to be consistent with the observed mean flows. Using the base of the near-surface shear layer as a probe of the rotational influence, we are further able to show that the characteristic length scale of deep convective motions must be no smaller than 5.5-30 Mm. These results are compatible with convection models but suggest that the efficiency of the turbulent transport assumed in advection-dominated flux-transport dynamo models is generally not consistent with the mean flows they employ. Title: Numerical models of sunspot formation and fine structure Authors: Rempel, M. Bibcode: 2012RSPTA.370.3114R Altcode: No abstract at ADS Title: Waves as the Source of Apparent Twisting Motions in Sunspot Penumbrae Authors: Bharti, L.; Cameron, R. H.; Rempel, M.; Hirzberger, J.; Solanki, S. K. Bibcode: 2012ApJ...752..128B Altcode: 2012arXiv1204.2221B The motion of dark striations across bright filaments in a sunspot penumbra has become an important new diagnostic of convective gas flows in penumbral filaments. The nature of these striations has, however, remained unclear. Here, we present an analysis of small-scale motions in penumbral filaments in both simulations and observations. The simulations, when viewed from above, show fine structure with dark lanes running outward from the dark core of the penumbral filaments. The dark lanes either occur preferentially on one side or alternate between both sides of the filament. We identify this fine structure with transverse (kink) oscillations of the filament, corresponding to a sideways swaying of the filament. These oscillations have periods in the range of 5-7 minutes and propagate outward and downward along the filament. Similar features are found in observed G-band intensity time series of penumbral filaments in a sunspot located near disk center obtained by the Broadband Filter Imager on board the Hinode. We also find that some filaments show dark striations moving to both sides of the filaments. Based on the agreement between simulations and observations we conclude that the motions of these striations are caused by transverse oscillations of the underlying bright filaments. Title: High-latitude Solar Torsional Oscillations during Phases of Changing Magnetic Cycle Amplitude Authors: Rempel, M. Bibcode: 2012ApJ...750L...8R Altcode: Torsional oscillations are variations of the solar differential rotation that are strongly linked to the magnetic cycle of the Sun. Helioseismic inversions have revealed significant differences in the high-latitude branch of torsional oscillations between cycle 23 and cycle 24. Here we employ a non-kinematic flux-transport dynamo model that has been used previously to study torsional oscillations and simulate the response of the high-latitude branch to a change in the amplitude of the magnetic cycle. It is found that a reduction of the cycle amplitude leads to an increase in the amplitude of differential rotation that is mostly visible as a drop in the high-latitude rotation rate. Depending on the amplitude of this adjustment the high-latitude torsional oscillation signal can become temporarily hidden due to the unknown changing mean rotation rate that is required to properly define the torsional oscillation signal. Title: Numerical Sunspot Models: Robustness of Photospheric Velocity and Magnetic Field Structure Authors: Rempel, M. Bibcode: 2012ApJ...750...62R Altcode: 2012arXiv1203.0534R MHD simulations of sunspots have successfully reproduced many aspects of sunspot fine structure as a consequence of magneto-convection in inclined magnetic field. We study how global sunspot properties and penumbral fine structure depend on the magnetic top boundary condition as well as on grid spacing. The overall radial extent of the penumbra is subject to the magnetic top boundary condition. All other aspects of sunspot structure and penumbral fine structure are resolved at an acceptable level starting from a grid resolution of 48 [24] km (horizontal [vertical]). We find that the amount of inverse polarity flux and the overall amount of overturning convective motions in the penumbra are robust with regard to both resolution and boundary conditions. At photospheric levels Evershed flow channels are strongly magnetized. We discuss in detail the relation between velocity and magnetic field structure in the photosphere and point out observational consequences. Title: Comparison of Multi-Height Observations with a 3D MHD Sunspot Model Authors: Jaeggli, S. A.; Lin, H.; Uitenbroek, H.; Rempel, M. Bibcode: 2012ASPC..456...67J Altcode: In sunspots the contribution to the horizontal pressure support from the curvature force and the geometrical height of formation which magnetic field measurements sample are poorly constrained observationally due to the effect of radiative transfer. In cool atmospheres, observations of the sunspot photosphere probe geometrically deeper layers, information on the magnetic field gradients cannot be easily derived even using multi-wavelength, multi-height observations. Recent MHD atmosphere models of sunspots analyzed with the Rybiki-Hummer radiative transfer code allow for direct comparison with simultaneous multi-height observations of the Fe I magnetic field diagnostics at 1565 and 630.2 nm in sunspots observed using the Facility Infrared Spectropolarimeter at the Dunn Solar Telescope. Title: Numerical calculation of convection with reduced speed of sound technique Authors: Hotta, H.; Rempel, M.; Yokoyama, T.; Iida, Y.; Fan, Y. Bibcode: 2012A&A...539A..30H Altcode: 2012arXiv1201.1061H Context. The anelastic approximation is often adopted in numerical calculations with low Mach numbers, such as those including stellar internal convection. This approximation requires so-called frequent global communication, because of an elliptic partial differential equation. Frequent global communication is, however, negative factor for the parallel computing performed with a large number of CPUs.
Aims: We test the validity of a method that artificially reduces the speed of sound for the compressible fluid equations in the context of stellar internal convection. This reduction in the speed of sound leads to longer time steps despite the low Mach number, while the numerical scheme remains fully explicit and the mathematical system is hyperbolic, thus does not require frequent global communication.
Methods: Two- and three-dimensional compressible hydrodynamic equations are solved numerically. Some statistical quantities of solutions computed with different effective Mach numbers (owing to the reduction in the speed of sound) are compared to test the validity of our approach.
Results: Numerical simulations with artificially reduced speed of sound are a valid approach as long as the effective Mach number (based on the lower speed of sound) remains less than 0.7. Title: Properties of Umbral Dots as Measured from the New Solar Telescope Data and MHD Simulations Authors: Kilcik, A.; Yurchyshyn, V. B.; Rempel, M.; Abramenko, V.; Kitai, R.; Goode, P. R.; Cao, W.; Watanabe, H. Bibcode: 2012ApJ...745..163K Altcode: 2011arXiv1111.3997K We studied bright umbral dots (UDs) detected in a moderate size sunspot and compared their statistical properties to recent MHD models. The study is based on high-resolution data recorded by the New Solar Telescope at the Big Bear Solar Observatory and three-dimensional (3D) MHD simulations of sunspots. Observed UDs, living longer than 150 s, were detected and tracked in a 46 minute long data set, using an automatic detection code. A total of 1553 (620) UDs were detected in the photospheric (low chromospheric) data. Our main findings are (1) none of the analyzed UDs is precisely circular, (2) the diameter-intensity relationship only holds in bright umbral areas, and (3) UD velocities are inversely related to their lifetime. While nearly all photospheric UDs can be identified in the low chromospheric images, some small closely spaced UDs appear in the low chromosphere as a single cluster. Slow-moving and long-living UDs seem to exist in both the low chromosphere and photosphere, while fast-moving and short-living UDs are mainly detected in the photospheric images. Comparison to the 3D MHD simulations showed that both types of UDs display, on average, very similar statistical characteristics. However, (1) the average number of observed UDs per unit area is smaller than that of the model UDs, and (2) on average, the diameter of model UDs is slightly larger than that of observed ones. Title: Helioseismology of a Realistic Magnetoconvective Sunspot Simulation Authors: Braun, D. C.; Birch, A. C.; Rempel, M.; Duvall, T. L. Bibcode: 2012ApJ...744...77B Altcode: We compare helioseismic travel-time shifts measured from a realistic magnetoconvective sunspot simulation using both helioseismic holography and time-distance helioseismology, and measured from real sunspots observed with the Helioseismic and Magnetic Imager instrument on board the Solar Dynamics Observatory and the Michelson Doppler Imager instrument on board the Solar and Heliospheric Observatory. We find remarkable similarities in the travel-time shifts measured between the methodologies applied and between the simulated and real sunspots. Forward modeling of the travel-time shifts using either Born or ray approximation kernels and the sound-speed perturbations present in the simulation indicates major disagreements with the measured travel-time shifts. These findings do not substantially change with the application of a correction for the reduction of wave amplitudes in the simulated and real sunspots. Overall, our findings demonstrate the need for new methods for inferring the subsurface structure of sunspots through helioseismic inversions. Title: Sunspot Modeling: From Simplified Models to Radiative MHD Simulations Authors: Rempel, Matthias; Schlichenmaier, Rolf Bibcode: 2011LRSP....8....3R Altcode: We review our current understanding of sunspots from the scales of their fine structure to their large scale (global) structure including the processes of their formation and decay. Recently, sunspot models have undergone a dramatic change. In the past, several aspects of sunspot structure have been addressed by static MHD models with parametrized energy transport. Models of sunspot fine structure have been relying heavily on strong assumptions about flow and field geometry (e.g., flux-tubes, "gaps", convective rolls), which were motivated in part by the observed filamentary structure of penumbrae or the necessity of explaining the substantial energy transport required to maintain the penumbral brightness. However, none of these models could self-consistently explain all aspects of penumbral structure (energy transport, filamentation, Evershed flow). In recent years, 3D radiative MHD simulations have been advanced dramatically to the point at which models of complete sunspots with sufficient resolution to capture sunspot fine structure are feasible. Here, overturning convection is the central element responsible for energy transport, filamentation leading to fine structure, and the driving of strong outflows. On the larger scale these models are also in the progress of addressing the subsurface structure of sunspots as well as sunspot formation. With this shift in modeling capabilities and the recent advances in high resolution observations, the future research will be guided by comparing observation and theory. Title: Testing Helioseismic Measurements of the Solar Meridional Flow with Numerical Simulations Authors: Hartlep, T.; Zhao, J.; Kosovichev, A. G.; Mansour, N. N.; Rempel, M.; Pipin, V. Bibcode: 2011AGUFMSH52B..03H Altcode: The meridional flow is of fundamental importance for understanding magnetic flux transport in the solar interior. Reliable measurements of the flow could provide important constraints for dynamo theories. The actual shape and strength of the meridional flow, particularly in the deep interior, remains unknown. Detecting such weak flows with a speed of 10-20 m/s in the deep solar interior is a challenging problem for helioseismology. Numerical simulations of helioseismic wave propagation provide means for testing and calibrating measurement techniques, and can help increase our confidence in the inferences obtained from helioseismic inversions. We have developed a 3D numerical spectral code to simulate the propagation of acoustic waves in the whole-Sun. With this code, we simulate the propagation of stochastic wave fields given mean meridional flows of different strength and circulation patterns (including flow models with deep and shallow stagnation points). Our helioseismic measurement techniques are based on estimating acoustic travel times from wave-field cross-correlations (time-distance helioseismology method). We investigate various cross-correlation schemes, and study the sensitivity of acoustic travel times to the depth and speed of the meridional flow. Using the numerical simulation results we discuss the prospects of measuring the Sun's meridional flow from Solar Dynamics Observatory (SDO/HMI) data. Title: Numerical simulations of the subsurface structure of sunspots Authors: Rempel, M.; Cheung, M.; Birch, A. C.; Braun, D. C. Bibcode: 2011AGUFMSH52B..02R Altcode: Knowledge of the subsurface magnetic field and flow structure of sunspots is essential for understanding the processes involved in their formation, dynamic evolution and decay. Information on the subsurface structure can be obtained by either direct numerical modeling or helioseismic inversions. Numerical simulations have reached only in recent years the point at which entire sunspots or even active regions can be modeled including all relevant physical processes such as 3D radiative transfer and a realistic equation of state. We present in this talk results from a series of different models: from simulations of individual sunspots (with and without penumbrae) in differently sized computational domains to simulations of the active region formation process (flux emergence). It is found in all models that the subsurface magnetic field fragments on an intermediate scale (larger than the scale of sunspot fine structure such as umbral dots); most of these fragmentations become visible as light bridges or flux separation events in the photosphere. The subsurface field strength is found to be in the 5-10 kG range. The simulated sunspots are surrounded by large scale flows, the most dominant and robust flow component is a deep reaching outflow with an amplitude reaching about 50% of the convective RMS velocity at the respective depth. The simulated sunspots show helioseismic signatures (frequency dependent travel time shifts) similar to those in observed sunspots. On the other hand it is clear from the simulations that these signatures originate in the upper most 2-3 Mm of the convection zone, since only there substantial perturbations of the wave speed are present. The contributions from deeper layers are insignificant, in particular a direct comparison between an 8 Mm and 16 Mm deep simulation leads to indiscernible helioseismic differences. The National Center for Atmospheric Research is sponsored by the National Science Foundation. This work is in part supported through the NASA SDO Science Center. Title: The role of magnetic field in supergranular scale selection Authors: Lord, J. W.; Rast, M. P.; Rempel, M. Bibcode: 2011AGUFMSH53C..03L Altcode: We examine the role of the magnetic field in solar surface convection using the MURaM radiative MHD code. Using two 74x74x16 Mm simulations, one without magnetic field and one with an initially uniform and vertical 10 Gauss field, we investigate the role of magnetic field in supergranular scale selection. We find that the simulation with magnetic field has two peaks in the photospheric kinetic energy spectrum, one corresponding to granular size scales and a second peak near 24 Mm, while the purely hydrodynamic simulation has a single peak near the size scale of granulation (Figure 1). We examine two possible physical mechanisms which may underlie this increased power at low wavenumbers: the decreased opacity in magnetic elements near the photosphere which increases the radiative cooling there and the coupling, by regions of high magnetic flux density in convective downflows, of deeper larger scale motions to the photosphere. These mechanisms imply two very different processes. The first suggests that supergranulation is organized in the photosphere where radiation escapes the system (top down) and the second suggests that the large scale convection deep in the sun influences the scales observed in the photosphere (bottom up). Temporal cross correlation is used to examine which direction information is moving during pattern formation across scales. Additionally, a series of experiments were conducted to isolate individual physical effects, artificially increasing and decreasing the radiative losses in regions of strong magnetic flux, reducing the importance of magnetic tension, and constraining the box depth to understand the sensitivity of the size scales observed to the boundary conditions imposed. Title: Properties of Umbral Dots as Measured from the New Solar Telescope Data and MHD Simulations Authors: Yurchyshyn, V.; Kilcik, A.; Rempel, M.; Abramenko, V.; Kitai, R.; Goode, P. R.; Cao, W.; Watanabe, H. Bibcode: 2011sdmi.confE..86Y Altcode: We studied bright umbral dots (UDs) detected in the main sunspot of AR NOAA 11108 and compare their statistical properties to a state-of-the-art MHD model of a sunspot. The study is based on high resolution data recorded on September 20, 2010 by the New Solar Telescope (NST) at Big Bear Solar Observatory and 3D MHD simulations of sunspots. The 46 min data set included photospheric (0.3nm TiO filter centered at 705.7 nm) and chromospheric (0.025nm Hα Lyot filter) adaptive optics corrected and speckle reconstructed images. Bright UDs, living longer than 150 s, were detected and tracked using an automatic UD detection code. Total 1553 (620) UDs were detected in the photospheric (chromospheric) data. Our main findings are: i) none of the analyzed UDs is of an exact circular shape, ii) the diameter-intensity relationship only works for bright umbral areas, and iii) UD velocities inversely related to their life time. Comparison of photospheric and chromospheric data showed that nearly all photospheric UDs can be identified in the chromospheric images. However, it appears that some small closely spaced UDs appear in the chromospheric images as a single cluster, which may lead to the underestimation of the total number of detected chromospheric UDs. Also, while slow moving and long living UDs seem to exist in both chromosphere and photosphere, fast moving and short living ones are detected mainly in the photospheric images. Comparison of model and observed data shows that both types of UDs display very similar statistical characteristics. The main difference between parameters of model and observed UDs is that i) the average number of observed UDs per unit area is smaller than that of the model UDs, and ii) on average, the diameter of model UDs is slightly larger than that of observed ones. Title: Subsurface Magnetic Field and Flow Structure of Simulated Sunspots Authors: Rempel, Matthias Bibcode: 2011ApJ...740...15R Altcode: 2011arXiv1106.6287R We present a series of numerical sunspot models addressing the subsurface field and flow structure in up to 16 Mm deep domains covering up to two days of temporal evolution. Changes in the photospheric appearance of the sunspots are driven by subsurface flows in several Mm depth. Most of magnetic field is pushed into a downflow vertex of the subsurface convection pattern, while some fraction of the flux separates from the main trunk of the spot. Flux separation in deeper layers is accompanied in the photosphere with light bridge formation in the early stages and formation of pores separating from the spot at later stages. Over a timescale of less than a day we see the development of a large-scale flow pattern surrounding the sunspots, which is dominated by a radial outflow reaching about 50% of the convective rms velocity in amplitude. Several components of the large scale flow are found to be independent from the presence of a penumbra and the associated Evershed flow. While the simulated sunspots lead to blockage of heat flux in the near surface layers, we do not see compelling evidence for a brightness enhancement in their periphery. We further demonstrate that the influence of the bottom boundary condition on the stability and long-term evolution of the sunspot is significantly reduced in a 16 Mm deep domain compared to the shallower domains considered previously. Title: Mechanisms of sunspot formation Authors: Cheung, M. C. M.; Rempel, M. Bibcode: 2011sdmi.confE..34C Altcode: We present numerical MHD simulations that model the rise of magnetic flux tubes through the upper 16 Mm of the solar convection zone and into the photosphere. Due to the strong stratification (a density contrast of 10^4), the emerging field is initially dispersed over a wide area. Nevertheless, the dispersed flux is eventually able to reorganize into coherent spots with photospheric field strengths of 3 kG. In the models, sunspot formation is weakly sensitive to the initial subsurface field strength and to the presence of magnetic twist. As a consequence sunspots can form from untwisted flux tubes with as little as 5 kG average field strength at 16 Mm depth. The physical mechanisms which enables this robust formation process to occur will be discussed. Title: Can Overturning Motions in Penumbral Filaments BE Detected? Authors: Bharti, Lokesh; Schuessler, Manfred; Rempel, Matthias Bibcode: 2011sdmi.confE..79B Altcode: Numerical simulations indicate that the filamentation of sunspot penumbrae and the associated systematic outflow (the Evershed effect) are due to convectively driven fluid motions constrained by the inclined magnetic field. We investigate whether these motions, in particular the upflows in the bright filaments and the downflows at their edges, can be reliably observed with existing instrumentation. We use a snapshot from a sunspot simulation to calculate two-dimensional maps of synthetic line profiles for the spectral lines Fe I 7090.4 Å and C I 5380.34 Å. The maps are spatially and spectrally degraded according to typical instrument properties. Line-of-sight velocities are determined from line bisector shifts. We find that the detectability of the convective flows is strongly affected by spatial smearing, particularly so for the downflows. Furthermore, the line-of-sight velocities are dominated by the Evershed flow unless the observation is made very near the disk center. These problems may have compromised recent attempts to detect overturning penumbral convection. Lines with a low formation height are best suited for detecting the convective flows. Title: Can Overturning Motions in Penumbral Filaments Be Detected? Authors: Bharti, Lokesh; Schüssler, Manfred; Rempel, Matthias Bibcode: 2011ApJ...739...35B Altcode: 2011arXiv1107.0398B Numerical simulations indicate that the filamentation of sunspot penumbrae and the associated systematic outflow (the Evershed effect) are due to convectively driven fluid motions constrained by the inclined magnetic field. We investigate whether these motions, in particular the upflows in the bright filaments and the downflows at their edges, can be reliably observed with existing instrumentation. We use a snapshot from a sunspot simulation to calculate two-dimensional maps of synthetic line profiles for the spectral lines Fe I 7090.4 Å and C I 5380.34 Å. The maps are spatially and spectrally degraded according to typical instrument properties. Line-of-sight velocities are determined from line bisector shifts. We find that the detectability of the convective flows is strongly affected by spatial smearing, particularly so for the downflows. Furthermore, the line-of-sight velocities are dominated by the Evershed flow unless the observation is made very near the disk center. These problems may have compromised recent attempts to detect overturning penumbral convection. Lines with a low formation height are best suited for detecting the convective flows. Title: Comparison of numerical simulations and observations of helioseismic MHD waves in sunspots Authors: Parchevsky, K. V.; Zhao, J.; Kosovichev, A. G.; Rempel, M. Bibcode: 2011IAUS..273..422P Altcode: Numerical 3D simulations of MHD waves in magnetized regions with background flows are very important for the understanding of propagation and transformation of waves in sunspots. Such simulations provide artificial data for testing and calibration of helioseismic techniques used for analysis of data from space missions SOHO/MDI, SDO/HMI, and HINODE. We compare with helioseismic observations results of numerical simulations of MHD waves in different models of sunspots. The simulations of waves excited by a localized source provide a detailed picture of the interaction of the MHD waves with the magnetic field and background flows (deformation of the waveform, wave transformation, amplitude variations and anisotropy). The observed cross-covariance function represents an effective Green's function of helioseismic waves. As an initial step, we compare it with simulations of waves generated by a localized source. More thorough analysis implies using multiple sources and comparison of the observed and simulated cross-covariance functions. We plan to do such calculations in the nearest future. Both, the simulations and observations show that the wavefront inside the sunspot travels ahead of a reference ``quiet Sun'' wavefront, when the wave enters the sunspot. However, when the wave passes the sunspot, the time lag between the wavefronts becomes unnoticeable. Title: Towards physics-based helioseismic inversions of subsurface sunspot structure Authors: Braun, D. C.; Birch, A. C.; Crouch, A. D.; Rempel, M. Bibcode: 2011IAUS..273..379B Altcode: Numerical computations of wave propagation through sunspot-like magnetic field structures are critical to developing and testing methods to deduce the subsurface structure of sunspots and active regions. We show that helioseismic analysis applied to the MHD sunspot simulations of Rempel and collaborators, as well as to translation-invariant models of umbral-like fields, yield wave travel-time measurements in qualitative agreement with those obtained in real sunspots. However, standard inversion methods applied to these data fail to reproduce the true wave-speed structure beneath the surface of the model. Inversion methods which incorporate direct effects of the magnetic field, including mode conversion, may be required. Title: 3D numerical MHD modeling of sunspots with radiation transport Authors: Rempel, Matthias Bibcode: 2011IAUS..273....8R Altcode: 2010arXiv1011.0981R Sunspot fine structure has been modeled in the past by a combination of idealized magneto-convection simulations and simplified models that prescribe the magnetic field and flow structure to a large degree. Advancement in numerical methods and computing power has enabled recently 3D radiative MHD simulations of entire sunspots with sufficient resolution to address details of umbral dots and penumbral filaments. After a brief review of recent developments we focus on the magneto-convective processes responsible for the complicated magnetic structure of the penumbra and the mechanisms leading to the driving of strong horizontal outflows in the penumbra (Evershed effect). The bulk of energy and mass is transported on scales smaller than the radial extent of the penumbra. Strong horizontal outflows in the sunspot penumbra result from a redistribution of kinetic energy preferring flows along the filaments. This redistribution is facilitated primarily through the Lorentz force, while horizontal pressure gradients play only a minor role. The Evershed flow is strongly magnetized: While we see a strong reduction of the vertical field, the horizontal field component is enhanced within filaments. Title: A more realistic representation of overshoot at the base of the solar convective envelope as seen by helioseismology Authors: Christensen-Dalsgaard, J.; Monteiro, M. J. P. F. G.; Rempel, M.; Thompson, M. J. Bibcode: 2011MNRAS.414.1158C Altcode: 2011MNRAS.tmp..440C; 2011arXiv1102.0235C The stratification near the base of the Sun's convective envelope is governed by processes of convective overshooting and element diffusion, and the region is widely believed to play a key role in the solar dynamo. The stratification in that region gives rise to a characteristic signal in the frequencies of solar p modes, which has been used to determine the depth of the solar convection zone and to investigate the extent of convective overshoot. Previous helioseismic investigations have shown that the Sun's spherically symmetric stratification in this region is smoother than that in a standard solar model without overshooting, and have ruled out simple models incorporating overshooting, which extend the region of adiabatic stratification and have a more-or-less abrupt transition to subadiabatic stratification at the edge of the overshoot region. In this paper we consider physically motivated models which have a smooth transition in stratification bridging the region from the lower convection zone to the radiative interior beneath. We find that such a model is in better agreement with the helioseismic data than a standard solar model. Title: Numerical Simulations of Sunspots: From the Scale of Sine Structure to the Scale of Active Regions Authors: Rempel, Matthias D. Bibcode: 2011SPD....42.1001R Altcode: 2011BAAS..43S.1001R Over that past five years magneto-convective sunspot models have seen a dramatic improvement to the point at which simulations of entire sunspots with sufficient detail for resolving sunspot fine structure are possible. After a brief review of recent developments I will focus on three different classes of numerical sunspot models. 1.) Sunspot simulations at the highest currently affordable resolution that focus on details of sunspot fine structure: I will highlight the magneto-convective processes that are responsible for the energy transport, filamentation and driving of the Evershed flow in sunspot penumbrae. 2.) Sunspot models at lower resolution that can be evolved for time scales of several days in computational domains with horizontal extents beyond 50 Mm: These models start to address the subsurface field and flow structure

of sunspots and their surroundings as well as processes related to sunspot decay. In addition these simulations are used as a testbed for helioseismic inversion methods. 3.) Sunspot models on the scale of active regions: These models capture the last stages of the flux emergence and sunspot formation process in the upper most 10 to 20 Mm of the convection zone. After the initial flux dispersal due to the strong expansion of emerging flux a re-amplification of flux into 3 kG sunspots is found as a robust result.

The National Center for Atmospheric Research is sponsored by the National

Science Foundation. Title: Towards Reliable Physics-based Helioseismic Inversions of Sunspot Structure Authors: Braun, Douglas; Birch, A.; Crouch, A.; Clack, C.; Dombroski, D.; Rempel, M.; Duvall, T., Jr. Bibcode: 2011SPD....42.1603B Altcode: 2011BAAS..43S.1603B Inversion methods capable of reliably probing the subsurface structure beneath regions of strong magnetic fields, such as sunspots, remain elusive. We will review progress of a SDO Science Center project, funded to (among other goals) develop and evaluate new methods for this problem. Progress to date has included extensive production of magneto-convective sunspot models for the testing and validation of existing methods, for which a 27 hour run of artificial photospheric Dopplergrams is available online to the community. We will also summarize progress on the use of magnetostatic models for the development and testing of novel inversion methods designed to distinguish between magnetic field and thermal perturbations.

This work is supported by NASA contracts NNH09CE41C and NNG07EI51C. Title: Local Helioseismology of Magnetoconvective Sunspot Simulations and the Reliability of Standard Inversion Methods Authors: Braun, Douglas; Birch, A.; Rempel, M.; Duvall, T.; J. Bibcode: 2011SPD....42.1607B Altcode: 2011BAAS..43S.1607B Controversy exists in the interpretation and modeling of helioseismic signals in and around magnetic regions like sunspots. We show the results of applying local helioseismic inversions to travel-time shift measurements from realistic magnetoconvective sunspot simulations. We compare travel-time maps made from several simulations, using different measurements (helioseismic holography and center-annulus time distance helioseismology), and made on real sunspots observed with the HMI instrument onboard the Solar Dynamics Observatory. We find remarkable similarities in the travel-time perturbations measured between: 1) simulations extending both 8 and 16 Mm deep, 2) the methodology (holography or time-distance) applied, and 3) the simulated and real sunspots. The application of RLS inversions, using Born approximation kernels, to narrow frequency-band travel-time shifts from the simulations demonstrates that standard methods fail to reliably reproduce the true wave speed structure. These findings emphasize the need for new methods for inferring the subsurface structure of active regions. Artificial Dopplergrams from our simulations are available to the community at www.hao.ucar.edu under "Data" and "Sunspot Models." This work is supported by NASA under the SDO Science Center project (contract NNH09CE41C). Title: Penumbral Fine Structure and Driving Mechanisms of Large-scale Flows in Simulated Sunspots Authors: Rempel, M. Bibcode: 2011ApJ...729....5R Altcode: 2011arXiv1101.2200R We analyze in detail the penumbral structure found in a recent radiative magnetohydrodynamic simulation. Near τ = 1, the simulation produces penumbral fine structure consistent with the observationally inferred interlocking comb structure. Fast outflows exceeding 8 km s-1 are present along almost horizontal stretches of the magnetic field; in the outer half of the penumbra, we see opposite polarity flux indicating flux returning beneath the surface. The bulk of the penumbral brightness is maintained by small-scale motions turning over on scales shorter than the length of a typical penumbral filament. The resulting vertical rms velocity at τ = 1 is about half of that found in the quiet Sun. Radial outflows in the sunspot penumbra have two components. In the uppermost few 100 km, fast outflows are driven primarily through the horizontal component of the Lorentz force, which is confined to narrow boundary layers beneath τ = 1, while the contribution from horizontal pressure gradients is reduced in comparison to granulation as a consequence of anisotropy. The resulting Evershed flow reaches its peak velocity near τ = 1 and falls off rapidly with height. Outflows present in deeper layers result primarily from a preferred ring-like alignment of convection cells surrounding the sunspot. These flows reach amplitudes of about 50% of the convective rms velocity rather independent of depth. A preference for the outflow results from a combination of Lorentz force and pressure driving. While the Evershed flow dominates by velocity amplitude, most of the mass flux is present in deeper layers and likely related to a large-scale moat flow. Title: The Need for Physics-based Inversions of Sunspot Structure and Flows Authors: Braun, D. C.; Birch, A. C.; Crouch, A. D.; Rempel, M. Bibcode: 2011JPhCS.271a2010B Altcode: Current controversy exists in the interpretation and modeling of helioseismic signals in and around magnetic regions like sunspots. Unresolved issues include the dependence of the sign of both the inferred flows and wave speed on the type of filtering used, and the discrepancy between the relatively deep two-layer wave-speed models derived from standard time-distance methods and shallow, positive wave-speed models derived using forward models which include effects of mode conversion To make full use of the year-round, almost limb-to-limb, coverage provided by the Solar Dynamics Observatory, an efficient and reliable inversion method incorporating possible magnetic effects and the currently unexplained sensitivity to methodology is critical. Title: Solar Convection Zone Dynamics Authors: Rempel, Matthias Bibcode: 2011sswh.book...23R Altcode: 2010arXiv1010.5858R A comprehensive understanding of the solar magnetic cycle requires detailed modeling of the solar interior including the maintenance and variation of large scale flows (differential rotation and meridional flow), the solar dynamo and the flux emergence process connecting the magnetic field in the solar convection zone with magnetic field in the photosphere and above. Due to the vast range of time and length scales encountered, a single model of the entire convection zone is still out of reach. However, a variety of aspects can be modeled through a combined approach of 3D MHD models and simplified descriptions. We will briefly review our current theoretical understanding of these processes based on numerical models of the solar interior. Title: Sunspot Seismology with the Solar Dynamics Observatory Helioseismic and Magnetic Imager Authors: Braun, D. C.; Birch, A. C.; Crouch, A. D.; Clack, C.; Dombroski, D.; Rempel, M. Bibcode: 2010AGUFMSH14A..05B Altcode: The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) promises to yield detailed information about the subsurface dynamics and structure of solar active regions. A SDO Science Center was recently funded and initiated by NASA to (among other goals) enable the reliable measurements of subsurface flow, magnetic field, and sound speed in regions of strong magnetic fields. Using analyses of sunspots observed with HMI/SDO, we illustrate the challenges of this goal and suggest a plan for the development and implementation of new physics-based modeling of the subsurface structure of sunspots. Key components of this effort will be discussed, including numerical forward modeling of the wave propagation through model sunspots. These efforts incorporate both magnetostatic and magneto-convective models. This work is supported by the NASA SDO Science Center and Heliophysics GI programs through contracts NNH09CE41C and NNG07EI51C. Title: Interaction of MHD Waves with Sunspots Authors: Parchevsky, K.; Zhao, J.; Kosovichev, A. G.; Rempel, M. Bibcode: 2010AGUFM.S32A..07P Altcode: Understanding of MHD wave propagation, transformation and scattering by sunspots and their interaction with the non-uniform background magnetic field and flows is very important for improving helioseismic inversion procedures. Such simulations also provide artificial data for testitng and calibration techniques used for analysis of data from space missions SOHO/MDI, SDO/HMI, and HINODE. We developed 3D linear MHD code for numerical simulation of excitation and propagation of MHD waves in non-uniform medium in presence of the background magnetic field and flows. We present simulations of MHD wave propagation in magnetostatic and dynamic models of sunspots. We consider separately two cases when the waves are excited by point sources, located at different distances from the spot, and by stochastic noise source. The results are compared with the waveforms of the cross-correlation function extracted from the observational data. We discuss the differences between the models and observations in terms of the amplitude variations and travel-time shifts. Comparison of the simulations with helioseismic observations allows us to test the sunspot and helioseismic models, and suggest improvements. The numerically simulated helioseismic data are publicly accessible for the helioseismic community for testing and verification of various ambient noise imaging techniques of helioseismology (time-distance, holography, and ring diagrams). Title: Formation of Solar Active Regions (Invited) Authors: Rempel, M. Bibcode: 2010AGUFMSH42A..02R Altcode: The flux emergence process transporting magnetic field from the solar interior into the photosphere and beyond is central to our understanding of solar magnetism. However, due to the wast range of length and time scales as well as different physical regimes encountered from the base of the solar convection zone to the solar corona, a fully coherent picture of this process does not yet exist. In this talk I review models addressing the flux emergence within the bulk of the convection zone as well as models of the last stages of flux emergence and active region formation in the upper most 10-20 Mm of the convection zone and photopshere. I will discuss the prospects of coupling these models in the near future. The latter had been hampered in the past primarily by the fact that realistic MHD simulations of the upper convection zone and photosphere were restricted to rather small domains compared to the typical scale of an active region. Over that past 5 years a combination of advancement in numerical methods and high performance computing has enabled numerical simulations on the scale of entire sunspots with sufficient resolution to capture the essence of sunspot fine structure. Currently these simulations are expanded even further to the scale of active regions to address the flux emergence process and active region formation in the photosphere. The National Center for Atmospheric Research is sponsored by the National Science Foundation. This work is in part supported by the NASA SDO Science Center. Title: Discovery of a 1.6 Year Magnetic Activity Cycle in the Exoplanet Host Star ι Horologii Authors: Metcalfe, T. S.; Basu, S.; Henry, T. J.; Soderblom, D. R.; Judge, P. G.; Knölker, M.; Mathur, S.; Rempel, M. Bibcode: 2010ApJ...723L.213M Altcode: 2010arXiv1009.5399M The Mount Wilson Ca HK survey revealed magnetic activity variations in a large sample of solar-type stars with timescales ranging from 2.5 to 25 years. This broad range of cycle periods is thought to reflect differences in the rotational properties and the depths of the surface convection zones for stars with various masses and ages. In 2007, we initiated a long-term monitoring campaign of Ca II H and K emission for a sample of 57 southern solar-type stars to measure their magnetic activity cycles and their rotational properties when possible. We report the discovery of a 1.6 year magnetic activity cycle in the exoplanet host star ι Horologii and obtain an estimate of the rotation period that is consistent with Hyades membership. This is the shortest activity cycle so far measured for a solar-type star and may be related to the short-timescale magnetic variations recently identified in the Sun and HD 49933 from helioseismic and asteroseismic measurements. Future asteroseismic observations of ι Hor can be compared to those obtained near the magnetic minimum in 2006 to search for cycle-induced shifts in the oscillation frequencies. If such short activity cycles are common in F stars, then NASA's Kepler mission should observe their effects in many of its long-term asteroseismic targets. Title: Modeling the Subsurface Structure of Sunspots Authors: Moradi, H.; Baldner, C.; Birch, A. C.; Braun, D. C.; Cameron, R. H.; Duvall, T. L.; Gizon, L.; Haber, D.; Hanasoge, S. M.; Hindman, B. W.; Jackiewicz, J.; Khomenko, E.; Komm, R.; Rajaguru, P.; Rempel, M.; Roth, M.; Schlichenmaier, R.; Schunker, H.; Spruit, H. C.; Strassmeier, K. G.; Thompson, M. J.; Zharkov, S. Bibcode: 2010SoPh..267....1M Altcode: 2009arXiv0912.4982M; 2010SoPh..tmp..171M While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this article, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out a helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by Gizon et al. (2009a, 2009b). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat. Title: Simulation of the Formation of a Solar Active Region Authors: Cheung, M. C. M.; Rempel, M.; Title, A. M.; Schüssler, M. Bibcode: 2010ApJ...720..233C Altcode: 2010arXiv1006.4117C We present a radiative magnetohydrodynamics simulation of the formation of an active region (AR) on the solar surface. The simulation models the rise of a buoyant magnetic flux bundle from a depth of 7.5 Mm in the convection zone up into the solar photosphere. The rise of the magnetic plasma in the convection zone is accompanied by predominantly horizontal expansion. Such an expansion leads to a scaling relation between the plasma density and the magnetic field strength such that B vprop rhov1/2. The emergence of magnetic flux into the photosphere appears as a complex magnetic pattern, which results from the interaction of the rising magnetic field with the turbulent convective flows. Small-scale magnetic elements at the surface first appear, followed by their gradual coalescence into larger magnetic concentrations, which eventually results in the formation of a pair of opposite polarity spots. Although the mean flow pattern in the vicinity of the developing spots is directed radially outward, correlations between the magnetic field and velocity field fluctuations allow the spots to accumulate flux. Such correlations result from the Lorentz-force-driven, counterstreaming motion of opposite polarity fragments. The formation of the simulated AR is accompanied by transient light bridges between umbrae and umbral dots. Together with recent sunspot modeling, this work highlights the common magnetoconvective origin of umbral dots, light bridges, and penumbral filaments. Title: Seismic Discrimination of Thermal and Magnetic Anomalies in Sunspot Umbrae Authors: Lindsey, C.; Cally, P. S.; Rempel, M. Bibcode: 2010ApJ...719.1144L Altcode: Efforts to model sunspots based on helioseismic signatures need to discriminate between the effects of (1) a strong magnetic field that introduces time-irreversible, vantage-dependent phase shifts, apparently connected to fast- and slow-mode coupling and wave absorption and (2) a thermal anomaly that includes cool gas extending an indefinite depth beneath the photosphere. Helioseismic observations of sunspots show travel times considerably reduced with respect to equivalent quiet-Sun signatures. Simulations by Moradi & Cally of waves skipping across sunspots with photospheric magnetic fields of order 3 kG show travel times that respond strongly to the magnetic field and relatively weakly to the thermal anomaly by itself. We note that waves propagating vertically in a vertical magnetic field are relatively insensitive to the magnetic field, while remaining highly responsive to the attendant thermal anomaly. Travel-time measurements for waves with large skip distances into the centers of axially symmetric sunspots are therefore a crucial resource for discrimination of the thermal anomaly beneath sunspot umbrae from the magnetic anomaly. One-dimensional models of sunspot umbrae based on compressible-radiative-magnetic-convective simulations such as by Rempel et al. can be fashioned to fit observed helioseismic travel-time spectra in the centers of sunspot umbrae. These models are based on cooling of the upper 2-4 Mm of the umbral subphotosphere with no significant anomaly beneath 4.5 Mm. The travel-time reductions characteristic of these models are primarily a consequence of a Wilson depression resulting from a strong downward buoyancy of the cooled umbral medium. Title: Spectropolarimetric analysis of 3D MHD sunspot simulations Authors: Borrero, J. M.; Rempel, M.; Solanki, S. K. Bibcode: 2010AN....331..567B Altcode: We have employed 3D non-grey MHD simulations of sunspots to compute theoretical Stokes profiles and compare the levels of circular and linear polarization in the simulations with those observed in a real sunspot. We find that the spatial distribution and average values of these quantities agree very well with the observations, although the polarization levels in the simulations are slightly larger. This can be explained by a slightly larger magnetic field strength or a larger temperature gradient in the simulated penumbra as compared to the observations. Title: Developing Physics-Based Procedures for Local Helioseismic Probing of Sunspots and Magnetic Regions Authors: Birch, Aaron; Braun, D. C.; Crouch, A.; Rempel, M.; Fan, Y.; Centeno, R.; Toomre, J.; Haber, D.; Hindman, B.; Featherstone, N.; Duvall, T., Jr.; Jackiewicz, J.; Thompson, M.; Stein, R.; Gizon, L.; Cameron, R.; Saidi, Y.; Hanasoge, S.; Burston, R.; Schunker, H.; Moradi, H. Bibcode: 2010AAS...21630805B Altcode: We have initiated a project to test and improve the local helioseismic techniques of time-distance and ring-diagram analysis. Our goals are to develop and implement physics-based methods that will (1) enable the reliable determinations of subsurface flow, magnetic field, and thermal structure in regions of strong magnetic fields and (2) be quantitatively tested with realistic solar magnetoconvection simulations in the presence of sunspot-like magnetic fields. We are proceeding through a combination of improvements in local helioseismic measurements, forward modeling of the helioseismic wavefield, kernel computations, inversions, and validation through numerical simulations. As improvements over existing techniques are made they will be applied to the SDO/HMI observations. This work is funded through the the NASA Heliophysics Science Division through the Solar Dynamics Observatory (SDO) Science Center program. Title: Numerical Simulations of Sunspot Fine Structure Authors: Rempel, Matthias D. Bibcode: 2010AAS...21621105R Altcode: Sunspot fine structure has been modeled in the past by a combination of idealized magneto-convection simulations and simplified models that prescribe the magnetic field and flow structure to a large degree. Advancement in numerical methods and computing power has enabled recently 3D radiative MHD simulations of entire sunspots with sufficient resolution to address details of umbral dots and penumbral filaments. After a brief review of recent developments I will focus on the magneto-convective processes responsible for the complicated magnetic structure of the penumbra and the mechanisms leading to the driving of strong horizontal outflows (Evershed effect). Overturning convective motions are the central element for understanding sunspot fine structure. The expansion of upflowing plasma leads to a strong reduction of the magnetic field strength allowing for overturning convection, which weakens the magnetic field further due to flux expulsion. The latter has a stronger effect on the vertical magnetic field component, leading to the formation of elongated filaments with increased inclination angle. Strong horizontal outflows can be explained through a redistribution of kinetic energy preferring flows along the filaments. This redistribution is facilitated primarily through the Lorentz force, horizontal pressure gradients play only a minor role. In the near surface layers energy is primarily transported by convective motions turning over laterally, the contribution from large scale flows is negligible.

The National Center for Atmospheric Research is sponsored by the National Science Foundation. Title: Activity Cycles of Southern Asteroseismic Targets Authors: Metcalfe, Travis S.; Judge, P. G.; Basu, S.; Henry, T. J.; Soderblom, D. R.; Knoelker, M.; Rempel, M. Bibcode: 2010AAS...21542416M Altcode: 2010BAAS...42..333M The Mount Wilson Ca HK survey revealed magnetic activity variations in a large sample of solar-type stars with timescales ranging from 2.5 to 25 years. This broad range of cycle periods is thought to reflect differences in the rotational properties and the depths of the surface convection zones for stars with various masses and ages. Asteroseismic data will soon provide direct measurements of these quantities for individual stars, but many of the most promising targets are in the southern sky (e.g., alpha Cen A & B, beta Hyi, mu Ara, tau Cet, nu Ind), while long-term magnetic activity cycle surveys are largely confined to the north. In 2007 we began using the SMARTS 1.5-m telescope to conduct a long-term monitoring campaign of Ca II H & K emission for a sample of 57 southern solar-type stars to measure their magnetic activity cycles and their rotational properties when possible. This sample includes the most likely southern asteroseismic targets to be observed by the Stellar Oscillations Network Group (SONG), currently scheduled to begin operations in 2012. We present selected results from the first two years of the survey, and from the longer time baseline sampled by a single-epoch survey conducted in 1992. Title: Radiative MHD Modeling of Sunspot Fine Structure Authors: Rempel, M. Bibcode: 2009ASPC..415..351R Altcode: For a long time 3D radiative MHD simulations of sunspots were out of reach. With increasing computing power there has been recently substantial progress in modeling magneto-convection in strong magnetic field regions and complete sunspots including the transition from umbra toward plage-like solar granulation. 3D simulations point toward a unified understanding of sunspot fine structure in terms of a magneto convection process in a background field with varying inclination angle. We summarize here briefly the most recent developments. Title: Group Discussion: Solar Activity: The Role of Convection, the Tachocline and the Dynamo, and Applications of Data Assimilation Authors: Rempel, M.; Dikpati, M. Bibcode: 2009ASPC..416..551R Altcode: We summarize opinions expressed and outstanding issues established during the group discussion on current understanding of the physics of the solar and stellar convection zones, including dynamos and the solar supergranulation. This includes discussion of prospective developments in data assimilation that are hoped will lead to deeper insight into some of the outstanding issues. Title: Radiative MHD simulations of sunspot structure Authors: Rempel, M.; Schuessler, M.; Cameron, R.; Knoelker, M. Bibcode: 2009AGUFMSH53B..07R Altcode: For a long time radiative MHD simulations of entire sunspots from first principles were out of reach due to insufficient computing resources. Over the past 4 years simulations have evolved from 6x6x2 Mm size domains focusing on the details of umbral dots to simulations covering a pair of opposite polarity sunspots in a 100x50x6 Mm domain. Numerical simulations point toward a common magneto convective origin of umbral dots and filaments in the inner and outer penumbra. Most recent simulations also capture the processes involved in the formation of an extended outer penumbra with strong horizontal outflows averaging around 5 km/s in the photosphere. In this talk I will briefly review the progress made in this field over the past 4 years and discuss in detail the magneto convective origin of penumbral fine structure as well as the Evershed flow. Title: Numerical sunspot models - subsurface structure and helioseismic forward modeling (Invited) Authors: Rempel, M.; Birch, A. C.; Braun, D. C. Bibcode: 2009AGUFMSH11B..02R Altcode: The magnetic and thermal subsurface structure of sunspots has been debated for decades. While local helioseismic inversions allow in principle to constrain the subsurface structure of sunspots, a full inversion is still not possible due to the complicated interaction between waves and magnetic field. As an alternative it is possible to address this problem through forward modeling. Over the past few years numerical MHD models of entire sunspots including radiative transfer and a realistic equation of state have become possible. These simulations include p-modes excited by convection and the full interaction of these modes with the magnetic and thermal structure of the sunspot. In this talk I will present recent progress in MHD modeling of sunspots with special emphasis on the thermal and magnetic structure of numerical sunspot models. It turns out that modeled sunspots so far impose rather shallow perturbations to sound and fast mode speeds in the upper most 2 Mm. Nevertheless the seismic signatures are very similar to observed sunspots. Title: Radiative MHD simulation of an Emerging Flux Region Authors: Cheung, C.; Rempel, M.; Title, A. M.; Schuessler, M. Bibcode: 2009AGUFMSH51A1267C Altcode: We present a radiation magnetohydrodynamics (MHD) simulation of the birth of an active region. The simulation models the rise of a magnetic flux bundle from the convection zone into the solar photosphere. Observational properties of the simulation are consistent with recent, high-cadence and high spatial resolution observations of emerging flux regions taken by Hinode/SOT. Observational properties common to both simulation and observation include the hierarchical formation of progressively larger photospheric magnetic structures, the formation and disappearance of light bridges, umbral dots as well as penumbral filaments. Title: Radiative-MHD Simulations of Sunspot Structure Authors: Rempel, M. Bibcode: 2009ASPC..416..461R Altcode: For a long time 3D numerical simulations of sunspots were out of reach. With increasing computing power there has been recently substantial progress in modeling magneto-convection in strong magnetic field regions and complete sunspots including the transition from umbra toward plage-like solar granulation. We summarize here briefly the most recent developments and discuss future directions. Title: Radiative MHD simulations of sunspot structure Authors: Rempel, M.; Schüssler, M.; Cameron, R.; Knölker, M. Bibcode: 2009iac..talk..192R Altcode: 2009iac..talk..106R No abstract at ADS Title: Radiative MHD Simulations of Sunspot Structure-Challenges and recent developments Authors: Rempel, Matthias Bibcode: 2009AIPC.1171..315R Altcode: For a long time 3D radiative MHD simulations of sunspots were out of reach. With increasing computing power there has been recently substantial progress in modeling magneto-convection in strong magnetic field regions and complete sunspots including the transition from umbra toward plage like solar granulation. 3D simulations point toward a unified understanding of sunspot fine structure in terms of a magneto convection process in a background field with varying inclination angle. We summarize here briefly the most recent developments. Title: Activity Cycles of Southern Asteroseismic Targets Authors: Metcalfe, T. S.; Judge, P. G.; Basu, S.; Henry, T. J.; Soderblom, D. R.; Knoelker, M.; Rempel, M. Bibcode: 2009arXiv0909.5464M Altcode: The Mount Wilson Ca HK survey revealed magnetic activity variations in a large sample of solar-type stars with timescales ranging from 2.5 to 25 years. This broad range of cycle periods is thought to reflect differences in the rotational properties and the depths of the surface convection zones for stars with various masses and ages. Asteroseismic data will soon provide direct measurements of these quantities for individual stars, but many of the most promising targets are in the southern sky (e.g., alpha Cen A & B, beta Hyi, mu Ara, tau Cet, nu Ind), while long-term magnetic activity cycle surveys are largely confined to the north. In 2007 we began using the SMARTS 1.5-m telescope to conduct a long-term monitoring campaign of Ca II H & K emission for a sample of 57 southern solar-type stars to measure their magnetic activity cycles and their rotational properties when possible. This sample includes the most likely southern asteroseismic targets to be observed by the Stellar Oscillations Network Group (SONG), currently scheduled to begin operations in 2012. We present selected results from the first two years of the survey, and from the longer time baseline sampled by a single-epoch survey conducted in 1992. Title: Creation and destruction of magnetic field Authors: Rempel, Matthias Bibcode: 2009hppl.book...42R Altcode: No abstract at ADS Title: Penumbral Structure and Outflows in Simulated Sunspots Authors: Rempel, M.; Schüssler, M.; Cameron, R. H.; Knölker, M. Bibcode: 2009Sci...325..171R Altcode: 2009arXiv0907.2259R Sunspots are concentrations of magnetic field on the visible solar surface that strongly affect the convective energy transport in their interior and surroundings. The filamentary outer regions (penumbrae) of sunspots show systematic radial outward flows along channels of nearly horizontal magnetic field. These flows were discovered 100 years ago and are present in all fully developed sunspots. By using a comprehensive numerical simulation of a sunspot pair, we show that penumbral structures with such outflows form when the average magnetic field inclination to the vertical exceeds about 45 degrees. The systematic outflows are a component of the convective flows that provide the upward energy transport and result from anisotropy introduced by the presence of the inclined magnetic field. Title: Radiative MHD Simulations of Sunspot Structure Authors: Rempel, Matthias D.; Schuessler, M.; Cameron, R.; Knoelker, M. Bibcode: 2009SPD....40.0604R Altcode: We summarize the recent progress made in magneto convection simulations of sunspot structure. Over the past 4 years simulations have evolved from local 6x6x2 Mm size domains focusing on the details of umbral dots to simulations covering a pair of opposite polarity spots in a 100x50x6 Mm domain. The simulations point out the common magneto convective origin of umbral dots and filaments in the inner penumbra and most recently also reveal the processes involved in the formation of an extended outer penumbra with strong horizontal outflows averaging around 5 km/s in the photosphere. Title: Helioseismology of a Realistic MHD Sunspot Simulation Authors: Braun, Douglas; Birch, A. C.; Rempel, M. Bibcode: 2009SPD....40.0303B Altcode: We have recently measured travel times and absorption of p modes propagating through a realistic numerical model of solar convection in the presence of a sunspot-like structure. Both the mean travel-time perturbations and the absorption in the simulation are remarkably similar to those observed in typical sunspots. Therefore, simulations of this type provide both the means to understand the physics behind the helioseismic observations and the opportunity to validate existing and future models of the subsurface structure of sunspots. We will compare helioseismic measurements made with the simulation with those of a typical sunspot observed with MDI. We will discuss the implications of these comparisons for structural inversions of sunspots and understanding the role of MHD mode conversion in interpreting helioseismic observations. This work is supported by NASA contracts NNH09CE41C and NNG07EI51C. Title: Helioseismic Inversions applied to a Realistic MHD Sunspot Simulation Authors: Birch, Aaron; Braun, D. C.; Rempel, M. Bibcode: 2009SPD....40.0713B Altcode: Local helioseismology applied to the realistic magneto-convection sunspot simulations of Rempel et al. produces solar-like wave travel times. We apply standard ray-theory based inversions to infer subsurface wave speed from these travel times. We find that the inferred wave-speed perturbations are similar to the wave-speed perturbations found from the analysis of typical sunspots observed with MDI. We show, however, that the ray theory inversions fail to retrieve the true time-averaged sound speed or fast-mode speed from the simulations. We propose some alternative strategies for inferring the subsurface structure of sunspots.

This work is supported by NASA contracts NNH09CE41C and NNG07EI51C. Title: Large Scale Flows in the Solar Convection Zone Authors: Brun, Allan Sacha; Rempel, Matthias Bibcode: 2009SSRv..144..151B Altcode: 2008SSRv..tmp..173B We discuss the current theoretical understanding of the large scale flows observed in the solar convection zone, namely the differential rotation and meridional circulation. Based on multi-D numerical simulations we describe which physical processes are at the origin of these large scale flows, how they are maintained and what sets their unique profiles. We also discuss how dynamo generated magnetic field may influence such a delicate dynamical balance and lead to a temporal modulation of the amplitude and profiles of the solar large scale flows. Title: Planetary Dynamos from a Solar Perspective Authors: Christensen, U. R.; Schmitt, D.; Rempel, M. Bibcode: 2009SSRv..144..105C Altcode: 2008SSRv..tmp..164C Direct numerical simulations of the geodynamo and other planetary dynamos have been successful in reproducing the observed magnetic fields. We first give an overview on the fundamental properties of planetary magnetism. We review the concepts and main results of planetary dynamo modeling, contrasting them with the solar dynamo. In planetary dynamos the density stratification plays no major role and the magnetic Reynolds number is low enough to allow a direct simulation of the magnetic induction process using microscopic values of the magnetic diffusivity. The small-scale turbulence of the flow cannot be resolved and is suppressed by assuming a viscosity far in excess of the microscopic value. Systematic parameter studies lead to scaling laws for the magnetic field strength or the flow velocity that are independent of viscosity, indicating that the models are in the same dynamical regime as the flow in planetary cores. Helical flow in convection columns that are aligned with the rotation axis play an important role for magnetic field generation and forms the basis for a macroscopic α-effect. Depending on the importance of inertial forces relative to rotational forces, either dynamos with a dominant axial dipole or with a small-scale multipolar magnetic field are found. Earth is predicted to lie close to the transition point between both classes, which may explain why the dipole undergoes reversals. Some models fit the properties of the geomagnetic field in terms of spatial power spectra, magnetic field morphology and details of the reversal behavior remarkably well. Magnetic field strength in the dipolar dynamo regime is controlled by the available power and found to be independent of rotation rate. Predictions for the dipole moment agree well with the observed field strength of Earth and Jupiter and moderately well for other planets. Dedicated dynamo models for Mercury, Saturn, Uranus and Neptune, which assume stably stratified layers above or below the dynamo region, can explain some of the unusual field properties of these planets. Title: Planetary Dynamos from a Solar Perspective Authors: Christensen, U. R.; Schmitt, D.; Rempel, M. Bibcode: 2009odsm.book..105C Altcode: Direct numerical simulations of the geodynamo and other planetary dynamos have been successful in reproducing the observed magnetic fields. We first give an overview on the fundamental properties of planetary magnetism. We review the concepts and main results of planetary dynamo modeling, contrasting them with the solar dynamo. In planetary dynamos the density stratification plays no major role and the magnetic Reynolds number is low enough to allow a direct simulation of the magnetic induction process using microscopic values of the magnetic diffusivity. The small-scale turbulence of the flow cannot be resolved and is suppressed by assuming a viscosity far in excess of the microscopic value. Systematic parameter studies lead to scaling laws for the magnetic field strength or the flow velocity that are independent of viscosity, indicating that the models are in the same dynamical regime as the flow in planetary cores. Helical flow in convection columns that are aligned with the rotation axis play an important role for magnetic field generation and forms the basis for a macroscopic α-effect. Depending on the importance of inertial forces relative to rotational forces, either dynamos with a dominant axial dipole or with a small-scale multipolar magnetic field are found. Earth is predicted to lie close to the transition point between both classes, which may explain why the dipole undergoes reversals. Some models fit the properties of the geomagnetic field in terms of spatial power spectra, magnetic field morphology and details of the reversal behavior remarkably well. Magnetic field strength in the dipolar dynamo regime is controlled by the available power and found to be independent of rotation rate. Predictions for the dipole moment agree well with the observed field strength of Earth and Jupiter and moderately well for other planets. Dedicated dynamo models for Mercury, Saturn, Uranus and Neptune, which assume stably stratified layers above or below the dynamo region, can explain some of the unusual field properties of these planets. Title: Radiative Magnetohydrodynamic Simulation of Sunspot Structure Authors: Rempel, M.; Schüssler, M.; Knölker, M. Bibcode: 2009ApJ...691..640R Altcode: 2008arXiv0808.3294R Results of a three-dimensional MHD simulation of a sunspot with a photospheric size of about 20 Mm are presented. The simulation has been carried out with the MURaM code, which includes a realistic equation of state with partial ionization and radiative transfer along many ray directions. The largely relaxed state of the sunspot shows a division in a central dark umbral region with bright dots and a penumbra showing bright filaments of about 2-3 Mm length with central dark lanes. By a process similar to the formation of umbral dots, the penumbral filaments result from magnetoconvection in the form of upflow plumes, which become elongated by the presence of an inclined magnetic field; the upflow is deflected in the outward direction while the magnetic field is weakened and becomes almost horizontal in the upper part of the plume near the level of optical depth unity. A dark lane forms owing to the piling up of matter near the cusp-shaped top of the rising plume that leads to an upward bulging of the surfaces of constant optical depth. The simulated penumbral structure corresponds well to the observationally inferred interlocking-comb structure of the magnetic field with Evershed outflows along dark-laned filaments with nearly horizontal magnetic field and overturning perpendicular ("twisting") motion, which are embedded in a background of stronger and less inclined field. Photospheric spectral lines are formed at the very top and somewhat above the upflow plumes, so that they do not fully sense the strong flow as well as the large field inclination and significant field strength reduction in the upper part of the plume structures. Title: Magnetic flux emergence on the Sun and Sun-like stars Authors: Rempel, Matthias; Fan, Yuhong; Birch, Aaron; Braun, Douglas Bibcode: 2009astro2010S..74R Altcode: 2009astro2010S..74F No abstract at ADS Title: Large Scale Flows in the Solar Convection Zone Authors: Brun, Allan Sacha; Rempel, Matthias Bibcode: 2009odsm.book..151B Altcode: We discuss the current theoretical understanding of the large scale flows observed in the solar convection zone, namely the differential rotation and meridional circulation. Based on multi-D numerical simulations we describe which physical processes are at the origin of these large scale flows, how they are maintained and what sets their unique profiles. We also discuss how dynamo generated magnetic field may influence such a delicate dynamical balance and lead to a temporal modulation of the amplitude and profiles of the solar large scale flows. Title: Dynamos and magnetic fields of the Sun and other cool stars, and their role in the formation and evolution of stars and in the habitability of planets Authors: Schrijver, Karel; Carpenter, Ken; Karovska, Margarita; Ayres, Tom; Basri, Gibor; Brown, Benjamin; Christensen-Dalsgaard, Joergen; Dupree, Andrea; Guinan, Ed; Jardine, Moira; Miesch, Mark; Pevtsov, Alexei; Rempel, Matthias; Scherrer, Phil; Solanki, Sami; Strassmeier, Klaus; Walter, Fred Bibcode: 2009astro2010S.262S Altcode: No abstract at ADS Title: Solar and stellar activity cycles Authors: Rempel, Matthias Bibcode: 2008JPhCS.118a2032R Altcode: A variety of different dynamo models have been proposed for the Sun. While the basic ingredients of the solar dynamo are known, there is no general agreement about the combination and the relative importance of these basic processes. Unfortunately observational constraints are not strong enough to clearly distinguish between different dynamo models. Studying stellar magnetism of the lower main-sequence allows us to impose additional constraints on the fundamental dynamo process and allows to investigate how the properties of dynamos change when rotation and convection zone depth are different from the solar values. We briefly summarize the current state of this field and give an outlook for future improvement including theoretical considerations, new observations and the contributions expected from asteroseismology. Title: 3D MHD Simulations of Sunspot Structure Authors: Rempel, M.; Schüssler, M. Bibcode: 2008ESPM...12..3.9R Altcode: We present results of a 3D MHD simulation of a sunspot with a photospheric size of about 20 Mm carried out with the MURaM MHD code. The simulation covers a time span of about 12 hours. The largely relaxed state of the sunspot shows a division in a central dark umbral region with bright dots and a penumbra showing bright filaments of about 3 to 4 Mm length with central dark lanes. By a process similar to the formation of umbral dots, the penumbral filaments result from magneto-convection in the form of upflow plumes, which become elongated by the presence of an inclined magnetic field: the upflow is deflected in the outward direction and bends down the magnetic field to become almost horizontal in the upper part of the plume near the level of optical depth unity. At the same time, roll-type motion leads to a flow perpendicular to the filament axis and to downflow near its edges. Expansion and flux expulsion leads to a strong reduction of the field strength in the upper part of the rising plume, where a dark lane forms owing to the piling up of matter near the cusp-shaped top and the upward bulging of the surfaces of constant optical depth. The simulated penumbral structure corresponds well to the observationally inferred interlocking-comb structure of the magnetic field with Evershed outflows along dark-laned filaments with nearly horizontal magnetic field and roll-type perpendicular motion, which are embedded in a background of stronger and less inclined field. Photospheric spectral lines are formed at the very top and somewhat above the upflow plumes, so that they do not fully sense the strong flow as well as the large field inclination and significant field strength reduction in the upper part of the plume structures. Title: Observation and Modeling of the Solar-Cycle Variation of the Meridional Flow Authors: Gizon, Laurent; Rempel, Matthias Bibcode: 2008SoPh..251..241G Altcode: 2008arXiv0803.0950G; 2008SoPh..tmp...58G We present independent observations of the solar-cycle variation of flows near the solar surface and at a depth of about 60 Mm, in the latitude range ± 45°. We show that the time-varying components of the meridional flow at these two depths have opposite sign, whereas the time-varying components of the zonal flow are in phase. This is in agreement with previous results. We then investigate whether the observations are consistent with a theoretical model of solar-cycle-dependent meridional circulation based on a flux-transport dynamo combined with a geostrophic flow caused by increased radiative loss in the active region belt (the only existing quantitative model). We find that the model and the data are in qualitative agreement, although the amplitude of the solar-cycle variation of the meridional flow at 60 Mm is underestimated by the model. Title: A solar mean field dynamo benchmark Authors: Jouve, L.; Brun, A. S.; Arlt, R.; Brandenburg, A.; Dikpati, M.; Bonanno, A.; Käpylä, P. J.; Moss, D.; Rempel, M.; Gilman, P.; Korpi, M. J.; Kosovichev, A. G. Bibcode: 2008A&A...483..949J Altcode: Context: The solar magnetic activity and cycle are linked to an internal dynamo. Numerical simulations are an efficient and accurate tool to investigate such intricate dynamical processes.
Aims: We present the results of an international numerical benchmark study based on two-dimensional axisymmetric mean field solar dynamo models in spherical geometry. The purpose of this work is to provide reference cases that can be analyzed in detail and that can help in further development and validation of numerical codes that solve such kinematic problems.
Methods: The results of eight numerical codes solving the induction equation in the framework of mean field theory are compared for three increasingly computationally intensive models of the solar dynamo: an αΩ dynamo with constant magnetic diffusivity, an αΩ dynamo with magnetic diffusivity sharply varying with depth and an example of a flux-transport Babcock-Leighton dynamo which includes a non-local source term and one large single cell of meridional circulation per hemisphere. All cases include a realistic profile of differential rotation and thus a sharp tachocline.
Results: The most important finding of this study is that all codes agree quantitatively to within less than a percent for the αΩ dynamo cases and within a few percent for the flux-transport case. Both the critical dynamo numbers for the onset of dynamo action and the corresponding cycle periods are reasonably well recovered by all codes. Detailed comparisons of butterfly diagrams and specific cuts of both toroidal and poloidal fields at given latitude and radius confirm the good quantitative agreement.
Conclusions: We believe that such a benchmark study will be a very useful tool since it provides detailed standard cases for comparison and reference. Title: Non-kinematic flux-transport dynamos with variable meridional flow Authors: Rempel, M. Bibcode: 2007AN....328.1096R Altcode: A single counter clockwise flow cell is the assumption underlying most flux-transport dynamo models to date. On the other hand, global 3D simulations of the solar convection zone by Miesch et al. indicate that the meridional flow is strongly variable and shows at a given time a multi-cellular flow structure, with only the long term average reflecting a more regular flow field. We investigate the influence of such a highly time variable meridional flow on a flux-transport dynamo model. In our model the differential rotation and meridional flow are driven self-consistently through a parameterization of the Reynolds-stress (Λ-effect) and also macroscopic Lorentz-force feedback is considered. We achieve the time variable flow by adding random fluctuations with a given correlation time and length scale to both components of the turbulent angular momentum flux. We find that a significant amount of random fluctuations can be tolerated before the dynamo loses its coherence, provided that the correlation time scale of the random component is significantly shorter than the cycle length. Stronger constraints on the amplitude of random fluctuations come from helioseismic constraints on the variability of differential rotation. Title: Joint Discussion 17 Highlights of recent progress in the seismology of the Sun and Sun-like stars Authors: Bedding, Timothy R.; Brun, Allan S.; Christensen-Dalsgaard, Jørgen; Crouch, Ashley; De Cat, Peter; García, Raphael A.; Gizon, Laurent; Hill, Frank; Kjeldsen, Hans; Leibacher, John W.; Maillard, Jean-Pierre; Mathis, S.; Rabello-Soares, M. Cristina; Rozelot, Jean-Pierre; Rempel, Matthias; Roxburgh, Ian W.; Samadi, Réza; Talon, Suzanne; Thompson, Michael J. Bibcode: 2007HiA....14..491B Altcode: The seismology and physics of localized structures beneath the surface of the Sun takes on a special significance with the completion in 2006 of a solar cycle of observations by the ground-based Global Oscillation Network Group (GONG) and by the instruments on board the Solar and Heliospheric Observatory (SOHO). Of course, the spatially unresolved Birmingham Solar Oscillation Network (BiSON) has been observing for even longer. At the same time, the testing of models of stellar structure moves into high gear with the extension of deep probes from the Sun to other solar-like stars and other multi-mode pulsators, with ever-improving observations made from the ground, the success of the MOST satellite, and the recently launched CoRoT satellite. Here we report the current state of the two closely related and rapidly developing fields of helio- and asteroseimology. Title: Origin of Solar Torsional Oscillations Authors: Rempel, Matthias Bibcode: 2007ApJ...655..651R Altcode: 2006astro.ph.10221R Helioseismology has revealed many details of solar differential rotation and its time variation, known as torsional oscillations. So far there is no generally accepted theoretical explanation for torsional oscillations, even though a close relation to the solar activity cycle is evident. On the theoretical side, nonkinematic dynamo models (including the Lorentz force feedback on differential rotation) have been used to explain torsional oscillations. In this paper we use a slightly different approach by forcing torsional oscillations in a mean field differential rotation model. Our aim is not a fully self-consistent model, but rather to point out a few general properties of torsional oscillations, and their possible origins, that are independent from a particular dynamo model. We find that the poleward-propagating high-latitude branch of the torsional oscillations can be explained as a response of the coupled differential rotation/meridional flow system to periodic forcing in midlatitudes of either mechanical (Lorentz force) or thermal nature. The speed of the poleward propagation sets constraints on the value of the turbulent viscosity in the solar convection zone to be less than 3×108 m2 s-1. We also show that the equatorward-propagating low-latitude branch is most likely not a consequence of mechanical forcing (Lorentz force) alone, but rather of thermal origin due to the Taylor-Proudman theorem. Title: The Uncombed Penumbra Authors: Borrero, J. M.; Rempel, M.; Solanki, S. K. Bibcode: 2006ASPC..358...19B Altcode: 2006astro.ph..2130B The uncombed penumbral model explains the structure of the sunspot penumbra in terms of thick magnetic fibrils embedded in a surrounding, magnetic atmosphere. This model has been successfully applied to explain the polarization signals emerging from the sunspot penumbra. Thick penumbral fibrils face some physical problems, however. In this contribution we will offer possible solutions to these shortcomings. Title: The Dynamical Disconnection of Sunspots from their Magnetic Roots Authors: Rempel, M.; Schüssler, M. Bibcode: 2006ASPC..354..148R Altcode: After a dynamically active emergence phase, magnetic flux at the solar surface soon ceases to show strong signs of the subsurface dynamics of its parent magnetic structure. This indicates that some kind of disconnection of the emerged flux from its roots in the deep convection zone should take place. We propose a mechanism for the dynamical disconnection of the surface flux based upon the buoyant upflow of plasma along the field lines. Such flows arise in the upper part of a rising flux loop during the final phases of its buoyant ascent towards the surface. The combination of the pressure buildup by the upflow and the cooling of the upper layers of an emerged flux tube by radiative losses at the surface lead to a progressive weakening of the magnetic field in several Mm depth. When the field strength has become sufficiently low, convective motions and the fluting instability disrupt the flux tube into thin, passively advected flux fragments, thus providing a dynamical disconnection of the emerged part from its roots. We substantiate this scenario by considering the quasi-static evolution of a sunspot model under the effects of radiative cooling, convective energy transport, and pressure buildup by a prescribed inflow at the bottom of the model. For inflow speeds in the range shown by simulations of thin flux tubes, we find that the disconnection takes place in a depth between two and six Mm for disconnection times up to three days. Title: Non-kinematic flux-transport dynamos and torsional oscillations Authors: Rempel, M. Bibcode: 2006ESASP.624E..18R Altcode: 2006soho...18E..18R No abstract at ADS Title: Time-varying component of the solar meridional flow Authors: Gizon, L.; Rempel, M. Bibcode: 2006ESASP.624E.129G Altcode: 2006soho...18E.129G No abstract at ADS Title: Solar Convection Zone Dynamics: How Sensitive Are Inversions to Subtle Dynamo Features? Authors: Howe, R.; Rempel, M.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R.; Larsen, R. M.; Schou, J.; Thompson, M. J. Bibcode: 2006ApJ...649.1155H Altcode: The nearly 10 year span of medium-degree helioseismic data from the Global Oscillation Network Group and the Michelson Doppler Imager has allowed us to study the evolving flows in the solar convection zone over most of solar cycle 23. Using two independent two-dimensional rotation inversion techniques and extensive studies of the resolution using artificial data from different assumed flow profiles, including those generated from sample mean field dynamo models, we attempt to assess the reality of certain features seen in the inferred rotation profiles. Our results suggest that the findings from observations of a substantial depth dependence of the phase of the zonal flow pattern in the low latitudes, and the penetration of the flows deep into the convection zone, are likely to be real rather than artifacts of the inversion process. Title: Non-kinematic flux-transport dynamos and torsional oscillations Authors: Rempel, M. Bibcode: 2006IAUJD..17E...6R Altcode: We present a non-kinematic, flux-transport dynamo model for the S un that combines a mean - field model for differential rotation and meridional flow with the mean - field induction equation. The induced magnetic field is allowed to feed back on differential rotation and meridional flow through the macroscopic Lorentz force, leading to solar cycle variations of zonal and meridional flows. We show that the dynamo saturates through this feedback at a field strength of around 10 - 2 0 kG and that the equator ward transport of field by the meridional flow at the base of the convection zone (essential for flux-transport dynamos) is not significantly reduced. The non-linear dynamo is capable of explaining the high- latitude branch of torsional oscillations (having correct amplitude and phase relation with respect to the magnetic butterfly diagram), but cannot explain the low- latitude branch through macroscopic Lorentz-force feedback. We present a compound model that includes a parameterisation of enhanced radiative losses in the active region belt (following the idea of Spruit 2003, Solar Physics 213, 1) and show that this can provide the correct oscillation pattern in low latitudes close to the surface. Thermally- driven inflows into the active region belt produced by this model are also consistent with observations. Title: Flux-Transport Dynamos with Lorentz Force Feedback on Differential Rotation and Meridional Flow: Saturation Mechanism and Torsional Oscillations Authors: Rempel, Matthias Bibcode: 2006ApJ...647..662R Altcode: 2006astro.ph..4446R In this paper we discuss a dynamic flux-transport dynamo model that includes the feedback of the induced magnetic field on differential rotation and meridional flow. We consider two different approaches for the feedback: mean field Lorentz force and quenching of transport coefficients such as turbulent viscosity and heat conductivity. We find that even strong feedback on the meridional flow does not change the character of the flux-transport dynamo significantly; however, it leads to a significant reduction of differential rotation. To a large degree independent of the dynamo parameters, the saturation takes place when the toroidal field at the base of the convection zone reaches between 1.2 and 1.5 T, and the energy converted into magnetic energy corresponds to about 0.1%-0.2% of the solar luminosity. The torsional oscillations produced through Lorentz force feedback on differential rotation show a dominant poleward propagating branch with the correct phase relation to the magnetic cycle. We show that incorporating enhanced surface cooling of the active region belt (as proposed by Spruit) leads to an equatorward propagating branch in good agreement with observations. Title: The uncombed penumbra Authors: Borrero, J. M.; Rempel, M.; Solanki, S. K. Bibcode: 2006astro.ph..2129B Altcode: The uncombed penumbral model explains the structure of the sunspot penumbra in terms of thick magnetic fibrils embedded in a magnetic surrounding atmosphere. This model has been successfully applied to explain the polarization signals emerging from the sunspot penumbra. Thick penumbral fibrils face some physical problems, however. In this contribution we will offer possible solutions to these shortcomings. Title: Transport of Toroidal Magnetic Field by the Meridional Flow at the Base of the Solar Convection Zone Authors: Rempel, Matthias Bibcode: 2006ApJ...637.1135R Altcode: 2006astro.ph.10133R In this paper we discuss the transport of toroidal magnetic field by a weak meridional flow at the base of the convection zone. We use the differential rotation and meridional flow model developed by Rempel and incorporate feedback of a purely toroidal magnetic field in two ways: directly through the Lorentz force (magnetic tension) and indirectly through quenching of the turbulent viscosity, which affects the parameterized turbulent angular momentum transport in the model. In the case of direct Lorentz force feedback, we find that a meridional flow with an amplitude of around 2 m s-1 can transport a magnetic field with a strength of 20-30 kG. Quenching of turbulent viscosity leads to deflection of the meridional flow from the magnetized region and a significant reduction of the transport velocity if the magnetic field is above equipartition strength. Title: How Sensitive are Rotation Inversions to Subtle Features of the Dynamo? Authors: Howe, R.; Rempel, M.; Christensen-Dalsgaard, J.; Schou, J.; Thompson, M. J.; Komm, R.; Hill, F. Bibcode: 2005ASPC..346...99H Altcode: Global rotation inversions can probe the pattern of zonal flows well into the convection zone. In this paper, we test the ability of the inversions to constrain the predictions of dynamo models. A flux-transport dynamo model, including a mean-field theory of differential rotation and allowing for feedback of the Lorentz force on differential rotation and meridional flow, was used to produce a 22-year cycle of simulated rotation profiles. These were then subjected to simulated inversions with realistic mode sets and errors, in order to test how well the subtle subsurface features of the input profile could be recovered. The preliminary results are quite encouraging. Title: Fighting the Taylor-Proudman constraint -- How to get differential rotation solar-like? Authors: Rempel, M. Bibcode: 2005ASPC..346...75R Altcode: We present a model for the solar differential rotation and meridional circulation based on a mean-field parametrization of the Reynolds-stresses that drive the differential rotation. We include the subadiabatic part of the tachocline and show that this, in conjunction with turbulent heat conductivity within the convection zone and upper overshoot region, provides the key physics to break the Taylor-Proudman constraint, which dictates normally differential rotation with contour lines parallel to the axis of rotation. We show that solar-like differential rotation with contour lines almost aligned with the radial direction is a very robust result of the model, which does not depend on the details of the Reynolds-stress and the assumed viscosity, as long as the Reynolds-stress transports angular momentum towards the equator. The meridional flow is more sensitive to the details of the assumed Reynolds-stress, but a one-cell flow, equatorward at the base of the convection zone and poleward in the upper half of the convection zone, is the preferred flow pattern for a variety of different assumptions concerning the Reynolds-stress. Incorporating the feedback of a toroidal magnetic field through Lorentz force into this models allows us to estimate up to which field strength meridional flow can transport toroidal magnetic field at the base of the convection zone equatorward. We find an upper limit of 2 to 3 T (20 to 30 kG) in our investigation. Title: Influence of Random Fluctuations in the Λ-Effect on Meridional Flow and Differential Rotation Authors: Rempel, Matthias Bibcode: 2005ApJ...631.1286R Altcode: 2006astro.ph.10132R We present a mean field model based on the approach taken by Rempel in order to investigate the influence of stochastic fluctuations in the Reynolds stresses on meridional flow and differential rotation. The stochastic fluctuations found in the meridional flow pattern directly resemble the stochastic fluctuations of the Reynolds stresses, while the stochastic fluctuations in the differential rotation are smaller by almost 2 orders of magnitude. It is further found that the correlation length and timescale of the stochastic fluctuations have only a weak influence on meridional flow, but a significant influence on the magnitude of variations in the differential rotation. We analyze the energy fluxes within the model to estimate timescales for the replenishment of differential rotation and meridional flow. We find that the timescale for the replenishment of differential rotation (~10 years) is nearly 4 orders of magnitude longer than the timescale for the replenishment of meridional flow, which explains the differences in the response to stochastic fluctuations of the Reynolds stress found for both flow fields. Title: The dynamical disconnection of sunspots from their magnetic roots Authors: Schüssler, M.; Rempel, M. Bibcode: 2005A&A...441..337S Altcode: 2005astro.ph..6654S After a dynamically active emergence phase, magnetic flux at the solar surface soon ceases to show strong signs of the subsurface dynamics of its parent magnetic structure. This indicates that some kind of disconnection of the emerged flux from its roots in the deep convection zone should take place. We propose a mechanism for the dynamical disconnection of the surface flux based upon the buoyant upflow of plasma along the field lines. Such flows arise in the upper part of a rising flux loop during the final phases of its buoyant ascent towards the surface. The combination of the pressure buildup by the upflow and the cooling of the upper layers of an emerged flux tube by radiative losses at the surface lead to a progressive weakening of the magnetic field in several Mm depth. When the field strength has become sufficiently low, convective motions and the fluting instability disrupt the flux tube into thin, passively advected flux fragments, thus providing a dynamical disconnection of the emerged part from its roots. We substantiate this scenario by considering the quasi-static evolution of a sunspot model under the effects of radiative cooling, convective energy transport, and pressure buildup by a prescribed inflow at the bottom of the model. For inflow speeds in the range shown by simulations of thin flux tubes, we find that the disconnection takes place in a depth between 2 and 6 Mm for disconnection times up to 3 days. Title: Concentration of Toroidal Magnetic Field in the Solar Tachocline by η-Quenching Authors: Gilman, Peter A.; Rempel, Matthias Bibcode: 2005ApJ...630..615G Altcode: 2005astro.ph..4003G We show that if the turbulent magnetic diffusivity used in solar dynamos is assumed to be ``quenched'' by increasing toroidal fields, much larger amplitude and more concentrated toroidal fields can be induced by differential rotation from an assumed poloidal field than if there is no quenching. This amplification and concentration mechanism is weakened and bounded by jXB feedbacks on the differential rotation. Nevertheless, it is strong enough to contribute to the creation of ~100 kG toroidal fields near the base of the convection zone, perhaps in conjunction with the ``exploding flux tube'' process. Such high fields are necessary for sunspots to occur in low solar latitudes. Title: Comments on "Full-sphere simulations of circulation-dominated solar dynamo: Exploring the parity issue" Authors: Dikpati, M.; Rempel, M.; Gilman, P. A.; MacGregor, K. B. Bibcode: 2005A&A...437..699D Altcode: Using two distinct simulation codes that respectively apply semi-implicit and fully explicit schemes, we perform calculations of a 2D kinematic Babcock-Leighton type flux-transport dynamo with Chatterjee et al.'s parameter settings. We show that their solutions are diffusion-dominated, rather than circulation-dominated as their title implies. We also have been unable to reproduce several properties of their dynamo solutions, namely we obtain a much faster cycle with ~ 4 times shorter period than theirs, with highly overlapping cycles; a polar field value of ∼ 2 kG if one has to produce a ~ 100 kG toroidal field at convection zone base; and quadrupolar parity as opposed to Chatterjee et al.'s dipolar parity solutions. Title: Solar Differential Rotation and Meridional Flow: The Role of a Subadiabatic Tachocline for the Taylor-Proudman Balance Authors: Rempel, M. Bibcode: 2005ApJ...622.1320R Altcode: 2006astro.ph..4451R We present a simple model for the solar differential rotation and meridional circulation based on a mean field parameterization of the Reynolds stresses that drive the differential rotation. We include the subadiabatic part of the tachocline and show that this, in conjunction with turbulent heat conductivity within the convection zone and overshoot region, provides the key physics to break the Taylor-Proudman constraint, which dictates differential rotation with contour lines parallel to the axis of rotation in case of an isentropic stratification. We show that differential rotation with contour lines inclined by 10°-30° with respect to the axis of rotation is a robust result of the model, which does not depend on the details of the Reynolds stress and the assumed viscosity, as long as the Reynolds stress transports angular momentum toward the equator. The meridional flow is more sensitive with respect to the details of the assumed Reynolds stress, but a flow cell, equatorward at the base of the convection zone and poleward in the upper half of the convection zone, is the preferred flow pattern. Title: Dynamos with feedback of of j x B force on meridional flow and differential rotation Authors: Rempel, M.; Dikpati, M.; MacGregor, K. Bibcode: 2005ESASP.560..913R Altcode: 2005csss...13..913R No abstract at ADS Title: How Sensitive are Rotation Inversions to Subtle Features of the Dynamo? Authors: Howe, R.; Rempel, M.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.; Schou, J.; Thompson, M. J. Bibcode: 2004ESASP.559..468H Altcode: 2004soho...14..468H No abstract at ADS Title: Overshoot at the Base of the Solar Convection Zone: A Semianalytical Approach Authors: Rempel, M. Bibcode: 2004ApJ...607.1046R Altcode: Despite the importance of overshoot at the base of the solar convection zone for the storage of strong toroidal magnetic field produced there by the solar dynamo, uncertainties concerning the depth and mean subadiabatic stratification remain large. Overshoot models based on the nonlocal mixing-length theory generally produce a shallow, weakly subadiabatic region with a sharp transition to the radiative interior, whereas several numerical simulations lead to significantly subadiabatic overshoot with penetration depth of more than a pressure scale height. We present a semianalytical convection zone/overshoot region model based on the assumption that the convective energy flux is governed by coherent downflow structures starting at the top of the domain and continuing all the way down into the overshoot region, which allows for modeling both the parameter regime addressed by nonlocal mixing-length approach and the regime addressed by numerical simulations. It turns out that the main differences between the nonlocal mixing-length approach and numerical simulations (nearly adiabatic vs. strongly subadiabatic overshoot) are caused by the much larger energy flux used in numerical simulations as a consequence of larger thermal diffusivities required by numerical constraints. The depth of the overshoot region is determined predominantly by the mixing between downflows and upflows in the convection zone. Furthermore, our model shows that the sharp transition between the nearly adiabatic overshoot and radiative interior, a typical result of the nonlocal mixing-length approach, can be avoided by assuming an ensemble of downflows with different strength. Title: Dynamos with feedback of jxB Force on Meridional Flow and Differential Rotation Authors: Rempel, M.; Dikpati, M.; MacGregor, K. Bibcode: 2004AAS...204.8802R Altcode: 2004BAAS...36..819R Recently, flux-transport dynamos have been successful in reproducing various observed features of the large scale solar magnetic fields. However, these studies addressed the transport of magnetic fields by the meridional circulation in a purely kinematic regime. The toroidal field strength at the base of the solar convection zone inferred from studies of rising magnetic flux tubes is around 100 KG and thus orders of magnitude larger than the equipartition field strength estimated from a meridional flow velocity of a few m/s. Therefore it is crucial for flux-transport dynamos to address the feedback of the jxB on the meridional flow. We present a "dynamic" dynamo model, in which we couple a mean-field Reynolds-stress approach for the differential rotation and meridional circulation with the axisymmetric dynamo equations. This provides a self-consistent model that allows to study the back-reaction of the mean-field Lorentz force of the dynamo generated field on differential rotation and meridional circulation. This model gives an estimate of the magnetic field strength up to which a transport of magnetic field by the weak meridional flow and amplification by the shear in the differential rotation is possible. Additional to this the model also provides solar cycle variations in differential rotation and meridional circulation, which can be compared to helioseismic data. We also show that the feedback of the Lorentz-force on the meridional flow can be included into a kinematic dynamo model in terms of a "quenching" of the stream function, which deflects the flow from regions of strong toroidal magnetic field. From both studies we conclude that flux-transport dynamos work even with strong feedback of the jxB force, primarily because of two reasons: 1) The transport of the weak poloidal magnetic field, which is the sources of strong toroidal field, is not affected strongly. 2) The meridional flow results from a small difference between large forces, so that the transport capability is much larger than a simple estimate based on equipartition argument.

This work is partially supported by NASA grants W-10107 and W-10175. The National Center for Atmospheric Research is sponsored by the National Science Foundation. Title: Stability Analysis of Tachocline Latitudinal Differential Rotation and Coexisting Toroidal Band Using a Shallow-Water Model Authors: Dikpati, Mausumi; Gilman, Peter A.; Rempel, Matthias Bibcode: 2003ApJ...596..680D Altcode: Recently global, quasi-two-dimensional instabilities of tachocline latitudinal differential rotation have been studied using a so-called shallow-water model. While purely hydrodynamic shallow-water type disturbances were found to destabilize only the overshoot tachocline, the MHD analysis showed that in the presence of a broad toroidal field, both the radiative and overshoot parts of the tachocline can be unstable. We explore here instability in the shallow-water solar tachocline with concentrated toroidal bands placed at a wide range of latitudes, emulating different phases of the solar cycle. In equilibrium, the poleward magnetic curvature stress of the band is balanced either by an equatorward hydrostatic pressure gradient or by the Coriolis force from a prograde jet inside the band. We find that toroidal bands placed almost at all latitudes make the system unstable to shallow-water disturbances. For bands without prograde jets, the instability persists well above 100 kG peak field, while a jet stabilizes the band at a field of ~40 kG. The jet imparts gyroscopic inertia to the toroidal band inhibiting it from unstably ``tipping'' its axis away from rotation axis. Like previously studied HD and MHD shallow-water instabilities in the tachocline, unstable shallow-water modes found here produce kinetic helicity and hence a tachocline α-effect these narrow kinetic helicity profiles should generate narrowly confined poloidal fields, which will help formation of the narrow toroidal field. Toroidal bands poleward of 15° latitude suppress midlatitude hydrodynamic α-effects. However, even strong toroidal bands equatorward of 15° allow this hydrodynamic α-effect. Such bands should occur during the late declining phase of a solar cycle and, thus, could help the onset of a new cycle by switching on the mid latitude α-effect. Title: Convective Overshoot at the Base of the Solar Convection Zone - a Semi-Analytical Approach Authors: Rempel, M. Bibcode: 2003SPD....34.2607R Altcode: 2003BAAS...35..855R Despite the importance of overshoot at the base of the solar convection zone for the storage of strong toroidal magnetic field produced there by the solar dynamo, the uncertainties concerning the depth and mean subadiabatic stratification are large. Overshoot models of the past, based on the non local mixing-length theory, generally produce a shallow weakly subadiabatic region with a sharp transition to the radiative interior, whereas several numerical simulations lead to significantly subadiabatic overshoot with penetration depth of more than a pressure scale height. I present a semi-analytical convection zone/overshoot model based on the assumption that the convective energy flux is governed by downflow structures with a low filling factor, which allows for modeling both, the parameter regime addressed by non-local mixing-length approach as well as the regime addressed by numerical simulations. It turns out that the main discrepancies between the non-local mixing-length approach and numerical simulations are due to the much larger energy flux used in numerical simulations. Furthermore this model shows that the sharp transition between the nearly adiabatic overshoot and radiative interior, a typical result of the non-local mixing-length approach which is in contradiction with helioseismology, can be avoided by assuming an ensemble of downflows with different strength (Mach number).

NCAR is sponsored by the National Science Foundation. Title: Storage and Equilibrium of Toroidal Magnetic Fields in the Solar Tachocline: A Comparison between MHD Shallow-Water and Full MHD Approaches Authors: Rempel, Matthias; Dikpati, Mausumi Bibcode: 2003ApJ...584..524R Altcode: Recently Dikpati & Gilman have shown, using a shallow-water model of the solar tachocline that allows the top surface to deform, that a tachocline with the observed broad differential rotation and a strong toroidal field is prolate. A strong toroidal field ring requires extra mass on its poleward side to provide a hydrostatic latitudinal pressure gradient to balance the poleward curvature stress. In a parallel study using a different approach, Rempel, Schüssler, & Tóth have shown that such a latitudinal pressure gradient is found in a strongly subadiabatic stratification, whereas a weakly subadiabatic stratification leads to a complementary equilibrium state of the overshoot tachocline in which the magnetic curvature stress is balanced by a prograde rotational jet inside the toroidal ring. We show that the shallow-water model with height deformation is a first-order approach to the equilibrium state found by Rempel, Schüssler, & Tóth for a strongly subadiabatic stratification. We also show that the shallow-water model can be generalized to allow for the equilibrium state found for a weakly subadiabatic stratification by suppressing the shell deformation associated with the toroidal field and allowing the differential rotation to be modified. Title: Thermal properties of magnetic flux tubes. II. Storage of flux in the solar overshoot region Authors: Rempel, M. Bibcode: 2003A&A...397.1097R Altcode: We consider the consequences of radiative heating for the storage of magnetic flux in the overshoot region at the bottom of the solar convection zone. In the first part of the paper, we study the evolution of axisymmetric flux tubes (flux rings), which are initially in neutrally buoyant mechanical equilibrium. Radiative heating leads to a slow upward drift of the flux ring with a velocity depending on the degree of subadiabaticity of the stratification. Maintaining the flux tubes within the overshoot region for time intervals comparable with the solar cycle period requires a strongly subadiabatic stratification with delta =nabla -nabla ad < -10-4, which is not predicted by most current overshoot models (e.g., Skaley & Stix \cite{skaley91}; van Ballegooijen \cite{Ballegooijen:1982b}; Schmitt et al. \cite{Schmitt:etal:1984}). The drag force exerted by equatorward flow due to meridional circulation permits states of mechanical and thermal equilibrium in the overshoot region, but these apply only to very thin magnetic flux tubes containing less than 1% of the flux of a large sunspot. In the second part, we consider the influence of radiative heating (and cooling) on magnetic flux stored in the form of a magnetic layer. In contrast to the case of isolated flux tubes, the suppression of the convective energy transport within the magnetic layer affects the overall stratification of the overshoot region. In the case of a quenching of the convective heat conductivity by a factor of the order 100, the overshoot layer receives a net cooling leading to a stronger subadiabaticity, so that values of delta < -10-4 are reached. The stabilization of the stratification relaxes the conditions for flux storage. Stronger quenching of the heat conductivity leads to larger temperature perturbations (of both signs) and to the destabilization of the upper part of the overshoot layer, with the likely consequence of rapid magnetic flux loss. Title: Structure of the magnetic field in the lower convection zone Authors: Schüssler, Manfred; Rempel, Matthias Bibcode: 2002ESASP.508..499S Altcode: 2002soho...11..499S The properties of the magnetic field and the convective flows near the base of the solar convection zone are crucial for understanding the working of the solar dynamo. We consider three aspects of this complex problem. (I) Magnetic flux needs to be stored against buoyant loss for a sufficiently long time in order to be amplified by the dynamo process. Convective pumping in strongly stratified convection is probably not sufficient for the strong fields (of order 105G) which have been inferred from the simulations of rising flux tubes. The required subadiabatically stratified storage region is likely to be generated by the asymmetric flow field (strong coherent downflows, weak upflows) characteristic for compressible convection in a stratified medium. (II) In a weakly subadiabatic region or a convective overshoot layer, the force equilibrium of a magnetic layer is very similar to that of an isolated flux tube: zero buoyancy and balance between the magnetic curvature (tension) force and the Coriolis force induced by a longitudinal flow along the field lines in a rotating system. In a strongly subadiabatic radiative region, a magnetic layer develops a different kind of force equilibrium, which involves buoyancy and a latitudinal pressure gradient. (III) A field of 105G is difficult to generate by convection or differential rotation. The outflow of plasma from an "exploded" flux tube provides an intensification mechanisms which is not limited by the Lorentz force and converts potential energy of a superadiabatic stratification into magnetic energy. Title: Equilibrium And Instability Of Toroidal Field Bands And Rotational Jets In The Solar Tachocline Authors: Gilman, P. A.; Rempel, M.; Dikpati, M. Bibcode: 2002AAS...200.0416G Altcode: 2002BAAS...34..645G Recently Dikpati & Gilman (2001, ApJ, 552, 348) have shown, using a shallow-water model of the solar tachocline that allows the top surface to deform, that a tachocline with the observed broad differential rotation and a strong toroidal field is prolate. A strong toroidal field ring requires extra mass on its poleward side to provide a hydrostatic latitudinal pressure gradient to balance the poleward curvature stress. In a parallel study using a different approach, Rempel et al (2000, A&A, 363, 789) have shown that a weakly subadiabatic stratification leads to a complementary equilibrium state of the overshoot tachocline in which the magnetic curvature stress is balanced by a prograde rotational jet inside the toroidal ring. We show that the shallow water model yields a similar equilibrium state if we suppress the shell deformation and allow the differential rotation to be modified. We are analyzing the stability of such an equilibrium tachocline by using the MHD shallow-water model of Gilman & Dikpati (2002, ApJ, submitted). We expect to show that the combination of toroidal band and rotational jet is virtually always unstable to disturbances with longitudinal wave number m>0, except perhaps when the band is extremely narrow. This instability could wipe out the jet, and lead to some poleward migration of the toroidal field, as well as the excitation of longitudinally periodic magnetic patterns that might provide sites for magnetic bouyancy to produce spots as well as other photospheric magnetic features. This work is supported by NASA grants W-19752 and S-10145-X. The National Center for Atmospheric Research is sponsored by the National Science Foundation. Title: Numerical Simulations of Convective Overshoot Authors: Rempel, M.; Rast, M. P. Bibcode: 2002AAS...200.0417R Altcode: 2002BAAS...34..646R The structure of the overshoot region at the base of solar convection zone is crucial to the storage of strong toroidal magnetic field produced there by the solar dynamo. Both the mean thermodynamic stratification and the statistical properties of the convective fluctuations affect the storage capabilities of the region. Overshoot models of the past, based on the non local mixing-length theory, generally produce a shallow weakly subadiabatic region with a steep transition to the radiative interior. A more recent estimation by Xiong & Deng (Mon. Not. R. Astron. Soc. 327, 1137) suggests a larger subadiabaticity and a smoother transition to the radiative gradient. Numerical studies have to date contributed little to constraining these simpler models, largely because they are unable to match the very low values of radiative conductivity found in the solar interior. The abnormally high values of conductivity generally employed lead to much more vigorous convection and much deeper convective penetration than anticipated. To address this deficiency directly we adopt a formulation which explicitly separates of the thermal conductivity into a turbulent and a radiative component, and employ a novel thermal relaxation scheme which accelerates the approach to equilibrium in the deep radiative layers even at very low values of the latter. This separation also enables adjustment of the convective properties apart from the radiative ones in the lower half of the convection zone. Preliminary results suggest that the structure of the overshoot region is highly sensitive to the properties of the convection in the lower half of the convection zone. NCAR is sponsored by the National Since Foundation. Title: Intensification of Magnetic Fields by Conversion of Potential Energy Authors: Rempel, M.; Schüssler, M. Bibcode: 2001ApJ...552L.171R Altcode: A strong superequipartition magnetic field strength on the order of 10 T (105 G) has been inferred at the bottom of the solar convection zone. We show that the ``explosion'' of weak magnetic flux tubes, which is caused by a sudden loss of pressure equilibrium in the flux loop rising through the superadiabatically stratified convection zone, provides a mechanism that leads to a strong field: the flow of high-entropy material out of the exploded loop leads to a significant intensification of the magnetic field in the underlying flux sheet at the bottom. In contrast to the amplification by differential rotation, this process converts the potential energy of the stratification into magnetic energy and thus is not dynamically limited by the back-reaction on the flow field via the Lorentz force. Title: Struktur und Ursprung starker Magnetfelder am Boden der solaren Konvektionszone Title: Struktur und Ursprung starker Magnetfelder am Boden der solaren Konvektionszone Title: Structure and origin of strong magnetic field at the base of the solar convection zone; Authors: Rempel, Matthias Dieter Bibcode: 2001PhDT.......204R Altcode: No abstract at ADS Title: Intensification of Magnetic Field in a Stellar Convection Zone by Conversion of Potential Energy Authors: Rempel, M.; Schüssler, M. Bibcode: 2001ASPC..248..165R Altcode: 2001mfah.conf..165R No abstract at ADS Title: Storage of a Strong Magnetic Field Below the Solar Convection Zone (CD-ROM Directory: contribs/rempel) Authors: Rempel, M.; Schüssler, M.; Moreno-Insertis, F.; Tóth, G. Bibcode: 2001ASPC..223..738R Altcode: 2001csss...11..738R No abstract at ADS Title: Storage of magnetic flux at the bottom of the solar convection zone Authors: Rempel, M.; Schüssler, M.; Tóth, G. Bibcode: 2000A&A...363..789R Altcode: We consider the mechanical equilibrium of a layer of axisymmetric toroidal magnetic field located in a subadiabatically stratified region near the bottom of the solar convection zone, with particular emphasis on the effects of spherical geometry. We determine equilibrium configurations and simulate numerically how these are reached from a non-equilibrium initial situation. While a subadiabatic stratification is essential for suppressing the buoyancy force, the latitudinal component of the magnetic curvature force is balanced by a latitudinal pressure gradient (in the case of a large subadiabaticity, as in the radiative interior) or by the Coriolis force due to a toroidal flow along the field lines (in the case of small subadiabaticity, as in a layer of convective overshoot). The latter case is found relevant for storing the magnetic flux generated by the solar dynamo. The corresponding equilibrium properties are similar to those of isolated magnetic flux tubes. Significant variations of the differential rotation at the bottom of the convection zone in the course of the solar cycle are expected for such a kind of equilibrium. Title: Stability of a flux tube model for prominences Authors: Rempel, M.; Schmitt, D.; Glatzel, W. Bibcode: 1999A&A...343..615R Altcode: We discuss the stability of a flux tube model for quiescent solar prominences. The main result is that the configurations are stable only up to a critical width (defined as the extension of the central part of the flux tube with prominence matter at low temperatures) of about 1 000 km to 3 000 km. The dependence of the critical width on the prominence parameters height, temperature, density contrast, external magnetic field, external gas pressure and external temperature is analysed. The normal modes and eigenfrequencies obtained numerically cover the range of observational data for prominence oscillations. Title: Storage of toroidal magnetic field below the solar convection zone Authors: Rempel, M.; Schüssler, M.; Moreno-Insertis, F. Bibcode: 1999AGAb...15R..74R Altcode: 1999AGM....15..J15R Simulations of erupting flux tubes in the thin flux tube approximation show that essential properties of sunspots can only be explained if the initial field strength of the flux tube at the base of the convection zone is about 10 T. Such strong magnetic field can only be stored below the solar convection zone in a subadiabatic stratification. We consider mechanical equilibria in form of magnetic flux tubes and magnetic sheets and discuss the influence of radiative and convective energy transport on these configurations. In the case of magnetic flux tubes, radiative inflow of heat leads to enhanced buoyancy which causes the flux tube to move upwards and leave the storage region. In the case of magnetic sheets, the compensation of the poleward directed magnetic tension force requires a deviation of the temperature from the hydrostatic background stratification. Convective energy transport disturbs the equilibrium and leads to thermal circulations.