Author name code: abbett ADS astronomy entries on 2022-09-14 author:"Abbett, William P." ------------------------------------------------------------------------ Title: Coupling a Global Heliospheric Magnetohydrodynamic Model to a Magnetofrictional Model of the Low Corona Authors: Hayashi, Keiji; Abbett, William P.; Cheung, Mark C. M.; Fisher, George H. Bibcode: 2021ApJS..254....1H Altcode: Recent efforts coupling our Sun-to-Earth magnetohydrodynamics (MHD) model and lower-corona magnetofrictional (MF) model are described. Our Global Heliospheric MHD (GHM) model uses time-dependent three-component magnetic field data from the lower-corona MF model as time-dependent boundary values. The MF model uses data-assimilation techniques to introduce the vector magnetic field data from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager, hence as a whole this simulation coupling structure is driven with actual observations. The GHM model employs a newly developed interface boundary treatment that is based on the concept of characteristics, and it properly treats the interface boundary sphere set at a height of the sub-Alfvénic lower corona (1.15 R in this work). The coupled model framework numerically produces twisted nonpotential magnetic features and consequent eruption events in the solar corona in response to the time-dependent boundary values. The combination of our two originally independently developed models presented here is a model framework toward achieving further capabilities of modeling the nonlinear time-dependent nature of magnetic field and plasma, from small-scale solar active regions to large-scale solar wind structures. This work is a part of the Coronal Global Evolutionary Model project for enhancing our understanding of Sun-Earth physics to help improve space weather capabilities. Title: The Coronal Global Evolutionary Model: Using HMI Vector Magnetogram and Doppler Data to Determine Coronal Magnetic Field Evolution Authors: Hoeksema, J. Todd; Abbett, William P.; Bercik, David J.; Cheung, Mark C. M.; DeRosa, Marc L.; Fisher, George H.; Hayashi, Keiji; Kazachenko, Maria D.; Liu, Yang; Lumme, Erkka; Lynch, Benjamin J.; Sun, Xudong; Welsch, Brian T. Bibcode: 2020ApJS..250...28H Altcode: 2020arXiv200614579H The Coronal Global Evolutionary Model (CGEM) provides data-driven simulations of the magnetic field in the solar corona to better understand the build-up of magnetic energy that leads to eruptive events. The CGEM project has developed six capabilities. CGEM modules (1) prepare time series of full-disk vector magnetic field observations to (2) derive the changing electric field in the solar photosphere over active-region scales. This local electric field is (3) incorporated into a surface flux transport model that reconstructs a global electric field that evolves magnetic flux in a consistent way. These electric fields drive a (4) 3D spherical magnetofrictional (SMF) model, either at high resolution over a restricted range of solid angles or at lower resolution over a global domain to determine the magnetic field and current density in the low corona. An SMF-generated initial field above an active region and the evolving electric field at the photosphere are used to drive (5) detailed magnetohydrodynamic (MHD) simulations of active regions in the low corona. SMF or MHD solutions are then used to compute emissivity proxies that can be compared with coronal observations. Finally, a lower-resolution SMF magnetic field is used to initialize (6) a global MHD model that is driven by an SMF electric field time series to simulate the outer corona and heliosphere, ultimately connecting Sun to Earth. As a demonstration, this report features results of CGEM applied to observations of the evolution of NOAA Active Region 11158 in 2011 February. Title: Modeling a Carrington-scale Stellar Superflare and Coronal Mass Ejection from {\kappa }^{1}{Cet} Authors: Lynch, Benjamin J.; Airapetian, Vladimir S.; DeVore, C. Richard; Kazachenko, Maria D.; Lüftinger, Teresa; Kochukhov, Oleg; Rosén, Lisa; Abbett, William P. Bibcode: 2019ApJ...880...97L Altcode: 2019arXiv190603189L Observations from the Kepler mission have revealed frequent superflares on young and active solar-like stars. Superflares result from the large-scale restructuring of stellar magnetic fields, and are associated with the eruption of coronal material (a coronal mass ejection, or CME) and energy release that can be orders of magnitude greater than those observed in the largest solar flares. These catastrophic events, if frequent, can significantly impact the potential habitability of terrestrial exoplanets through atmospheric erosion or intense radiation exposure at the surface. We present results from numerical modeling designed to understand how an eruptive superflare from a young solar-type star, κ 1 Cet, could occur and would impact its astrospheric environment. Our data-inspired, three-dimensional magnetohydrodynamic modeling shows that global-scale shear concentrated near the radial-field polarity inversion line can energize the closed-field stellar corona sufficiently to power a global, eruptive superflare that releases approximately the same energy as the extreme 1859 Carrington event from the Sun. We examine proxy measures of synthetic emission during the flare and estimate the observational signatures of our CME-driven shock, both of which could have extreme space-weather impacts on the habitability of any Earth-like exoplanets. We also speculate that the observed 1986 Robinson-Bopp superflare from κ 1 Cet was perhaps as extreme for that star as the Carrington flare was for the Sun. Title: MHD Simulation of a Superflare and Associated Carrington-Scale CME Event From the Young Sun Authors: Lynch, B. J.; Airapetian, V.; Kazachenko, M.; Lueftinger, T.; DeVore, C. R.; Abbett, W. P. Bibcode: 2018AGUFM.P43H3844L Altcode: Recent Kepler observations reveal frequent superflares on young active solar-like stars. We present preliminary simulation results for a global eruptive flare from the young-Sun analog Kappa-1 Cet. Our simulation magnetic field initialization is based on a low-order PFSS representation of the observed stellar magnetogram that provides a non-trivial dipolar magnetic field configuration with a significantly warped helmet streamer belt. We use a standard Parker [1958] isothermal solar wind for the coronal atmosphere and energize the closed-field stellar corona with idealized shearing flows parallel to the radial field polarity inversion line. We examine the energy evolution of the global superflare showing a release of 7.1e+33 erg of magnetic free energy over the course of 10 hours while the maximum kinetic energy increase of the CME eruption reaches 2.8e+33 erg, i.e. approximately the strength of the famous 1859 Carrington Event. We use a flare-ribbon geometric proxy to calculate a total unsigned flare reconnection flux of 2.2e+23 Mx and a peak reconnection rate of 8.0e+18 Mx/s. We examine various proxy measures of synthetic emission during the flare and discuss the potential for extreme space weather impacts on the early Earth associated with the CME-driven shock and the CME/ICME flux rope field structure and orientation. Title: Initiation of Superflares and Super-CMEs in Active Solar-type Stars Authors: Lynch, B. J.; Airapetian, V. S.; Kazachenko, M. D.; Lueftinger, T.; DeVore, C. R.; Abbett, W. P. Bibcode: 2018csc..confE..94L Altcode: Recent Kepler observations reveal frequent superflares on young active solar-like stars. We present preliminary simulation results for a global eruptive flare from the young-Sun analog Kappa-1 Cet. Our simulation magnetic field initialization is based on a low-order PFSS representation of the observed stellar magnetogram that provides a non-trivial dipolar magnetic field configuration with a significantly warped helmet streamer belt. We use a standard Parker [1958] isothermal solar wind for the coronal atmosphere and energize the closed-field stellar corona with idealized shearing flows parallel to the radial field polarity inversion line. We examine the energy evolution of the global superflare showing a release of 7.1e+33 erg of magnetic free energy over the course of 10 hours while the maximum kinetic energy increase of the CME eruption reaches 2.8e+33 erg, i.e. approximately the strength of the famous 1859 Carrington Event. We use a flare-ribbon geometric proxy to calculate a total unsigned flare reconnection flux of 2.2e+23 Mx and a peak reconnection rate of 8.0e+18 Mx/s. We examine various proxy measures of synthetic emission during the flare and discuss the potential for extreme space weather impacts on the early Earth associated with the CME-driven shock and the CME/ICME flux rope field structure and orientation. Title: Excess Lorentz Force in Major Solar Eruptions Authors: Sun, Xudong; Lynch, Benjamin; Abbett, William; Li, Yan Bibcode: 2018csc..confE..41S Altcode: The solar active region photospheric magnetic field evolves rapidly during major eruptive events, suggesting appreciable feedback from the corona. Using high-cadence vector magnetograms, multi-wavelength coronal imaging, and numerical simulation, we show how the observed photospheric "magnetic imprints" are highly structured in space and time, and how it can in principle be used to estimate the impulse of the Lorentz force that accelerates the coronal mass ejection (CME) plasma. In an archetypical event, the Lorentz force correlates well with the CME acceleration, but the total force impulse surprisingly exceeds the CME momentum by almost two orders of magnitude. Such a clear trend exists in about two thirds of the eruptions in our survey for Cycle 24. We propose a "gentle photospheric upwelling" scenario, where most of the Lorentz force is trapped in the lower atmosphere layer, counter-balanced by gravity of the upwelled mass. This unexpected effect dominates the momentum processes, but is negligible for the energy budget. We discuss how the upcoming high-sensitivity observations and new-generation numerical models may help elucidate the problem. Title: Using Convection Zone-to-Corona Models to Understand the Physics of the Solar Wind Authors: Abbett, W. P. Bibcode: 2015AGUFMSH13E..01A Altcode: How magnetic energy and flux emerges from the turbulent convective interior of the Sun into the solar atmosphere is of great importance to a number of challenging problems in Heliophysics. With the wealth of data from space-based and ground-based observatories, it is evident that solar magnetic fields span the entirety of the convection zone-to-corona system, and do not exist in isolation in a localized region, or interact only over a prescribed spatial scale. The challenge of modeling this system in its entirety is that the magnetic field not only spans multiple scales, but also regions whose physical conditions vary dramatically. In this overview, I will summarize recent progress in the effort to dynamically model the upper convection zone-to-corona system over large spatial scales, and will discuss applications of these new models to Solar Probe Plus science. Title: The Coronal Global Evolutionary Model: Using HMI Vector Magnetogram and Doppler Data to Model the Buildup of Free Magnetic Energy in the Solar Corona Authors: Fisher, G. H.; Abbett, W. P.; Bercik, D. J.; Kazachenko, M. D.; Lynch, B. J.; Welsch, B. T.; Hoeksema, J. T.; Hayashi, K.; Liu, Y.; Norton, A. A.; Dalda, A. Sainz; Sun, X.; DeRosa, M. L.; Cheung, M. C. M. Bibcode: 2015SpWea..13..369F Altcode: 2015arXiv150506018F The most violent space weather events (eruptive solar flares and coronal mass ejections) are driven by the release of free magnetic energy stored in the solar corona. Energy can build up on timescales of hours to days, and then may be suddenly released in the form of a magnetic eruption, which then propagates through interplanetary space, possibly impacting the Earth's space environment. Can we use the observed evolution of the magnetic and velocity fields in the solar photosphere to model the evolution of the overlying solar coronal field, including the storage and release of magnetic energy in such eruptions? The objective of CGEM, the Coronal Global Evolutionary Model, funded by the NASA/NSF Space Weather Modeling program, is to develop and evaluate such a model for the evolution of the coronal magnetic field. The evolving coronal magnetic field can then be used as a starting point for magnetohydrodynamic (MHD) models of the corona, which can then be used to drive models of heliospheric evolution and predictions of magnetic field and plasma density conditions at 1AU. Title: Modeling the Convection Zone-to-Corona System over Global Spatial Scales Authors: Abbett, W. P.; Bercik, D. J.; Fisher, G. H. Bibcode: 2014AGUFMSH44A..01A Altcode: How magnetic energy and flux emerges from the turbulent convective interior of the Sun into the solar atmosphere is of great importance to a number of challenging problems in solar physics. With the wealth of data from missions such as SDO, Hinode, and IRIS, it is evident that the dynamic interaction of magnetic structures at the photosphere and in the solar atmosphere occurs over a vast range of spatial and temporal scales. Emerging active regions often develop magnetic connections to other regions of activity some distance away on the solar disk, and always emerge into a global coronal field whose structural complexity is a function of the solar cycle. Yet even small-scale dynamic interactions (e.g., processes at granular or supergranular scales in the photosphere) can trigger rapid changes in the large-scale coronal field sufficient to power eruptive events such as coronal mass ejections, or solar flares. The challenge of modeling this system in its entirety is that the magnetic field not only spans multiple scales, but also regions whose physical conditions vary dramatically. We will summarize recent progress in the effort to dynamically model the upper convection zone-to-corona system over large spatial scales, and will present the latest results from a new, global radiative-MHD model of the upper convection zone-to-corona system, RADMHD2S. We will characterize the flux of electromagnetic energy into the solar atmosphere as flux systems of different scales dynamically interact, and discuss how physics-based models of the convection zone-to-corona system can be used to guide the development and testing of data-driven models. Title: Understanding Measures of Magnetic Activity Using Physics-based Models of the Solar Interior and Atmosphere Authors: Abbett, W. P.; Luhmann, J. G. Bibcode: 2014AGUFMSH13D4140A Altcode: Substantial progress has been made over the past decade in the effort to better understand how magnetic flux and energy is generated in the convective interior of the Sun, how it emerges into the solar atmosphere, and how manifestations of solar magnetic activity (such as sunspots, coronal mass ejections, and flares) are connected within a dynamic magnetic environment spanning the solar convection zone-to-corona system. Here, we present a brief overview of recent efforts to model the evolution of active region magnetic fields and sunspots over a range of physical conditions and spatial and temporal scales. We will focus on how dynamic, physics-based numerical models can be used to better understand observed relationships between different measures of solar activity as a function of time (e.g., sunspot activity and morphologies, unsigned magnetic flux measured at the photosphere, coronal X-ray emissivity). We will determine whether local physics-based models of active region evolution can be used to better constrain proxies of solar activity such as the sunspot number, which remains the only direct record available to trace the very long-term influence of the solar dynamo on the earth's environment. Title: RADMHD2S: A Global 3D Radiative-MHD Model of the Upper Convection Zone-to-Corona System Authors: Abbett, William P.; Bercik, David J Bibcode: 2014AAS...22412347A Altcode: We present the latest results from a new, global radiative-MHD model of the upper convection zone-to-corona system, RADMHD2S. The numerical methods build upon those of the RADMHD model of Abbett (2007) and Abbett & Fisher (2012), and significantly extend the capabilities of that code to allow for large-scale, sufficiently resolved, global calculations over a non-uniform, 3D curvilinear (spherical) mesh. RADMHD2S utilizes a high-order, non-dimensionally split, semi-implicit finite volume formalism to update the system of conservation equations in a way that properly propagates discontinuities in off-axis directions, while simultaneously preserving the 3D solenoidal constraint on the magnetic field. In addition, we will discuss improvements in the treatment of energetics, radiative transport, and cross-field diffusion that allow for more realistic data-driven modeling of the model's photosphere and chromosphere. Title: Buildup of Magnetic Shear and Free Energy during Flux Emergence and Cancellation Authors: Fang, Fang; Manchester, Ward, IV; Abbett, William P.; van der Holst, Bart Bibcode: 2012ApJ...754...15F Altcode: 2012arXiv1205.3764F We examine a simulation of flux emergence and cancellation, which shows a complex sequence of processes that accumulate free magnetic energy in the solar corona essential for the eruptive events such as coronal mass ejections, filament eruptions, and flares. The flow velocity at the surface and in the corona shows a consistent shearing pattern along the polarity inversion line (PIL), which together with the rotation of the magnetic polarities, builds up the magnetic shear. Tether-cutting reconnection above the PIL then produces longer sheared magnetic field lines that extend higher into the corona, where a sigmoidal structure forms. Most significantly, reconnection and upward-energy-flux transfer are found to occur even as magnetic flux is submerging and appears to cancel at the photosphere. A comparison of the simulated coronal field with the corresponding coronal potential field graphically shows the development of non-potential fields during the emergence of the magnetic flux and formation of sunspots. Title: Buildup of Free Energy for Eruptive Events during Flux Emergence Authors: Fang, Fang; Manchester, Ward, IV; Abbett, William P.; van der Holst, Bart Bibcode: 2012shin.confE..39F Altcode: In a simulation of magnetic flux emergence from the convection zone, a complex sequence of processes accumulate free magnetic energy in the solar corona essential for the eruptive events such as coronal mass ejections (CMEs), filament eruptions and flares. The flow velocity at the surface and in the corona shows a consistent shearing pattern along the polarity inversion line (PIL), which together with the rotation of the magnetic polarities, builds up the magnetic shear. Tether-cutting reconnection above the PIL then produces longer sheared magnetic field lines that extend higher into the corona, where a sigmoidal structure forms. Most significantly, reconnection and upward energy-flux transfer are found to occur even as magnetic flux is submerging and appears to cancel at the photosphere. A comparison of the simulated coronal field with the corresponding coronal potential field graphically shows the development of non-potential fields during the emergence of the magnetic flux and formation of sunspots. Title: An Improved 3D Radiative-MHD Model of the Convection Zone-to-Corona System Authors: Abbett, William P.; Bercik, D. J.; Kazachenko, M. Bibcode: 2012AAS...22020507A Altcode: We present the latest results from an improved radiative-MHD model of the convection zone-to-corona system. The numerical methods of the RADMHD model of Abbett & Fisher (2012) have been significantly updated so that the underlying finite volume scheme is (1) no longer dimensionally split along coordinate axes; (2) of much higher order accuracy using a three-dimensional 27-point stencil; and (3) capable of performing much larger scale calculations in both spherical polar coordinates and Cartesian coordinates. We will describe the improvements of the underlying scheme in detail, present a 3D dynamic convection zone-to-corona quiet Sun model using the new formalism, and compare the latest results with previous models. Title: A First Look at Magnetic Field Data Products from SDO/HMI Authors: Liu, Y.; Scherrer, P. H.; Hoeksema, J. T.; Schou, J.; Bai, T.; Beck, J. G.; Bobra, M.; Bogart, R. S.; Bush, R. I.; Couvidat, S.; Hayashi, K.; Kosovichev, A. G.; Larson, T. P.; Rabello-Soares, C.; Sun, X.; Wachter, R.; Zhao, J.; Zhao, X. P.; Duvall, T. L., Jr.; DeRosa, M. L.; Schrijver, C. J.; Title, A. M.; Centeno, R.; Tomczyk, S.; Borrero, J. M.; Norton, A. A.; Barnes, G.; Crouch, A. D.; Leka, K. D.; Abbett, W. P.; Fisher, G. H.; Welsch, B. T.; Muglach, K.; Schuck, P. W.; Wiegelmann, T.; Turmon, M.; Linker, J. A.; Mikić, Z.; Riley, P.; Wu, S. T. Bibcode: 2012ASPC..455..337L Altcode: The Helioseismic and Magnetic Imager (HMI; Scherrer & Schou 2011) is one of the three instruments aboard the Solar Dynamics Observatory (SDO) that was launched on February 11, 2010 from Cape Canaveral, Florida. The instrument began to acquire science data on March 24. The regular operations started on May 1. HMI measures the Doppler velocity and line-of-sight magnetic field in the photosphere at a cadence of 45 seconds, and the vector magnetic field at a 135-second cadence, with a 4096× 4096 pixels full disk coverage. The vector magnetic field data is usually averaged over 720 seconds to suppress the p-modes and increase the signal-to-noise ratio. The spatial sampling is about 0".5 per pixel. HMI observes the Fe i 6173 Å absorption line, which has a Landé factor of 2.5. These data are further used to produce higher level data products through the pipeline at the HMI-AIA Joint Science Operations Center (JSOC) - Science Data Processing (Scherrer et al. 2011) at Stanford University. In this paper, we briefly describe the data products, and demonstrate the performance of the HMI instrument. We conclude that the HMI is working extremely well. Title: Generation of electric currents via neutral-ion drag in the chromosphere and ionosphere Authors: Krasnoselskikh, V.; Abbett, W. P.; Hudson, H.; Vekstein, G.; Bale, S. D. Bibcode: 2012AIPC.1439...42K Altcode: We consider the generation of electric currents in the solar chromosphere. The ionization level in this region is generally supposed to be low. We show that the ambient electrons are magnetized even for weak magnetic fields (30 G), i.e. their gyrofrequency is larger than the collision frequency; ion motions continue to be dominated by ion-neutral collisions in this region. Under such conditions the ions are dragged by neutrals. As a result, the dynamics of magnetic field resembles frozen-in motion of the field with the neutral gas. On the other hand magnetized electrons drift under the action of the electric and magnetic fields induced in the reference frame of ions moving with the neutral gas. This relative motion of electrons and ions results in the generation of quite intense electric currents. The dissipation of these currents leads to the resistive electron heating and efficient gas ionization. Ionization by electron-neutral impact does not alter the dynamics of the heavy particles; thus the gas turbulent motions persist even when the plasma becomes fully ionized and the resistive current dissipation continues to heat electrons and ions. This heating process is so efficient that it can result in typical temperature increases with altitude as large as 0.1-0.3 eV/km. We conclude that this process can play a major role in the heating of the chromosphere and corona. We show that the physical conditions in the solar chromosphere, in particular the neutral and ion density dependencies upon altitude, are very similar to those in the lower ionosphere of the Earth. A very similar process of current generation occurs in the ionosphere after strong earthquakes, resulting in the generation of strong perturbations in the ionosphere. We then present well-known results of the observations of such perturbations, which allow an evaluation of the increment of the growth of the perturbations with altitude, making use of ionospheric sounding. These results are in perfect agreement with estimates obtained making use a model similar to ours. We consider that these observations clearly show the efficiency of the physical mechanisms discussed, and thus provide strong support for our ideas. Title: The Impact of the Chromosphere on Numerical Models of the Convection Zone-to-Corona System Authors: Abbett, W. P. Bibcode: 2012decs.confE..52A Altcode: This review will provide an overview of recent progress toward simulating the magnetic and energetic connection between the convection zone and corona with a particular emphasis on the effect of the chromosphere on the coupled system. We will discuss the challenges inherent in modeling the dynamics and energetics of the chromosphere, then review what 3D MHD simulations of the atmosphere are able to tell us about about the transport of magnetic flux and energy from below the visible surface into the low atmosphere and corona. We will explore how the dynamic chromosphere affects the structure and non-potentiality of the overlying coronal field, and what implications this may have to force-free models based on photospheric magnetograms. Title: Radiative Cooling in MHD Models of the Quiet Sun Convection Zone and Corona Authors: Abbett, W. P.; Fisher, G. H. Bibcode: 2012SoPh..277....3A Altcode: 2011arXiv1102.1035A We present a series of numerical simulations of the quiet-Sun plasma threaded by magnetic fields that extend from the upper convection zone into the low corona. We discuss an efficient, simplified approximation to the physics of optically thick radiative transport through the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Sun's atmosphere in an initially unipolar (open field) region. We find that the net Poynting flux below the surface is on average directed toward the interior, while in the photosphere and chromosphere the net flow of electromagnetic energy is outward into the solar corona. Overturning convective motions between these layers driven by rapid radiative cooling appears to be the source of energy for the oppositely directed fluxes of electromagnetic energy. Title: Can We Determine Electric Fields and Poynting Fluxes from Vector Magnetograms and Doppler Measurements? Authors: Fisher, G. H.; Welsch, B. T.; Abbett, W. P. Bibcode: 2012SoPh..277..153F Altcode: 2011arXiv1101.4086F The availability of vector-magnetogram sequences with sufficient accuracy and cadence to estimate the temporal derivative of the magnetic field allows us to use Faraday's law to find an approximate solution for the electric field in the photosphere, using a Poloidal-Toroidal Decomposition (PTD) of the magnetic field and its partial time derivative. Without additional information, however, the electric field found from this technique is under-determined - Faraday's law provides no information about the electric field that can be derived from the gradient of a scalar potential. Here, we show how additional information in the form of line-of-sight Doppler-flow measurements, and motions transverse to the line-of-sight determined with ad-hoc methods such as local correlation tracking, can be combined with the PTD solutions to provide much more accurate solutions for the solar electric field, and therefore the Poynting flux of electromagnetic energy in the solar photosphere. Reliable, accurate maps of the Poynting flux are essential for quantitative studies of the buildup of magnetic energy before flares and coronal mass ejections. Title: Momentum Distribution in Solar Flare Processes Authors: Hudson, H. S.; Fletcher, L.; Fisher, G. H.; Abbett, W. P.; Russell, A. Bibcode: 2012SoPh..277...77H Altcode: We discuss the consequences of momentum conservation in processes related to solar flares and coronal mass ejections (CMEs), in particular describing the relative importance of vertical impulses that could contribute to the excitation of seismic waves ("sunquakes"). The initial impulse associated with the primary flare energy transport in the impulsive phase contains sufficient momentum, as do the impulses associated with the acceleration of the evaporation flow (the chromospheric shock) or the CME itself. We note that the deceleration of the evaporative flow, as coronal closed fields arrest it, will tend to produce an opposite impulse, reducing the energy coupling into the interior. The actual mechanism of the coupling remains unclear at present. Title: Electric Fields and Poynting Fluxes from Vector Magnetograms Authors: Fisher, G. H.; Welsch, B. T.; Abbett, W. P. Bibcode: 2012decs.confE..75F Altcode: The availability of vector-magnetogram sequences with sufficient accuracy and cadence to estimate the temporal derivative of the magnetic field allows us to use Faraday's law to find an approximate solution for the electric field in the photosphere, using a Poloidal-Toroidal Decomposition (PTD) of the magnetic field and its partial time derivative. Without additional information, however, the electric field found from this technique is under-determined - Faraday's law provides no information about the electric field that can be derived from the gradient of a scalar potential. Here, we show how additional information in the form of line-of-sight Doppler-flow measurements, and motions transverse to the line-of-sight determined with ad-hoc methods such as local correlation tracking, can be combined with the PTD solutions to provide much more accurate solutions for the solar electric field, and therefore the Poynting flux of electromagnetic energy in the solar photosphere. Reliable, accurate maps of the Poynting flux are essential for quantitative studies of the buildup of magnetic energy before flares and coronal mass ejections. Title: Dynamic Coupling of Convective Flows and Magnetic Field during Flux Emergence Authors: Fang, Fang; Manchester, Ward, IV; Abbett, William P.; van der Holst, Bart Bibcode: 2012ApJ...745...37F Altcode: 2011arXiv1111.1679F We simulate the buoyant rise of a magnetic flux rope from the solar convection zone into the corona to better understand the energetic coupling of the solar interior to the corona. The magnetohydrodynamic model addresses the physics of radiative cooling, coronal heating, and ionization, which allow us to produce a more realistic model of the solar atmosphere. The simulation illustrates the process by which magnetic flux emerges at the photosphere and coalesces to form two large concentrations of opposite polarities. We find that the large-scale convective motion in the convection zone is critical to form and maintain sunspots, while the horizontal converging flows in the near-surface layer prevent the concentrated polarities from separating. The footpoints of the sunspots in the convection zone exhibit a coherent rotation motion, resulting in the increasing helicity of the coronal field. Here, the local configuration of the convection causes the convergence of opposite polarities of magnetic flux with a shearing flow along the polarity inversion line. During the rising of the flux rope, the magnetic energy is first injected through the photosphere by the emergence, followed by energy transport by horizontal flows, after which the energy is subducted back to the convection zone by the submerging flows. Title: Roles for Data Assimilation in Studying Solar Flares & CMEs Authors: Welsch, B. T.; Abbett, W. P.; Fisher, G. H. Bibcode: 2011AGUFMSH54A..05W Altcode: Solar flares and coronal mass ejections (CMEs) are driven by the sudden release of free magnetic energy stored in electric currents the solar corona. While there is a consensus that free energy enters the corona from the solar interior, there is ongoing debate about the physical processes primarily responsible for transporting free energy into the corona and / or triggering its release once there. Since direct measurements of the coronal vector magnetic field, necessary to quantify coronal currents, are currently not feasible, it is hoped that modeling of the coronal field can improve our understanding of processes that drive the corona to flare and produce CMEs. Many coronal modeling efforts employ spectropolarimetric observations of the photosphere, which can be used to infer magnetic fields and flows there; the model then relates these photospheric measurements to coronal currents. Observations of coronal emission structures might also usefully inform coronal field models. Here, I will discuss different approaches to modeling the coronal magnetic field, using both photospheric and other data sets, and possible roles for data assimilation. Title: Can we Determine Electric Fields and Poynting Fluxes from Vector Magnetograms and Doppler Measurements? Authors: Fisher, G. H.; Welsch, B. T.; Abbett, W. P. Bibcode: 2011AGUFMSH33C..07F Altcode: The availability of vector magnetogram sequences with sufficient accuracy and cadence to estimate the time derivative of the magnetic field allows us to use Faraday's law to find an approximate solution for the electric field in the photosphere, using a Poloidal-Toroidal Decomposition (PTD) of the magnetic field and its partial time derivative. Without additional information, however, the electric field found from this technique is under-determined -- Faraday's law provides no information about the electric field that can be derived the gradient of a scalar potential. Here, we show how additional information in the form of line-of-sight Doppler flow measurements, and motions transverse to the line-of-sight determined with ad-hoc methods such as local correlation tracking, can be combined with the PTD solutions to provide much more accurate solutions for the solar electric field, and therefore the Poynting flux of electromagnetic energy in the solar photosphere. Reliable, accurate maps of the Poynting flux are essential for quantitative studies of the buildup of magnetic energy before flares and coronal mass ejections. This work was supported by the NASA Heliophysics Theory Program, the NASA Living-With-a-Star Program, and the NSF Geosciences Directorate Title: The Effect of Subsurface Flows during Flux Emergence Authors: Fang, F.; Manchester, W. B.; Abbett, W. P.; van der Holst, B. Bibcode: 2011AGUFMSH54A..06F Altcode: Here we carry out magnetohydrodynamic simulations on the emergence of a buoyant magnetic flux rope through a realistic convection zone that extends 21 Mm below the photosphere and 21 Mm up into the corona, with solar thermodynamic processes taken into account. The total maximum magnetic flux at the photosphere reaches 6.85±1020 Mx, of the same order of magnitude of solar pores. The main aim of the simulations is to study the mechanism of the energy and magnetic flux transfer during the interaction between the subphotospheric flows and the rising magnetic flux rope. The magnetic flux emerges as bipoles on the photospheric and subphotospheric layers, then the bipoles are quickly pulled apart by the horizontal flows and concentrate in downdrafts. The coalescence of the small-scale bipoles and convective collapse in the near surface layers form the large-scale concentrated magnetic flux, i.e. solar pores. The horizontal flow also exhibits a coherent pattern of rotation, which extends into the convection zone. Vertical flow in the convection zone pushes down the endpoints of the flux rope and maintains the bipolar pores during the emergence. Analysis of the Poynting energy fluxes associated with vertical and horizontal flows shows that horizontal flow is the main contributor to the energy transfer from the convection into the corona, with a value of 6.78±1031 ergs at the photosphere within 8 hours. Title: Observational Analysis of Photospheric Magnetic Field Restructuring During Energetic Solar Flares Authors: Alvarado, J. D.; Buitrago, J. C.; Martinez Oliveros, J.; Lindsey, C. A.; Abbett, W. P.; Fisher, G. H. Bibcode: 2011AGUFMSH13B1944A Altcode: The magnetic field has proven to be the main driver in the behavior, dynamics and evolution of several solar atmospheric phenomena including sunspots, plages, faculae, CME's and flares. Observational evidence of photospheric magnetic field restructuring during energetic flares have shown an enhancement of the transversal field component suggesting an apparent relation between this process with the generation of ``sunquakes'', expanding ripples on the solar photosphere as a result of the momentum-energy transfer into the solar photosphere and subphotosphere. In this work we present a doppler and magnetic observational study of some recent energetic flaring events (X and M type of the 24th solar cycle) trying to find possible acoustic signatures and make a characterization of the photospheric magnetic field evolution during those flares, being this the observational basis of a future numerical modeling of the field restructuring during this phenomenon. Title: Coupling of Convective Flows and Emerging Magnetic Fields Authors: Fang, Fang; Manchester, Ward, IV; Abbett, William P.; van der Holst, Bart Bibcode: 2011sdmi.confE..31F Altcode: We carry out radiative MHD simulations on the rising process of a buoyant magnetic flux rope inside the convection zone and its further emergence into the upper atmosphere. Our model takes into account of the radiative cooling, coronal heating and the ionization. The emergence of the flux rope is accompanied by turbulent surrounding plasma flows. Analysis on the magnetic fluxes shows that the convective downflows play an important role in formation of the concentrated polarities in the convection zone. During the rising of the flux rope, the magnetic energy is first injected through the photosphere by the emergence, followed by energy transport by horizontal flows, after which the energy is subducted back to the convection zone by the submerging flows. Title: Radiative Cooling in MHD Models of the Quiet Sun Convection Zone and Corona Authors: Abbett, William; Fisher, George Bibcode: 2011shin.confE..10A Altcode: We present a series of numerical simulations of the quiet Sun plasma threaded by magnetic fields that extend from the upper convection zone into the low corona. We discuss an efficient, simplified approximation to the physics of optically thick radiative transport through the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Sun's atmosphere in an initially unipolar (open field) region. We find that the net Poynting flux below the surface is on average directed toward the interior, while in the photosphere and chromosphere the net flow of electromagnetic energy is outward into the solar corona. Overturning convective motions between these layers driven by rapid radiative cooling appears to be the source of energy for the oppositely directed fluxes of electromagnetic energy. Title: Can We Determine Electric Fields and Poynting Fluxes from Vector Magnetograms and Doppler Measurements? Authors: Fisher, George H.; Welsch, B. T.; Abbett, W. P. Bibcode: 2011SPD....42.1717F Altcode: 2011BAAS..43S.1717F The availability of vector-magnetogram sequences with sufficient accuracy and cadence to estimate the temporal derivative of the magnetic field allows us to use Faraday's law to find an approximate solution for the electric field in the photosphere, using a Poloidal--Toroidal Decomposition (PTD) of the magnetic field and its partial time derivative. Without additional information, however, the electric field found from this technique is under-determined -- Faraday's law provides no information about the electric field that can be derived the gradient of a scalar potential. Here, we show how additional information in the form of line-of-sight Doppler-flow measurements, and motions transverse to the line-of-sight determined with ad-hoc methods such as local correlation tracking, can be combined with the PTD solutions to provide much more accurate solutions for the solar electric field, and therefore the Poynting flux of electromagnetic energy in the solar photosphere. Reliable, accurate maps of the Poynting flux are essential for quantitative studies of the buildup of magnetic energy before flares and coronal mass ejections. Title: Modeling the Physical Connection Between the Solar Convection Zone and Corona Authors: Abbett, William P. Bibcode: 2011SPD....42.0101A Altcode: 2011BAAS..43S.0101A How magnetic energy and flux emerges from below the surface into the solar atmosphere is a topic ripe for theoretical and observational investigation, particularly in the SDO era. Data from this mission is showing us that magnetic fields from the interior emerge through the surface, and energize the dynamic chromosphere and corona over a wide range of spatial and temporal scales. The interplay between granular-scale magnetic features, and large-scale structures from decaying active regions, for example, are seen to affect the large-scale solar magnetic field in complex ways. Being able to model these interactions in a way that captures the disparate spatial and temporal scales of the convection zone-to-corona system while simultaneously allowing for direct comparison with observations would be of enormous value in the effort to better understand the physics of coronal heating, the energetics of the solar wind, and the onset of magnetic eruptions (among other phenomena). In this lecture, I will summarize current progress in the effort to model the magnetic and energetic connection between the solar interior and atmosphere, and will describe the limitations and challenges inherent to this holistic approach. Title: Generation of Electric Currents in the Chromosphere via Neutral-Ion Drag Authors: Krasnoselskikh, V.; Vekstein, G.; Hudson, H. S.; Bale, S. D.; Abbett, W. P. Bibcode: 2010ApJ...724.1542K Altcode: 2010arXiv1011.5834K We consider the generation of electric currents in the solar chromosphere where the ionization level is typically low. We show that ambient electrons become magnetized even for weak magnetic fields (30 G); that is, their gyrofrequency becomes larger than the collision frequency while ion motions continue to be dominated by ion-neutral collisions. Under such conditions, ions are dragged by neutrals, and the magnetic field acts as if it is frozen-in to the dynamics of the neutral gas. However, magnetized electrons drift under the action of the electric and magnetic fields induced in the reference frame of ions moving with the neutral gas. We find that this relative motion of electrons and ions results in the generation of quite intense electric currents. The dissipation of these currents leads to resistive electron heating and efficient gas ionization. Ionization by electron-neutral impact does not alter the dynamics of the heavy particles; thus, the gas turbulent motions continue even when the plasma becomes fully ionized, and resistive dissipation continues to heat electrons and ions. This heating process is so efficient that it can result in typical temperature increases with altitude as large as 0.1-0.3 eV km-1. We conclude that this process can play a major role in the heating of the chromosphere and corona. Title: Simulation of Flux Emergence in Solar Active Regions Authors: Fang, F.; Manchester, W. B.; Abbett, W. P.; van der Holst, B.; Schrijver, C. J. Bibcode: 2010AGUFMSH31A1781F Altcode: We present results of magnetohydrodynamic (MHD) simulations of magnetic flux emergence from the convection zone into the solar corona using BATSRUS. The MHD equations are modified to take account of the radiative terms, coronal heating and heat conduction. The implementation of non-ideal equation of state describes the partially ionized plasma in the convection zone. The simulations are carried out on a domain of active-region size of 30×30×40 Mm3, extending 20 Mm down into the convection zone. The magnetic fields are coupled with the convective motion during the emerging process, and concentrates in the downflow regions. A coherent shear pattern is formed in the lower corona during the rising. We also compare our model results at the photosphere with SDO/HMI vector magnetograms and illustrate the mechanism of flux emergence that give rise to complexity of the structures in active regions. Title: Generation of electric currents in the chromosphere via neutral-ion drag Authors: Krasnoselskikh, V.; Vekstein, G.; Hudson, H. S.; Bale, S.; Abbett, W. P. Bibcode: 2010AGUFMSH31C1810K Altcode: We consider the generation of electric currents in the solar chromosphere. The ionization level in this region is generally supposed to be low. We show that the ambient electrons become magnetized even for weak magnetic fields (30 G), i.e. their gyrofrequency becomes larger than the collision frequency; ion motions continue to be dominated by ion-neutral collisions in this region. Under such conditions the ions are dragged by neutrals and magnetic field dynamics resembles frozen-in motion of the field with the neutral gas. On the other hand magnetized electrons drift under the action of the electric and magnetic fields induced in the reference frame of ions moving with the neutral gas. This relative motion of electrons and ions results in the generation of quite intense electric currents. The dissipation of these currents leads to the resistive electron heating and efficient gas ionization. Ionization by electron-neutral impact does not alter the dynamics of the heavy particles; thus the gas turbulent motions continue even when the plasma becomes fully ionized and the resistive current dissipation continues to heat electrons and ions. This heating process is so efficient that it can result in typical temperature increases with altitude as large as 0.1-0.3 eV/km. We conclude that this process can play a major role in the heating of the chromosphere and corona. Title: A Simplified Treatment of Radiative Transfer in Large-scale Convection Zone-to-Corona Models Authors: Abbett, William P.; Fisher, G. H. Bibcode: 2010shin.confE...6A Altcode: We present the latest in a series of numerical simulations of quiet Sun magnetic fields that extend from the upper convection zone into the low corona. We apply an efficient, simplified treatment of the physics of optically-thick radiative transfer throughout the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Sun's upper atmosphere in an initially unipolar (open-field) region. We then compare these results with earlier simulations that use an ad-hoc, parameterized treatment of surface cooling. Title: Simulation of Flux Emergence from the Convection Zone to the Corona Authors: Fang, Fang; Manchester, Ward; Abbett, William P.; van der Holst, Bart Bibcode: 2010ApJ...714.1649F Altcode: 2010arXiv1003.6118F Here, we present numerical simulations of magnetic flux buoyantly rising from a granular convection zone into the low corona. We study the complex interaction of the magnetic field with the turbulent plasma. The model includes the radiative loss terms, non-ideal equations of state, and empirical corona heating. We find that the convection plays a crucial role in shaping the morphology and evolution of the emerging structure. The emergence of magnetic fields can disrupt the convection pattern as the field strength increases, and form an ephemeral region-like structure, while weak magnetic flux emerges and quickly becomes concentrated in the intergranular lanes, i.e., downflow regions. As the flux rises, a coherent shear pattern in the low corona is observed in the simulation. In the photosphere, both magnetic shearing and velocity shearing occur at a very sharp polarity inversion line. In a case of U-loop magnetic field structure, the field above the surface is highly sheared while below it is relaxed. Title: Determing Flow Fields Consistent with Vector Magnetic Evolution Authors: Welsch, Brian; Fisher, G. H.; Abbett, W. P.; Bercik, D. J. Bibcode: 2010AAS...21640112W Altcode: 2010BAAS...41..858W Sequences of photospheric vector magnetograms can be used to drive time-dependent models of magnetic evolution in the overlying atmosphere, as well as to investigate dynamics in the atmospheric layer imaged in the magnetograms. While several methods of estimating electric fields consistent with the observed evolution of the magnetic field normal to the magnetogram surface have been developed, these do not explicitly employ evolution of the horizontal field components in deriving electric fields. The recently developed poloidal- toroidal decomposition (PTD) method (Fisher et al. 2010) does use this extra information; PTD electric fields, however, are generally not ideal, so ideality must be imposed post facto. Here, we present formalism for deriving ideal electric fields consistent with vector magnetic evolution, assuming that the induction equation in the MHD approximation governs the magnetic evolution; accordingly, we term the approach "inductive vector driving", or IVD. This formalism can incorporate explicit resistive terms. Moreover, IVD allows direct inclusion of results from tracking methods, which can provide additional information regarding photospheric evolution. This work is supported by NASA's Heliophysics Theory Program and NSF's SHINE program. Title: Assimilating Measurements of the Photospheric Magnetic Field into MHD Models of the Solar Atmosphere Authors: Abbett, William P.; Fisher, G. H.; Welsch, B. T.; Bercik, D. J. Bibcode: 2010AAS...21640502A Altcode: 2010BAAS...41..889A We introduce a rudimentary assimilative technique that allows a time series of vector magnetograms to be directly incorporated into the active cells of a RADMHD model of the solar atmosphere. We apply this technique to a simplified large-scale model of NOAA AR-8210, a flare and CME-producing active region. We begin by relaxing an initial magnetic configuration based on the first in a series of IVM vector magnetograms from the Mees Solar Observatory at Haleakala HI. This low-beta, near force-free configuration is achieved by solving the MHD system in the presence of a time-dependent artificial damping that is reduced as the configuration relaxes. Once the magnetic and thermodynamic initial state is achieved, we advance the system using our assimilative technique applied to a 4 hour sequence of IVM magnetograms. In addition, we present a simple 3D MHD simulation of the response of the initial AR-8210 pre-flare model corona to flare energy deposited in the upper chromosphere near a sheared neutral line. Title: Estimating Electric Fields from Vector Magnetogram Sequences Authors: Fisher, George H.; Welsch, B. T.; Abbett, W. P.; Bercik, D. J. Bibcode: 2010AAS...21640113F Altcode: 2010BAAS...41..859F Determining the electric field distribution on the Sun's photosphere is essential for quantitative studies of how energy flows from the Sun's photosphere, through the corona, and into the heliosphere. This electric field also provides valuable input for data-driven models of the solar atmosphere and the Sun-Earth system. We show how observed vector magnetogram time series can be used to estimate the photospheric electric field. Our method uses a "poloidal-toroidal decomposition" (PTD) of the time derivative of the vector magnetic field. These solutions provide an electric field whose curl obeys all three components of Faraday's Law. The PTD solutions are not unique; the gradient of a scalar potential can be added to the PTD electric field without affecting consistency with Faraday's Law. We then present an iterative technique to determine a potential function consistent with ideal MHD evolution; but this field is also not a unique solution to Faraday's Law. Finally, we explore a variational approach that minimizes an energy functional to determine a unique electric field, a generalization of Longcope's "Minimum Energy Fit". The PTD technique, the iterative technique, and the variational technique are used to estimate electric fields from a pair of synthetic vector magnetograms taken from an MHD simulation; and these fields are compared with the simulation's known electric fields. The PTD and iteration techniques compare favorably to results from existing velocity inversion techniques. These three techniques are then applied to a pair of vector magnetograms of solar active region NOAA AR8210, to demonstrate the methods with real data. Title: Estimating Electric Fields from Vector Magnetogram Sequences Authors: Fisher, G. H.; Welsch, B. T.; Abbett, W. P.; Bercik, D. J. Bibcode: 2010ApJ...715..242F Altcode: 2009arXiv0912.4916F Determining the electric field distribution on the Sun's photosphere is essential for quantitative studies of how energy flows from the Sun's photosphere, through the corona, and into the heliosphere. This electric field also provides valuable input for data-driven models of the solar atmosphere and the Sun-Earth system. We show how observed vector magnetogram time series can be used to estimate the photospheric electric field. Our method uses a "poloidal-toroidal decomposition" (PTD) of the time derivative of the vector magnetic field. These solutions provide an electric field whose curl obeys all three components of Faraday's Law. The PTD solutions are not unique; the gradient of a scalar potential can be added to the PTD electric field without affecting consistency with Faraday's Law. We then present an iterative technique to determine a potential function consistent with ideal MHD evolution; but this field is also not a unique solution to Faraday's Law. Finally, we explore a variational approach that minimizes an energy functional to determine a unique electric field, a generalization of Longcope's "Minimum Energy Fit." The PTD technique, the iterative technique, and the variational technique are used to estimate electric fields from a pair of synthetic vector magnetograms taken from an MHD simulation; and these fields are compared with the simulation's known electric fields. The PTD and iteration techniques compare favorably to results from existing velocity inversion techniques. These three techniques are then applied to a pair of vector magnetograms of solar active region NOAA AR8210, to demonstrate the methods with real data. Careful examination of the results from all three methods indicates that evolution of the magnetic vector by itself does not provide enough information to determine the true electric field in the photosphere. Either more information from other measurements, or physical constraints other than those considered here are necessary to find the true electric field. However, we show it is possible to construct physically reasonable electric field distributions whose curl matches the evolution of all three components of B. We also show that the horizontal and vertical Poynting flux patterns derived from the three techniques are similar to one another for the cases investigated. Title: Improving large-scale convection-zone-to-corona models. Authors: Abbett, W. P.; Fisher, G. H. Bibcode: 2010MmSAI..81..721A Altcode: 2010arXiv1005.0641A We introduce two new methods that are designed to improve the realism and utility of large, active region-scale 3D MHD models of the solar atmosphere. We apply these methods to RADMHD, a code capable of modeling the Sun's upper convection zone, photosphere, chromosphere, transition region, and corona within a single computational volume. We first present a way to approximate the physics of optically-thick radiative transfer without having to take the computationally expensive step of solving the radiative transfer equation in detail. We then briefly describe a rudimentary assimilative technique that allows a time series of vector magnetograms to be directly incorporated into the MHD system. Title: Incorporating Magnetogram Data into Time-Dependent Coronal Field Models Authors: Fisher, G. H.; Abbett, W. P.; Bercik, D. J.; McTiernan, J. M.; Welsch, B. T. Bibcode: 2009AGUFMSM51A1340F Altcode: We briefly review our efforts to incorporate sequences of photospheric vector magnetograms into MHD simulations of coronal evolution, in an effort to create data-driven models of the coronal magnetic field. Such models should improve our understanding of flares and coronal mass ejections (CMEs), and might eventually lead to predictive capabilities. Title: 3D simulation of flux emergence from convective zone to corona with BATSRUS Authors: Fang, F.; Manchester, W. B.; Abbett, W. P.; van der Holst, B. Bibcode: 2009AGUFMSH41B1656F Altcode: To study the interaction between magnetic field and convective motion, we present a 3d simulation of the emergence of magnetic flux ropes from the convective zone into the corona, applying radiation terms and non-ideal equation of state table to BATSRUS code. To perform this simulation, we first generate a solar atmosphere, whose physical properties are comparable with Bercik(2002) data, with a turbulent convective zone. The upgoing convective motion is cooled down and stopped by the surface loss and sharp temperature decrease at photosphere. The magnetic flux is observed to concentrate at the intergranular lanes with downflowing plasma and decrease in the granules. We then heat up the corona to temperature of above 1MK, using an empirical relationship between heating and unsigned magnetic flux. In the high-temperature, low-density upper atmosphere, radiative loss term is approximated with optically thin limit and the radiative cooling curve is obtained from CHIANTI database. The Field aligned heat conduction is applied to channel heat flux along the magnetic field lines in corona and form a more realistic transition region. After producing a superadiabatic atmosphere matching the observed properties, we introduce a buoyant magnetic flux rope below the photosphere. The flux rope shows shear flow with velocity of 8km/s at the photosphere where it emerges. We then compare our results with previous simulations without convection (Manchester et al. 2004). Title: Estimating Electric Fields from Sequences of Vector Magnetograms Authors: Fisher, George H.; Welsch, Brian T.; Abbett, William P.; Bercik, David J. Bibcode: 2009shin.confE..10F Altcode: We describe a new technique for estimating the three-dimensional vector electric field in the solar atmosphere by using a time-sequence of vector magnetograms to find an electric field distribution that obeys all 3 components of Faraday's law. The technique uses a "poloidal-toroidal" decomposition (PTD) to describe the electric field in terms of two scalar functions. The "inductive" PTD solutions to Faraday's Law are not unique, however, since additional contributions to the electric field from a potential function have no effect on Faraday's law.

We then describe how estimates for the total electric field including both the inductive and potential components can be made by using variational techniques. The variational approach we develop is similar to Longcope's "Minimum Energy Fit" technique, in that the electric field obeys the vertical component of the magnetic induction equation, while also minimizing a positive definite functional. The purely potential part of the electric field can then be recovered by subtracting the PTD electric field from the total field. Title: Estimating Electric Fields from Vector Magnetogram Sequences Authors: Fisher, George H.; Welsch, B. T.; Abbett, W. P.; Bercik, D. J. Bibcode: 2009SPD....40.0605F Altcode: We describe a new technique for estimating the three-dimensional vector electric field in the solar atmosphere by using a time-sequence of vector magnetograms to find an electric field distribution that obeys all 3 components of Faraday's law. The technique uses a ``poloidal-toroidal'' decomposition (PTD) to describe the electric field in terms of two scalar functions. The ``inductive'' PTD solutions to Faraday's Law are not unique, however, since additional contributions to the electric field from a potential function have no effect on Faraday's law.

We then describe how estimates for the total electric field including both the inductive and potential components can be made by using variational techniques. The variational approach we develop is similar to Longcope's ``Minimum Energy Fit'' technique, in that the electric field obeys the vertical component of the magnetic induction equation, while also minimizing a positive definite functional. The purely potential part of the electric field can then be recovered by subtracting the PTD electric field from the total field. Title: The Dynamic Evolution of Quiet Sun Magnetic Fields Authors: Abbett, William P.; Fisher, G. H. Bibcode: 2009SPD....40.0903A Altcode: We present the latest in a series of numerical simulations of quiet Sun magnetic fields. The upper convection zone, photosphere, chromosphere, transition region, and corona are all included within a single computational domain that is sufficiently large to encompass a typical active region. We introduce a simplified treatment of the physics of optically-thick radiative transfer throughout the surface layers, and compare these results with an earlier, non-physics based parameterized treatment of radiative cooling. Title: Erratum: "Tests and Comparisons of Velocity-Inversion Techniques" (ApJ, 670, 1434 [2007]) Authors: Welsch, B. T.; Abbett, W. P.; DeRosa, M. L.; Fisher, G. H.; Georgoulis, M. K.; Kusano, K.; Longcope, D. W.; Ravindra, B.; Schuck, P. W. Bibcode: 2008ApJ...680..827W Altcode: No abstract at ADS Title: The Dynamic Evolution of Active Region Magnetic Fields in the Solar Atmosphere Authors: Abbett, W. P.; Fisher, G. H.; Welsch, B. T.; Bercik, D. J. Bibcode: 2008AGUSMSH31A..08A Altcode: We present the latest results from a series of three-dimensional MHD simulations of active region magnetic fields. The computational domain extends from the upper convection zone out into the corona, and includes the highly-stratified layers of the photosphere, chromosphere, and transition region. We characterize the effects of convective turbulence on large-scale magnetic structures, the magnetic connectivity between sub-surface and coronal fields, and the energetics of the low atmosphere and corona. Title: Using Ideal Electric Fields Estimated from Vector Magnetogram Sequences to Drive Coronal MHD Simulations Authors: Welsch, B. T.; Fisher, G. H.; Abbett, W. P.; Bercik, D. J. Bibcode: 2008AGUSMSH54A..04W Altcode: Dynamic models of the coronal magnetic field show promise as space weather forecasting tools. Such models should be driven by electric fields derived from sequences of photospheric vector magnetograms, the only routine measurements of the solar magnetic field currently available. Previous studies derived flows --- or, equivalently, ideal electric fields --- consistent with evolution of the normal photospheric field, which could be used in "component driving" of an MHD model, i.e., enforcing consistent evolution of the observed and modeled normal magnetic fields. In this extension of the component-driving approach, we demonstrate how to derive ideal electric fields consistent with the observed evolution of both the normal and horizontal magnetic field, useful for "vector driving," i.e., enforcing consistency between all three components of the observed and model photospheric magnetic vectors. To drive an MHD model, this "ideal vector driving" (IVD) approach amount to specification of both the velocity (perpendicular the magnetic field) and its vertical derivative at the model's bottom boundary. The IVD method can incorporate results from local/ tracking methods (e.g., LCT or DAVE) and/or results from global methods (e.g., MEF or poloidal-toroidal decomposition [PTD]). We have applied this new approach to "synthetic magnetograms" extracted from MHD simulations (where the magnetic and electric fields are exactly known), as well as to a four-hour sequence of vector magnetograms from NOAA AR 8210, on 01 May 1998, just prior to an M-class flare and geoeffective CME. Title: Inferring Photospheric Velocity Fields Using a Combination of Minimum Energy Fit, Local Correlation Tracking, and Doppler Velocity Authors: Ravindra, B.; Longcope, D. W.; Abbett, W. P. Bibcode: 2008ApJ...677..751R Altcode: The minimum energy fit (MEF), a velocity inversion technique, infers all components of the photospheric velocity that are consistent with the induction equation. From the set of consistent velocity fields, it selects the smallest overall flow speed by minimizing a kinetic energy functional. If partial velocity information is available from other measurements, it can be incorporated into the MEF methodology by minimizing the squared difference from that data. We incorporate the partial velocity information provided by local correlation tracking (LCT) technique and Doppler velocity measurements. We test the incorporation of these auxiliary velocity fields using the simulated magnetograms and velocitygrams. To the known velocity field we compare the results obtained from the MEF alone, the MEF with LCT constraints, and the MEF with LCT and Doppler information. We find that the combination of MEF with LCT and vertical velocity yields the best agreement. We also apply these three methods to actual vector magnetograms of AR 8210 obtained by the Imaging Vector Magnetograph. The results suggest that in this active region the helicity and energy fluxes are dominated by the horizontal rather than the vertical components of the velocity. Title: Connecting the Quiet-Sun Convection Zone and Corona Authors: Abbett, W. P. Bibcode: 2008ASPC..383..327A Altcode: We present the first results of a new numerical model designed to simultaneously evolve the upper convection zone and low-corona within a single computational domain. We characterize (1) the properties of a quiet-Sun model atmosphere that forms as a result of the action of a convective dynamo; (2) the efficacy of parameterized cooling as a means of approximating the physics of optically-thick radiative transfer in the model chromosphere; (3) the magnetic and thermodynamic properties of the quiet-Sun atmosphere, and the magnetic connectivity between the turbulent sub-surface layers and corona; and (4) the properties of horizontally-directed magnetic fields in the low atmosphere. Title: Tests and Comparisons of Velocity-Inversion Techniques Authors: Welsch, B. T.; Abbett, W. P.; De Rosa, M. L.; Fisher, G. H.; Georgoulis, M. K.; Kusano, K.; Longcope, D. W.; Ravindra, B.; Schuck, P. W. Bibcode: 2007ApJ...670.1434W Altcode: Recently, several methods that measure the velocity of magnetized plasma from time series of photospheric vector magnetograms have been developed. Velocity fields derived using such techniques can be used both to determine the fluxes of magnetic energy and helicity into the corona, which have important consequences for understanding solar flares, coronal mass ejections, and the solar dynamo, and to drive time-dependent numerical models of coronal magnetic fields. To date, these methods have not been rigorously tested against realistic, simulated data sets, in which the magnetic field evolution and velocities are known. Here we present the results of such tests using several velocity-inversion techniques applied to synthetic magnetogram data sets, generated from anelastic MHD simulations of the upper convection zone with the ANMHD code, in which the velocity field is fully known. Broadly speaking, the MEF, DAVE, FLCT, IM, and ILCT algorithms performed comparably in many categories. While DAVE estimated the magnitude and direction of velocities slightly more accurately than the other methods, MEF's estimates of the fluxes of magnetic energy and helicity were far more accurate than any other method's. Overall, therefore, the MEF algorithm performed best in tests using the ANMHD data set. We note that ANMHD data simulate fully relaxed convection in a high-β plasma, and therefore do not realistically model photospheric evolution. Title: The Magnetic Connection between the Convection Zone and Corona in the Quiet Sun Authors: Abbett, W. P. Bibcode: 2007ApJ...665.1469A Altcode: To understand the dynamic, magnetic, and energetic connection between the convectively unstable layers below the visible surface of the Sun and the overlying solar corona, we have developed a new three-dimensional magnetohydrodynamic code capable of simultaneously evolving a model convection zone and corona within a single computational volume. As a first application of this numerical model, we present a series of simulations of the quiet Sun in a domain that encompasses both the upper convection zone and low corona. We investigate whether the magnetic field generated by a convective surface dynamo can account for some of the observed properties of the quiet-Sun atmosphere. We find that (1) it is possible to heat a model corona to X-ray-emitting temperatures with the magnetic fields generated from a convective dynamo and an empirically based heating mechanism consistent with the observed relationship between X-ray emission and magnetic flux observed at the visible surface; (2) within the limitations of our numerical models of the quiet Sun, resistive and viscous dissipation alone are insufficient to maintain a hot corona; (3) the quiet-Sun model chromosphere is a dynamic, non-force-free layer that exhibits a temperature reversal in the convective pattern in the relatively low density layers above the photosphere; (4) the majority of the unsigned magnetic flux lies below the model photosphere in the convectively unstable portion of the domain; (5) horizontally directed magnetic structures thread the low atmosphere, often connecting relatively distant concentrations of magnetic flux observed at the surface; and (6) low-resolution photospheric magnetograms can significantly underestimate the amount of unsigned magnetic flux threading the quiet-Sun photosphere. Title: The Dynamic Evolution of Quiet Sun Magnetic Fields in the Solar Atmosphere Authors: Abbett, William P. Bibcode: 2007AAS...210.9109A Altcode: 2007BAAS...39..205A We present the latest results from a series of three-dimensional MHD simulations of the Quiet Sun magnetic field. The computational domain extends from the upper convection zone out into the corona, and includes the highly-stratified layers of the photosphere, chromosphere, and transition region. Our study focuses on the following questions: Can the magnetic field generated by a convective surface dynamo heat a model corona to soft X-ray emitting temperatures? Do physical processes such as resistive and viscous dissipation supply the necessary heating throughout the model atmosphere, or is an additional empirically-based heating mechanism required? What is the magnetic connection between the flux threading the model photosphere, and that filling the model corona? Can the magnetic field in the dynamic models be successfully reproduced by static extrapolations? Title: Active Region Magnetic Fields in the Solar Interior Authors: Abbett, W. P.; Fisher, G. H. Bibcode: 2006ASPC..354..135A Altcode: We present a brief review of recent efforts to understand the life-cycle of active region magnetic fields with an emphasis on what photospheric observations can tell us about the evolution of large-scale magnetic structures deep in the convective interior. A critical component of these efforts is to understand the dynamic connection between magnetic fields (at both large and small scales) observed threading the solar atmosphere and their sub-surface counterparts. We conclude our survey by presenting early results from a new numerical model capable of self-consistently incorporating both sub-photospheric layers and the low solar corona into a single computational domain. Title: Are Convective Dynamos Responsible for the Minimum X-ray Fluxes Observed in the Sun and Late-Type Main Sequence Stars? Authors: Bercik, D. J.; Fisher, G. H.; Johns-Krull, C. M.; Abbett, W. P.; Lundquist, L. L. Bibcode: 2006ASPC..354..127B Altcode: We extend the investigation of tet{Bercik05} to the case of a non-rotating solar-type reference star. Using three-dimensional numerical simulations of a turbulent dynamo driven by convection and the empirical relationship of tet{Pevtsov03}, we predict the level of X-ray emission from such a convective turbulent dynamo, and find that our results are consistent with quiet Sun observations. This implies that it is plausible that the Sun may have a rotation-independent convective dynamo working together with the large-scale dynamo believed to be responsible for the solar cycle. Title: Simulations of the Quiet Sun Magnetic Field: From the Upper Convection Zone into the Corona Authors: Abbett, William P. Bibcode: 2006SPD....37.0701A Altcode: 2006BAAS...38..227A We present the latest in a series of simulationsdesigned to directly investigate whether the magneticfield generated by a convective dynamo in the upperconvection zone can account for the observedproperties of the Quiet Sun magnetic field andatmosphere. The simulations are performed usinga new numerical code capable of evolving a modelsolar atmosphere that extends from the upper convectionzone into the low corona. This code is a parallel,semi-implicit solver capable of accomodating thespatial and temporal disparities intrinsic to thiscombined system. Title: Radiative Hydrodynamic Models of Optical and Ultraviolet Emission from M Dwarf Flares Authors: Allred, Joel C.; Hawley, Suzanne L.; Abbett, William P.; Carlsson, Mats Bibcode: 2006ApJ...644..484A Altcode: 2006astro.ph..3195A We report on radiative hydrodynamic simulations of M dwarf stellar flares and compare the model predictions to observations of several flares. The flares were simulated by calculating the hydrodynamic response of a model M dwarf atmosphere to a beam of nonthermal electrons. Radiative back-warming through numerous soft X-ray, extreme-ultraviolet, and ultraviolet transitions are also included. The equations of radiative transfer and statistical equilibrium are treated in non-LTE for many transitions of hydrogen, helium, and the Ca II ion, allowing the calculation of detailed line profiles and continuum radiation. Two simulations were carried out, with electron beam fluxes corresponding to moderate and strong beam heating. In both cases we find that the dynamics can be naturally divided into two phases: an initial gentle phase in which hydrogen and helium radiate away much of the beam energy and an explosive phase characterized by large hydrodynamic waves. During the initial phase, lower chromospheric material is evaporated into higher regions of the atmosphere, causing many lines and continua to brighten dramatically. The He II 304 line is especially enhanced, becoming the brightest line in the flaring spectrum. The hydrogen Balmer lines also become much brighter and show very broad line widths, in agreement with observations. We compare our predicted Balmer decrements to decrements calculated for several flare observations and find the predictions to be in general agreement with the observations. During the explosive phase both condensation and evaporation waves are produced. The moderate flare simulation predicts a peak evaporation wave of ~130 km s-1 and a condensation wave of ~30 km s-1. The velocity of the condensation wave matches velocities observed in several transition region lines. The optical continuum also greatly intensifies, reaching a peak increase of 130% (at 6000 Å) for the strong flare, but does not match observed white-light spectra. Title: Radiative Hydrodynamic Models of the Optical and Ultraviolet Emission from Solar Flares Authors: Allred, Joel C.; Hawley, Suzanne L.; Abbett, William P.; Carlsson, Mats Bibcode: 2005ApJ...630..573A Altcode: 2005astro.ph..7335A We report on radiative hydrodynamic simulations of moderate and strong solar flares. The flares were simulated by calculating the atmospheric response to a beam of nonthermal electrons injected at the apex of a one-dimensional closed coronal loop and include heating from thermal soft X-ray, extreme ultraviolet, and ultraviolet (XEUV) emission. The equations of radiative transfer and statistical equilibrium were treated in non-LTE and solved for numerous transitions of hydrogen, helium, and Ca II, allowing the calculation of detailed line profiles and continuum emission. This work improves on previous simulations by incorporating more realistic nonthermal electron beam models and includes a more rigorous model of thermal XEUV heating. We find that XEUV back-warming contributes less than 10% of the heating, even in strong flares. The simulations show elevated coronal and transition region densities resulting in dramatic increases in line and continuum emission in both the UV and optical regions. The optical continuum reaches a peak increase of several percent, which is consistent with enhancements observed in solar white-light flares. For a moderate flare (~M class), the dynamics are characterized by a long gentle phase of near balance between flare heating and radiative cooling, followed by an explosive phase with beam heating dominating over cooling and characterized by strong hydrodynamic waves. For a strong flare (~X class), the gentle phase is much shorter, and we speculate that for even stronger flares the gentle phase may be essentially nonexistent. During the explosive phase, synthetic profiles for lines formed in the upper chromosphere and transition region show blueshifts corresponding to a plasma velocity of ~120 km s-1, and lines formed in the lower chromosphere show redshifts of ~40 km s-1. Title: Convective Dynamos and the Minimum X-Ray Flux in Main-Sequence Stars Authors: Bercik, D. J.; Fisher, G. H.; Johns-Krull, Christopher M.; Abbett, W. P. Bibcode: 2005ApJ...631..529B Altcode: 2005astro.ph..6027B The objective of this paper is to investigate whether a convective dynamo can account quantitatively for the observed lower limit of X-ray surface flux in solar-type main-sequence stars. Our approach is to use three-dimensional numerical simulations of a turbulent dynamo driven by convection to characterize the dynamic behavior, magnetic field strengths, and filling factors in a nonrotating stratified medium and to predict these magnetic properties at the surface of cool stars. We use simple applications of stellar structure theory for the convective envelopes of main-sequence stars to scale our simulations to the outer layers of stars in the F0-M0 spectral range, which allows us to estimate the unsigned magnetic flux on the surface of nonrotating reference stars. We find agreement between our G0 star calculations and the observed unsigned magnetic flux density in the quiet Sun. With these magnetic flux estimates we use the recent results of Pevtsov et al. to predict the level of X-ray emission from such a turbulent dynamo and find that our results compare well with observed lower limits of surface X-ray flux. If we scale our predicted X-ray fluxes to Mg II fluxes, we also find good agreement with the observed lower limit of chromospheric emission in K dwarfs. This suggests that dynamo action from a convecting, nonrotating plasma is a viable alternative to acoustic heating models as an explanation for the basal emission level seen in chromospheric, transition-region, and coronal diagnostics from late-type stars. Title: Turbulent Dynamos and the Minimum X-ray Flux in Solar-Type Main Sequence Stars Authors: Bercik, D. J.; Fisher, G. H.; Johns-Krull, C. M.; Abbett, W. P. Bibcode: 2005AGUSMSP43B..01B Altcode: We investigate whether a small-scale turbulent dynamo can account quantitatively for the observed lower limit of X-ray surface flux in solar-type main sequence stars. Our approach is to use 3D numerical simulations of a turbulent dynamo driven by convection to characterize the dynamic behavior, magnetic field strengths, and filling factors in a non-rotating stratified medium, and to predict these magnetic properties at the surface of cool stars. We use simple applications of stellar structure theory for the convective envelopes of main-sequence stars to scale our simulations to the outer layers of stars in the F0--M0 spectral range, which allows us to estimate the unsigned magnetic flux on the surface of non-rotating reference stars. With these estimates we use the observed magnetic flux--X-ray flux correlation of Pevtsov et al. (2003) to predict the level of X-ray emission from such a turbulent dynamo, and find that our results compare well with observed lower limits of surface X-ray flux. This suggests that dynamo action from a convecting, non-rotating plasma is a viable alternative to acoustic heating models as an explanation for the basal emission level seen in chromospheric, transition region, and coronal diagnostics from late-type stars. Title: 3D MHD Simulations of Magnetic Flux Emergence in Active Regions Authors: Abbett, W. P. Bibcode: 2005AGUSMSP41A..11A Altcode: We report on the progress of 3D simulations of active region magnetic flux emergence (and decay) through the stratified, sub-photospheric layers of the upper convection zone into the solar atmosphere and low corona. We use a recently-developed 3D semi-implicit MHD code (with a non-uniform, adaptive mesh) to address the inherent stiffness of the system of equations, and will compare our results with similar studies using second-order accurate, fully explicit numerical schemes. Title: The photospheric boundary of Sun-to-Earth coupled models Authors: Abbett, W. P.; Mikić, Z.; Linker, J. A.; McTiernan, J. M.; Magara, T.; Fisher, G. H. Bibcode: 2004JASTP..66.1257A Altcode: 2004JATP...66.1257A The least understood component of the Sun-to-Earth coupled system is the solar atmosphere—the visible layers of the Sun that encompass the photosphere, chromosphere, transition region and low corona. Coronal mass ejections (CMEs), principal drivers of space weather, are magnetically driven phenomena that are thought to originate in the low solar corona. Their initiation mechanism, however, is still a topic of great debate. If we are to develop physics-based models with true predictive capability, we must progress beyond simulations of highly idealized magnetic configurations, and develop the techniques necessary to incorporate observations of the vector magnetic field at the solar photosphere into numerical models of the solar corona. As a first step toward this goal, we drive the SAIC coronal model with the complex magnetic fields and flows that result from a sub-photospheric MHD simulation of an emerging active region. In particular, we successfully emerge a twisted Ω-loop into a pre-existing coronal arcade.

To date, it is not possible to directly measure the magnetic field in the solar corona. Instead, we must rely on non-potential extrapolations to generate the twisted, pre-eruptive coronal topologies necessary to initiate data-driven MHD simulations of CMEs. We therefore investigate whether a non-constant-α force-free extrapolation can successfully reproduce the magnetic features of a self-consistent MHD simulation of flux emergence through a stratified model atmosphere. We generate force-free equilibria from simulated photospheric and chromospheric vector magnetograms, and compare these results to the MHD calculation. We then apply these techniques to an IVM (Mees Solar Observatory) vector magnetogram of NOAA active-region 8210, a source of a number of eruptive events on the Sun. Title: The Dynamic Evolution of Twisted Magnetic Flux Tubes in a Three-dimensional Convecting Flow. II. Turbulent Pumping and the Cohesion of Ω-Loops Authors: Abbett, W. P.; Fisher, G. H.; Fan, Y.; Bercik, D. J. Bibcode: 2004ApJ...612..557A Altcode: We present a set of three-dimensional MHD simulations using the anelastic approximation of active region-scale flux ropes embedded in a turbulent, stratified model convection zone. We simulate the evolution of Ω-loops and other magnetic structures of varying field strengths, helicities, and morphologies in both rotating and nonrotating background states. We show that if the magnetic energy of a flux tube is weak relative to the kinetic energy density of strong downdrafts, convective flows dominate the evolution, flux tubes of any shape rapidly lose cohesion, and the magnetic field redistributes itself throughout the domain over timescales characteristic of convective turnover. We determine the conditions under which magnetic tension resulting from field line twist can provide the force necessary to prevent a relatively weak flux tube from losing cohesion during its ascent through the turbulent convection zone. Our simulations show that there is no initial tendency for a horizontal magnetic flux tube or layer to be preferentially transported in one vertical direction over the other solely as a result of the presence of an asymmetric vertical flow field. However, as the simulations progress, there is a transient net transport of magnetic flux into the lower half of the computational domain as the distribution of the magnetic field changes and flux is expelled from cell centers into converging downflows and intergranular lanes. This pumping mechanism is weak and uncorrelated with the degree of vertical flow asymmetry. We find that the strong turbulent pumping evident in simulations of penetrative convection-the efficient transport of magnetic flux to the base of the convection zone over several local turnover times-does not manifest itself in a closed domain in the absence of a convective overshoot layer. Thus, we suggest that this rapid redistribution of flux is primarily due to the penetration of magnetic flux into the stable layer where it remains over a timescale that far exceeds that of convective turnover. We also find that different treatments of the viscosity of a Newtonian fluid-in which the coefficient of either kinematic or dynamic viscosity is held constant throughout the domain-do not affect the global average evolution of embedded magnetic structures, although the details of the evolution may differ between models. Title: ILCT: Recovering Photospheric Velocities from Magnetograms by Combining the Induction Equation with Local Correlation Tracking Authors: Welsch, B. T.; Fisher, G. H.; Abbett, W. P.; Regnier, S. Bibcode: 2004ApJ...610.1148W Altcode: We present three methods for deriving the velocity field in magnetized regions of the Sun's photosphere. As a preliminary step, we introduce a Fourier-based local correlation tracking (LCT) routine that we term ``FLCT.'' By explicitly employing the observation made by Démoulin & Berger, that results determined by LCT applied to magnetograms involve a combination of all components of the velocity and magnetic fields, we show that a three-component velocity field can be derived, in a method we term algebraic decomposition, or ADC. Finally, we introduce ILCT, a method that enforces consistency between the normal component of the induction equation and results obtained from LCT. When used with photospheric vector magnetograms, ILCT determines a three-component photospheric velocity field suitable for use with time sequences of such magnetograms to drive boundary conditions for MHD simulations of the solar corona. We present results from these methods applied to vector magnetograms of NOAA AR 8210 on 1998 May 1. Title: Radiative Hydrodynamic Simulations of Solar and Stellar Flares Authors: Allred, J. C.; Hawley, S. L.; Abbett, W. P. Bibcode: 2004AAS...204.0305A Altcode: 2004BAAS...36..671A We have constructed radiative hydrodynamic simulations of the effects of flare heating on model solar and dMe stellar atmospheres. The heating is assumed to be driven by a beam of non-thermal electrons originating in the corona and impacting on the lower transition region and chromosphere. We use thick target bremsstrahlung fits to RHESSI hard X-ray observations of the July 23, 2002 and February 26, 2002 flares to model the electron beam. Our simulations include detailed calculations of numerous bound-bound and bound-free transitions which we compare with line profiles measured during flares on the Sun and on the dMe star AD Leo. We also investigate the possibility that the 511 keV emission line is produced from a significant amount of material at transition region temperatures. Title: ILCT: Combining Local Correlation Tracking with the Magnetic Induction Equation Authors: Fisher, G. H.; Welsch, B. T.; Abbett, W. P.; Regnier, S. Bibcode: 2004AAS...204.8805F Altcode: 2004BAAS...36..820F In order to use sequences of vector magnetogram data as input to MHD simulations of the solar atmosphere, one must ensure that the data is consistent with the MHD induction equation. We describe a new technique, ILCT, that uses local correlation tracking to determine a 3-D flow field that is consistent with the ideal MHD induction equation. The flow fields are thus suitable for incorporation into the photospheric boundary of an MHD simulation of the solar atmosphere. Title: HST, EUVE and Ground-Based Observations of Flares on AD Leo Authors: Allred, J. C.; Hawley, S. L.; Johns-Krull, C. M.; Fisher, G. H.; Abbett, W. P.; Avgoloupis, S. I.; Seiradakis, J. H. Bibcode: 2004IAUS..219..829A Altcode: No abstract at ADS Title: Radiative Hydrodynamic Models of Solar White Light Flares Authors: Allred, J. C.; Hawley, S. L.; Abbett, W. P.; Fisher, G. H.; Hudson, H. S.; Metcalf, T. R. Bibcode: 2003AGUFMSH22A0175A Altcode: We report on theoretical radiative hydrodynamic simulations of solar white light flares. The solar atmosphere is modeled in detail from the transition region to the photosphere. The coronal pressure and X-ray backheating are included self-consistently. Flare heating is assumed to be from an electron beam which is modeled for several white light flares using data from RHESSI, TRACE and Yohkoh. We also investigate the possibility that the 511 keV line width is produced from a significant column depth of atmosphere at transition region temperatures. We compare our new solar flare models to previous results, and to models of M dwarf stellar flares. Title: Temperature, Density, and Magnetic Field Reconstructions of Active Region Coronae Authors: Lundquist, L. L.; Fisher, G. H.; Régnier, S.; Liu, Y.; Abbett, W. P. Bibcode: 2003AGUFMSH42B0509L Altcode: We present simulated coronal emission pictures of some case-study solar active regions, including NOAA-designated regions 8210 and 8038. The simulated emissions are calculated from a 3-d temperature, density, and magnetic field model of the corona based on first principles. The method involves a static energy balance along individual coronal loops, with the heating term taken from a given coronal heating theory. The predicted emissions can be compared with observed X-ray and UV satellite images. By comparing the predictions of various heating theories with observations, we can determine constraints on the probable mechanisms of coronal heating. The model is also useful for a variety of other applications, such as testing of coronal magnetic field extrapolation techniques, calculations of wave propagation and shock phenomena, and testing assumptions about the spatial distribution of heating along loops. This work was supported by a DoD/AFOSR MURI grant, "Understanding Magnetic Eruptions and their Interplanetary Consequences." Title: I+LCT: A Method for Determining Photospheric Flows from Magnetograms Authors: Welsch, B. T.; Fisher, G. H.; Abbett, W. P. Bibcode: 2003AGUFMSH22A0177W Altcode: Coronal mass ejections (CME's) are magnetically-driven reconfigurations of plasma in the low-β solar corona; they are the primary drivers of space weather. One way to investigate coronal field evolution before and during such events involves driving MHD simulations of the coronal magnetic field using data from time series of vector magnetograms. Doing so requires specification of a three-component velocity field at the simulated photosphere, consistent with the observed magnetic field evolution in that layer. Unfortunately, such velocity data are not generally available. We have developed a method that finds photospheric plasma velocities consistent with both the flows derived by the familiar techinique of local correlation tracking (LCT), and the field evolution described by z-component of the induction equation. We present results obtained by applying this ``I+LCT'' technique to vector magnetograms, and to ``false'' magnetograms obtained from MHD simulations of photospheric field evolution. Title: Turbulent Magnetic Field Generation in Rotating Stars Authors: Bercik, D. J.; Abbett, W. P.; Fisher, G. H.; Fan, Y. Bibcode: 2003AGUFMSH42B0536B Altcode: Observationally, it has been found that magnetic activity is a strong function of rotation rate. The connection between rotation and dynamo-generated fields is not well understood, however. The typical interface dynamo theory applied to the Sun to describe its activity cycle assumes the existence of a velocity shear layer. Such a model is inappropriate for fully convective stars that are nevertheless active, such as late-type M and L stars and pre-main sequence T Tauri stars; in these stars a turbulent dynamo is generally believed to be the mechanism of magnetic field generation. We investigate the connection between observed activity behavior and magnetic field generation in fully convective stars through a series of simulations of the turbulent dynamo. The simulations were performed in a Cartesian domain using ANMHD, a 3D MHD anelastic code. We compare the resulting magnetic topologies for a series of Rossby numbers and comment on the implications for the sizes of coronal loops and activity levels. Title: Incorporating Vector Magnetic Field Measurements into MHD Models of the Solar Atmosphere Authors: Abbett, W. P. Bibcode: 2003AGUFMSM11A..03A Altcode: We report on our efforts to incorporate high cadence vector magnetic field measurements of the CME and flare producing active region NOAA 8210 (observed from April 28 to May 2 1998) into the photospheric boundary layers of our 3D MHD models of the solar atmosphere. We find that it is is essential to be able to specify an initial model atmosphere that is both consistent with soft X-ray observations of the corona and with observed vector magnetic field measurements at the photosphere. Further, MHD codes require that certain components of the flowfield be specified at the lower boundary in such a way as to self-consistently update the model photosphere between each successive magnetogram. We will present the results of our application of several techniques to infer the velocity field of magnetized plasma in the photosphere using a time-series of IVM vector magnetograms of NOAA 8210, and will present the results from our latest attempt to model this complex active region. Title: Multiwavelength Observations of Flares on AD Leonis Authors: Hawley, Suzanne L.; Allred, Joel C.; Johns-Krull, Christopher M.; Fisher, George H.; Abbett, William P.; Alekseev, Ilya; Avgoloupis, Stavros I.; Deustua, Susana E.; Gunn, Alastair; Seiradakis, John H.; Sirk, Martin M.; Valenti, Jeff A. Bibcode: 2003ApJ...597..535H Altcode: We report results from a multiwavelength observing campaign conducted during 2000 March on the flare star AD Leo. Simultaneous data were obtained from several ground- and space-based observatories, including observations of eight sizable flares. We discuss the correlation of line and continuum emission in the optical and ultraviolet wavelength regimes, as well as the flare energy budget, and we find that the emission properties are remarkably similar even for flares of very different evolutionary morphology. This suggests a common heating mechanism and atmospheric structure that are independent of the detailed evolution of individual flares. We also discuss the Neupert effect, chromospheric line broadening, and velocity fields observed in several transition region emission lines. The latter show significant downflows during and shortly after the flare impulsive phase. Our observations are broadly consistent with the solar model of chromospheric evaporation and condensation following impulsive heating by a flux of nonthermal electrons. These data place strong constraints on the next generation of radiative hydrodynamic models of stellar flares. Title: The March 2000 AD Leo Flare Campaign Authors: Hawley, S. L.; Johns-Krull, C. M.; Fisher, G. H.; Abbett, W. P.; Seiradakis, J. H.; Avgoloupis, S. I. Bibcode: 2003csss...12..975H Altcode: Flares are by their nature random and unpredictable events and flare observations are often the serendipitous result of programs designed for other scientific endeavors. Thus, few observations of flares covering multiple wavelength regimes, with both spectroscopic and photometric information, are available to test stellar flare models. Occasionally, a bold and reckless team will put together a flare campaign, employing suitable statistical arguments to convince the relevant telescope allocation committees that such a campaign will prove fruitful, while hoping desperately for the combination of clear weather, working instruments and cooperative star necessary to warrant the herculean organizational effort. We report here on one such campaign, conducted during March, 2000 on the dM3e flare star AD Leo. Title: A Magnetohydrodynamic Test of the Wang-Sheeley Model Authors: Ledvina, S. A.; Luhmann, J. G.; Abbett, W. P. Bibcode: 2003AIPC..679..323L Altcode: The Wang-Sheeley relationship relates the solar wind speed at the Earth to the divergence rate of open magnetic flux tubes in the solar corona. This relationship is based on a statistically significant correlation between the flux tube divergence parameter ``fs'' derived from a photospheric field-based potential field source surface model, and satellite observations of the solar wind speed. The fast solar wind emanates from regions of small magnetic divergence, while slow solar wind comes from regions of high magnetic divergence. Arge and Pizzo [2] improved the reliability of the method by relating the coronal flux tube expansion factor to the solar wind speed at the source surface instead of the satellite. We use a three-dimensional MHD model of the solar corona to further investigate the implications of the Wang-Sheeley relationship for solar wind acceleration. The results suggest what additional heating and momentum inputs may be necessary in an MHD model to obtain the observed relationship between flux tube divergence and solar wind speed. Title: A Temperature and Density Model of the Solar Corona Authors: Lundquist, L. L.; Regnier, S.; Abbett, W. P.; Fisher, G. H. Bibcode: 2003SPD....34.0404L Altcode: 2003BAAS...35..811L We have developed the foundations of a 3-d global temperature and density model of the solar corona based on first principles. The method involves a static energy balance along individual coronal loops, with the heating term taken from a given coronal heating theory. We use the model to create synthetic emission images of active regions for comparison with observed X-ray and UV satellite images. The technique will enable us to perform a statistical study of active region heating with Yohkoh data from the last decade, comparing observations with the predicted emission measures and X-ray morphologies for different heating theories. The model is also useful for a variety of other applications, such as calculations of wave propagation and shock phenomena, testing of coronal magnetic field extrapolation techniques such as the potential and FFF models, and testing assumptions about the spatial distribution of heating along loops.

We have applied the technique to two cases: a simulated emerged active region, and NOAA active region 8210. These cases employ a heating term derived from the empirical relationship of Pevtsov et al. (2003) relating soft X-ray luminosity to total unsigned magnetic flux for a wide range of solar and stellar magnetic features. We present results from these two cases, including a comparison of the synthetic emission images of AR 8210 with Yohkoh SXT data. This work was supported by a DoD/AFOSR MURI grant, "Understanding Magnetic Eruptions and their Interplanetary Consequences." Title: Can Simulations of Active Region Magnetic Fields Lead to a Simplified Model of Turbulent Pumping? Authors: Abbett, W. P.; Fisher, G. H.; Fan, Y.; Bercik, D. J. Bibcode: 2003SPD....34.1905A Altcode: 2003BAAS...35..842A We present a series of 3-D MHD simulations in the anelastic approximation of active region scale magnetic flux ropes embedded in a highly stratified, turbulent model convection zone. The numerical calculations are carried out over long time scales (of order a solar rotation time) at high magnetic Reynolds numbers and suggest that the process of ``turbulent pumping'' --- the tendency for magnetic flux to be efficiently transported from surface layers to the base of the convection zone --- does not manifest itself in the absence of a convective overshoot layer. If the overshoot layer is present, we suggest a simple, statistical model (similar to a 1-D, depth-dependent eddy-diffusivity treatment with a characteristic time-scale of supergranulation) that describes the average properties of the flux storage process. Title: Comparison of the Coronal Magnetic Field Derived from PFSS and MHD Models Authors: Ledvina, S. A.; Luhmann, J. G.; Li, Y.; Abbett, W. P. Bibcode: 2003SPD....34.0601L Altcode: 2003BAAS...35..817L The coronal magnetic field determines many properties of the solar corona such as the location of the heliospheric current sheet and regions of high and low speed solar wind. Thus understanding the structure of the coronal magnetic field is crucial to the understanding of space weather. Several models use a synoptic map to derive the structure of the coronal field out to several solar radii. One such model is the potential field source surface model (PFSS). This model neglects electric currents between the photosphere and a "source surface" (typically 2.5 Rs). At the source surface the field lines are forced to be radial in order to mimic the effects of the solar wind. In contrast MHD models try to self-consistently derive the coronal field and the plasma properties of the corona. We compare the coronal magnetic field structures derived by the PFSS and MHD models in order to understand what role dynamical effects may have on the field structure. Title: Modeling of the Turbulent Dynamo Authors: Bercik, D. J.; Fisher, G. H.; Abbett, W. P. Bibcode: 2003SPD....34.1904B Altcode: 2003BAAS...35R.842B We report on the development progress of a 3-D spherical anelastic MHD code (SANMHD) that will be used to study the turbulent dynamo in solar and stellar interiors. SANMHD is a complement to the existing Cartesian anelastic MHD code, ANMHD; to model the interaction between penetrative turbulent convection and magnetic field deep in the interior of stars, it becomes necessary to consider a gravitationally stratified atmosphere in a spherical geometry. We discuss issues regarding the creation of a highly modular code that is portable across multiple platforms, code structuring to allow the flexibility to investigate a variety of physical scenarios and testing strategies. Title: The Dynamic Evolution of Twisted Magnetic Flux Tubes in a Three-dimensional Convecting Flow. I. Uniformly Buoyant Horizontal Tubes Authors: Fan, Y.; Abbett, W. P.; Fisher, G. H. Bibcode: 2003ApJ...582.1206F Altcode: We present three-dimensional numerical simulations of the dynamic evolution of uniformly buoyant, twisted horizontal magnetic flux tubes in a three-dimensional stratified convective velocity field. Our calculations are relevant to understanding how stratified convection in the deep solar convection zone may affect the rise and the structure of buoyant flux tubes that are responsible for the emergence of solar active regions. We find that in order for the magnetic buoyancy force of the tube to dominate the hydrodynamic force due to the convective downflows, the field strength B of the flux tube needs to be greater than (Hp/a)1/2Beq~3Beq, where Hp is the pressure scale height, a is the tube radius, and Beq is the field strength in equipartition with the kinetic energy density of the strong downdrafts. For tubes of equipartition field strength (B=Beq), the dynamic evolution depends sensitively on the local condition of the convective flow. Sections of the tube in the paths of strong downdrafts are pinned down to the bottom despite their buoyancy, while the rise speed of sections within upflow regions is significantly boosted; Ω-shaped emerging tubes can form between downdrafts. Although flux tubes with B=Beq are found to be severely distorted by convection, the degree of distortion obtained from our simulations is not severe enough to clearly rule out the Ω-tubes that are able to emerge between downdrafts as possible progenitors of solar active regions. As the initial field strength of the tube becomes higher than the critical value of ~(Hp/a)1/2Beq given above, the dynamic evolution converges toward the results of previous simulations of the buoyant rise of magnetic flux tubes in a static, adiabatically stratified model solar convection zone. Tubes with 10 times the equipartition field strength are found to rise unimpeded by the downdrafts and are not significantly distorted by the three-dimensional convective flow. Title: A Coupled Model for the Emergence of Active Region Magnetic Flux into the Solar Corona Authors: Abbett, W. P.; Fisher, G. H. Bibcode: 2003ApJ...582..475A Altcode: We present a set of numerical simulations that model the emergence of active region magnetic flux into an initially field-free model corona. We simulate the buoyant rise of twisted magnetic flux tubes initially positioned near the base of a stable stratified model convection zone and use the results of these calculations to drive a three-dimensional magnetohydrodynamic model corona. The simulations show that time-dependent subsurface flows are an important component of the dynamic evolution and subsequent morphology of an emerging magnetic structure. During the initial stages of the flux emergence process, the overlying magnetic field differs significantly from a force-free state. However, as the runs progress and boundary flows adjust, most of the coronal field-with the exception of those structures located relatively close to the model photosphere-relaxes to a more force-free configuration. Potential field extrapolations do not adequately represent the magnetic structure when emerging active region fields are twisted. In the dynamic models, if arched flux ropes emerge with nonzero helicity, the overlying field readily forms sigmoid-shaped structures. However, the chirality of the sigmoid and other details of its structure depend on the observer's vantage point and the location within a given loop of emitting plasma. Thus, sigmoids may be an unreliable signature of the sign and magnitude of magnetic twist. Title: Comparison of the Coronal Magnetic Field Derived from PFSS and MHD Models Authors: Ledvina, S. A.; Luhmann, J. G.; Li, Y.; Abbett, W. P. Bibcode: 2002AGUFMSH52A0456L Altcode: The coronal magnetic field determines many properties of the solar corona such as the location of the heliospheric current sheet and regions of high and low speed solar wind. Thus understanding the structure of the coronal magnetic field is crucial to the understanding of space weather. Several models use a synoptic map to derive the structure of the coronal field out to several solar radii. One such model is the potential field source surface model (PFSS). This model neglects electric currents between the photosphere and a "source surface" (typically 2.5 Rs). At the source surface the field lines are forced to be radial in order to mimic the effects of the solar wind. In contrast MHD models try to self-consistently derive the coronal field and the plasma properties of the corona. We compare the coronal magnetic field structures derived by the PFSS and MHD models in order to understand what role dynamical effects may have on the field structure. Title: The Dynamic Evolution of Twisted Omega-loops in a 3-D Convecting Flow Authors: Abbett, W. P.; Fan, Y.; Fisher, G. H. Bibcode: 2002AGUFMSH52A0474A Altcode: We present the latest results from 3D MHD simulations (in the anelastic approximation) of buoyant magnetic flux tubes interacting with turbulent convection in the solar interior. We focus our study on active region scale flux ropes and Omega-loops, and perform a large parameter space study of the effects of not only initial field strength, but twist and loop geometry on the morphology and dynamics of sub-surface magnetic structures. We also investigate the effects of different numerical treatments of viscosity, and quantify the amount of magnetic field in each simulation that succumbs to the effects of turbulent pumping. Title: The Rise of Twisted Horizontal Flux Tubes in a 3D Convecting Flow Authors: Fan, Y.; Abbett, W. P.; Fisher, G. H. Bibcode: 2002AAS...200.0306F Altcode: 2002BAAS...34..642F We present 3D numerical simulations of the dynamic evolution of twisted horizontal magnetic flux tubes in a stratified convecting convection zone. We investigate how the trajectory, rise velocity, and cohesion of the buoyant flux tubes are affected by the 3D stratified convection. It is found that the field strength of the magnetic flux tube needs to be significantly above the value of equipartition with the kinetic energy of convection in order for the flux tube to rise cohesively to the top of the stratified domain. These simulations add further support to the strong toroidal field strength ( ~ 5 x 104 G to 105 G) at the base of the solar convection zone, suggested by previous thin flux tube calculations of emerging flux tubes through the solar convective envelope. NCAR is sponsored by the National Science Foundation. Part of this work was carried out while the authors were participating in the solar magnetic field program held at ITP, UCSB. Title: A Magnetohydrodynamic Test of the Wang-Sheeley Model Authors: Ledvina, S. A.; Abbett, W. P.; Luhmann, J. G. Bibcode: 2002AAS...200.5714L Altcode: 2002BAAS...34Q.739L The Wang-Sheeley empirical model enables the calculation of the solar wind speed at Earth from the divergence of magnetic flux tubes in a synoptic map-based potential field source surface model of the coronal magnetic field. The formula used for this purpose was derived from observations of the solar wind speed at 1 AU. According to the model, fast solar wind emanates from regions of small magnetic field divergence, while slow solar wind comes from high divergence regions. Arge and Pizzo (2000) recently improved the Wang-Sheeley formula by taking the stream interaction effects between the Sun and 1 AU into account. We use a three-dimensional MHD model of the solar corona to test the assumptions of the Wang- Sheeley model and the improvements made by Arge and Pizzo for various magnetic configurations. These results provide insight into what additional coronal heating may be implied for different flux tube geometries in order to obtain the observed relationship with solar wind speed. Title: Numerical Simulations of Magnetic Flux Emergence in Active Regions Authors: Abbett, W. P. Bibcode: 2002AAS...200.7906A Altcode: 2002BAAS...34..780A Understanding the sub-photospheric structure and dynamics of emerging active region magnetic fields, and how these fields are coupled to structures observed above the photosphere, is important to a variety of ongoing research projects in both the solar physics and space science communities (for example, the effort to predict the onset of intense episodes of solar activity such as CMEs and flares). Over the past decade, much progress has been made by using 2-D MHD codes and the 1-D ``thin flux tube'' approximation to describe the evolution of buoyant magnetic flux tubes in the solar interior. However, in recent years, the rapid evolution of computer technology, coupled with advances in computational algorithms, have made it possible to use physically self-consistent, 3-D MHD numerical simulations to model the evolution of strong magnetic fields through stratified model convection zones without the restrictive assumptions of earlier models. This review will summarize efforts to use modern 3-D codes as tools to test predictions of earlier theoretical models and to interpret observational data. The emphasis will be on the progress made in modeling emerging magnetic flux in the solar interior; however, a brief overview of recent efforts to couple sub-photospheric simulations to models of the solar atmosphere and corona will also be presented. Title: New coupled models of emerging magnetic flux in active regions Authors: Abbett, W.; Ledvina, S.; Fisher, G. Bibcode: 2002ocnd.confE..22A Altcode: No abstract at ADS Title: How do emerging magnetic fields affect the solar coronal field configuration? Authors: LI, Y.; Luhmann, J. G.; Abbett, W.; Linker, J.; Lionello, R.; Mikic, Z. Bibcode: 2001AGUFMSH11C0719L Altcode: Experiments are carried out to study the coronal field response to an emerging active region into a simple background global magnetic field using potential field source surface models. The emerging active region used is the radial component of the magnetic field of an emerging flux rope from an ANMHD simulation. When the active region is emerging into a dipole field, it introduces polar coronal hole extensions, warps the source surface neutral lines, and changes the field line connections. The active region internal field line connections are also changed to be different from an isolated active region. The relative strength of the background and active region affect the extent of the changes that occur. The field distribution of the background global field is important, and different background with the same emerging active region may result in different coronal features. A few examples of different background fields with the emerging active region will be presented and compared. A global MHD simulation is also in preparation using the same global magnetic field with the emerging active region as the boundary condition. Title: A Magnetohydrodynamic Test of the Wang-Sheeley Model Authors: Ledvina, S. A.; Abbett, W. P.; Li, Y.; Luhmann, J. G. Bibcode: 2001AGUFMSH31A0695L Altcode: The Wang-Sheeley empirical model relates the solar wind speed observed at the Earth with the divergence rate of magnetic flux tubes expanding in the solar corona. This model is based on a statistically significant correlation between an open flux tube divergence parameter "fs" derived from photospheric field synoptic maps, and satellite observations of the solar wind speed. They found that the fast solar wind emanates from regions of small magnetic divergence, while slow solar wind comes from regions of high magnetic divergence. Arge and Pizzo (2000) have since improved the reliability of the Wang-Sheeley model by including an empirical function that relates the magnetic expansion factor to the solar wind speed at the source surface, and a scheme to account for stream interactions as the solar wind propagates outward. We use a three-dimensional MHD model of the solar corona to empirically test the Wang-Sheely model and the improvements made by Arge and Pizzo. These results may provide insight into what additional heating may be necessary in different flux tube geometries in order to obtain to the observed relationship with solar Title: Flux-loss of buoyant ropes interacting with convective flows Authors: Dorch, S. B. F.; Gudiksen, B. V.; Abbett, W. P.; Nordlund, Å. Bibcode: 2001A&A...380..734D Altcode: 2001astro.ph.10205D We present 3-d numerical magneto-hydrodynamic simulations of a buoyant, twisted magnetic flux rope embedded in a stratified, solar-like model convection zone. The flux rope is given an initial twist such that it neither kinks nor fragments during its ascent. Moreover, its magnetic energy content with respect to convection is chosen so that the flux rope retains its basic geometry while being deflected from a purely vertical ascent by convective flows. The simulations show that magnetic flux is advected away from the core of the flux rope as it interacts with the convection. The results thus support the idea that the amount of toroidal flux stored at or near the bottom of the solar convection zone may currently be underestimated. Title: New Coupled Models of Magnetic Flux in Active Regions Authors: Abbett, W. P.; Ledvina, S. A.; Fisher, G. H.; MacNeice, P. Bibcode: 2001AGUFMSH11C0727A Altcode: We report progress in our efforts to use the publicly available domain decomposition and adaptive mesh refinement framework ``PARAMESH'' to couple our 3D anelastic MHD (ANMHD) model of active region magnetic flux in the solar convection zone with a simple, fully compressible ZEUS3D MHD model of the photosphere, transition region, and low corona. Title: 3-D MHD Simulations of Flux Tube Emergence Authors: Abbett, W. P.; Fisher, G. H. Bibcode: 2001AGUSM..SH41A10A Altcode: We present initial results from coupled 3-D MHD simulations of twisted magnetic flux tubes that have risen through a model solar convection zone and emerged into the lower corona. We use the anelastic code ``ANMHD'' to simulate the rise of buoyant flux tubes through the solar convection zone, and use this data to generate a photospheric boundary that drives a simple simulation of the solar transition region and corona using a modified version of the publicly available code ``ZEUS3D'' Title: Initial Behavior of a Buoyant Magnetic Flux Tube Imbedded in a Rotating Medium Authors: Fisher, G. H.; Abbett, W. P. Bibcode: 2001AGUSM..SP51B11F Altcode: In a non-rotating medium with gravity, an initially stationary, buoyant, untwisted magnetic flux tube will generate 2 counter-rotating vortices as it begins rising. In a 2-D geometry, these vortices ultimately split the flux tube into two fragments, which then repel one another. The trajectory of the flux tube fragments can be predicted extremely well by using a simple analytical treatment based on the initial behavior of the flux tube (see e.g. Longcope, Fisher, and Arendt 1996, Ap.J. 464, 999). Numerical simulations in both 2-D and 3-D geometries show that rotation dramatically changes this behavior, acting to strongly suppress magnetic flux tube fragmentation (see e.g. Wissink et al. 2000, Ap.J. 536, 982 and Abbett, Fisher, & Fan 2001, Ap. J. 546, 1194). Coriolis forces deflect the motions that otherwise would result in strong circulation around the flux tube fragments. In the same spirit as the analytical treatment of Longcope, Fisher & Arendt, we derive equations that describe the initial flow pattern for a 2-D buoyant, untwisted magnetic flux tube rising in a rotating medium, and compare these results to those from numerical simulations. Title: The Emergence of Magnetic Flux in Active Regions Authors: Abbett, W. P.; Fisher, G. H.; Fan, Y. Bibcode: 2001IAUS..203..225A Altcode: Over the past decade, ``thin flux tube'' models have proven successful in explaining many properties of active regions in terms of magnetic flux tube dynamics in the solar interior. Unfortunately, recent, more sophisticated two-dimensional MHD simulations of the emergence of magnetic flux have shown that many of the assumptions adopted in the thin flux tube approximation are invalid. For example, unless the flux tubes exhibit a large amount of initial field line twist --- and observations of emerging active regions suggest they do not --- they will fragment (break apart) before they are able to emerge through the surface. We attempt to resolve this paradox using a number of 3-D MHD simulations (in the anelastic approximation) that describe the rise and fragmentation of twisted magnetic flux tubes. We find that the degree of fragmentation of an evolving Omega-loop depends strongly on the three-dimensional geometry of the tube --- the greater the apex curvature, the lesser the degree of fragmentation for a fixed amount of initial twist. We also find that the Coriolis force plays a dynamically important role in the evolution and emergence of magnetic flux. We are able to infer general observational characteristics of the emerging flux, and compare our theoretical data with recent observations. Title: The Effects of Rotation on the Evolution of Rising Omega Loops in a Stratified Model Convection Zone Authors: Abbett, W. P.; Fisher, G. H.; Fan, Y. Bibcode: 2001ApJ...546.1194A Altcode: 2000astro.ph..8501A We present three-dimensional MHD simulations of buoyant magnetic flux tubes that rise through a stratified model convection zone in the presence of solar rotation. The equations of MHD are solved in the anelastic approximation, and the results are used to determine the effects of solar rotation on the dynamic evolution of an Ω-loop. We find that the Coriolis force significantly suppresses the degree of fragmentation at the apex of the loop during its ascent toward the photosphere. If the initial axial field strength of the tube is reduced, then, in the absence of forces due to convective motions, the degree of apex fragmentation is also reduced. Our simulations confirm the results of thin flux-tube calculations that show the leading polarity of an emerging active region positioned closer to the equator than the trailing polarity and the trailing leg of the loop oriented more vertically than the leading leg. We show that the Coriolis force slows the rise of the tube and induces a retrograde flow in both the magnetized and unmagnetized plasma of an emerging active region. Observationally, we predict that this flow will appear to originate at the leading polarity and will terminate at the trailing polarity. Title: Erratum: The Three-dimensional Evolution of Rising, Twisted Magnetic Flux Tubes in a Gravitationally Stratified Model Convection Zone Authors: Abbett, W. P.; Fisher, G. H.; Fan, Y. Bibcode: 2000ApJ...542.1119A Altcode: In the article ``The Three-dimensional Evolution of Rising, Twisted Magnetic Flux Tubes in a Gravitationally Stratified Model Convection Zone'' by W. P. Abbett, G. H. Fisher, and Y. Fan (ApJ, 540, 548 [2000]), an error was introduced into one of the equations during the production process. A cross product symbol was mistakenly removed from equation (2). The corrected equation is as follows: ρ0(∂v/∂t+v˙∇v)= -∇p11g + 1/4π (∇XB)XB+∇˙Π. The Press sincerely apologizes for this error. Title: The Three-dimensional Evolution of Rising, Twisted Magnetic Flux Tubes in a Gravitationally Stratified Model Convection Zone Authors: Abbett, W. P.; Fisher, G. H.; Fan, Y. Bibcode: 2000ApJ...540..548A Altcode: 2000astro.ph..4031A We present three-dimensional numerical simulations of the rise and fragmentation of twisted, initially horizontal magnetic flux tubes that evolve into emerging Ω-loops. The flux tubes rise buoyantly through an adiabatically stratified plasma that represents the solar convection zone. The MHD equations are solved in the anelastic approximation, and the results are compared with studies of flux-tube fragmentation in two dimensions. We find that if the initial amount of field line twist is below a critical value, the degree of fragmentation at the apex of a rising Ω-loop depends on its three-dimensional geometry: the greater the apex curvature of a given Ω-loop, the lesser the degree of fragmentation of the loop as it approaches the photosphere. Thus, the amount of initial twist necessary for the loop to retain its cohesion can be reduced substantially from the two-dimensional limit. The simulations also suggest that, as a fragmented flux tube emerges through a relatively quiet portion of the solar disk, extended crescent-shaped magnetic features of opposite polarity should form and steadily recede from one another. These features eventually coalesce after the fragmented portion of the Ω-loop emerges through the photosphere. Title: 3D MHD Simulation of Flux Tube Dynamics: Comparison with Thin Flux Tube Models Authors: Fisher, G. H.; Abbett, W. P.; Fan, Y. Bibcode: 2000SPD....31.0135F Altcode: 2000BAAS...32..807F We have used the anelastic 3D MHD code ``ANMHD'' to perform simulations of emerging magnetic flux tubes moving in a gravitationally stratified background model representing the solar convection zone. The MHD model is computed within a local Cartesian geometry, with Coriolis forces included, using the f-plane approximation. The evolution of flux tubes computed with the code will be compared and contrasted with results computed with the thin flux tube approximation. This work was supported by NASA and NSF. Title: The Cohesion of 3-D Magnetic Flux Tubes in a Rotating, Stratified Model Convection Zone Authors: Abbett, W. P.; Fisher, G.; Fan, Y. Bibcode: 2000SPD....31.0136A Altcode: 2000BAAS...32..807A We present the latest results from a series of 3-D MHD simulations in the anelastic approximation that describe the rise of magnetic flux tubes through an adiabatically stratified model convection zone. The effects of solar rotation and the Coriolis force are included in the models. The simulations begin with initially horizontal magnetic flux tubes which subsequently evolve into Omega-loops. We find that the degree of ``fragmentation'' at the apex of a rising Omega-loop depends strongly on both the three-dimensional geometry of the loop, and on the field strength along the axis of the initial tube. Loops with a relatively high degree of apex curvature, and of moderate to low initial axial field strength retain their cohesion throughout their rise toward the photosphere --- even in the absence of initial field line twist. We are able to infer general observational characteristics of the emerging flux, and compare our theoretical data with recent observations of active regions. This work was funded by NSF grants AST 98-19727 and ATM 98-96316, and by NASA grant NAGS-8468. The computations were partially supported by the National Center for Atmospheric Research, and the National Computational Science Alliance. Title: Magnetic flux tubes inside the sun Authors: Fisher, G. H.; Fan, Y.; Longcope, D. W.; Linton, M. G.; Abbett, W. P. Bibcode: 2000PhPl....7.2173F Altcode: Bipolar magnetic active regions are the largest concentrations of magnetic flux on the Sun. In this paper, the properties of active regions are investigated in terms of the dynamics of magnetic flux tubes which emerge from the base of the solar convection zone, where the solar cycle dynamo is believed to operate, to the photosphere. Flux tube dynamics are computed with the ``thin flux tube'' approximation, and by using magnetohydrodynamics simulation. Simulations of active region emergence and evolution, when compared with the known observed properties of active regions, have yielded the following results: (1) The magnetic field at the base of the convection zone is confined to an approximately toroidal geometry with a field strength in the range 3-10×104 G. The latitude distribution of the toroidal field at the base of the convection zone is more or less mirrored by the observed active latitudes; there is not a large poleward drift of active regions as they emerge. The time scale for emergence of an active region from the base of the convection zone to the surface is typically 2-4 months. (2) The tilt of active regions is due primarily to the Coriolis force acting to twist the diverging flows of the rising flux loops. The dispersion in tilts is caused primarily by the buffeting of flux tubes by convective motions as they rise through the interior. (3) Coriolis forces also bend active region flux tube shapes toward the following (i.e., antirotational) direction, resulting in a steeper leg on the following side as compared to the leading side of an active region. When the active region emerges through the photosphere, this results in a more rapid separation of the leading spots away from the magnetic neutral line as compared to the following spots. This bending motion also results in the neutral line being closer to the following magnetic polarity. (4) The properties of the strongly sheared, flare productive δ-spot active regions can be accounted for by the dynamics of highly twisted Ω loops that succumb to the helical kink instability as they emerge through the solar interior. Title: Dynamic Models of Optical Emission in Impulsive Solar Flares Authors: Abbett, William P.; Hawley, Suzanne L. Bibcode: 1999ApJ...521..906A Altcode: No abstract at ADS Title: Non-LTE Dynamic Models of Optical Emission During Solar Flares Authors: Abbett, W. P. Bibcode: 1999AAS...194.2206A Altcode: 1999BAAS...31..860A The results from a non-LTE radiative-hydrodynamic model of a flare loop, from its apex in the corona to its footpoints in the photosphere, are presented. The effects of non-thermal heating of the lower solar atmosphere by accelerated electrons during the impulsive phase, and the subsequent effects of soft X-ray irradiation of the chromosphere from the flare-heated transition region and corona during the beginning of the gradual phase are investigated. During the impulsive phase, the models show a significant continuum (or ``white light'') brightening resulting from increased hydrogen recombination radiation in the upper chromosphere at the point where the accelerated electrons deposit the bulk of their energy. Additionally, the models produce a measurable time lag between the brightening of the near wings of H-alpha and the brightening of the Paschen continuum. This work was funded in part by NSF grants AST 96-16886 and AST 94-57455. The computations were partially supported by the National Computational Science Alliance, and utilized the NCSA SGI/CRAY Power Challenge Array. Title: Dynamical Solar Flare Model Atmospheres Authors: Abbett, W. P.; Hawley, S. L. Bibcode: 1999ASPC..158..212A Altcode: 1999ssa..conf..212A No abstract at ADS Title: A Theoretical Investigation of Optical Emission in Solar Flares Authors: Abbett, William Paul Bibcode: 1998PhDT.........1A Altcode: 1998PhDT........91A; 1998PhDT........87A A dynamic theoretical model of a flare loop from its footpoints in the photosphere to its apex in the corona is presented, and the effects of non-thermal heating of the lower atmosphere by accelerated electrons and soft X-ray irradiation from the flare heated transition region and corona are investigated. Important transitions of hydrogen, helium, and singly ionized calcium and magnesium are treated in non-LTE. Three main conclusions are drawn from the models. First, even the strongest of impulsive events can be described as having two phases: a gentle phase characterized by a state of near equilibrium, and an explosive phase characterized by large material flows, and strong hydrodynamic waves and shocks. During the gentle phase, one or possibly two temperature 'plateaus' form in the upper chromosphere. The line emission generated in these regions produces profiles that are generally symmetric and undistorted, in contrast to emission produced during the explosive phase, where large velocity gradients that occur in the upper atmosphere produce line profiles that are highly asymmetric and show large emission peaks and troughs. Second, a significant continuum (or 'white light') brightening results from increased hydrogen recombination radiation in the upper chromosphere at the point where the accelerated electrons deposit the bulk of their energy. Third, there exists a measurable time lag between the brightening of the near wings of Hα and the brightening of the Paschen continuum. This delay is controlled by the amount of time it takes for electron densities in the upper chromosphere to become high enough, and the densities of hydrogen atoms in high energy bound states to become low enough, to allow the number of recombinations to dominate the number of photoionizations in the region. Title: Non-LTE Radiative-hydrodynamic Models of Solar Flares Authors: Abbett, William P.; Hawley, Suzanne L. Bibcode: 1997BAAS...29Q1120A Altcode: No abstract at ADS Title: Solar Convection: Comparison of Numerical Simulations and Mixing-Length Theory Authors: Abbett, William P.; Beaver, Michelle; Davids, Barry; Georgobiani, Dali; Rathbun, Pamela; Stein, Robert F. Bibcode: 1997ApJ...480..395A Altcode: We compare the results of realistic numerical simulations of convection in the superadiabatic layer near the solar surface with the predictions of mixing-length theory. We find that the peak values of such quantities as the temperature gradient, the temperature fluctuations, and the velocity fluctuations, as well as the entropy jump in the simulation, can be reproduced by mixing-length theory for a ratio of mixing length to pressure scale height α ~ 1.5. However, local mixing-length theory neither reproduces the profiles of these variables with depth nor allows penetration of convective motions into the overlying stable photosphere.