Author name code: fluri ADS astronomy entries on 2022-09-14 author:"Fluri, D.M." ------------------------------------------------------------------------ Title: Polarimetry of Extrasolar Planets Authors: Berdyugin, A.; Berdyugina, S.; Fluri, D.; Piirola, V. Bibcode: 2011ASPC..449..389B Altcode: Polarimetry is a powerful technique for detecting directly the starlight that is scattered in a planetary atmosphere and, thus, possesses information on its geometry, chemistry, and thermodynamics. Recently, we have started a polarimetric survey of nearby planetary systems with hot Jupiters closely orbiting their host stars using the DiPol polarimeter at the KVA telescope and the TurPol polarimeter at the Nordic Optical Telescope, La Palma. Here we present our first results and discuss orbital parameters of the HD 189733 system and scattering properties of its planet. Title: NLTE modeling of Stokes vector center-to-limb variations in the CN violet system Authors: Shapiro, A. I.; Fluri, D. M.; Berdyugina, S. V.; Bianda, M.; Ramelli, R. Bibcode: 2011A&A...529A.139S Altcode: 2011arXiv1103.2524S Context. The solar surface magnetic field is connected with and even controls most of the solar activity phenomena. Zeeman effect diagnostics allow for measuring only a small fraction of the fractal-like structured magnetic field. The remaining hidden magnetic fields can only be accessed with the Hanle effect.
Aims: Molecular lines are very convenient for applying the Hanle effect diagnostics thanks to the broad range of magnetic sensitivities in a narrow spectral region. With the UV version of the Zurich Imaging Polarimeter ZIMPOL II installed at the 45 cm telescope of the Istituto Ricerche Solari Locarno (IRSOL), we simultaneously observed intensity and linear polarization center-to-limb variations in two spectral regions containing the (0, 0) and (1, 1) bandheads of the CN B2Σ - X2Σ system. Here we present an analysis of these observations.
Methods: We have implemented coherent scattering in molecular lines into an NLTE radiative transfer code. A two-step approach was used. First, we separately solved the statistical equilibrium equations and compute opacities and intensity while neglecting polarization. Then we used these quantities as input for calculating scattering polarization and the Hanle effect.
Results: We have found that it is impossible to fit the intensity and polarization simultaneously at different limb angles in the framework of standard 1D modeling. The atmosphere models that provide correct intensity center-to-limb variations fail to fit linear polarization center-to-limb variations due to lacking radiation-field anisotropy. We had to increase the anisotropy by means of a specially introduced free parameter. This allows us to successfully interpret our observations. We discuss possible reasons for underestimating the anisotropy in the 1D modeling. Title: Polarized Reflected Light from the Exoplanet HD189733b: First Multicolor Observations and Confirmation of Detection Authors: Berdyugina, S. V.; Berdyugin, A. V.; Fluri, D. M.; Piirola, V. Bibcode: 2011ApJ...728L...6B Altcode: 2011arXiv1101.0059B We report the first multicolor polarimetric measurements (UBV bands) for the hot Jupiter HD189733b and confirm our previously reported detection of polarization in the B band. The wavelength dependence of polarization indicates the dominance of Rayleigh scattering with a peak in the blue B and U bands of ~10-4 ± 10-5 and at least a factor of two lower signal in the V band. The Rayleigh-like wavelength dependence, also detected in the transmitted light during transits, implies a rapid decrease of the polarization signal toward longer wavelengths. Therefore, the nondetection by Wiktorowicz, based on a measurement integrated within a broad passband covering the V band and partly covering the B and R bands, is inconclusive and consistent with our detection in B. We discuss possible sources of the polarization and demonstrate that effects of incomplete cancellation of stellar limb polarization due to starspots or tidal perturbations are negligible as compared with scattering polarization in the planetary atmosphere. We compare the observations with a Rayleigh-Lambert model and determine effective radii and geometrical albedos for different wavelengths. We find a close similarity of the wavelength-dependent geometrical albedo with that of the Neptune atmosphere, which is known to be strongly influenced by Rayleigh and Raman scattering. Our result establishes polarimetry as a reliable means for directly studying exoplanetary atmospheres. Title: Sunspot Umbra Atmosphere from Full Stokes Inversion Authors: Wenzel, R.; Berdyugina, S. V.; Fluri, D. M.; Arnaud, J.; Sainz-Dalda, A. Bibcode: 2010ASPC..428..117W Altcode: 2010arXiv1003.5114W Sunspots are prominent manifestations of the solar cycle and provide key constraints for understanding its operation. Also, knowing the internal structure of sunspots allows us to gain insights on the energy transport in strong magnetic fields and, thus, on the processes inside the convection zone, where solar magnetic fields are generated and amplified before emerging at the surface on various scales, even during solar minima. In this paper, we present results of a spectropolarimetric analysis of a sunspot observed during the declining phase of solar cycle 23. By inversion of the full Stokes spectra, observed in several spectral regions in the optical at the THEMIS facility, we infer the height dependence of physical quantities such as the temperature and the magnetic field strength for different sunspot regions. The simultaneous use of atomic (Fe I 5250.2 and 5250.6 Å) and highly temperature-sensitive molecular (TiO 7055 Å and MgH 5200 Å) lines allows us to improve a model of the sunspot umbra. Title: Orbital parameters of extrasolar planets derived from polarimetry Authors: Fluri, D. M.; Berdyugina, S. V. Bibcode: 2010A&A...512A..59F Altcode: 2010arXiv1001.3091F Context. Polarimetry of extrasolar planets becomes a new tool for their investigation, which requires the development of diagnostic techniques and parameter case studies.
Aims: Our goal is to develop a theoretical model which can be applied to interpret polarimetric observations of extrasolar planets. Here we present a theoretical parameter study that shows the influence of the various involved parameters on the polarization curves. Furthermore, we investigate the robustness of the fitting procedure. We focus on the diagnostics of orbital parameters and the estimation of the scattering radius of the planet.
Methods: We employ the physics of Rayleigh scattering to obtain polarization curves of an unresolved extrasolar planet. Calculations are made for two cases: (i) assuming an angular distribution for the intensity of the scattered light as from a Lambert sphere and for polarization as from a Rayleigh-type scatterer; and (ii) assuming that both the intensity and polarization of the scattered light are distributed according to the Rayleigh law. We show that the difference between these two cases is negligible for the shapes of the polarization curves. In addition, we take the size of the host star into account, which is relevant for hot Jupiters orbiting giant stars.
Results: We discuss the influence of the inclination of the planetary orbit, the position angle of the ascending node, and the eccentricity on the linearly polarized light curves both in Stokes Q/I and U/I. We also analyze errors that arise from the assumption of a point-like star in numerical modeling of polarization as compared to consistent calculations accounting for the finite size of the host star. We find that errors due to the point-like star approximation are reduced with the size of the orbit, but still amount to about 5% for known hot Jupiters. Recovering orbital parameters from simulated data is shown to be very robust even for very noisy data because the polarization curves react sensitively to changes in the shape and orientation of the orbit.
Conclusions: The proposed model successfully diagnoses orbital parameters of extrasolar planets and can also be applied to predict polarization curves of known exoplanets. Polarization curves of extrasolar planets thus provide an ideal tool to determine parameters that are difficult to obtain with other methods, namely inclination and position angle of the ascending node of orbits as well as true masses of extrasolar planets. Title: Nonlinear deconvolution with deblending: a new analyzing technique for spectroscopy Authors: Sennhauser, C.; Berdyugina, S. V.; Fluri, D. M. Bibcode: 2009A&A...507.1711S Altcode: Context: Spectroscopy data in general often deals with an entanglement of spectral line properties, especially in the case of blended line profiles, independently of how high the quality of the data may be. In stellar spectroscopy and spectropolarimetry, where atomic transition parameters are usually known, the use of multi-line techniques to increase the signal-to-noise ratio of observations has become common practice. These methods extract an average line profile by means of either least squares deconvolution (LSD) or principle component analysis (PCA). However, only a few methods account for the blending of line profiles, and when they do, they assume that line profiles add linearly.
Aims: We abandon the simplification of linear line-adding for Stokes I and present a novel approach that accounts for the nonlinearity in blended profiles, also illuminating the process of a reasonable deconvolution of a spectrum. Only the combination of those two enables us to treat spectral line variables independently, constituting our method of nonlinear deconvolution with deblending (NDD). The improved interpretation of a common line profile achieved compensates for the additional expense in calculation time, especially when it comes to the application to (Zeeman) doppler imaging (ZDI).
Methods: By examining how absorption lines of different depths blend with each other and describing the effects of line-adding in a mathematically simple, yet physically meaningful way, we discover how it is possible to express a total line depth in terms of a (nonlinear) combination of contributing individual components. Thus, we disentangle blended line profiles and underlying parameters in a truthful manner and strongly increase the reliability of the common line patterns retrieved.
Results: By comparing different versions of LSD with our NDD technique applied to simulated atomic and molecular intensity spectra, we are able to illustrate the improvements provided by our method to the interpretation of the recovered mean line profiles. As a consequence, it is possible for the first time to retrieve an intrinsic line pattern from a molecular band, offering the opportunity to fully include them in a NDD-based ZDI. However, we also show that strong line broadening deters the existence of a unique solution for heavily blended lines such as in molecular bandheads. Title: Zeeman-Doppler Imaging of Stellar Magnetic Fields with Atomic and Molecular Lines Authors: Sennhauser, C.; Berdyugina, S. V.; Fluri, D. M. Bibcode: 2009ASPC..405..543S Altcode: We have developed a new code for Zeeman-Doppler Imaging (ZDI) of stellar magnetic fields using the Occamian approach for solving inverse problems. The inversions are applied to Stokes I and V parameter sets obtained by solving the full set of polarized radiative transfer equations for both atomic and molecular lines. For the first time we demonstrate that molecular polarization strongly constrains the ZDI maps and is crucial for obtaining a realistic solution from Stokes I and V only observed at a few stellar rotational phases. We also present an enhanced LSD technique, which allows analytic separation of blended line profiles. The resulting LSD profiles are free from systematic effects induced by blends, which are typical for other multi-line techniques. Title: Solar Magnetic Field Diagnostics with the Molecular Hanle Effect Authors: Shapiro, A. I.; Fluri, D. M.; Berdyugina, S. V. Bibcode: 2009ASPC..405..343S Altcode: Weak entangled magnetic fields with mixed polarity occupy the main part of the quiet solar photosphere. While the Zeeman effect diagnostics fail to measure such fields due to cancellation in polarization, the Hanle effect, accessible through the second solar spectrum, provides us with a very sensitive tool for studying the distribution of weak magnetic fields on the Sun. Molecular lines are valuable for magnetic field diagnostics thanks to their broad range of magnetic sensitivities within narrow spectral regions, so that the differential Hanle effect can be employed, which greatly reduces the model dependence of deduced magnetic field strengths. Here we present our recent results on the diagnostic of solar turbulent magnetic fields with the help of CN transitions in the violet system. In addition, we have implemented modeling of coherent scattering in molecular lines into a non-LTE radiative transfer code. Together with the Hanle effect theory this provides us with a realistic model for studying turbulent magnetic fields. Title: FeH -- A Valuable Magnetic Diagnostic Tool Authors: Afram, N.; Berdyugina, S. V.; Fluri, D. M. Bibcode: 2009ASPC..405..349A Altcode: Transitions of the FeH molecule are dominating features in the near-infrared spectra of sunspots, starspots and red and brown dwarfs. Their remarkable magnetic sensitivity provides an excellent opportunity to study magnetic fields in these cool objects. However, the absence of an adequate theoretical model of the molecule capable to reproduce its observed magnetic properties limits the usage of these transitions in solar and stellar magnetic studies. Here we present the first successful semi-empirical model of the FeH F4Δ -- X4Δ system based on the Hamiltonian for the intermediate Hund's case (a-b) and a perturbation from a nearby electronic state, resulting in modification of the spin-orbit and spin-spin coupling. Our model is able to reproduce the broadening of FeH lines due to the Zeeman effect and their polarization signatures detected in sunspots and starspots and, for the first time, provides reliable Landé factors. This opens a door for developing further applications for red and brown dwarfs. Title: LSD-a nonlinear approach Authors: Sennhauser, C.; Berdyugina, S. V.; Fluri, D. M. Bibcode: 2009AIPC.1094..732S Altcode: 2009csss...15..732S Stellar spectra usually are very limited in the signal-to-noise ratio (SNR) that can be obtained. In order to increase their informative value, different techniques have been developed in the past ten years which combine multiple spectral lines by cutting out individual line profiles and analysing them by means of least-squares errors or PCA. They usually neglect that the bulk of lines are blended, resulting in artificial broadening of the retrieved common line pattern, while those that care to disentangle blended profiles assume linear line adding.

Based on the well-known least-squares deconvolution (LSD) method, we developed a new technique, which truly accounts for blended profiles and deconvolves them in a physically meaningful way by taking into account the nonlinearity when abandoning the regime of optically thin lines. The so-called interpolation formula by M. Minnaert is a unique tool to describe a line profile both in the optically thin and the optically thick regime. It enables us to write a total line depth in terms of a (nonlinear) combination of contributing individual components.

Applying different versions of LSD, among them our nonlinear (NL-) LSD, to simulated atomic and molecular intensity spectra shows the unrivaled functionality of our new method in terms of interpretability of the retrieved common line pattern. For the first time it is possible to recover an intrinsic line pattern from a molecular band. Title: Sunspot Model Atmosphere from Inversion of Stokes Profiles Authors: Wenzel, R.; Berdyugina, V. S.; Fluri, D. M.; Arnaud, J.; Sainz Dalda, A. Bibcode: 2008ESPM...12.2.24W Altcode: We present results of a spectropolarimetric analysis of sunspots. By inversion of full Stokes spectra observed in serveral spectral regions in the optical at the THEMIS facility we infer the height dependence of physical quantities such as the temperature, LOS velocity and magnetic field for different sunspot regions. The wide spectral range and the use of TiO and MgH transitions, which are extremely temperature sensitive and can be treated in LTE even in higher layers, allow us to extend and improve a sunspot model atmosphere. Title: The FeH F4Δ-X4Δ system. Creating a valuable diagnostic tool to explore solar and stellar magnetic fields Authors: Afram, N.; Berdyugina, S. V.; Fluri, D. M.; Solanki, S. K.; Lagg, A. Bibcode: 2008A&A...482..387A Altcode: Context: Lines of diatomic molecules are ideal tools for studying cool stellar atmospheres and the internal structure of sunspots and starspots, given their temperature and pressure sensitivities, which are typically higher than in atomic lines. The Wing-Ford FeH F4Δ-X4Δ system represents such a diatomic molecule that is, in addition, highly sensitive to magnetic fields. The current theoretical description of those transitions that include the involved molecular constants, however, are only based on intensity measurements because polarimetric observations have not been available until now, which limits their diagnostic value. Furthermore, the theory has so far been optimized to reproduce energy levels and line strengths without taking magnetic sensitivities into account.
Aims: The FeH F4Δ-X4Δ system is produced by transitions between two electronic states with the coupling of the angular momenta that is intermediate between limiting Hund's cases (a) and (b). Our goal is to investigate the diagnostic capabilities of the current theoretical description of the molecule FeH.
Methods: Using the most precise available Hamiltonian, we carried out the perturbation calculation of the molecular Zeeman effect for this transition and computed the Landé factors of the energy levels and of transitions. We extracted Landé factors from a comparison of observed and calculated Stokes I and V profiles. Certain spectral lines, most frequently with high magnetic sensitivity, exhibited discrepancies between the theory and observations. We extended the theoretical model with a semi-empirical approach to obtain a diagnostic tool that is able to reproduce many of the interesting spectral lines.
Results: We find that the current theory successfully reproduces the magnetic properties of a large number of lines in the FeH F4Δ-X4Δ system and that the modified Hamiltonian allows us to synthesize and successfully reproduce the most sensitive lines. Thus, our observations have provided valuable constraints for determining empirical molecular constants and Landé factors.
Conclusions: The FeH F4Δ-X4Δ system is found to be a very sensitive magnetic diagnostic tool. Polarimetric data of these lines, in contrast to intensity measurements, provide us with more direct and detailed information to study the coolest parts of sunspot and starspot umbrae, as well as cool active dwarfs. Title: First Direct Detection of Magnetic Fields in Starspots and Stellar Chromospheres Authors: Berdyugina, S. V.; Fluri, D. M.; Afram, N.; Suwald, F.; Petit, P.; Arnaud, J.; Harrington, D. M.; Kuhn, J. R. Bibcode: 2008ASPC..384..175B Altcode: 2008csss...14..175B; 2007astro.ph..3559B Here we report on the first detection of circular polarization in molecular lines formed in cool magnetic regions (starspots) and in chromospheric emission lines formed in hot plages on the surfaces of active stars.

Our survey of G-K-M stars included young main-sequence dwarfs and RS~CVn-type giants and subgiants. All stars were found to possess surface magnetic fields producing Stokes V LSD signals in atomic lines of 0.05% to 0.5%. Several stars clearly showed circular polarization in molecular lines of 0.1% to 1%. The molecular Stokes V signal is reminiscent of that observed in sunspots. Chromospheric magnetic fields were detected on most active targets in Stokes~V profiles of emission lines with peak polarization up to 2%. The observed molecular circular polarization on M dwarfs indicates single-polarity magnetic fields covering at least 10% of the stellar disk. Smaller signals on K stars imply that their magnetic fields are apparently weaker, more entangled than on M dwarfs, or more diluted by the bright photosphere. Title: First Detection of Polarized Scattered Light from an Exoplanetary Atmosphere Authors: Berdyugina, S. V.; Berdyugin, A. V.; Fluri, D. M.; Piirola, V. Bibcode: 2008ApJ...673L..83B Altcode: 2007arXiv0712.0193B We report the first direct detection of an exoplanet in the visible polarized light. The transiting planet HD 189733b is one of the very hot Jupiters with shortest periods and, thus, smallest orbits, which makes them ideal candidates for polarimetric detections. We obtained polarimetric measurements of HD 189733 in the B band well distributed over the orbital period and detected two polarization maxima near planetary elongations with a peak amplitude of ~2 × 10-4. Assuming Rayleigh scattering, we estimated the effective size of the scattering atmosphere (Lambert sphere) to be 1.5 ± 0.2 RJ, which is 30% larger than the radius of the opaque body previously inferred from transits. If the scattering matter fills the planetary Roche lobe, the lower limit of the geometrical albedo can be estimated as 0.14. The phase dependence of polarization indicates that the planetary orbit is oriented almost in a north-south direction with a longitude of ascending node Ω = (16° or 196°) ± 8°. We obtain independent estimates of the orbit inclination i = 98° ± 8° and eccentricity e = 0.0 (with an uncertainty of 0.05), which are in excellent agreement with values determined previously from transits and radial velocities. Our findings clearly demonstrate the power of polarimetry and open a new dimension in exploring exoplanetary atmospheres even for systems without transits. Title: Hanle effect in the CN violet system with LTE modeling Authors: Shapiro, A. I.; Berdyugina, S. V.; Fluri, D. M.; Stenflo, J. O. Bibcode: 2007A&A...475..349S Altcode: 2007arXiv0709.2515S Context: Weak entangled magnetic fields with mixed polarity occupy the main part of the quiet Sun. The Zeeman effect diagnostics fails to measure such fields because of cancellation in circular polarization. However, the Hanle effect diagnostics, accessible through the second solar spectrum, provides us with a very sensitive tool for studying the distribution of weak magnetic fields on the Sun.
Aims: Molecular lines are very strong and even dominate in some regions of the second solar spectrum. The CN B {}2 Σ - X {}2 Σ system is one of the richest and most promising systems for molecular diagnostics and well suited for the application of the differential Hanle effect method. The aim is to interpret observations of the CN B {}2 Σ - X {}2 Σ system using the Hanle effect and to obtain an estimation of the magnetic field strength.
Methods: We assume that the CN molecular layer is situated above the region where the continuum radiation is formed and employ the single-scattering approximation. Together with the Hanle effect theory this provides us with a model that can diagnose turbulent magnetic fields.
Results: We have succeeded in fitting modeled CN lines in several regions of the second solar spectrum to observations and obtained a magnetic field strength in the range from 10-30 G in the upper solar photosphere depending on the considered lines.

Tables [see full textsee full textsee full textsee full text]-[see full textsee full textsee full textsee full text] are only available in electronic form at http://www.aanda.org Title: A New Mechanism for Polarizing Light from Obscured Stars Authors: Kuhn, J. R.; Berdyugina, S. V.; Fluri, D. M.; Harrington, D. M.; Stenflo, J. O. Bibcode: 2007ApJ...668L..63K Altcode: 2007arXiv0708.0599K Recent spectropolarimetric observations of Herbig Ae/Be stellar systems show linear polarization variability with wavelength and epoch near their obscured Hα emission. Surprisingly, this polarization is not coincident with the Hα emission peak but is variable near the absorptive part of the line profile. With a new and novel model, we show here that this is evidence of optical pumping-anisotropy of the incident radiation that leads to a linear polarization-dependent optical depth within the intervening hydrogen wind or disk cloud. This effect can yield a larger polarization signal than scattering polarization in these systems. Title: First polarimetric observations and modeling of the FeH F4Δ-X4Δ system Authors: Afram, N.; Berdyugina, S. V.; Fluri, D. M.; Semel, M.; Bianda, M.; Ramelli, R. Bibcode: 2007A&A...473L...1A Altcode: 2007arXiv0708.0298A Context: Lines of diatomic molecules are typically much more temperature and pressure sensitive than atomic lines, which makes them ideal, complementary tools for studying cool stellar atmospheres as well as the internal structure of sunspots and starspots. The FeH F^4Δ-X^4Δ system represents such an example that exhibits in addition a large magnetic field sensitivity. However, the current theoretical descriptions of these transitions including the molecular constants involved are only based on intensity measurements because polarimetric observations have not been available so far, which limits their diagnostic value. Furthermore, the theory was optimized to reproduce energy levels and line strengths without taking the magnetic sensitivities into account.
Aims: We present for the first time spectropolarimetric observations of the FeH F^4Δ-X^4Δ system measured in sunspots to investigate their diagnostic capabilities for probing solar and stellar magnetic fields. In particular, we investigate whether the current theoretical model of FeH can reproduce the observed Stokes profiles including their magnetic properties.
Methods: The polarimetric observations of the FeH F^4Δ-X^4Δ system in Stokes I and V are compared with synthetic Stokes profiles modeled with radiative transfer calculations. This allows us to infer the temperature and the magnetic field strength of the observed sunspots.
Results: We find that the current theory successfully reproduces the magnetic properties of a large number of lines in the FeH F^4Δ-X^4Δ system. In a few cases the observations indicate a larger Zeeman splitting than predicted by the theory. There, our observations have provided additional constraints, which allowed us to determine empirical molecular constants.
Conclusions: The FeH F^4Δ-X^4Δ system is found to be a very sensitive magnetic diagnostic tool. Polarimetric data of these lines, in contrast to intensity measurements, provide us with more direct and detailed information to study the coolest parts of sunspot and starspot umbrae, and cool active dwarfs. Title: Molecular Hanle effect in the Paschen-Back regime Authors: Shapiro, A. I.; Fluri, D. M.; Berdyugina, S. V.; Stenflo, J. O. Bibcode: 2007A&A...461..339S Altcode: Context: The second solar spectrum resulting from coherent scattering is a main tool for diagnostics of turbulent magnetic fields on the Sun. Scattering on diatomic molecules plays an important role in forming this spectrum and even dominates in some spectral regions.
Aims: In a magnetic field electronic states of a molecule are often perturbed via the Paschen-Back effect. Sometimes this perturbation can completely change the spectrum, not only quantitatively, but even qualitatively. Here we calculate molecular scattering properties taking into account the Paschen-Back effect.
Methods: Starting with the Hund's case (a) wave functions as a basis we obtain with the perturbation theory wave functions of the intermediate Hund's case (a-b) in a magnetic field. Using new, perturbed values of the Landé factors and transition amplitudes we calculate the Mueller matrix for coherent scattering at diatomic molecules in the intermediate Hund's case (a-b) and look for the effects that can be caused by the Paschen-Back effect.
Results: We have found a considerable deviation from the Zeeman regime and discuss here the quantitative and qualitative effects on observed polarization signals for the CN B {}2 Σ - X {}2 Σ and MgH B' {}2 Σ - X {}2 Σ systems as examples. Title: Molecular Hanle effect in the Paschen-Back regime: theory and application Authors: Shapiro, A. I.; Berdyugina, S. V.; Fluri, D. M.; Stenflo, J. O. Bibcode: 2007msfa.conf..317S Altcode: The second solar spectrum resulting from coherent scattering is a main tool for diagnostics of turbulent magnetic fields on the Sun. Scattering on diatomic molecules plays an important role in forming this spectrum and even dominates in some spectral regions. In a magnetic field electronic states of a molecule are often perturbed via the Paschen-Back effect. Sometimes this perturbation can completely change the spectrum, not only quantitatively, but even qualitatively. Here we calculate molecular scattering properties taking into account the Paschen-Back effect. We calculate the Mueller matrix for coherent scattering at diatomic molecules in the intermediate Hund's case (a-b) and look for the effects that can be caused by the Paschen-Back effect. We have found a considerable deviation from the Zeeman regime and discuss here the quantitative and qualitative effects on observed polarization signals for the CN B 2 [Sigma] - X 2 [Sigma] system as an example. We show an application of the Hanle effect for the interpretation of observations of Title: Spectro-polarimetry of a sunspot simultaneously in atomic and molecular lines. Authors: Arnaud, J.; Berdyugina, S. V.; Fluri, D. M.; Afram, N. Bibcode: 2007MmSAI..78...89A Altcode: We performed with THEMIS spectro-polarimetric observations simultaneously in various atomic and molecular lines. We present the observations and discuss an important aspect of spectro-polarimetric data reduction: the recentering of the frames in the spectral direction needed before substracting spectra to extract polarized Stokes parameters. We conclude that THEMIS has the unique capability, among present time large solar telescope, of providing polarization data almost free from instrumental effects. Title: Spectro-Polarimetry of a Sunspot in Atomic and Molecular Lines with THEMIS Authors: Arnaud, J.; Berdyugina, S. V.; Fluri, D. M.; Afram, N.; Solanki, S. K.; Raouafi, N. -E. Bibcode: 2006ASPC..358..319A Altcode: We present spectro-polarimetric observations of a sunspot, which were recorded simultaneously with THEMIS in various atomic and molecular lines. These observations include the first full Stokes measurements of the band-head of TiO around 7055 Å. Title: Molecular Diagnostics of the Internal Structure of Starspots and Sunspots Authors: Afram, N.; Berdyugina, S. V.; Fluri, D. M.; Solanki, S. K.; Lagg, A.; Petit, P.; Arnaud, J. Bibcode: 2006ASPC..358..375A Altcode: We have analyzed the usefulness of molecules as a diagnostic tool for studying solar and stellar magnetism with the molecular Zeeman and Paschen-Back effects. In the first part we concentrate on molecules that are observed in sunspots such as MgH and TiO. We present calculated molecular line profiles obtained by assuming magnetic fields of 2-3 kG and compare these synthetic Stokes profiles with spectro-polarimetric observations in sunspots. The good agreement between the theory and observations allows us to turn our attention in the second part to starspots to gain insight into their internal structure. We investigate the temperature range in which the selected molecules can serve as indicators for magnetic fields on highly active cool stars and compare synthetic Stokes profiles with our recent observations. Title: The Molecular Paschen-Back Effect Authors: Berdyugina, S. V.; Fluri, D. M.; Solanki, S. K. Bibcode: 2006ASPC..358..329B Altcode: The molecular Paschen-Back effect (PBE) lacks a detailed description since the problem was first addressed by Hill in 1929. However, many diatomic molecules exhibit the PBE at field strengths typical of sunspots and active cool stars. Recently we have presented a complete theoretical description of the molecular PBE in Hund's cases (a), (b), and all intermediate cases. This description allows us to compute the splitting of levels of any multiplicity and the transitions between them. We find that in the partial PBE regime strongly asymmetric Stokes profiles are produced, whose strengths and asymmetries depend sensitively on the magnetic field. Also, the strength of the forbidden and satellite transitions increases rapidly with field strength, while the strength of the main branch transitions decreases. These signatures hold promise to form the basis of new diagnostics of solar and stellar magnetic fields. Title: Polarized Scattering in Strong Chromospheric Lines: Theory and Its Confrontation with Observations Authors: Fluri, D. M.; Holzreuter, R.; Stenflo, J. O. Bibcode: 2006ASPC..358..237F Altcode: We present the current status of modeling scattering polarization in strong lines and compare it to observations. First, we discuss how the emergent polarization profile depends directly on the source function gradient and the anisotropy of the radiation field. This explains naturally the formation of the triplet peak structure often observed in these strong lines. Then, we investigate the Ca II K line which is of particular interest since it forms high in the chromosphere. The degree of its scattering polarization depends sensitively on atmospheric properties and even provides observational evidence for the presence of cool components in the chromosphere. Therefore, polarized scattering in Ca II K might provide a long searched for, second observational tool (apart from CO molecules) to access the coolest parts of the chromosphere. Title: Detection of the Molecular Zeeman Effect in Circular Polarization on Cool Active Stars Authors: Berdyugina, S. V.; Petit, P.; Fluri, D. M.; Afram, N.; Arnaud, J. Bibcode: 2006ASPC..358..381B Altcode: 2007astro.ph..3560B We report on the first ever detection of circular polarization in molecular lines forming in magnetic regions on the surfaces of active stars. The new observations were obtained with the high-resolution spectro-polarimeter ESPaDOnS recently installed at the Canada-France-Hawaii Telescope. In July 2005 we carried out a survey of 17 G-K-M stars including active main-sequence dwarfs and RS CVn-type giants and subgiants. All stars were found to possess surface magnetic fields producing average atomic Stokes-V signals of 0.05% to 0.5%. Three stars clearly showed circular polarization in molecular lines of 0.5% to 1%. The molecular Stokes-V signal is reminiscent of that observed in sunspots. Title: Hanle Effect in the Paschen-Back Regime Authors: Shapiro, A. I.; Fluri, D. M.; Berdyugina, S. V.; Stenflo, J. O. Bibcode: 2006ASPC..358..311S Altcode: The second solar spectrum resulting from coherent scattering is an important tool for the diagnostics of turbulent magnetic fields on the Sun. Molecular scattering plays an important role in forming this spectrum, and even dominates in some spectral regions. We present a theory that allows us to calculate the Mueller matrix for coherent scattering from diatomic molecules in Hund's intermediate coupling case (a-b) for arbitrary molecular transitions. We performed the calculation of the molecular Hanle effect in the Paschen-Back regime. We found significant differences from the Zeeman regime, and as an example we discuss here, both qualitatively and quantitatively, the effects on observed polarization signals for the CN violet system. Title: First Polarimetric Measurements and Modeling of the Paschen-Back Effect in CaH Transitions Authors: Berdyugina, S. V.; Fluri, D. M.; Ramelli, R.; Bianda, M.; Gisler, D.; Stenflo, J. O. Bibcode: 2006ApJ...649L..49B Altcode: 2006astro.ph.10588B We report the first spectropolarimetric observations and modeling of CaH transitions in sunspots. We have detected strong polarization signals in many CaH lines from the A-X system, and we provide the first successful fit to the observed Stokes profiles using the previously developed theory of the Paschen-Back effect in arbitrary electronic states of diatomic molecules and polarized radiative transfer in molecular lines in stellar atmospheres. We analyze the CaH Stokes profiles together with quasi-simultaneous observations in TiO bands and conclude that CaH provides a valuable diagnostic of magnetic fields in sunspots, starspots, cool stars, and brown dwarfs. Title: Ca II K polarization as a diagnostic of temperature bifurcation Authors: Holzreuter, R.; Fluri, D. M.; Stenflo, J. O. Bibcode: 2006A&A...449L..41H Altcode: Aims.We compute the linearly polarized spectrum of Ca II K caused by coherent scattering and exploit the line for chromospheric diagnosis, with particular attention to temperature bifurcation, by comparing the theory with solar observations.Methods.We numerically solve the statistical equilibrium equations and the radiative transfer equation taking into account polarized coherent scattering with partial frequency redistribution. All calculations are performed in 1D within a plane-parallel atmosphere.Results.We find strong evidence of a chromospheric temperature bifurcation. This suggests that the linearly polarized spectrum of Ca II K might become a valuable tool to study cool components and the dynamics of the chromosphere independently of observations of molecular CO lines and millimeter and sub-millimeter continua. Title: The molecular Zeeman effect and diagnostics of solar and stellar magnetic fields. III. Theoretical spectral patterns in the Paschen-Back regime Authors: Berdyugina, S. V.; Braun, P. A.; Fluri, D. M.; Solanki, S. K. Bibcode: 2005A&A...444..947B Altcode: Many diatomic molecules present in the atmospheres of the Sun and cool stars exhibit the Paschen-Back effect at field strengths typical of sunspots and active cool stars. Here we present a complete theoretical description of the molecular Paschen-Back efect in Hund's cases (a), (b) and all cases intermediate to them. This description allows us to compute the splitting of levels of any multiplicity and the transitions between them. We also introduce a generalized description of the effective magnetic Landé factor applicable not just in the Zeeman regime, but also in the Paschen-Back regime. We find that in the regime of the partial Paschen-Back effect strongly asymmetric Stokes profiles are produced, whose strengths and asymmetries depend sensitively on the magnetic field. In the regime of the complete Paschen-Back effect the profiles become symmetric again (although they may be strongly shifted). The strength of the forbidden and satellite transitions increases rapidly with field strength in the partial Paschen-Back regime, while the strength of the main branch transitions decreases. These signatures hold promise to form the basis of new diagnostics of solar and stellar magnetic fields. Title: Interpretation of Solar and Stellar Activity in terms of Dynamo Modes Authors: Fluri, D. M.; Berdyugina, S. V. Bibcode: 2005ASPC..346..167F Altcode: The magnetic activity on active, cool stars and on the Sun is spatially organized on large scales and exhibits cyclic behavior on various time scales. In particular, the biggest active regions tend to appear mainly at two preferred longitudes on opposite sides. Therefore, a physical mechanism has to exist that breaks the axial symmetry of the global magnetic field. This implies that in addition to the axisymmetric dipole a non-axisymmetric dynamo mode should be excited in the Sun. We discuss possible dynamo mode configurations that can explain the patterns observed both on stars and the Sun. Title: Scattering polarization in strong chromospheric lines. I. Explanation of the triplet peak structure Authors: Holzreuter, R.; Fluri, D. M.; Stenflo, J. O. Bibcode: 2005A&A...434..713H Altcode: Although the triplet polarization structure of the Na I D2 and Ca I 4227 Å lines in the second solar spectrum has been known for more than two decades, a clear and consistent explanation has been lacking. Here we show that the qualitative profile shape may be explained in terms of the anisotropy of the radiation field and partial frequency redistribution (PRD) effects. The complicated frequency and depth dependence of the anisotropy can be understood in terms of simple arguments that involve the source function gradient and boundary effects. We show in particular that the triplet peak structure of the polarization profile of Na I D2 has basically the same origin as for the Ca I 4227 Å line. Hyperfine structure and lower-level atomic polarization only modify the core polarization without altering the overall qualitative features. For our calculations we adopt a numerical method that combines the advantages of both the classical formalism with integral source function and the density-matrix formalism. In a first step, a multi-level, PRD-capable MALI code, which solves the statistical equilibrium and the radiative transfer equation self-consistently, computes intensity, opacities and collision rates. Keeping these quantities fixed, we obtain the scattering polarization in a second step by solving the radiative transfer equation for the transitions of interest with the classical formalism, which assumes a two-level atomic model with unpolarized lower level. Quantum interferences and lower-level atomic polarization are included in terms of a wavelength dependent polarizability W_2, which is independently obtained with the density-matrix formalism. Title: Comparison between KPVT/SPM and SoHO/MDI magnetograms with an application to solar irradiance reconstructions Authors: Wenzler, T.; Solanki, S. K.; Krivova, N. A.; Fluri, D. M. Bibcode: 2004A&A...427.1031W Altcode: To be able to use both space- and ground-based solar magnetograms and construct long time series of derived parameters it is important to cross-calibrate them so that we can estimate their reliability and combine them. Using two different techniques, we compare magnetograms as well as continuum images recorded by the Spectropolarimeter (SPM) on Kitt Peak and the Michelson Doppler Interferometer (MDI) on board SoHO. We find that the result obtained depends on the method used. The method we favour gives almost identical umbral and penumbral areas and very similar total magnetic fluxes in faculae. The magnetic fluxes in umbrae and penumbrae returned by the two instruments, however, differ considerably. We also demonstrate that SPM data can be employed to reconstruct total solar irradiance variations with almost the same accuracy as recently shown for MDI data. Title: Flip-Flops as Observational Signatures of Different Dynamo Modes in Cool Stars Authors: Fluri, D. M.; Berdyugina, S. V. Bibcode: 2004SoPh..224..153F Altcode: 2005SoPh..224..153F Cool, rapidly rotating stars exhibit enhanced magnetic activity with cyclic behavior on various time scales. In particular, the longitude of the dominant activity region switches quasi-periodically by 180∘, which is known as the "flip-flop" phenomenon. In the present paper we introduce a new approach for the interpretation of stellar cycles based on light curve modeling with dipole and quadrupole dynamo modes. We discuss the observational signatures of different combinations of the dynamo modes. The proposed simple model is able to reproduce the basic properties of long-term photometric behavior of active stars and allows us to study different mechanisms resulting in flip-flops. Title: Evidence for the Hanle effect in molecular lines Authors: Berdyugina, S. V.; Fluri, D. M. Bibcode: 2004A&A...417..775B Altcode: In many wavelength regions molecular lines dominate the second solar spectrum that results from coherent scattering. Scattering polarization is modified by magnetic fields via the Hanle effect. This allows us to explore the magnetic field regime with weak field strengths and mixed polarities, which is not seen with the Zeeman effect and thus contains complementary information. Molecular lines are particularly well suited to diagnose such turbulent fields because they exhibit a broad range of magnetic sensitivities within narrow spectral regions. Thus, it is possible to employ the technique of the differential Hanle effect, i.e. to obtain field strengths by observing polarization ratios in various lines. We have identified one R- and one P-triplet of C2 at 5140 Å and 5141 Å, respectively, that satisfy all conditions to be used in the differential Hanle effect. Based on these lines we have developed a model that can diagnose turbulent magnetic fields using the Hanle effect. The tool is sensitive over a broad range of magnetic field strengths from a few Gauss up to several hundred Gauss. This tool has allowed us to find a significant Hanle depolarization of C2 lines in quiet Sun observations, which corresponds to a magnetic field strength of 15±3 G. Title: First Evidence for the Hanle Effect in Molecular Lines Authors: Fluri, D. M.; Berdyugina, S. V. Bibcode: 2004IAUS..219..674F Altcode: 2003IAUS..219E.189F Magnetic fields influence and drive the activity in stellar atmospheres. In the optical they can be measured via Zeeman and Hanle effect which are relevant in different magnetic field regimes and thus complement each other. The Zeeman effect is sensitive to the net magnetic flux in the resolution element whereas the Hanle effect allows to detect weak directed or entangled magnetic fields. On the Sun Hanle effect is observed in prominences in strong chromospheric lines as well as in many photospheric lines. Especially in the photosphere Hanle effect observations have led to a new paradigm of the magnetic field structure. There 99 percent of the volume are filled by relatively weak entangled fields of the order of a few Gauss to which Zeeman effect observations are pracitcally blind but which are clearly detected by the Hanle effect. We find that molecular lines are particularly well suited for magnetic field diagnostics with the Hanle effect. In molecular bands closeby lines with different sensitivities to the magnetic field form under very similar conditions and can be observed in a single image. Therefore many potential instrumental and physical sources of errors can be eliminated. Title: An operator perturbation method for polarized line transfer. VI. Generalized PALI method for Hanle effect with partial frequency redistribution and collisions Authors: Fluri, D. M.; Nagendra, K. N.; Frisch, H. Bibcode: 2003A&A...400..303F Altcode: A generalized iteration method is presented to solve the polarized line transfer equation for a two-level-atom in an arbitrarily oriented, weak magnetic field. The polarized redistribution matrix employed accounts self-consistently for collisions as well as the presence of a weak magnetic field responsible for the Hanle effect. The proposed numerical method of solution is based on a Polarized Approximate Lambda Iteration (PALI) method. A Fourier decomposition of the radiation field and of the phase matrix with respect to the azimuthal angle reduces the complexity of the problem. A generalized core-wing technique is proposed, which permits an efficient implementation of the frequency domain structure inherent in the polarized redistribution matrix. The numerical method is tested for its accuracy and efficiency by comparing with the existing methods. Title: Depolarizing lines in the Sun's spectrum Authors: Fluri, D. M.; Stenflo, J. O. Bibcode: 2003A&A...398..763F Altcode: The majority of all lines in the solar spectrum depolarize the continuum. Here we present a theoretical analysis of the depolarizing lines. In a parameter survey where we vary the details of line formation such as height of formation, we find that absorption and scattering lines have entirely different behavior. While the depolarization by absorption lines rapidly decreases with increasing height of formation, the depolarization by scattering lines increases with height of formation. We interpret the results in terms of a simple qualitative model that contains the relevant physics and support it with quantitative calculations. The main relevant quantities are the anisotropy of the radiation field, which varies over the line profile, and the probability that a photon undergoes polarized scattering above the height where the atmosphere becomes optically thin. For lines with intrinsic polarization we find that the coupling between continuum and line polarization can be neglected. Title: Numerical Methods for Solving the Polarized Line Transfer Equations with Partial Frequency Redistribution Authors: Nagendra, K. N.; Frisch, H.; Fluri, D. M. Bibcode: 2003ASPC..307..227N Altcode: No abstract at ADS Title: Radiative Transfer in Na I D2 and D1 Authors: Fluri, D. M.; Holzreuter, R.; Klement, J.; Stenflo, J. O. Bibcode: 2003ASPC..307..263F Altcode: No abstract at ADS Title: Radiative transfer with polarized scattering in the magnetized solar atmosphere Authors: Fluri, Dominique Martin Bibcode: 2003PhDT.......147F Altcode: No abstract at ADS Title: Modelling solar irradiance variations: separate models for the network and active region faculae Authors: Wenzler, T.; Solanki, S. K.; Fluri, D. M.; Frutiger, C.; Fligge, M.; Ortiz, A. Bibcode: 2002ESASP.508..231W Altcode: 2002soho...11..231W In order to determine to what extent solar surface magnetism affects solar irradiance we need to reconstruct the irradiance from magnetograms. This process requires the use of model atmospheres. Here we present two model atmospheres describing faculae in active regions and the network. The models have been constructed such that they reproduce various data sets simultaneously. Title: Depolarizing Lines in the Solar Spectrum Authors: Fluri, D. M.; Stenflo, J. O. Bibcode: 2001ASPC..236..205F Altcode: 2001aspt.conf..205F No abstract at ADS Title: Continuum polarization and blend lines in the solar spectrum Authors: Fluri, D. M.; Stenflo, J. O. Bibcode: 1999ASSL..243..171F Altcode: 1999sopo.conf..171F No abstract at ADS Title: Continuum polarization in the solar spectrum Authors: Fluri, D. M.; Stenflo, J. O. Bibcode: 1999A&A...341..902F Altcode: We present a theoretical study of the continuum polarization due to radiative scattering in the visible solar spectrum. The results from nine different solar model atmospheres are compared. The center-to-limb variation (CLV) as well as the wavelength dependence of the continuum polarization are determined, and the sources of the dependence on the model atmospheres are identified. The key physical quantities turn out to be the scattering coefficient and the temperature gradient in the layer where the polarization is formed. A simple analytical function that approximates the CLV of the theoretical continuum polarization for every wavelength in the visible is found. This is based in first approximation on the assumption that the scattering layer producing the polarization is optically thin and lies above the layer of formation of the continuum intensity. Applications of the analytical function range from determinations of the instrumental zero-level of the polarization scale to diagnostic work using empirical center-to-limb curves to constrain the solar model atmospheres.