Author name code: landi-deglinnocenti ADS astronomy entries on 2022-09-14 author:"Landi Degl'Innocenti, Egidio" ------------------------------------------------------------------------ Title: Forbidden Line Polarimetry to Detect the Evolution of the Coronal Magnetic Field Authors: Li, H.; Landi Degl'Innocenti, E.; Qu, Z. Q. Bibcode: 2019ASPC..526..173L Altcode: Most of the activity in the solar corona is dominated by magnetic fields. However, the diagnostics of magnetic fields in the corona is still challenging, simply because the field is very weak. The forbidden line polarimetry technique was first suggested by Charvin (1965) to determine the orientation of the coronal magnetic field projected on the plane of sky. In this paper, we adopt the quantum theory for the generation and transfer of polarized radiation, in the framework of the density matrix formalism, and we present the linearly polarized coronal emission in forbidden lines resulting from models of the coronal magnetic field based on the potential field assumption. The results indicate that the forbidden line polarimetry technique may provide a possible way to investigate the polarity reversal of the coronal magnetic field during the solar cycle. Title: PeNCIL: A Wire Grid Polarimeter at 121.6 nm Authors: Landini, F.; Romoli, M.; Baccani, C.; Adam, G.; Dinescu, A.; Meneghin, A.; Scippa, A.; Pancrazzi, M.; Focardi, M.; Baglioni, R.; Landi Degl'Innocenti, E. Bibcode: 2019ASPC..526..341L Altcode: The magnetic field in corona can be measured through the Hanle effect, which is the magnetic field induced modification of the linear polarization signals resulting from the scattering of anisotropic radiation. The H I Lyα 121.6 nm is the most intense emission line of the EUV coronal spectrum and is highly sensitive to the Hanle effect. Through the comparison between the measured and the expected polarization in this line it is possible to infer the magnetic field in corona. PeNCIL (Polarimetry with Nanowires for Coronal Imaging of Lyα) may constitute the ideal candidate to measure the linear polarization of the whole Lyα 121.6 nm corona. It is a transmitting polarimeter optimized for the Lyα 121.6 nm line, thought as part of an internally occulted coronagraph to be flown aboard a future small solar mission or a sounding rocket. It is a light device, completely free of mechanical moving parts, composed of a fixed MgF2 quarter wave retarder, a nano-wire grid polarizer (nano-WGP), and a MgF2 variable retarder modulated through a calibrated piezo-clamp (PCVR). The nano-WGP and the PCVR are the two main components of PeNCIL and represent a first-ever achievement in the history of technology development for VUV. This paper addresses the status of the project with particular emphasis on the design and manufacturing of the nano-WGP and PCVR. Title: Relaxation Phenomena Due to Collisions with Neutral Perturbers in Hyperfine Structure Multiplets Authors: Landi Degl'Innocenti, E.; Belluzzi, L. Bibcode: 2019ASPC..526...29L Altcode: A connection is established between the depolarizing rates, due to collisions with neutral perturbers, of the statistical tensors of a hyperfine structure multiplet and those of the statistical tensors of the parent fine structure level. This connection is described by a simple equation involving a 12-j symbol of the second kind. An application is performed to derive an analytical expression for the scattering matrix of a hyperfine structured two-level atom in the presence of collisions and a magnetic field. Numerical results are presented. Title: Experimental Testing of Scattering Polarization Models Authors: Li, W.; Casini, R.; Tomczyk, S.; Landi Degl'Innocenti, E.; Marsell, B. Bibcode: 2018ApJ...867L..22L Altcode: 2018arXiv181107090L We realized a laboratory experiment to study the scattering polarization of the Na I D-doublet at 589.0 and 589.6 nm in the presence of a magnetic field. This work was stimulated by solar observations of that doublet, which have proven particularly challenging to explain through available models of polarized line formation, even to the point of casting doubts on our very understanding of the underlying physics. The purpose of the experiment was to test a quantum theory for the polarized scattering of spectrally flat incident radiation, on which much of the current magnetic diagnostics of stellar atmospheres is based. The experiment has confirmed the predictions of that theory, and its adequacy for the modeling of scattering polarization under flat-spectrum illumination. Title: Experimental testing of scattering polarization models Authors: Li, Wenxian; Casini, Roberto; Tomczyk, Steven; Landi Degl'Innocenti, Egidio; Marsell, Brandan Bibcode: 2018AAS...23212305L Altcode: We realized a laboratory experiment to study the polarization of the Na I doublet at 589.3 nm, in the presence of a magnetic field. The purpose of the experiment is to test the theory of scattering polarization for illumination conditions typical of astrophysical plasmas. This work was stimulated by solar observations of the Na I doublet that have proven particularly challenging to reproduce with current models of polarized line formation, even casting doubts on our very understanding of the physics of scattering polarization on the Sun. The experiment has confirmed the fundamental correctness of the current theory, and demonstrated that the "enigmatic'' polarization of those observations is exclusively of solar origin. Title: The Physics and Diagnostic Potential of Ultraviolet Spectropolarimetry Authors: Trujillo Bueno, Javier; Landi Degl'Innocenti, Egidio; Belluzzi, Luca Bibcode: 2018smf..book..183T Altcode: No abstract at ADS Title: The Physics and Diagnostic Potential of Ultraviolet Spectropolarimetry Authors: Trujillo Bueno, Javier; Landi Degl'Innocenti, Egidio; Belluzzi, Luca Bibcode: 2017SSRv..210..183T Altcode: 2017SSRv..tmp...15T The empirical investigation of the magnetic field in the outer solar atmosphere is a very important challenge in astrophysics. To this end, we need to identify, measure and interpret observable quantities sensitive to the magnetism of the upper chromosphere, transition region and corona. This paper provides an overview of the physics and diagnostic potential of spectropolarimetry in permitted spectral lines of the ultraviolet solar spectrum, such as the Mg ii h and k lines around 2800 Å, the hydrogen Lyman-α line at 1216 Å, and the Lyman-α line of He ii at 304 Å. The outer solar atmosphere is an optically pumped vapor and the linear polarization of such spectral lines is dominated by the atomic level polarization produced by the absorption and scattering of anisotropic radiation. Its modification by the action of the Hanle and Zeeman effects in the inhomogeneous and dynamic solar atmosphere needs to be carefully understood because it encodes the magnetic field information. The circular polarization induced by the Zeeman effect in some ultraviolet lines (e.g., Mg ii h & k) is also of diagnostic interest, especially for probing the outer solar atmosphere in plages and more active regions. The few (pioneering) observational attempts carried out so far to measure the ultraviolet spectral line polarization produced by optically pumped atoms in the upper chromosphere, transition region and corona are also discussed. We emphasize that ultraviolet spectropolarimetry is a key gateway to the outer atmosphere of the Sun and of other stars. Title: Polarization of Coronal Forbidden Lines Authors: Li, Hao; Landi Degl'Innocenti, Egidio; Qu, Zhongquan Bibcode: 2017ApJ...838...69L Altcode: Since the magnetic field is responsible for most manifestations of solar activity, one of the most challenging problems in solar physics is the diagnostics of solar magnetic fields, particularly in the outer atmosphere. To this end, it is important to develop rigorous diagnostic tools to interpret polarimetric observations in suitable spectral lines. This paper is devoted to analyzing the diagnostic content of linear polarization imaging observations in coronal forbidden lines. Although this technique is restricted to off-limb observations, it represents a significant tool to diagnose the magnetic field structure in the solar corona, where the magnetic field is intrinsically weak and still poorly known. We adopt the quantum theory of polarized line formation developed in the framework of the density matrix formalism, and synthesize images of the emergent linear polarization signal in coronal forbidden lines using potential-field source-surface magnetic field models. The influence of electronic collisions, active regions, and Thomson scattering on the linear polarization of coronal forbidden lines is also examined. It is found that active regions and Thomson scattering are capable of conspicuously influencing the orientation of the linear polarization. These effects have to be carefully taken into account to increase the accuracy of the field diagnostics. We also found that linear polarization observation in suitable lines can give valuable information on the long-term evolution of the magnetic field in the solar corona. Title: Radiative Transfer Modeling of the Enigmatic Scattering Polarization in the Solar Na I D1 Line Authors: Belluzzi, Luca; Trujillo Bueno, Javier; Landi Degl'Innocenti, Egidio Bibcode: 2015ApJ...814..116B Altcode: 2015arXiv151105801B The modeling of the peculiar scattering polarization signals observed in some diagnostically important solar resonance lines requires the consideration of the detailed spectral structure of the incident radiation field as well as the possibility of ground level polarization, along with the atom's hyperfine structure and quantum interference between hyperfine F-levels pertaining either to the same fine structure J-level, or to different J-levels of the same term. Here we present a theoretical and numerical approach suitable for solving this complex non-LTE radiative transfer problem. This approach is based on the density-matrix metalevel theory (where each level is viewed as a continuous distribution of sublevels) and on accurate formal solvers of the transfer equations and efficient iterative methods. We show an application to the D-lines of Na i, with emphasis on the enigmatic D1 line, pointing out the observable signatures of the various physical mechanisms considered. We demonstrate that the linear polarization observed in the core of the D1 line may be explained by the effect that one gets when the detailed spectral structure of the anisotropic radiation responsible for the optical pumping is taken into account. This physical ingredient is capable of introducing significant scattering polarization in the core of the Na i D1 line without the need for ground-level polarization. Title: The Physics of Polarization Authors: Landi Degl'Innocenti, Egidio Bibcode: 2015IAUS..305....1L Altcode: 2015IAUS..305....1D The introductory lecture that has been delivered at this Symposium is a condensed version of an extended course held by the author at the XII Canary Island Winter School from November 13 to November 21, 2000. The full series of lectures can be found in Landi Degl'Innocenti (2002). The original reference is organized in 20 Sections that are here itemized: 1. Introduction, 2. Description of polarized radiation, 3. Polarization and optical devices: Jones calculus and Muller matrices, 4. The Fresnel equations, 5. Dichroism and anomalous dispersion, 6. Polarization in everyday life, 7. Polarization due to radiating charges, 8. The linear antenna, 9. Thomson scattering, 10. Rayleigh scattering, 11. A digression on Mie scattering, 12. Bremsstrahlung radiation, 13. Cyclotron radiation, 14. Synchrotron radiation, 15. Polarization in spectral lines, 16. Density matrix and atomic polarization, 17. Radiative transfer and statistical equilibrium equations, 18. The amplification condition in polarized radiative transfer, and 19. Coupling radiative transfer and statistical equilibrium equations. Title: Isotropic Inelastic Collisions in a Multiterm Atom with Hyperfine Structure Authors: Belluzzi, Luca; Landi Degl'Innocenti, Egidio; Trujillo Bueno, Javier Bibcode: 2015ApJ...812...73B Altcode: A correct modeling of the scattering polarization profiles observed in some spectral lines of diagnostic interest, the sodium doublet being one of the most important examples, requires taking hyperfine structure (HFS) and quantum interference between different J-levels into account. An atomic model suitable for taking these physical ingredients into account is the so-called multiterm atom with HFS. In this work, we introduce and study the transfer and relaxation rates due to isotropic inelastic collisions with electrons, which enter the statistical equilibrium equations (SEE) for the atomic density matrix of this atomic model. Under the hypothesis that the electron-atom interaction is described by a dipolar operator, we provide useful relations between the rates describing the transfer and relaxation of quantum interference between different levels (whose numerical values are in most cases unknown) and the usual rates for the atomic level populations, for which experimental data and/or approximate theoretical expressions are generally available. For the particular case of a two-term atom with HFS, we present an analytical solution of the SEE for the spherical statistical tensors of the upper term, including both radiative and collisional processes, and we derive the expression of the emission coefficient in the four Stokes parameters. Finally, an illustrative application to the Na i D1 and D2 lines is presented. Title: Recurrent flares in active region NOAA 11283 Authors: Romano, P.; Zuccarello, F.; Guglielmino, S. L.; Berrilli, F.; Bruno, R.; Carbone, V.; Consolini, G.; de Lauretis, M.; Del Moro, D.; Elmhamdi, A.; Ermolli, I.; Fineschi, S.; Francia, P.; Kordi, A. S.; Landi Degl'Innocenti, E.; Laurenza, M.; Lepreti, F.; Marcucci, M. F.; Pallocchia, G.; Pietropaolo, E.; Romoli, M.; Vecchio, A.; Vellante, M.; Villante, U. Bibcode: 2015A&A...582A..55R Altcode: Context. Flares and coronal mass ejections (CMEs) are solar phenomena that are not yet fully understood. Several investigations have been performed to single out their related physical parameters that can be used as indices of the magnetic complexity leading to their occurrence.
Aims: In order to shed light on the occurrence of recurrent flares and subsequent associated CMEs, we studied the active region NOAA 11283 where recurrent M and X GOES-class flares and CMEs occurred.
Methods: We use vector magnetograms taken by HMI/SDO to calculate the horizontal velocity fields of the photospheric magnetic structures, the shear and the dip angles of the magnetic field, the magnetic helicity flux distribution, and the Poynting fluxes across the photosphere due to the emergence and the shearing of the magnetic field.
Results: Although we do not observe consistent emerging magnetic flux through the photosphere during the observation time interval, we detected a monotonic increase of the magnetic helicity accumulated in the corona. We found that both the shear and the dip angles have high values along the main polarity inversion line (PIL) before and after all the events. We also note that before the main flare of X2.1 GOES class, the shearing motions seem to inject a more significant energy than the energy injected by the emergence of the magnetic field.
Conclusions: We conclude that the very long duration (about 4 days) of the horizontal displacement of the main photospheric magnetic structures along the PIL has a primary role in the energy release during the recurrent flares. This peculiar horizontal velocity field also contributes to the monotonic injection of magnetic helicity into the corona. This process, coupled with the high shear and dip angles along the main PIL, appears to be responsible for the consecutive events of loss of equilibrium leading to the recurrent flares and CMEs.

A movie associated to Fig. 4 is available in electronic form at http://www.aanda.org Title: Polarimetric shapes of spectral lines in solar observations Authors: Landi Degl'Innocenti, Egidio Bibcode: 2014AdSpR..54.1272L Altcode: A century has elapsed since the first observation of the polarimetric profile of a line of the solar spectrum. Since then, dramatic progress has been made in the instrumentation, which is now reaching unprecedented levels of sensitivity in the measurement of polarization signals in solar spectral lines. At the same time, the theoretical framework needed for the interpretation of polarimetric observations has steadily evolved from the pioneering methods, based on simple formulae, to the sophisticated structure that is nowadays used with success in the interpretation of solar observations. The present paper is intended to give a historical perspective of the evolution of this research field and of its major achievements, with particular emphasis on the role played by the magnetic field in determining the polarimetric shapes of spectral lines. Title: Theoretical Schemes for the Interpretation of Solar Polarimetric Observations: An Overview and Some New Ideas Authors: Landi Degl'Innocenti, E.; Belluzzi, L. Bibcode: 2014ASPC..489...99L Altcode: The theoretical scheme based on the density matrix formalism, and self-consistently derived from the principles of Quantum Electrodynamics, is presently one of the most solid frameworks for the interpretation of solar polarimetric observations. This scheme has been highly successful, mainly for the interpretation of polarimetric signals that can be described in the so-called limit of complete frequency redistribution (CRD). However, it suffers from the severe limitation that partial frequency redistribution (PRD) effects cannot be accounted for. The metalevel theory can handle PRD effects, but all the attempts for its generalization to account consistently for collisions and lower-level coherences have failed. The redistribution matrix approach is very suitable for taking PRD effects into account. However, it can consistently describe only two-level atoms with unpolarized lower level. New heuristic approaches have been proposed for treating two-term atoms, but they are based on rather crude approximations and their validity and physical consistency are far from being firmly established. Some few reflections that may lead to the establishment of a self-consistent set of equations, fully derived from first principles, are put forward. These reflections are based on the introduction of the Fourier transform of the density matrix. Title: Frequency Redistribution Function for the Polarized Two-term Atom Authors: Casini, R.; Landi Degl'Innocenti, M.; Manso Sainz, R.; Landi Degl'Innocenti, E.; Landolfi, M. Bibcode: 2014ApJ...791...94C Altcode: 2014arXiv1406.6129C We present a generalized frequency redistribution function for the polarized two-term atom in an arbitrary magnetic field. This result is derived within a new formulation of the quantum problem of coherent scattering of polarized radiation by atoms in the collisionless regime. The general theory, which is based on a diagrammatic treatment of the atom-photon interaction, is still a work in progress. However, the results anticipated here are relevant enough for the study of the magnetism of the solar chromosphere and of interest for astrophysics in general.

The National Center for Atmospheric Research is sponsored by the National Science Foundation. Title: Atomic Spectroscopy and Radiative Processes Authors: Landi Degl'Innocenti, E. Bibcode: 2014asrp.book.....L Altcode: No abstract at ADS Title: Theoretical formulation of Doppler redistribution in scattering polarization within the framework of the velocity-space density matrix formalism Authors: Belluzzi, L.; Landi Degl'Innocenti, E.; Trujillo Bueno, J. Bibcode: 2013A&A...552A..72B Altcode: 2013arXiv1302.2887B Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications when adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a two-level atom with infinitely sharp upper and lower levels, and we derive the corresponding statistical equilibrium equations, neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as RI) is derived starting from the statistical equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches. Title: Isotropic inelastic and superelastic collisional rates in a multiterm atom Authors: Belluzzi, L.; Landi Degl'Innocenti, E.; Trujillo Bueno, J. Bibcode: 2013A&A...551A..84B Altcode: 2013arXiv1302.0990B The spectral line polarization of the radiation emerging from a magnetized astrophysical plasma depends on the state of the atoms within the medium, whose determination requires considering the interactions between the atoms and the magnetic field, between the atoms and photons (radiative transitions), and between the atoms and other material particles (collisional transitions). In applications within the framework of the multiterm model atom (which accounts for quantum interference between magnetic sublevels pertaining either to the same J-level or to different J-levels within the same term) collisional processes are generally neglected when solving the master equation for the atomic density matrix. This is partly due to the lack of experimental data and/or of approximate theoretical expressions for calculating the collisional transfer and relaxation rates (in particular the rates for interference between sublevels pertaining to different J-levels, and the depolarizing rates due to elastic collisions). In this paper we formally define and investigate the transfer and relaxation rates due to isotropic inelastic and superelastic collisions that enter the statistical equilibrium equations for the atomic density matrix of a multiterm atom. Under the hypothesis that the interaction between the collider and the atom can be described by a dipolar operator, we provide expressions that relate the collisional rates for interference between different J-levels to the usual collisional rates for J-level populations, for which experimental data or approximate theoretical expressions are generally available. We show that the rates for populations and interference within the same J-level reduce to those previously obtained for the multilevel model atom (where quantum interference is assumed to be present only between magnetic sublevels pertaining to any given J-level). Finally, we apply the general equations to the case of a two-term atom with unpolarized lower term, illustrating the impact of inelastic and superelastic collisions on the scattering line polarization through radiative transfer calculations in a slab of stellar atmospheric plasma anisotropically illuminated by the photospheric radiation field. Title: Spectropolarimetry with new generation solar telecopes Authors: Landi Degl'Innocenti, E. Bibcode: 2013MmSAI..84..391L Altcode: Next generation solar telescopes will provide the possibility of performing solar observations at unprecedented levels of spectral, spatial, and tempoarl resolution, combined with very high polarimetric sensitivity. This talk will concentrate on the new diagnostic possibilities that will be opened by these telescopes to the solar scientific community, with particular emphasis on the diagnostics of the magnetic field vector. Also, I will discuss the ultimate limitations due to the pysical complexity of the solar atmosphere and to radiative transfer effects. Title: Spectropolarimetric signatures of anisotropic velocity distributions of optically thin coronal UV lines Authors: Khan, A.; Landi Degl'Innocenti, E. Bibcode: 2012A&A...543A.158K Altcode: Context. Many interpretations of observations with the Ultraviolet Coronagraph Spectrometer (UVCS) operating aboard the Solar and Heliospheric Observatory (SOHO) have suggested that there are variations in particle velocity distributions. In this paper, we investigate their spectropolarimetric signatures.
Aims: We uncover the spectropolarimetric signatures of anisotropic velocity distribution functions after a line-of-sight (LOS) integration of both the 1215.16 Å Lα line and the 1032 Å O vi line.
Methods: We perform a forward modelling of the resonance scattering of neutral hydrogen atoms and O5+ ions in the presence of anisotropic velocity distribution functions using a self-consistent 2.5-dimensional, magnetohydrodynamics global coronal model. We analyse the most important observables in spectropolarimetry, i.e., the rotation of the plane of linear polarisation, and de-or hyperpolarisation after a LOS integration.
Results: The spectropolarimetric signatures of anisotropic velocity distributions do survive the LOS integration, and are to be found in the region where there are non-radial solar outflows, i.e., from mid-way between the poles and the equator and down to the equator, in some cases starting from the photosphere all the way out to almost 2 R⊙. We consider the cases of w⊥ = 2w and w∥ = w or w ⊥ = w and w∥ = 2w, where w is the local thermal velocity of either neutral hydrogen atoms or O5+ ions, and where w⊥ and w∥ characterise the perpendicular and parallel distributions of the components of the velocity with respect to the magnetic field, respectively. We find that the rotation angles reach values of roughly ± 15 degrees, and should in principle be measurable.
Conclusions: Our results show that it should be possible to distinguish anisotropic velocity distribution functions on the condition that one samples as extensive a region of the plane of the sky as possible. The effects of the anisotropy are in most cases seen all the way out to 2 R⊙, and we therefore recommend that the observations be made as far away from the photosphere as possible in order to avoid the possible contamination by active regions. It will in most cases, however, be extremely hard to determine the sense of the anisotropy using only spectropolarimetry. Title: Solar magnetism eXplorer (SolmeX). Exploring the magnetic field in the upper atmosphere of our closest star Authors: Peter, Hardi; Abbo, L.; Andretta, V.; Auchère, F.; Bemporad, A.; Berrilli, F.; Bommier, V.; Braukhane, A.; Casini, R.; Curdt, W.; Davila, J.; Dittus, H.; Fineschi, S.; Fludra, A.; Gandorfer, A.; Griffin, D.; Inhester, B.; Lagg, A.; Landi Degl'Innocenti, E.; Maiwald, V.; Sainz, R. Manso; Martínez Pillet, V; Matthews, S.; Moses, D.; Parenti, S.; Pietarila, A.; Quantius, D.; Raouafi, N. -E.; Raymond, J.; Rochus, P.; Romberg, O.; Schlotterer, M.; Schühle, U.; Solanki, S.; Spadaro, D.; Teriaca, L.; Tomczyk, S.; Trujillo Bueno, J.; Vial, J. -C. Bibcode: 2012ExA....33..271P Altcode: 2011arXiv1108.5304P; 2011ExA...tmp..134P The magnetic field plays a pivotal role in many fields of Astrophysics. This is especially true for the physics of the solar atmosphere. Measuring the magnetic field in the upper solar atmosphere is crucial to understand the nature of the underlying physical processes that drive the violent dynamics of the solar corona—that can also affect life on Earth. SolmeX, a fully equipped solar space observatory for remote-sensing observations, will provide the first comprehensive measurements of the strength and direction of the magnetic field in the upper solar atmosphere. The mission consists of two spacecraft, one carrying the instruments, and another one in formation flight at a distance of about 200 m carrying the occulter to provide an artificial total solar eclipse. This will ensure high-quality coronagraphic observations above the solar limb. SolmeX integrates two spectro-polarimetric coronagraphs for off-limb observations, one in the EUV and one in the IR, and three instruments for observations on the disk. The latter comprises one imaging polarimeter in the EUV for coronal studies, a spectro-polarimeter in the EUV to investigate the low corona, and an imaging spectro-polarimeter in the UV for chromospheric studies. SOHO and other existing missions have investigated the emission of the upper atmosphere in detail (not considering polarization), and as this will be the case also for missions planned for the near future. Therefore it is timely that SolmeX provides the final piece of the observational quest by measuring the magnetic field in the upper atmosphere through polarimetric observations. Title: HAZEL: HAnle and ZEeman Light Authors: Asensio Ramos, Andrés; Trujillo Bueno, Javier; Landi Degl'Innocenti, E. Bibcode: 2011ascl.soft09004A Altcode: A big challenge in solar and stellar physics in the coming years will be to decipher the magnetism of the solar outer atmosphere (chromosphere and corona) along with its dynamic coupling with the magnetic fields of the underlying photosphere. To this end, it is important to develop rigorous diagnostic tools for the physical interpretation of spectropolarimetric observations in suitably chosen spectral lines. HAZEL is a computer program for the synthesis and inversion of Stokes profiles caused by the joint action of atomic level polarization and the Hanle and Zeeman effects in some spectral lines of diagnostic interest, such as those of the He I 1083.0 nm and 587.6 nm (or D3) multiplets. It is based on the quantum theory of spectral line polarization, which takes into account in a rigorous way all the relevant physical mechanisms and ingredients (optical pumping, atomic level polarization, level crossings and repulsions, Zeeman, Paschen-Back and Hanle effects). The influence of radiative transfer on the emergent spectral line radiation is taken into account through a suitable slab model. The user can either calculate the emergent intensity and polarization for any given magnetic field vector or infer the dynamical and magnetic properties from the observed Stokes profiles via an efficient inversion algorithm based on global optimization methods. Title: Solar coronal magnetic field diagnostics through polarimetric forward modelling of the Hanle effect Authors: Khan, A.; Landi Degl'Innocenti, E. Bibcode: 2011A&A...532A..70K Altcode: Context. Progress in the solution to some of the most outstanding open problems of solar physics, such as coronal heating, solar wind acceleration, the generation and triggering of explosive events like flares and CMEs, hinges on the provision of a more stringent estimate of the solar magnetic field coordinates.
Aims: We seek a way to infer the magnetic field of the solar atmosphere. A very promising way of doing this is by using the Hanle effect in resonance scattering in the Lα line of the solar atmosphere.
Methods: By forward modelling the known scattering effects in the presence of magnetic fields, i.e. rotation of the plane of polarisation and depolarisation of the linear polarisation parameters, and by comparing them to observations, one could potentially uncover the magnetic morphology and restrict its intensity range. We simulate the effects of simple dipole configurations along the coordinate axes and analyse the outcome through two kinds of graphs (i.e. the difference in angle of the plane of linear polarisation with respect to the field-free case, and the relative depolarisation).
Results: The graphs are either symmetric, anti-symmetric or asymmetric with respect to the (y,z) plane. This is explained by invoking two symmetry operations and taking into account that the magnetic field is a pseudovector. We also show the polarimetric effects of active regions and use them pairwise with the magnetic field due to dipoles to analyse the polarimetric signatures of magnetic field line loops. Inspired by the famous TRACE image, we finally show what one could expect from polarimetry performed on the region of the solar atmosphere displayed in the image.
Conclusions: By combining the two complementary remote sensing techniques, i.e. the Zeeman and the Hanle effect, in all thinkable ways with tracers such as the images revealed by TRACE, SOHO, STEREO, etc., we hope one day to be able to infer the solar magnetic field coordinates. Much theoretical and instrumental work still lies ahead, however. Title: Vector magnetic field and vector current density in and around the δ-spot NOAA 10808† Authors: Bommier, Véronique; Landi Degl'Innocenti, Egidio; Schmieder, Brigitte; Gelly, Bernard Bibcode: 2011IAUS..273..338B Altcode: The context is that of the so-called ``fundamental ambiguity'' (also azimuth ambiguity, or 180° ambiguity) in magnetic field vector measurements: two field vectors symmetrical with respect to the line-of-sight have the same polarimetric signature, so that they cannot be discriminated. We propose a method to solve this ambiguity by applying the ``simulated annealing'' algorithm to the minimization of the field divergence, added to the longitudinal current absolute value, the line-of-sight derivative of the magnetic field being inferred by the interpretation of the Zeeman effect observed by spectropolarimetry in two lines formed at different depths. We find that the line pair Fe I λ 6301.5 and Fe I λ 6302.5 is appropriate for this purpose. We treat the example case of the δ-spot of NOAA 10808 observed on 13 September 2005 between 14:25 and 15:25 UT with the THEMIS telescope. Besides the magnetic field resolved map, the electric current density vector map is also obtained. A strong horizontal current density flow is found surrounding each spot inside its penumbra, associated to a non-zero Lorentz force centripetal with respect to the spot center (i.e., oriented towards the spot center). The current wrapping direction is found to depend on the spot polarity: clockwise for the positive polarity, counterclockwise for the negative one. This analysis is made possible thanks to the UNNOFIT2 Milne-Eddington inversion code, where the usual theory is generalized to the case of a line (Fe I λ 6301.5) that is not a normal Zeeman triplet line (like Fe I λ 6302.5). Title: Spectropolarimetric forward modelling of the lines of the Lyman-series using a self-consistent, global, solar coronal model Authors: Khan, A.; Belluzzi, L.; Landi Degl'Innocenti, E.; Fineschi, S.; Romoli, M. Bibcode: 2011A&A...529A..12K Altcode: Context. The presence and importance of the coronal magnetic field is illustrated by a wide range of phenomena, such as the abnormally high temperatures of the coronal plasma, the existence of a slow and fast solar wind, the triggering of explosive events such as flares and CMEs.
Aims: We investigate the possibility of using the Hanle effect to diagnose the coronal magnetic field by analysing its influence on the linear polarisation, i.e. the rotation of the plane of polarisation and depolarisation.
Methods: We analyse the polarisation characteristics of the first three lines of the hydrogen Lyman-series using an axisymmetric, self-consistent, minimum-corona MHD model with relatively low values of the magnetic field (a few Gauss).
Results: We find that the Hanle effect in the above-mentioned lines indeed seems to be a valuable tool for analysing the coronal magnetic field. However, great care must be taken when analysing the spectropolarimetry of the Lα line, given that a non-radial solar wind and active regions on the solar disk can mimic the effects of the magnetic field, and, in some cases, even mask them. Similar drawbacks are not found for the Lβ and Lγ lines because they are more sensitive to the magnetic field. We also briefly consider the instrumental requirements needed to perform polarimetric observations for diagnosing the coronal magnetic fields.
Conclusions: The combined analysis of the three aforementioned lines could provide an important step towards better constrainting the value of solar coronal magnetic fields. Title: Polarized Radiative Transfer: from Solar Applications to Laboratory Experiments Authors: Landi Degl'Innocenti, E.; Belluzzi, L.; Bommier, V. Bibcode: 2011ASPC..437...45L Altcode: The theory of radiative transfer for polarized radiation, developed from Quantum Electrodynamics for the interpretation of solar observations, predicts the existence of a variety of physical phenomena that, in many cases, would deserve being directly tested through laboratory experiments, also in view of possible practical applications. In this report we will focus on the description of some of these atomic-physics phenomena that have been disregarded, or overlooked, in terrestrial laboratories. Title: Magnetic Field, Density Current, and Lorentz Force Full Vector Maps of the NOAA 10808 Double Sunspot: Evidence of Strong Horizontal Current Flows in the Penumbra Authors: Bommier, V.; Landi Degl'Innocenti, E.; Schmieder, B.; Gelly, B. Bibcode: 2011ASPC..437..491B Altcode: The context is that of the so-called “fundamental ambiguity” (also azimuth ambiguity, or 180° ambiguity) in magnetic field vector measurements: two field vectors symmetrical with respect to the line-of-sight have the same polarimetric signature, so that they cannot be discriminated. We propose a method to solve this ambiguity by applying the “simulated annealing” algorithm to the minimization of the field divergence, added to the longitudinal current absolute value, the line-of-sight derivative of the magnetic field being inferred by the interpretation of the Zeeman effect observed by spectropolarimetry in two lines formed at different depths. We find that the line pair Fe I λ 6301.5 and Fe I λ 6302.5 is appropriate for this purpose. We treat the example case of the δ-spot of NOAA 10808 observed on 13 September 2005 between 14:25 and 15:25 UT with the THEMIS telescope. Besides the magnetic field resolved map, the electric current density vector map is also obtained. A strong horizontal current density flow is found surrounding each spot inside its penumbra, associated to a non-zero Lorentz force centripetal with respect to the spot center (i.e., oriented towards the spot center). The current wrapping direction is found to depend on the spot polarity: clockwise for the positive polarity, counterclockwise for the negative one. This analysis is made possible thanks to the UNNOFIT2 Milne-Eddington inversion code, where the usual theory is generalized to the case of a line Fe I λ 6301.5) that is not a normal Zeeman triplet line (like Fe I λ 6302.5). Title: On the Sensitivity of Partial Redistribution Scattering Polarization Profiles to Various Atmospheric Parameters Authors: Sampoorna, M.; Trujillo Bueno, J.; Landi Degl'Innocenti, E. Bibcode: 2010ApJ...722.1269S Altcode: 2010arXiv1008.2585S This paper presents a detailed study of the scattering polarization profiles formed under partial frequency redistribution (PRD) in two thermal models of the solar atmosphere. Particular attention is given to understanding the influence of several atmospheric parameters on the emergent fractional linear polarization profiles. The shapes of these Q/I profiles are interpreted in terms of the anisotropy of the radiation field, which in turn depends on the source function gradient that sets the angular variation of the specific intensity. We define a suitable frequency integrated anisotropy factor for PRD that can be directly related to the emergent linear polarization. We show that complete frequency redistribution is a good approximation to model weak resonance lines. We also show that the emergent linear polarization profiles can be very sensitive to the thermal structure of the solar atmosphere and, in particular, to spatial variations of the damping parameter. Title: Magnetic field diagnostics through the second solar spectrum: a spectroscopic analysis of the most polarizing atomic lines Authors: Belluzzi, L.; Landi Degl'Innocenti, E. Bibcode: 2010MmSAI..81..710B Altcode: Detailed observations of the second solar spectrum have shown a complex phenomenology whose detailed interpretation is still in a preliminary phase. The only certain thing is that the observed polarization is due to the phenomenon of resonance scattering. It is well known that such polarization can be strongly modified by the presence of a magnetic field through the so-called Hanle effect. It then follows that the second solar spectrum is, at least potentially, a fundamental instrument for diagnosing the intensity and topology of the weak magnetic fields lying in the higher layers of the solar atmosphere. Obviously, to fully exploit such potential, it is absolutely necessary to arrive at the correct theoretical interpretation, a task that has been revealed to involve many difficulties. We present an analysis of the second solar spectrum, carried out with the aim of investigating its general properties. The most interesting results concern an empirical classification of the wide variety of polarization signals that are observed, and the formulation of three empirical laws describing a series of properties common to the strongest signals. Title: The Physical Origin and the Diagnostic Potential of the Scattering Polarization in the Li I Resonance Doublet at 6708 Å Authors: Belluzzi, Luca; Landi Degl'Innocenti, Egidio; Trujillo Bueno, Javier Bibcode: 2009ApJ...705..218B Altcode: 2009arXiv0909.3748B High-sensitivity measurements of the linearly polarized solar limb spectrum produced by scattering processes in quiet regions of the solar atmosphere showed that the Q/I profile of the lithium doublet at 6708 Å has an amplitude ~10-4 and a curious three-peak structure, qualitatively similar to that found and confirmed by many observers in the Na I D2 line. Given that a precise measurement of the scattering polarization profile of the lithium doublet lies at the limit of the present observational possibilities, it is worthwhile to clarify the physical origin of the observed polarization, its diagnostic potential, and what kind of Q/I shapes can be expected from theory. To this end, we have applied the quantum theory of atomic level polarization taking into account the hyperfine structure of the two stable isotopes of lithium, as well as the Hanle effect of a microturbulent magnetic field of arbitrary strength. We find that quantum interferences between the sublevels pertaining to the upper levels of the D2 and D1 line transitions of lithium do not cause any observable effect on the emergent Q/I profile. Our theoretical calculations show that only two Q/I peaks can be expected, with the strongest one caused by the D2 line of 7Li I and the weakest one due to the D2 line of 6Li I. Interestingly, we find that these two peaks in the theoretical Q/I profile stand out clearly only when the kinetic temperature of the thin atmospheric region that produces the emergent spectral line radiation is lower than 4000 K. The fact that such a thin atmospheric region is located around a height of 200 km in standard semi-empirical models, where the kinetic temperature is about 5000 K, leads us to suggest that the most likely Q/I profile produced by the Sun in the lithium doublet should be slightly asymmetric and dominated by the 7Li I peak. Title: The quiet Sun magnetic field observed with ZIMPOL on THEMIS. I. The probability density function Authors: Bommier, V.; Martínez González, M.; Bianda, M.; Frisch, H.; Asensio Ramos, A.; Gelly, B.; Landi Degl'Innocenti, E. Bibcode: 2009A&A...506.1415B Altcode: Context: The quiet Sun magnetic field probability density function (PDF) remains poorly known. Modeling this field also introduces a magnetic filling factor that is also poorly known. With these two quantities, PDF and filling factor, the statistical description of the quiet Sun magnetic field is complex and needs to be clarified.
Aims: In the present paper, we propose a procedure that combines direct determinations and inversion results to derive the magnetic field vector and filling factor, and their PDFs.
Methods: We used spectro-polarimetric observations taken with the ZIMPOL polarimeter mounted on the THEMIS telescope. The target was a quiet region at disk center. We analyzed the data by means of the UNNOFIT inversion code, with which we inferred the distribution of the mean magnetic field α B, α being the magnetic filling factor. The distribution of α was derived by an independent method, directly from the spectro-polarimetric data. The magnetic field PDF p(B) could then be inferred. By introducing a joint PDF for the filling factor and the magnetic field strength, we have clarified the definition of the PDF of the quiet Sun magnetic field when the latter is assumed not to be volume-filling.
Results: The most frequent local average magnetic field strength is found to be 13 G. We find that the magnetic filling factor is related to the magnetic field strength by the simple law α = B_1/B with B1 = 15 G. This result is compatible with the Hanle weak-field determinations, as well as with the stronger field determinations from the Zeeman effect (kGauss field filling 1-2% of space). From linear fits, we obtain the analytical dependence of the magnetic field PDF. Our analysis has also revealed that the magnetic field in the quiet Sun is isotropically distributed in direction.
Conclusions: We conclude that the quiet Sun is a complex medium where magnetic fields having different field strengths and filling factors coexist. Further observations with a better polarimetric accuracy are, however, needed to confirm the results obtained in the present work.

Based on observations made with the French-Italian telescope THEMIS operated by the CNRS and CNR on the island of Tenerife in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Present address: Instituto de Astrofísica de Canarias, vía Láctea s/n, 38205 La Laguna, Tenerife, Spain. Title: Stellar Spectropolarimetry with Retarder Waveplate and Beam Splitter Devices Authors: Bagnulo, S.; Landolfi, M.; Landstreet, J. D.; Landi Degl'Innocenti, E.; Fossati, L.; Sterzik, M. Bibcode: 2009PASP..121..993B Altcode: Nighttime polarimetric measurements are often obtained very close to the limits of the instrumental capabilities. It is important to be aware of the possible sources of spurious polarization, and to adopt data reduction techniques that best compensate for the instrumental effects intrinsic to the design of the most common polarimeters adopted for nighttime observations. We define a self-consistent framework starting from the basic definitions of the Stokes parameters, and we present an analytical description of the data reduction techniques commonly used with a polarimeter (consisting of a retarder wave plate and a Wollaston prism) to explore their advantages and limitations. We first consider an ideal polarimeter in which all optical components are perfectly defined by their nominal characteristics. We then introduce deviations from the nominal behavior of the polarimetric optics, and develop an analytical model to describe the polarization of the outgoing radiation. We study and compare the results of two different data reduction methods, one based on the differences of the signals, and one based on their ratios, to evaluate the residual amount of spurious polarization. We show that data reduction techniques may fully compensate for small deviations of the polarimetric optics from their nominal values, although some important (first-order) corrections have to be adopted for linear polarization data. We include a detailed discussion of quality checking by means of null parameters. We present an application to data obtained with the FORS1 instrument of the ESO VLT, in which we have detected a significant amount of cross talk between circular and linear polarization. We show that this cross-talk effect is not due to the polarimetric optics themselves, but is most likely caused by spurious birefringence due to the instrument’s collimator lens. Title: Mn I Lines with Hyperfine Structure Synthesized in Realistic Quiet-Sun Atmospheres Authors: Viticchié, B.; Sánchez Almeida, J.; Landi Degl'Innocenti, E.; Berrilli, F. Bibcode: 2009ASPC..405..319V Altcode: We present the first synthesis of Mn I lines in realistic multi-component magnetized quiet Sun atmospheres, including variation of magnetic field strength, magnetic field direction, plasma velocity, and coupling between magnetic field and thermodynamics. All synthesized Mn I lines weaken for strong magnetic fields. A detailed analysis of the Mn I λ5538 line shows that the Weak Field Approximation (WFA) breaks down at 400~G, and that kG magnetic fields produce Stokes V profiles with amplitudes up to two orders of magnitude smaller than those predicted by the WFA. Consequently, the polarization emerging from an atmosphere in which weak (hG) and strong (kG) fields coexist is biased towards the hG field polarization. When including velocity gradients, profiles showing important asymmetries are produced, and these profiles cannot be obtained using single-component magnetized model atmospheres. We synthesize Mn I lines presenting very different hyperfine structure (HFS) patterns, and all of them reproduce the observed Stokes I profiles in a really satisfactory way. Title: The Sensitivity of the Second Solar Spectrum of the Li I 6708 Å Doublet to the Lithium Isotopic Abundance and to a Microturbulent Magnetic Field Authors: Belluzzi, L.; Landi Degl'Innocenti, E.; Trujillo Bueno, J. Bibcode: 2009ASPC..405..107B Altcode: The second solar spectrum offers a novel diagnostic window not only to explore the magnetic field of our nearest star, but also to determine the atomic and isotopic abundances in the solar atmosphere. A very interesting example, concerning this second aspect, is the Li I resonance doublet at 6708~Å. Here we present a detailed theoretical investigation, carried out within the framework of the density matrix formalism, on the atomic physics that is involved in the generation of the observed Q/I profile, which is the result of a complex blend of the D_1 and D_2 lines of the two stable isotopes of lithium (^6Li and ^7Li), both showing hyperfine structure. We discuss the diagnostic potential of this linear polarization profile for the determination of the lithium isotopic abundance in the quiet Sun, and we investigate the magnetic sensitivity of this profile to a microturbulent magnetic field. Title: Radiative Transfer for Polarized Radiation: a Personal, Historical Overview Authors: Landi Degl'Innocenti, E. Bibcode: 2009ASPC..405...57L Altcode: Almost a century has elapsed since the first application of spectro-polarimetry to the diagnostic of solar magnetic fields. Since then, dramatic progress has been made in the instrumentation, which is now reaching unprecedented levels of sensitivity in the measurement of polarization signals in spectral lines. At the same time, the theoretical framework needed for the interpretation of polarimetric observations has steadily evolved from the pioneering methods based on simple formulae to a sophisticated structure which is nowadays used with success in the interpretation of solar observations. The present paper is intended to give a personal, historical perspective of the evolution of this research field and of its major achievements. Title: Observations of the Joint Action of the Hanle and Zeeman Effects in the D_2 Line of Ba II Authors: Ramelli, R.; Bianda, M.; Trujillo Bueno, J.; Belluzzi, L.; Landi Degl'Innocenti, E. Bibcode: 2009ASPC..405...41R Altcode: 2009arXiv0906.2320R We show a selection of high-sensitivity spectropolarimetric observations obtained over the last few years in the Ba II D_2-line with the Zürich Imaging Polarimeter (ZIMPOL) attached to the Gregory Coudé Telescope of IRSOL. The measurements were collected close to the solar limb, in several regions with varying degree of magnetic activity. The Stokes profiles we have observed show clear signatures of the joint action of the Hanle and Zeeman effects, in very good qualitative agreement with the theoretical expectations. Polarimetric measurements of this line show to be very well suited for magnetic field diagnostics of the lower solar chromosphere, from regions with field intensities as low as 1 gauss to strongly magnetized ones having kG field strengths. Title: A spectroscopic analysis of the most polarizing atomic lines of the second solar spectrum Authors: Belluzzi, L.; Landi Degl'Innocenti, E. Bibcode: 2009A&A...495..577B Altcode: We present an analysis of the second solar spectrum, as plotted in graphical form in the three volumes of the atlas “The Second Solar Spectrum”, in the wavelength range between 3160 Å and 6995 Å. All the strongest positive linear polarization signals produced by atomic spectral lines are identified, and their amplitudes are listed, along with the most relevant spectroscopic properties of the lines. The various signals are divided into five classes according to the shape of their Q/I profiles. Three empirical rules are formulated from the analysis of the amplitude and shape of the various signals, and of the spectroscopic properties of the spectral lines.

Tables 1 and 2 are only available in electronic form at http://www.aanda.org Title: Spettroscopia atomica e processi radiativi Authors: Landi degl'Innocenti, Egidio Bibcode: 2009sapr.book.....L Altcode: 2009sapr.book.....D No abstract at ADS Title: Advanced Forward Modeling and Inversion of Stokes Profiles Resulting from the Joint Action of the Hanle and Zeeman Effects Authors: Asensio Ramos, A.; Trujillo Bueno, J.; Landi Degl'Innocenti, E. Bibcode: 2008ApJ...683..542A Altcode: 2008arXiv0804.2695A A big challenge in solar and stellar physics in the coming years will be to decipher the magnetism of the solar outer atmosphere (chromosphere and corona) along with its dynamic coupling with the magnetic fields of the underlying photosphere. To this end, it is important to develop rigorous diagnostic tools for the physical interpretation of spectropolarimetric observations in suitably chosen spectral lines. Here we present a computer program for the synthesis and inversion of Stokes profiles caused by the joint action of atomic level polarization and the Hanle and Zeeman effects in some spectral lines of diagnostic interest, such as those of the He I 10830 Å and 5876 Å (or D3) multiplets. It is based on the quantum theory of spectral line polarization, which takes into account in a rigorous way all the relevant physical mechanisms and ingredients (optical pumping, atomic level polarization, level crossings and repulsions, Zeeman, Paschen-Back, and Hanle effects). The influence of radiative transfer on the emergent spectral line radiation is taken into account through a suitable slab model. The user can either calculate the emergent intensity and polarization for any given magnetic field vector or infer the dynamical and magnetic properties from the observed Stokes profiles via an efficient inversion algorithm based on global optimization methods. The reliability of the forward modeling and inversion code presented here is demonstrated through several applications, which range from the inference of the magnetic field vector in solar active regions to determining whether or not it is canopy-like in quiet chromospheric regions. This user-friendly diagnostic tool called "HAZEL" (from HAnle and ZEeman Light) is offered to the astrophysical community, with the hope that it will facilitate new advances in solar and stellar physics. Title: Modelling the incomplete Paschen-Back effect in the spectra of magnetic Ap stars Authors: Stift, M. J.; Leone, F.; Landi Degl'Innocenti, E. Bibcode: 2008MNRAS.385.1813S Altcode: 2008arXiv0801.2740S; 2008MNRAS.tmp..265S We present preliminary results of a systematic investigation of the incomplete Paschen-Back effect in magnetic Ap stars. A short overview of the theory is followed by a demonstration of how level splittings and component strengths change with magnetic field strength for some lines of special astrophysical interest. Requirements are set out for a code which allows the calculation of full Stokes spectra in the Paschen-Back regime, and the behaviour of Stokes I and V profiles of transitions in the multiplet 74 of FeII is discussed in some detail. It is shown that the incomplete Paschen-Back effect can lead to notable line shifts which strongly depend on total multiplet strength, magnetic field strength and field direction. Ghost components (which violate the normal selection rule on J) show up in strong magnetic fields but are probably unobservable. Finally it is shown that measurements of the integrated magnetic field modulus Hs are not adversely affected by the Paschen-Back effect, and that there is a potential problem in (magnetic) Doppler mapping if lines in the Paschen-Back regime are treated in the Zeeman approximation. Title: Quiet-Sun Magnetic Field Measurements Based on Lines with Hyperfine Structure Authors: Sánchez Almeida, J.; Viticchié, B.; Landi Degl'Innocenti, E.; Berrilli, F. Bibcode: 2008ApJ...675..906S Altcode: 2007arXiv0710.5393S The Zeeman pattern of Mn I lines is sensitive to hyperfine structure (HFS), and because of this, they respond to hectogauss magnetic field strengths differently than the lines commonly used in solar magnetometry. This peculiarity has been employed to measure magnetic field strengths in quiet-Sun regions, assuming the magnetic field to be constant over a resolution element. This assumption is clearly insufficient, biasing the measurements. The diagnostic potential of Mn I lines can be fully exploited only after one understands the sense and magnitude of such bias. We present the first syntheses of Mn I lines in realistic quiet-Sun model atmospheres. The Mn I lines weaken with increasing field strength. In particular, kilogauss magnetic concentrations produce Mn I λ5538 circular polarization signals (Stokes V) that can be up to 2 orders of magnitude smaller than what the weak magnetic field approximation predicts. The polarization emerging from an atmosphere having weak and strong fields is biased toward the weak fields, and HFS features characteristic of weak fields show up even when the magnetic flux and energy are dominated by kilogauss fields. For the HFS feature of Mn I λ5538 to disappear, the filling factor of kilogauss fields has to be larger than the filling factor of subkilogauss fields. Since the Mn I lines are usually weak, Stokes V depends on magnetic field inclination according to the simple cosine law. Atmospheres with unresolved velocities produce very asymmetric line profiles, which cannot be reproduced by simple one-component model atmospheres. Using the HFS constants available in the literature, we reproduce the observed line profiles of nine lines with varied HFS patterns. Title: Magnetic Field Vector Measurements with THEMIS Authors: Bommier, V.; González, M. J. M.; Schmieder, B.; Landi Degl'Innocenti, E. Bibcode: 2008ASPC..383..123B Altcode: The aim of the present work is twofold: a) to validate the Milne-Eddington UNNOFIT inversion by comparing its results with those of the SIR inversion, which is in LTE but does not assumes the Milne-Eddington atmosphere; b) to present a decrease of the network local average magnetic field strength in the vicinity of a filament/prominence, observed before its disppearance, suggesting that the disappearance results from a weakening of the magnetic support. Title: The Magnetic Sensitivity of the Ba II D1 and D2 Lines of the Fraunhofer Spectrum Authors: Belluzzi, Luca; Trujillo Bueno, Javier; Landi Degl'Innocenti, Egidio Bibcode: 2007ApJ...666..588B Altcode: 2007arXiv0704.3979B The physical interpretation of the spectral line polarization produced by the joint action of the Hanle and Zeeman effects offers a unique opportunity to obtain empirical information about hidden aspects of solar and stellar magnetism. To this end, it is important to achieve a complete understanding of the sensitivity of the emergent spectral line polarization to the presence of a magnetic field. Here we present a detailed theoretical investigation on the role of resonance scattering and magnetic fields on the polarization signals of the Ba II D1 and D2 lines of the Fraunhofer spectrum at 4934 and 4554 Å, respectively. We adopt a three-level model of Ba II, and we take into account the hyperfine structure that is shown by the 135Ba and 137Ba isotopes. Despite their relatively small abundance (18%), the contribution coming from these two isotopes is indeed fundamental for the interpretation of the polarization signals observed in these lines. We consider an optically thin slab model, through which we can investigate in a rigorous way the essential physical mechanisms involved (resonance polarization, Zeeman, Paschen-Back, and Hanle effects), avoiding complications due to radiative transfer effects. We assume the slab to be illuminated from below by the photospheric solar continuum radiation field, and we investigate the radiation scattered at 90°, both in the absence and in the presence of magnetic fields, deterministic and microturbulent. We show in particular the existence of a differential magnetic sensitivity of the three-peak Q/I profile that is observed in the D2 line in quiet regions close to the solar limb, which is of great interest for magnetic field diagnostics. Title: Simulation of Magneto-Optical Filter Transmission Profiles Authors: Severino, G.; Oliviero, M.; Landi Degl'Innocenti, E. Bibcode: 2007ASPC..368..617S Altcode: We present a numerical simulation of a potassium Magneto-Optical Filter (MOF) enabling to compute the filter transmission. The results of the simulation are compared with experimental transmission profiles at different heating temperatures, measured with a diode laser system. The comparison reveals a significant amount of agreement but also shows some important differences. Title: Polarimetric Properties of the D2 Lines of Alkali Atoms Authors: Belluzzi, L.; Landi Degl'Innocenti, E.; Trujillo Bueno, J. Bibcode: 2007ASPC..368..311B Altcode: We present a theoretical investigation on the influence of a deterministic magnetic field on the linear and circular polarization of the Na I, K I, and Ba II D2 lines. We describe the three ions by means of a three-level atomic model, and we take into account the hyperfine structure which is shown by some isotopes. We focus on the ``solar prominence case'', in which an optically thin slab of chromospheric plasma, situated 7000 km above the visible solar ``surface'', and permeated by a magnetic field of given strength and orientation, is illuminated from below by the continuum photospheric radiation field. Title: Is the Solar Intranetwork Field a Resolved Turbulent Field? Authors: Bommier, V.; Landi Degl'Innocenti, E.; Landolfi, M.; Molodij, G. Bibcode: 2007ASPC..370...81B Altcode: The spectropolarimetric map observed below an active region filament on 7 December 2003 in the Fe I 6302.5 Å line has been inverted by using the UNNOFIT code of Landolfi et al. (1984), improved by the introduction of a magnetic filling factor parameter. The magnetic and non-magnetic theoretical atmospheres, mixed in the proportion given by the filling factor, are derived from the same set of parameters, except for the presence (or absence) of a magnetic field. The fundamental ambiguity is not solved. The results make clearly appear two regimes, corresponding to two ranges of filling factors: (a) the network zone extended to spatially broad lanes, having a field about 20°-30° from the vertical, with a homogeneous azimuth. In this zone the filling factor may be high, typically 10%-20% on the network itself and decreasing on both sides. (b) the intranetwork zone, where the field is turbulent and the filling factor typically 2% as expected by several authors. In both regions the field strength is found of the order of 1 kGauss. No clear difference in field strength is found between both zone types, they differ only by field direction homogeneity and filling factor. The turbulent nature of the intranetwork field has been confirmed by an independent inversion of Fe I 6301.5 Å. Title: Standard Stars for Linear Polarization Observed with FORS1 Authors: Fossati, L.; Bagnulo, S.; Mason, E.; Landi Degl'Innocenti, E. Bibcode: 2007ASPC..364..503F Altcode: We present the analysis of the observations of standard stars for linear polarization obtained from 1999 to 2005 within the context of the calibration plan of the FORS1 instrument of the ESO VLT. We have considered observations carried out both in imaging polarimetric and in spectropolarimetric mode. Broadband polarization was obtained in the Bessel BVRI filters; spectropolarimetry was obtained with various grisms covering different optical ranges and with a typical resolution of a few hundreds. Spectropolarimetric data have been convolved with the transmission functions of the Bessel filters, which enabled us to calculate polarization values equivalent to broadband polarization measurements in imaging mode. Finally, for each star, instrument mode, and for each Bessel filter band, we have calculated an average polarization value obtained after filtering all available data with a kσ-clipping algorithm. Title: Polarimetric Standardization Authors: Landi Degl'Innocenti, E.; Bagnulo, S.; Fossati, L. Bibcode: 2007ASPC..364..495L Altcode: 2006astro.ph.10262L The use of polarimetric techniques is nowadays widespread among solar and stellar astronomers. However, notwithstanding the recommandations that have often been made about the publication of polarimetric results in the astronomical literature, we are still far from having a standard protocol on which to conform. In this paper we review the basic definitions and the physical significance of the Stokes parameters, and we propose a standardization of the measurement of polarized radiation. Title: UNNOFIT inversion of spectro-polarimetric maps observed with THEMIS Authors: Bommier, V.; Landi Degl'Innocenti, E.; Landolfi, M.; Molodij, G. Bibcode: 2007A&A...464..323B Altcode: Aims:We inverted a spectropolarimetric scan of an active region and a filament (240× 340 arcsec) achieved with THEMIS on 7 December 2003 in the two lines Fe I 6302.5 and 6301.5 Å.
Methods: The inversion was achieved for each line separately by using the UNNOFIT code of Landolfi and Landi Degl'Innocenti, and was improved by introducing a magnetic filling-factor parameter. The magnetic and non-magnetic theoretical atmospheres, mixed in the proportion given by the filling factor, were derived from the same set of parameters, except for the presence (or absence) of a magnetic field. The fundamental ambiguity is not solved.
Results: The tests run with UNNOFIT show that the magnetic field strength B and the magnetic filling factor α cannot be separately recovered by the inversion in Fe I 6302.5, but that their product α B, which is the local average magnetic field, is recovered. The magnetic flux is only its longitudinal component. In addition, the results make two regimes clearly appear, corresponding to two ranges of local average magnetic field strength as measured in 6302.5: (a) the network, having a field inclined of about 20°-30° from the vertical in 6302.5 (spread more but non-horizontal in 6301.5), with a homogeneous azimuth. In this zone the local average field strength in 6302.5 is higher than 45 Gauss; (b) the internetwork, where the field is turbulent (with a horizontal trend, spread more at lower altitudes), and the 6302.5 local average field strength is lower than 45 Gauss (about 20 Gauss).
Conclusions: .The two lines display coherent results, in particular for the magnetic-field azimuth. From this coherence we conclude that the turbulence of the 20 Gauss internetwork field has a solar origin.

Based on observations made with the French-Italian telescope THEMIS operated by the CNRS and CNR on the island of Tenerife in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Title: Polarization properties of resonance scattering in molecular bands. The intermediate (a-b) coupling regime Authors: Landi Degl'Innocenti, E. Bibcode: 2007A&A...461....1L Altcode: The polarimetric properties of the phenomenon of resonance scattering in molecular bands are analyzed in detail for the general case where both the lower and upper electronic states of the molecule are described in the coupling scheme intermediate between Hund's cases (a) and (b). A semi-analytical expression is derived for the line polarizability factor in the special case where atomic polarization is neglected in the lower electronic state, and particular attention is devoted to clarifying the role played by the phenomenon of Λ-doubling, which turns out to be particularly relevant in the case of Π - Σ transitions. The expression for the line polarizability factor is derived for both cases where the energy eigenvectors are expressed as a linear combination of the eigenvectors relative to Hund's case (a) and of those relative to Hund's case (b). Such expressions are then combined with the corresponding expressions of the Einstein coefficient and of the Landé factors to obtain an estimate of the linear polarization signals to be expected in molecular bands observed at the solar limb either in the quiet atmosphere or in magnetic regions. Illustrative results are shown for the bands of MgH and of C2 around 5100 Å. Title: The Hanle and Zeeman Effects in the Ba II D2 Line Authors: Belluzzi, L.; Trujillo Bueno, J.; Landi Degl'Innocenti, E. Bibcode: 2006ASPC..358..459B Altcode: We present a theoretical investigation on the influence of the magnetic field on the linear and circular polarization of the Ba II D2 line at 4554 Å, through the Hanle and Zeeman effects. We show in particular the existence of a differential magnetic sensitivity of the three-peak structure of the Q/I profile observed for this line, which is of interest for magnetic field diagnostics. Title: UNNOFIT Inversion of Spectro-Polarimetric Maps Observed with THEMIS Authors: Bommier, V.; Landi Degl'Innocenti, E.; Landolfi, M.; Molodij, G. Bibcode: 2006ASPC..358..119B Altcode: This paper presents the inversion of a spectro-polarimetric scan (240 arcsec×340 arcsec) of an active region and a filament, obtained with THEMIS, on December 7, 2003, in the two Fe I lines at 6302.5 Å and 6301.5 Å. The inversion was applied to each line separately, using the UNNOFIT code of tet{b13 La84}, improved by the introduction of a magnetic filling factor parameter. The magnetic and non-magnetic theoretical atmospheres, mixed in the proportion given by the filling factor, are derived from the same set of parameters, except for the presence (or absence) of a magnetic field. The fundamental ambiguity is not solved. The tests run with UNNOFIT show that the magnetic field strength, B, and the magnetic filling factor, α, cannot be separately recovered by the inversion of Fe I 6302.5 Å, but that their product, α B, which is the local average magnetic field, is recovered. The magnetic flux is only its longitudinal component. Our results also reveal two distinct regimes, corresponding to two different ranges of local average magnetic field strength as inferred from Fe I 6302.5 Å: a) The network, having a field inclined of about 20°-30° from the vertical in Fe I 6302.5 Å (more spreaded, but non-horizontal in Fe I 6301.5 Å), with a homogeneous azimuth. In this zone, the local average field strength in Fe I 6302.5 Å is larger than 45 G. b) The internetwork, where the field is turbulent (with a horizontal trend, more spreaded at lower altitudes), and with local average field strength in Fe I 6302.5 Å smaller than 45 G. The two lines gives coherent results, in particular in magnetic field azimuth. From this we conclude that the turbulence of the internetwork field is of solar origin. This work has been presented in detail by tet{b13 Bo06}. Title: Multi-Line Determination of the Turbulent Magnetic Field from the Second Solar Spectrum of MgH Authors: Bommier, V.; Landi Degl'Innocenti, E.; Molodij, G. Bibcode: 2006ASPC..358..317B Altcode: This paper presents an analysis of the Q1,2(6{-}12) lines of the Q band of the A2Π-X2Σ+ (0,0) transition of MgH, whose linear polarization was measured with THEMIS, on November 21, 2004, in a quiet region of the Sun (North pole), 4 arcsec inside the solar limb. This analysis is performed as follows: a) The Hanle effect parameter, ΓH, is derived by applying the differential Hanle effect method between the two extreme pairs of lines. Assuming no depolarizing collisions, a magnetic field strength follows, which is found to be 9.2 G, in agreement with previous observations of the same kind. b) This ΓH parameter is entered in a code solving the non-LTE polarized radiative transfer equations, and the other depolarizing parameter, namely the depolarizing collision rate, is then derived by adjusting the computed polarization to the observed one. Thus an average value of the rate per colliding hydrogen atom α(2)=1.20×10-9 cm3 s-1 is obtained for the upper levels of the 12 lines (with a standard deviation of 0.21×10-9 cm3 s-1). The corresponding model-dependent depolarizing rate is D(2)=(4.2 ± 0.7)×107 s-1 at h=200 km. c) This depolarizing rate is now introduced in the conversion of the ΓH parameter in terms of magnetic field strength: an average turbulent field strength of 29 ± 12 G is derived as the final value, at a height h=200 ± 80 km where the polarization is formed. The Hönl-London factors of the lines under interest have been recalculated, leading to detect an error of a factor 2 in the recent literature. The derived value B=29 ± 12 G at h=200 ± 80 km is in fairly good agreement with previous determinations based on the interpretation of the Sr I 4607 Å limb polarization, which has led to fields in the range 35-60 G. Given the error bars, it seems unnecessary to put forward different formation regions for the Sr I and MgH lines. This work has been presented in detail by tet{b14 Bo06}, under the title ``Collisional influence on the differential Hanle effect method applied to the second solar spectrum of the A2Π-X2Σ+ (0,0) band of MgH.'' Title: Interpretation of the Second Solar Spectrum of the Sr I 4607 Å Line Observed at THEMIS and Pic-du-Midi Authors: Derouich, M.; Bommier, V.; Malherbe, J. -M.; Landi Degl'Innocenti, E.; Molodij, G.; Sahal-Bréchot, S. Bibcode: 2006ASPC..358..120D Altcode: The Hanle effect is the only tool available for measuring turbulent (i.e., spatially unresolved) magnetic fields at the surface of the quiet Sun. The Hanle-effect diagnostics relies on the discrepancy between the linear polarization calculated in the absence of a magnetic field and the observed polarization. We interpreted the linear polarization of the Sr I 4607 Å line, observed at THEMIS (December 7-9, 2002) and Pic-du-Midi (May 14, 2004), in terms of the Hanle effect. We present here the main results of this study. In particular, we stress the importance of a proper adjustment of the theoretical intensity profile to the observed one, through the application of a zero-field model, the magnetic field being determined in a second step from the line-center polarization degree. With the spatial resolution

and coverage of the Pic-du-Midi data (1 arcsec resolution, 132 distances from the limb), we can also attain depth probing of the turbulent magnetic strength, and we discuss whether this can vary within the range of heights of formation for the line center. Title: Polarizability Factors for Molecular Bands Authors: Landi Degl'Innocenti, E. Bibcode: 2006ASPC..358..293L Altcode: The polarimetric properties of resonance scattering in molecular bands are studied in detail for the general case where both the lower and upper electronic states of the molecule are described in the intermediate coupling scheme between Hund's cases (a) and (b). Starting from the diagonalization of the atomic Hamiltonian, and introducing suitable numerical coefficients for the description of the energy eigenvectors, we give semi-analytical expressions for the polarizability factors under the hypothesis of the absence of atomic polarization in the lower electronic state. Similar expressions are also given for the Einstein coefficients, and the Landé factors of all the lines pertaining to a molecular band. This allows to provide approximate expressions for the linear polarization observed at the solar limb in weak molecular lines and for its modification due to the Hanle effect. Title: Collisional influence on the differential Hanle effect method applied to the second solar spectrum of the A2Π-X2Σ+ (0, 0) band of MgH Authors: Bommier, V.; Landi Degl'Innocenti, E.; Feautrier, N.; Molodij, G. Bibcode: 2006A&A...458..625B Altcode: Aims.This paper presents an analysis of the Q1,2(6-12) lines of the Q band of the A2Π-X2Σ+ (0, 0) transition of MgH, whose linear polarization was measured 4 arcsec inside the solar limb in a quiet region (North Pole) with THEMIS on 21 November 2004.
Methods: .This analysis is performed as follows: a) the Hanle effect ΓH parameter is derived by applying the differential Hanle effect method between the two extreme pairs of lines. Assuming no depolarizing collisions, a magnetic field strength follows, which is found to be 9.2 Gauss, in agreement with previous observations of the same kind; b) this ΓH parameter is entered in a code solving the NLTE polarized radiative transfer equations, and the other depolarizing parameter, namely the depolarizing collision rate, is then derived by adjusting the computed polarization to the observed one. Thus an average value of the rate per colliding hydrogen atom α(2)=1.20 × 10-9 cm3 s-1 is obtained for the upper levels of the 12 lines (standard deviation 0.21 × 10-9 cm3 s-1). The corresponding model-dependent depolarizing rate is D(2)=(4.2 ± 0.7) × 107 s-1 at h=200 km; c) this depolarizing rate is now introduced in the conversion of the ΓH parameter in terms of magnetic field strength: an average turbulent field strength of 29 ± 12 Gauss is derived as the final value, at height h=200 ± 80 km where the polarization is formed. The Hönl-London factors of the lines under interest have been recalculated, leading to detect an error of a factor 2 in the recent literature.
Results: .The derived value B=29 ± 12 Gauss at h=200 ± 80 km is in fairly good agreement with the previous determinations based on the interpretation of the Sr I 4607 Å limb polarization, which has led to fields in the range 35-60 Gauss.
Conclusions: .Given the error bars, it seems unnecessary to put forward different formation regions for the Sr I and MgH lines. Title: Standard stars for linear polarization Authors: Fossati, L.; Bagnulo, S.; Mason, E.; Landi Degl'Innocenti, E. Bibcode: 2006astro.ph.10637F Altcode: We present the analysis of the observations of standard stars for linear polarization obtained from 1999 to 2005 within the context of the calibration plan of the FORS1 instrument of the ESO VLT. We have considered observations carried out both in imaging polarimetric and in spectropolarimetric mode. Broadband polarization was obtained in the Bessel BVRI filters; spectropolarimetry was obtained with various grisms covering different optical ranges and with a typical resolution of a few hundreds. Spectropolarimetric data have been convolved with the transmission functions of the Bessel filters, which enabled us to calculate polarization values equivalent to broadband polarization measurements in imaging mode. Finally, for each star, instrument mode, and for each Bessel filter band, we have calculated an average polarization value obtained after filtering all available data with a k-sigma clipping algorithm. Title: Second solar spectrum of the Sr I 4607 Å line: depth probing of the turbulent magnetic field strength in a quiet region Authors: Derouich, M.; Bommier, V.; Malherbe, J. M.; Landi Degl'Innocenti, E. Bibcode: 2006A&A...457.1047D Altcode: Aims.This paper is devoted to an interpretation of Quiet-Sun, spatially-resolved spectropolarimetric observations of the Hanle effect in terms of turbulent weak magnetic field determination.
Methods: . Observations: the slit was positioned perpendicular to the limb, and the spatial resolution along the slit was 1 arcsec, leading to a depth probing along 132 different limb distances. The new polarimeter of the Pic-du-Midi Turret Dome was used on May 14, 2004 to observe a quiet region at the East limb equator in the resonance line of neutral Strontium at 4607 Å.
Results: . For each limb distance, we properly adjusted the theoretical intensity profile obtained by applying a zero-field model to the observed one. Micro- and macroturbulent velocities were thus derived (average values v{micro}=1.77 km s-1 and v{macro}=1.95 km s-1). The magnetic field was determined in a second step by interpreting the Hanle effect on the line center linear polarization degree. The depolarizing collisions with neutral hydrogen were taken fully into account through a semi-classical calculation of their rates. An average value of B=38 Gauss was thus derived. Finally, error bars on the magnetic field values were evaluated from a) the polarimetric inaccuracy, b) the limb distance determination inaccuracy, and c) the uncertainty on our theoretical collisional depolarizing rates that we evaluated. This combination leads to 10-20% as total relative error on the magnetic field determination by the Hanle effect method. Since the inaccuracy due to the model itself was hard to properly evaluate, it was ignored. An uncertainty of ±60 km on the line formation depth was, however, derived from the contribution functions. The magnetic field is found to increase slowly with height in the height range 220-300 km above τ5000=1 and then decrease in the height range 300-370 km.
Title: Erratum: ``Polynomial Approximants for the Calculation of Polarization Profiles in the He I 10830 Å Multiplet'' (ApJS, 160, 312 [2005]) Authors: Socas-Navarro, H.; Trujillo Bueno, J.; Landi Degl'Innocenti, E. Bibcode: 2006ApJS..166..441S Altcode: In our published paper there is an error in the order of the rows in Tables 1 through 6. We stated in the paper that the components are sorted in the order of increasing wavelengths in the linear Zeeman splitting (LZS) regime. However, in the published tables the values for the σ+ and σ- components appear reversed. As a result, researchers trying to implement our polynomial approximants might apply the incomplete Paschen-Back splitting (IPBS) corrections to the wrong components. To avoid any possible confusion, here we reproduce the tables with the correct sorting (i.e., in the order of increasing wavelengths in the LZS regime). For clarity, we have also replaced the σ+/- notation with σred/blue.

We thank Rebecca Centeno for bringing this error to our attention. Title: Determination of the Magnetic Field Vector via the Hanle and Zeeman Effects in the He I λ10830 Multiplet: Evidence for Nearly Vertical Magnetic Fields in a Polar Crown Prominence Authors: Merenda, L.; Trujillo Bueno, J.; Landi Degl'Innocenti, E.; Collados, M. Bibcode: 2006ApJ...642..554M Altcode: The magnetic field is the key physical quantity responsible for the formation, stability, and evolution of solar prominences (ribbons of cool dense gas embedded in the hot tenuous corona). Therefore, it is important to obtain good empirical knowledge of the three-dimensional structure of prominence magnetic fields. Here we show how the magnetic field vector can be inferred via the physical interpretation of spectropolarimetric observations in the He I λ10830 multiplet. To this end, we have developed an inversion code based on the quantum theory of the Hanle and Zeeman effects and on a few modeling assumptions. We show an application to full Stokes vector observations of a polar crown prominence that, in the slit-jaw Hα image, showed nearly vertical plasma structures. Our results provide evidence for magnetic fields on the order of 30 G inclined by about 25° with respect to the local solar vertical direction. Of additional interest is that the inferred nearly vertical magnetic field vector appears to be slightly rotating around a fixed direction in space as one proceeds along the direction of the spectrograph's slit. While these results provide new light on the three-dimensional geometry of the magnetic fields that confine the plasma of polar crown prominences, they also urge us to develop improved solar prominence models and to pursue new diagnostic investigations. Title: A qualitative interpretation of the second solar spectrum of Ce ll Authors: Manso Sainz, R.; Landi Degl'Innocenti, E.; Trujillo Bueno, J. Bibcode: 2006A&A...447.1125M Altcode: 2005astro.ph.11011M This is a theoretical investigation on the formation of the linearly polarized line spectrum of ionized cerium in the sun. We calculate the scattering line polarization pattern emergent from a plane-parallel layer of Ce ii atoms illuminated from below by the photospheric radiation field, taking into account the differential pumping induced in the various magnetic sublevels by the anisotropic radiation field. We find that the line polarization pattern calculated with this simple model is in good qualitative agreement with reported observations. Interestingly, the agreement improves when some amount of atomic level depolarization is considered. We find that the best fit to the observations corresponds to the situation where the ground and metastable levels are depolarized to about one fifth of the corresponding value obtained in the absence of any depolarizing mechanism. One possibility to have this situation is that the depolarizing rate value of elastic collisions is exactly D=10^6~s-1, which is rather unlikely. Therefore, we interpret that fact as due to the presence of a turbulent magnetic field in the limit of saturated Hanle effect for the lower-levels. For this turbulent magnetic field we obtain a lower limit of 0.8 Gauss and an upper limit of 200-300 Gauss. Title: The scientific case for spectropolarimetry from space: a novel diagnostic window on cosmic magnetic fields Authors: Trujillo Bueno, J.; Landi Degl'Innocenti, E.; Casini, R.; Martínez Pillet, V. Bibcode: 2005ESASP.588..203T Altcode: 2005tssc.conf..203T No abstract at ADS Title: Determination of the Magnetic Field Vector in a Polar Crown Prominence via the Hanle and Zeeman Effects in the He I 10830 Å Multiplet. Authors: Merenda, L.; Trujillo Bueno, J.; Landi Degl'Innocenti, E.; Collados, M. Bibcode: 2005ESASP.596E..18M Altcode: 2005ccmf.confE..18M No abstract at ADS Title: The Scientific Case for Quantum Spectropolarimetry from Space Authors: Trujillo Bueno, J.; Landi Degl'Innocenti, E.; Casini, R.; Martínez Pillet, V. Bibcode: 2005ESASP.596E...4T Altcode: 2005ccmf.confE...4T No abstract at ADS Title: Polynomial Approximants for the Calculation of Polarization Profiles in the He I 10830 Å Multiplet Authors: Socas-Navarro, H.; Trujillo Bueno, J.; Landi Degl'Innocenti, E. Bibcode: 2005ApJS..160..312S Altcode: 2005astro.ph..5321S The He I multiplet at 10830 Å is formed in the incomplete Paschen-Back regime for typical conditions found in solar and stellar atmospheres. The positions and strengths of the various components that form the Zeeman structure of this multiplet in the Paschen-Back regime are approximated here by polynomials. The fitting errors are smaller than ~10-2 mÅ in the component positions and ~10-3 in the relative strengths. The approximant polynomials allow for a very fast implementation of the incomplete Paschen-Back regime in numerical codes for the synthesis and inversion of polarization profiles in this important multiplet. Title: Dichroic Masers Due to Radiation Anisotropy and the Influence of the Hanle Effect on the Circumstellar SiO Polarization Authors: Asensio Ramos, A.; Landi Degl'Innocenti, E.; Trujillo Bueno, J. Bibcode: 2005ApJ...625..985A Altcode: 2005astro.ph..2405A The theory of the generation and transfer of polarized radiation, mainly developed for interpreting solar spectropolarimetric observations, allows us to reconsider, in a more rigorous and elegant way, a physical mechanism that has been suggested some years ago to interpret the high degree of polarization often observed in astronomical masers. This mechanism, for which the name of ``dichroic maser'' is proposed, can operate when a low-density molecular cloud is illuminated by an anisotropic source of radiation (e.g., a nearby star). Here we investigate completely unsaturated masers and show that selective stimulated emission processes are capable of producing highly polarized maser radiation in a nonmagnetic environment. The polarization of the maser radiation is linear and is directed tangentially to a ring equidistant to the central star. We show that the Hanle effect due to the presence of a magnetic field can produce a rotation (from the tangential direction) of the polarization by more that 45° for some selected combinations of the strength, inclination, and azimuth of the magnetic field vector. However, these very same conditions produce a drastic inhibition of the maser effect. The rotations of about 90° observed in SiO masers in the evolved stars TX Cam by Kemball & Diamond and IRC +10011 by Desmurs and coworkers may then be explained by a local modification of the anisotropy of the radiation field, being transformed from mainly radial to mainly tangential. Title: Full Stokes Spectropolarimetry of Hα in Prominences Authors: López Ariste, A.; Casini, R.; Paletou, F.; Tomczyk, S.; Lites, B. W.; Semel, M.; Landi Degl'Innocenti, E.; Trujillo Bueno, J.; Balasubramaniam, K. S. Bibcode: 2005ApJ...621L.145L Altcode: We report on spectropolarimetric observations of Hα in prominences made with the Télescope Héliographique pour l'Etude du Magnétisme et des Instabilités Solaires and the High Altitude Observatory/Advanced Stokes Polarimeter. Stokes Q and U show the expected profile shape from resonance scattering polarization and the Hanle effect. In contrast, most of the time, Stokes V does not show the antisymmetric profile shape typical of the Zeeman effect but a profile that indicates the presence of strong atomic orientation in the hydrogen levels, to an extent that cannot be explained by invoking the alignment-to-orientation transfer mechanism induced by the prominence magnetic field. We found that the largest signal amplitudes of Stokes V (comparable to that of Stokes Q and U) could be produced by a process of selective absorption of circularly polarized radiation from the photosphere, which requires that the prominence be in the vicinity of an active region. Although recent observations of active region filaments indicate such a selective absorption mechanism as a plausible explanation of the anomalous signals observed, the particular set of conditions that must be met suggest that a different explanation may be required to explain the almost ubiquitous symmetric V signal observed in Hα prominences. Therefore, we speculate that an alternative mechanism inducing strong atomic orientation at the observed level could be due to the presence of electric fields inducing an electric Hanle effect on Hα. Although we are still working toward a careful modeling of this effect, including both electric and magnetic fields, we present some preliminary considerations that seem to support this possibility. Title: Interpretation of second solar spectrum observations of the Sr I 4607 Å line in a quiet region: Turbulent magnetic field strength determination Authors: Bommier, V.; Derouich, M.; Landi Degl'Innocenti, E.; Molodij, G.; Sahal-Bréchot, S. Bibcode: 2005A&A...432..295B Altcode: This paper presents and interprets some observations of the limb polarization of Sr I 4607 Å obtained with the spectropolarimeter of the French-Italian telescope THEMIS in quiet regions close to the solar North Pole on 2002 December 7-9. The linear polarization was measured for a series of limb distances ranging from 4 to 160 arcsec, corresponding to heights of optical depth unity in the line core ranging from about 330 to 220 km, respectively, above the τ5000=1 level. To increase the polarimetric sensitivity, the data were averaged along the spectrograph slit (one arcmin long) set parallel to the solar limb. Since the data show no rotation of the linear polarization direction with respect to the limb direction, the observed depolarization is ascribed to the Hanle effect of a turbulent weak magnetic field, the zero-field polarization being derived from a model. The interpretation is performed by means of an algorithm which describes the process of line formation in terms of the atomic density matrix formalism, the solar atmosphere being described by an empirical, plane-parallel model. The collisional rates entering the model (inelastic collisions with electrons, elastic depolarizing collisions with neutral hydrogen), have been computed by applying fast semi-classical methods having a typical accuracy of the order of 20% or better (see Derouich [CITE]), leading to 6% inaccuracy on the magnetic field strength determination. We assume a unimodal distribution for the intensity of the turbulent field. The computed intensity profile has been adjusted to the observed one in both depth and width, by varying both microturbulent and macroturbulent velocities. The best adjustment is obtained for respectively 1.87 km s-1 (micro) and 1.78 km s-1 (macro). The evaluation of the magnetic depolarization leads then to the average value of 46 Gauss for the turbulent magnetic field strength, with a gradient of -0.12 Gauss/km. Our results are in very good agreement with the value of 60 Gauss determined at large μ, in the volume-filling field case, by Trujillo Bueno et al. ([CITE], Nature, 430, 326), using a 3D magneto-convective simulation. This validates our method.

Based on observations made with the french-italian telescope THEMIS operated by CNRS and CNR on the island of Tenerife in the spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Title: The Hanle and Zeeman Effects in Solar Spicules: A Novel Diagnostic Window on Chromospheric Magnetism Authors: Trujillo Bueno, J.; Merenda, L.; Centeno, R.; Collados, M.; Landi Degl'Innocenti, E. Bibcode: 2005ApJ...619L.191T Altcode: 2005astro.ph..1533T; 2005astro.ph..1533B An attractive diagnostic tool for investigating the magnetism of the solar chromosphere is the observation and theoretical modeling of the Hanle and Zeeman effects in spicules, as shown in this Letter for the first time. Here we report on spectropolarimetric observations of solar chromospheric spicules in the He I λ10830 multiplet and on their theoretical modeling accounting for radiative transfer effects. We find that the magnetic field in the observed (quiet-Sun) spicular material at a height of about 2000 km above the visible solar surface has a strength of the order of 10 G and is inclined by approximately 35deg with respect to the local vertical direction. Our empirical finding based on full Stokes vector spectropolarimetry should be taken into account in future magnetohydrodynamical simulations of spicules. Title: Second solar spectrum observed at the Pic-du-Midi: depth probing of the turbulent magnetic field intensity in a quiet region. Authors: Derouich, M.; Malherbe, J. M.; Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Bréchot, S. Bibcode: 2004sf2a.conf..113D Altcode: 2004sf2a.confE.346D The installation of a new polarimeter at the Turret Dome of the Pic-du-Midi has permitted new observations of the "second solar spectrum" (which is the spectrum of the linear polarization observed near the solar limb), having a spatial resolution. On 2003 October 25, we have observed a quiet region located at the East limb equator, in the resonance line of neutral strontium at 4607 Å. The slit was positioned perpendicular to the limb: recording various limb distances provides a depth probing of the solar atmosphere. The intensity of the turbulent magnetic field has been derived from the Hanle effect interpretation, which is actually the only method for vectorial weak field determination. The theoretical profiles to be compared to the observed ones have been obtained by applying the atomic density matrix formalism (Landi Degl'Innocenti E., Bommier V., & Sahal-Bréchot S., 1990). The various collisional coefficients have been computed by applying semi-classical methods that are accurate to 20% or better: the one from Seaton (1962) and Sahal-Bréchot (1969a, 1969b) for the collisions with electrons, responsible for the inelastic transitions, and the one developed by Anstee & O'Mara (1991, 1995) for line broadening computations, generalized to the collisional depolarization by Derouich et al. (2003; see also Derouich, 2004), for the elastic collisions with neutral hydrogen atoms. The results have been found in full agreement with those previously obtained with THEMIS without any spatial resolution (at 9 limb distances). With the spatial resolution that we have now at the Pic-du-Midi (1 arcsec, 138 limb distances), it appears that the turbulent magnetic field intensity does not vary with depth, in the line formation region that ranges from ~200 to ~300 km above the tau5000=1 level. Title: Concerning the Existence of a ``Turbulent'' Magnetic Field in the Quiet Sun Authors: Manso Sainz, Rafael; Landi Degl'Innocenti, Egidio; Trujillo Bueno, Javier Bibcode: 2004ApJ...614L..89M Altcode: 2004astro.ph..8360M We report on the a5F-y5Fo multiplet of Ti I and its interest for the study of ``turbulent'' magnetic fields in the quiet solar photosphere. In particular, we argue that the sizable scattering polarization signal of the 4536 Å line (whose lower and upper levels have Landé factors equal to zero), relative to the rest of the lines in the multiplet, gives direct evidence for the existence of a ubiquitous, unresolved magnetic field. We cannot determine precisely the strength of the magnetic field, but its very existence is evidenced by the differential Hanle effect technique that this Ti I multiplet provides. Title: Signatures of Incomplete Paschen-Back Splitting in the Polarization Profiles of the He I λ10830 Multiplet Authors: Socas-Navarro, H.; Trujillo Bueno, J.; Landi Degl'Innocenti, E. Bibcode: 2004ApJ...612.1175S Altcode: 2004astro.ph..9005S We investigate the formation of polarization profiles induced by a magnetic field in the He I multiplet at 10830 Å. Our analysis considers the Zeeman splitting in the incomplete Paschen-Back regime. The effects turn out to be important and produce measurable signatures on the profiles, even for fields significantly weaker than the level-crossing field (~400 G). When compared to profiles calculated with the usual linear Zeeman effect, the incomplete Paschen-Back profiles exhibit the following conspicuous differences: (1) a non-Doppler blueshift of the Stokes V zero-crossing wavelength of the blue component; (2) area and peak asymmetries, even in the absence of velocity and magnetic gradients; and (3) a ~25% reduction in the amplitude of the red component. These features do not vanish in the weak-field limit. The spectral signatures that we analyze in this paper may be found in previous observations published in the literature. Title: Polarization in Spectral Lines Authors: Landi Degl'Innocenti, E.; Landolfi, M. Bibcode: 2004ASSL..307.....L Altcode: 2004psl..book.....L The scientific research based on spectropolarimetric techniques is undergoing a phase of rapid growth. Instruments of unprecedented sensitivity are nowadays available, particularly for solar observations. To fully exploit the rich diagnostic content of such observations, it is necessary to understand the physical mechanisms involved in the generation and transfer of polarized radiation in astrophysical (or laboratory) plasmas. After an introductory part based on classical physics, this book tackles the subject by a rigorous quantum-mechanical approach. The transfer equations for polarized radiation and the statistical equilibrium equations for the atomic density matrix are derived directly from the principles of Quantum Electrodynamics. The two sets of equations are then used to present a number of applications, mainly concerning the diagnostics of solar magnetic fields. This book is primarily addressed to scientists working in the field of spectropolarimetry. It may also serve as a textbook for a course at the graduate or advanced undergraduate level.

Link: https://www.springer.com/gb/book/9781402024146 Title: Successful Measurement of the Full Magnetic Vector Near the Base of the Solar Corona Authors: Solanki, S. K.; Lagg, A.; Woch, J.; Krupp, N.; Landi Degl'Innocenti, E.; Collados, M. Bibcode: 2003AGUFMSH41D..05S Altcode: The measurement of coronal fields has in the past generally been restricted to the field strength or to only some of the components of the magnetic vector. We present here a technique for measuring the full magnetic vector near the base of the solar corona. As an application we report on observations of a developing active region with ongoing magnetic flux emergence. The data allow the first measurement of the 3-D structure of magnetic loops. They also provide the first detection of an electric current sheet located near the base of the solar corona. Such current sheets or tangential discontinuities of the coronal magnetic field have long been thought to be a major source of coronal heating. Title: The Differential Saturation Mechanism: an Application of the Zeeman Effect to the Diagnostic of Magnetic Fields Authors: Landi Degl'Innocenti, E. Bibcode: 2003EAS.....9...71L Altcode: A review of broad-band polarimetric observations is presented, from the first systematic observations of Jean-Louis Leroy in sunpots and active regions to the more recent applications concerning the polarization diagrams of chemically peculiar stars. The historical evolution of the interpretation is also discussed, with particular emphasis on the differential saturation mechanism and on its physical meaning. Title: Diagnostic of turbulent magnetic fields in solar quiet regions by their Hanle effect in the Sr I 4607Å line Authors: Derouich, M.; Bommier, V.; Landi Degl'Innocenti, E.; Molodij, G.; Sahal-Bréchot, S. Bibcode: 2003sf2a.conf..113D Altcode: 2003sf2a.confE..42D Stokes parameters of the resonance Sr I 4607 Å line were observed with the solar THEMIS telescope in December 2002, close to the limb of the sun at the North pole. They are interpreted in terms of turbulent magnetic field. The Interpretation requires a non-LTE radiative transfer calculations of the Stokes parameters. The contributions of depolarizing isotropic collisions with neutral hydrogen and inelastic collisions with electrons as well as the radiative processes are taken into account in the statistical equilibrium equations in order to identify weak magnetic fields by their depolarizing Hanle effect. The values of depth-dependent magnetic field, derived from observations at different distances from the solar limb, are given. These observations and the magnetic field results are in agreement with other measurements also obtained with THEMIS, and interpreted by using a different formalism (Faurobert M., Arnaud J., Vigneau J., Frisch H., 2001, A&A 378, 627). Title: Theory of Polarization: What's Next? Authors: Landi Degl'Innocenti, E. Bibcode: 2003ASPC..307..593L Altcode: No abstract at ADS Title: Towards the Understanding of the Second Solar Spectrum of Ti I Authors: Manso Sainz, R.; Landi Degl'Innocenti, E. Bibcode: 2003ASPC..307..425M Altcode: No abstract at ADS Title: The Zeeman effect: applications to solar physics Authors: Landi Degl'Innocenti, E. Bibcode: 2003AN....324..393L Altcode: This contribution is intended to give a brief review of some of the results concerning the Zeeman effect which have been recently published in the literature or which appear to be particularly relevant at the light of recent technological improvements in observations. The arguments emphasized are the Zeeman effect in molecular lines, the asymmetries observed in Stokes profiles from sunspots, and the interpretation of spectropolarimetric observations in the infrared. Title: Case Studies in Resonance Polarization and the Hanle Effect Authors: Landolfi, M.; Landi Degl'Innocenti, E. Bibcode: 2003ASPC..307..241L Altcode: No abstract at ADS Title: Resonance Scattering Polarization in Molecular Lines Authors: Landi Degl'Innocenti, E. Bibcode: 2003ASPC..307..164L Altcode: No abstract at ADS Title: A qualitative interpretation of the second solar spectrum of Ti I Authors: Manso Sainz, R.; Landi Degl'Innocenti, E. Bibcode: 2002A&A...394.1093M Altcode: The first theoretical investigation of the formation of the linearly polarized solar line spectrum of a complex atom, neutral titanium, is presented. The process of formation of line polarization is modeled by simply considering a plane-parallel layer of Ti I atoms illuminated from below by the photospheric radiation field, and accounting for the differential pumping induced in the various magnetic sublevels by the anisotropic radiation field. The calculated line polarization pattern is in good qualitative agreement with reported observations, thus showing that the generation of population imbalances between magnetic sublevels due to the radiation field anisotropy is the basic physical mechanism responsible for the observed polarization pattern in the Fraunhofer spectrum of Ti I. The role of depolarizing collisions on the polarized spectrum of Ti I is also investigated. Title: On the Atomic Polarization of the Ground Level of Na I Authors: Casini, Roberto; Landi Degl'Innocenti, Egidio; Landolfi, Marco; Trujillo Bueno, Javier Bibcode: 2002ApJ...573..864C Altcode: 2002astro.ph..4341C In a recent Letter, we showed the remarkable result that the atomic alignment of the levels P1/2 and S1/2 of the D1 line of Na I is practically destroyed in the presence of magnetic fields sensibly larger than 10 G, irrespective of the field direction. In this paper, we analytically demonstrate that this property is a consequence of the decoupling of the electronic and nuclear angular momenta J and I in the excited state P3/2, which is achieved when the Zeeman splitting from the local magnetic field becomes much larger than the typical hyperfine separation for that level. Title: The Physical Origin of the Scattering Polarization of the Na I D Lines in the Presence of Weak Magnetic Fields Authors: Trujillo Bueno, Javier; Casini, Roberto; Landolfi, Marco; Landi Degl'Innocenti, Egidio Bibcode: 2002ApJ...566L..53T Altcode: 2002astro.ph..1389T We demonstrate that the atomic alignment of the hyperfine-structure components of the ground-level S1/2 of Na I and of the upper-level P1/2 of the D1 line are practically negligible for magnetic strengths B>10 G and virtually zero for B>~100 G. This occurs independently of the magnetic field inclination on the stellar surface (also, in particular, for vertical fields). Consequently, the characteristic antisymmetric linear polarization signature of the scattered light in the D1 line is practically suppressed in the presence of magnetic fields larger than 10 G, regardless of their inclination. Remarkably, we find that the scattering polarization amplitude of the D2 line increases steadily with the magnetic strength, for vertical fields above 10 G, while the contribution of the alignment to the polarization of the D1 line rapidly decreases. Therefore, we suggest that spectropolarimetric observations of the ``quiet'' solar chromosphere showing significant linear polarization peaks in both D1 and D2 cannot be interpreted in terms of one-component magnetic field models, implying that the magnetic structuring of the solar chromosphere could be substantially more complex than previously thought. Title: Selective absorption processes as the origin of puzzling spectral line polarization from the Sun Authors: Trujillo Bueno, J.; Landi Degl'Innocenti, E.; Collados, M.; Merenda, L.; Manso Sainz, R. Bibcode: 2002Natur.415..403T Altcode: 2002astro.ph..1409T Magnetic fields play a key role in most astrophysical systems, from the Sun to active galactic nuclei. They can be studied through their effects on atomic energy levels, which produce polarized spectral lines. In particular, anisotropic radiation `pumping' processes (which send electrons to higher atomic levels) induce population imbalances that are modified by weak magnetic fields. Here we report peculiarly polarized light in the HeI 10,830-Å multiplet observed in a coronal filament located at the centre of the solar disk. We show that the polarized light arises from selective absorption from the ground level of the triplet system of helium, and that it implies the presence of magnetic fields of the order of a few gauss that are highly inclined with respect to the solar radius vector. This disproves the common belief that population imbalances in long-lived atomic levels are insignificant in the presence of inclined fields of the order of a few gauss, and opens up a new diagnostic window for the investigation of solar magnetic fields. Title: The physics of polarization Authors: Landi Degl'Innocenti, Egidio Bibcode: 2002apsp.conf....1L Altcode: This course is intended to give a description of the basic physical concepts which underlie the study and the interpretation of polarization phenomena. Apart from a brief historical introduction (Sect. 1), the course is organized in three parts. A first part (Sects. 2 - 6) covers the most relevant facts about the polarization phenomena that are typically encountered in laboratory applications and in everyday life. In Sect. 2, the modern description of polarization in terms of the Stokes parameters is recalled, whereas Sect. 3 is devoted to introduce the basic tools of laboratory polarimetry, such as the Jones calculus and the Mueller matrices. The polarization phenomena which are met in the reflection and refraction of a beam of radiation at the separation surface between two dielectrics, or between a dielectric and a metal, are recalled in Sect. 4. Finally, Sect. 5 gives an introduction to the phenomena of dichroism and of anomalous dispersion and Sect. 6 summarizes the polarization phenomena that are commonly encountered in everyday life. The second part of this course (Sects. 7-14) deals with the description, within the formalism of classical physics, of the spectro-polarimetric properties of the radiation emitted by accelerated charges. Such properties are derived by taking as starting point the Liénard and Wiechert equations that are recalled and discussed in Sect. 7 both in the general case and in the non-relativistic approximation. The results are developed to find the percentage polarization, the radiation diagram, the cross-section and the spectral characteristics of the radiation emitted in different phenomena particularly relevant from the astrophysical point of view. The emission of a linear antenna is derived in Sect. 8. The other Sections are devoted to Thomson scattering (Sect. 9), Rayleigh scattering (Sect. 10), Mie scattering (Sect. 11), bremsstrahlung radiation (Sect. 12), cyclotron radiation (Sect. 13), and synchrotron radiation (Sect. 14). Finally, the third part (Sects. 15-19) is devoted to give a sketch of the theory of the generation and transfer of polarized radiation in spectral lines. After a general introduction to the argument (Sect. 15), the concepts of density-matrix and of atomic polarization are illustrated in Sect. 16. In Sect. 17, a parallelism is established, within the framework of the theory of stellar atmospheres, between the usual formalism, which neglects polarization phenomena, and the more involved formalism needed for the interpretation of spectro-polarimetric observations. Some consequences of the radiative transfer equations for polarized radiation, pointing to the importance of dichroism phenomena in establishing the amplification condition via stimulated emission, are discussed in Sect. 18. The last section (Sect. 19) is devoted to introduce the problem of finding a self-consistent solution of the radiative transfer equations for polarized radiation and of the statistical equilibrium equations for the density matrix (non-LTE of the 2nd kind). Title: Magnetic Field Diagnostic Techniques Based on the Zeeman and Hanle Effects Authors: Landi Degl'Innocenti, E. Bibcode: 2001ASPC..248...73L Altcode: 2001mfah.conf...73L No abstract at ADS Title: The Paschen-Back Effect on Fine and Hyperfine Structure: Impact on Polarized Spectra of Ap and Bp Stars Authors: Landolfi, M.; Bagnulo, S.; Landi Degl'Innocenti, M.; Landi Degl'Innocenti, E. Bibcode: 2001ASPC..248..349L Altcode: 2001mfah.conf..349L No abstract at ADS Title: Evidence for ground-level atomic polarization in the solar atmosphere Authors: Landi Degl'Innocenti, E. Bibcode: 1999ASSL..243...61L Altcode: 1999sopo.conf...61L No abstract at ADS Title: Evidence against turbulent and canopy-like magnetic fields in the solar chromosphere Authors: Landi degl'Innocenti, Egidio Bibcode: 1998Natur.392..256L Altcode: Measurements of the degree of polarization of light in the spectral lines emitted by gas near the Sun's limb (its outer edge) can be used to investigate the electron densities and magnetic field strengths in the solar atmosphere; these quantities are important for determining the balance and transport of energy through the Sun's atmosphere. Recent measurements, revealed a surprising degree of polarization in the sodium doublet; these observations have remained an enigma. Here I report a mechanism that may explain these observations, in which it is assumed that the populations of the magnetic sublevels of the electronic ground state of the sodium atom are not equal: this leads to ground-level atomic polarization. This mechanism explains very well the observed line shapes, and implies that depolarization does not occur in the solar chromosphere, which would seem to rule out the existence of turbulent magnetic fields and of horizontal, canopy-like fields stronger than~0.01G. This is difficult to understand, because there is substantial evidence from othertypes of observation for both types of field. There are obviously aspects of the Sun's atmosphere that remain very poorly understood. Title: Spectropolarimetry of the solar atmosphere Authors: Landi Degl'Innocenti, E. Bibcode: 1998MmSAI..69..605L Altcode: No abstract at ADS Title: Constraints on the magnetic configuration of AP stars from simple features of observed quantities. Authors: Landolfi, M.; Bagnulo, S.; Landi Degl'Innocenti, M.; Landi Degl'Innocenti, E.; Leroy, J. L. Bibcode: 1997A&A...322..197L Altcode: According to the oblique rotator model, the time variations of the quantities usually employed to investigate the magnetic configuration of Ap stars (mean longitudinal field, mean surface field, broad band linear polarization) are described by simple laws. For each quantity, certain typical features can easily be identified. We show that these features set definite constraints on the magnetic configuration. Title: Linear Polarization Due to Lower Level Depopulation Pumping in Stellar Atmospheres Authors: Trujillo Bueno, Javier; Landi Degl'Innocenti, Egidio Bibcode: 1997ApJ...482L.183T Altcode: The possible generation of linear polarization in spectral lines due to depopulation-pumping processes in stellar atmospheres is investigated within the framework of a quantum electrodynamic theory for the transfer of polarized radiation based on the atomic density-matrix formalism. It is shown that the radiation field's anisotropy in solar-like atmospheres induces population imbalances among the lower level sublevels of optical line transitions. The depolarizing rates that are assumed to model some typical spectral lines are not capable of completely destroying such a lower level atomic alignment, and the corresponding linear polarization signals are found to lie above the sensitivity limit of some recently developed spectropolarimeters. Title: Theoretical polarization profiles of optically-thick hydrogen lines from slabs in the presence of electric and magnetic fields Authors: Casini, R.; Landi Degl'Innocenti, E. Bibcode: 1997A&AS..122..149C Altcode: The theory of formation of hydrogen lines in the presence of stationary electric and magnetic fields is applied to the calculation of the emerging Stokes profiles from a slab of hydrogen plasma, for different optical thicknesses of the slab. The calculations are performed assuming different analytical dependences of the source function on the optical depth. Typical results for hydrogen lines of interest in solar plasmas investigation are then shown. Title: (Erratum) LTE radiative transfert for polarized hydrogen lines in the weak-field regime. Authors: Casini, R.; Landi Degl'Innocenti, E. Bibcode: 1996A&A...313.1027C Altcode: Erratum to Astron. Astrophys. 308, 335-344 (1996). Title: Line Asymmetries and the Microstructure of Photospheric Magnetic Fields Authors: Sanchez Almeida, J.; Landi Degl'Innocenti, E.; Martinez Pillet, V.; Lites, B. W. Bibcode: 1996ApJ...466..537S Altcode: A systematic structuring of magnetic fields over scales much smaller than the mean free path of photospheric photons may be responsible for the observed asymmetrical Stokes profiles. We explore this possibility by deriving the radiative transfer equation for microstructured magnetic atmospheres (the MISMA approximation). This equation is subsequently employed to show that very schematic MISMA scenarios for the penumbrae of sunspots, plage and network regions, and internetwork regions produce Stokes profiles that have the observed asymmetries. The details of these model atmospheres are of secondary importance, but the ease of generating the type of observed asymmetries with MISMAs is significant, so the existence of MISMAs deserves serious consideration. Should such microstructures exist, the techniques currently employed to infer properties of the solar photosphere need to be revised. MISMAs are also of concern for the physics of the photosphere itself. These two topics are briefly discussed. Title: Linear polarimetry of AP stars. VI. A modified dipolar model consistent with the observations. Authors: Leroy, J. L.; Landolfi, M.; Landi Degl'Innocenti, E. Bibcode: 1996A&A...311..513L Altcode: While some Ap variables display a linear polarization variation very similar to that computed for a pure magnetic dipole, several Ap stars show conspicuous peculiarities which must be interpreted in terms of departures from the standard, oblique rotator model (we have shown previously that abundances anomalies are not sufficient to explain odd polarization diagrams). We have designed an inversion method, based on a residues minimization process, which allows us to build the map of the magnetic peculiarities at the surface of non-dipolar stars. As the linear polarization is but weakly sensitive to the variations of the field modulus, we interpret the polarization anomalies in terms of inclination changes of the lines of force within their meridian plane. Keeping the magnetic equator as a plane of symmetry, we show that it is sufficient to assume slightly expanded lines of force, over some parts of the magnetic equator, to explain most peculiar polarization curves (Figs. 2 to 7). Such regions, where the lines of force expand outwards, seem to occur preferentially in the vicinity of the rotation poles for those stars having a β angle not far from 90deg. In the case of β CrB, which was studied previously in detail (Leroy, 1995), this region nearly coincides with the equatorial patch of enhanced field strength, which must be postulated to explain the surface field measurements. The present study, which also provides unambiguous determinations of the i and β angles for 15 stars, marks the provisional end of our investigation based on broadband linear polarization measurements. We expect that similar measurements, having a good spectral resolution, will be available soon: they will yield more severe observational constraints enabling a more detailed modeling work. However, we think that the series of articles which ends with the present paper has demonstrated the great value of linear polarization data and may have opened fruitful research tracks bearing on the magnetic structure of Ap stars. Title: LTE radiative transfer for polarized hydrogen lines in the weak-field regime. Authors: Casini, R.; Landi Degl'Innocenti, E. Bibcode: 1996A&A...308..335C Altcode: In this paper we investigate the radiative-transfer problem for polarized hydrogen lines in the regime of weak electric and magnetic fields, and under the hypothesis of LTE. A standard perturbation method is applied which reduces the vector radiative-transfer equation to a set of four de-coupled ODEs for each order of approximation. Our derivation enables us to use previous results for the first- and second-order moments of the polarization profiles of hydrogen lines in the presence of electric and magnetic fields, also accounting for the fine structure contribution. We then get to a generalization of the weak-field solution for the purely magnetic case, which had already been obtained in the literature under the same hypotheses and through the same perturbation approach. Title: Multipolar magnetic fields in rotating AP stars: modeling of observable quantities. Authors: Bagnulo, S.; Landi Degl'Innocenti, M.; Landi Degl'Innocenti, E. Bibcode: 1996A&A...308..115B Altcode: Magnetic field is present in most of the chemically peculiar stars of the upper main sequence. For a long time, the component of the magnetic field along the line of sight and the magnetic field modulus, averaged on the stellar disk, were the only diagnostic contents of the observational techniques. Recent developments in the application of the theory of line formation, joined to the increased sensitivity of instrumental techniques, augmented the number of observable quantities related to the magnetic fields of such a class of stars. On the other hand, the analytical modeling techniques, that is, the capability to reproduce the observable quantities - predicted by a given magnetic configuration - through simple analytical formulae, is still limited only to some of the quantities nowadays measurable and for the simplest magnetic configurations. This work gives a contribution in order to fill this gap. Through the formalism of the spherical tensorial calculus, analytical formulae for most of the observable quantities are provided for a magnetic field of arbitrary complexity. Namely, the magnetic field is thought of as originated by a multipolar expansion of arbitrary order (dipole, plus quadrupole, plus octupole, ...) and it is expressed through spherical tensors and spherical harmonics. By using such a formalism, it is straightforward to carry on the integration over the stellar disk of the particular combinations of the magnetic field components which represent the observable quantities. The mean longitudinal magnetic field, the so-called mean asymmetry of the longitudinal magnetic field and the mean quadratic magnetic field, together with the quantities related to the observed broadband linear polarization, are expressed through suitable sums of terms including the spherical components of tensors describing the magnetic configuration. These sums can numerically be performed, or they can be further developed in order to provide simpler analytical expressions in the case of a defined multipolar expansion: in particular, such simpler analytical expressions are given in the case of a magnetic field due to the superposition of a dipole with a quadrupole. Finally, few diagrams of the observable quantities predicted by such a configuration are shown. Title: The density matrix approach to polarized radiative transfer Authors: Landi Degl'innocenti, E. Bibcode: 1996SoPh..164...21L Altcode: The density matrix approach to polarized radiative transfer is reviewed, with particular emphasis on the physical assumptions that are at the basis of the recent developments achieved by means of this formalism. In particular it is shown that two of the basic hypotheses (the hypothesis of neglecting correlation effects between thermal velocity and density matrix, and the hypothesis of neglecting atomic polarization in the atomic ground level) are highly questionable for the description of resonance polarization -and its modifications due to the presence of a magnetic field- in spectral lines formed in the solar atmosphere. Title: The polarization-free approximation Authors: Trujillo Bueno, J.; Landi Degl'Innocenti, E. Bibcode: 1996SoPh..164..135T Altcode: The development of effective iterative methods capable of accurately solving NLTE Stokes transfer problems is of considerable importance for the investigation of solar and stellar magnetic fields. After briefly indicating the iterative approach which is being presently pursued for the exact solution of such problems, the particular regime where polarization signals can only be due to the Zeeman effect is considered in some detail. By means of NLTE Stokes transfer calculations for a two-level atomic model it is first shown that the currently-used field-free approximation (Rees, 1969) cannot be safely applied in the presence of magnetic field gradients. Such gradients lead to changes in the shape and width of the line profiles and they can produce non-negligible effects on the atomic level populations and line source functions. A new approximate method is then proposed, which does not require the actual solution of the Stokes vector transfer equation and is practically as fast as the field-free one. This polarization-free approximation provides a fairly good account of the effects of homogeneous and inhomogeneous magnetic fields on the statistical equilibrium and is very easy to implement in any existing non-magnetic, multi-level transfer code. Title: The first and second order moments of the polarization profiles of hydrogen lines Authors: Casini, R.; Landi Degl'Innocenti, E. Bibcode: 1996SoPh..164...91C Altcode: The main properties of the first- and second-order moments of polarized hydrogen lines, forming in the presence of stationary electric and magnetic fields, are reviewed. The analytical results presented here apply directly to the case of optically-thin emission lines in the LTE regime. Some applications of such results to electric- and magnetic-field diagnostics in (solar) plasmas are then briefly considered. Title: Net Circular Polarization in Magnetic Spectral Lines Produced by Velocity Gradients: Some Analytical Results Authors: Landolfi, M.; Landi Degl'innocenti, E. Bibcode: 1996SoPh..164..191L Altcode: The net circular polarization in a spectral line due to the combined effect of magnetic fields and velocity gradients is analyzed for a few schematic situations. In some particular cases, its dependence on the magnetic field, velocity field and line parameters can be expressed analytically. Title: Non-LTE Polarized Radiative Transfer in Intermediate Magnetic Fields: Numerical Problems and Results Authors: Bommier, V.; Landi Degl'Innocenti, E. Bibcode: 1996SoPh..164..117B Altcode: This paper presents some numerical results relative to a solution, based on the density matrix formalism, of the non-LTE, polarized radiative transfer problem for a two-level atom. The results concern the atomic upper level population and alignment, and the emergent radiation Stokes profiles, for a plane-parallel, static, isothermal atmosphere embedded in a magnetic field of intermediate strength, such that the Zeeman splitting has to be taken into account in the line profile. Zeeman coherences are neglected, whereas magneto-optical effects are taken into account, resulting in a full 4×4 absorption matrix. Induced emission is neglected and complete frequency redistribution, in the rest and laboratory frames, is assumed. Pure Doppler absorption profile (gaussian shape) has also been assumed. The presentation of the results is preceded by a brief discussion of their accuracy and of the numerical difficulties that were met in the solution of the problem. Title: Linear polarimetry of AP stars. IV. The influence of deviations from a pure dipolar model. Authors: Leroy, J. L.; Landolfi, M.; Landi Degl'Innocenti, M.; Landi Degl'Innocenti, E.; Bagnulo, S.; Laporte, P. Bibcode: 1995A&A...301..797L Altcode: In the previous papers of this series we have described a new observational program of broadband linear polarimetry aimed at Ap stars. At the same time, we have established a canonical model, based on the oblique rotator geometry, which describes successfully the main features of the observed polarization: in some cases the linear polarization data, combined with the classical circular polarization measurements, allow one to determine the characteristic parameters which define the oblique dipolar rotator. However, we have also observed polarization diagrams that depart clearly from those predicted by the canonical model, which means that it is not always possible to rely on a pure dipolar model (nor on a combination of a dipole plus a linear quadrupole parallel to the dipole). Although an interpretation of the polarization peculiarities in terms of magnetic `anomalies' (i.e. deviations from the dipolar configuration) is quite natural, one must also take into account the possible influence of local abundance inhomogeneities. Therefore, we have first studied the sensitivity of the polarized signal (which is known to be due to the differential saturation of Zeeman components in spectral lines) to a variation of the metallic absorption spectrum. Then we have examined how a local enhancement (or reduction) of the polarization produced by a dipolar magnetic field affects the Fourier spectrum of the observed polarization signal. Finally, we have designed an inversion program making possible the recovery - under certain restrictions - of the spatial modulations of the polarization generated by a dipole, which are necessary to explain `odd' polarimetric data. This program has been applied to the data gathered from three stars (49 Cam, β CrB, HD 71866). As far as the last star is concerned, none of the spatial modulations considered was able to reproduce the observations. On the contrary, good solutions are found for the other two. However, if one interprets the variations of the polarization as the result of abundance variations, which must correspond to a modulation of the absorption spectrum, a contradiction arises, especially for β CrB, because the observed spectral variability of these stars is too small to account for our computed maps. Therefore, non-canonical polarization diagrams must essentially be interpreted in terms of magnetic anomalies, not of abundance anomalies: in other words, the peculiarities of the polarization diagrams are likely to result mainly from departures of the magnetic configuration from the pure dipolar configuration. Title: Properties of the second-order moments of the polarization profiles of hydrogen lines. Authors: Casini, R.; Landi Degl'Innocenti, E. Bibcode: 1995A&A...300..309C Altcode: In this paper we give the expressions for the second-order moments of the polarization profiles, for any hydrogen line which is formed in the presence of external electric and magnetic fields. These quantities are directly related to the dispersions of the polarization profiles and are useful whenever the centers-of-gravity method cannot be applied, as in the case of the linear Stark effect or, more generally, when investigating the linear-polarization profiles. An analytical definition of the modulation of the polarization signals is given in order to provide an unambiguous way to estimate the sensitivity of a line to the electric and magnetic fields. Then, relevant properties of the modulations are examined in typical regimes of the external fields. Title: Linear polarimetry of AP stars. III. A diagnostic method for the magnetic structure of rotating stars. Authors: Bagnulo, S.; Landi Degl'Innocenti, E.; Landolfi, M.; Leroy, J. L. Bibcode: 1995A&A...295..459B Altcode: A method for the diagnostic of magnetic fields in Ap stars is presented. It is based on the joint interpretation of traditional circular polarization observations (giving B_l_, the longitudinal magnetic field averaged over the stellar surface) and of broadband linear polarization observations. The method consists in a numerical, best-fit algorithm which takes into account the possibility of describing the time variation of broadband linear polarization by means of analytical expressions. The algorithm has been checked against numerical simulations and has shown to be reliable especially for the determination of the magnetic configuration of the star. Two applications have been considered for the stars HD 24712 and HD 71866 by interpreting new broadband linear polarization observations together with circular polarization data available in the literature. Title: Properties of the first-order moments of the polarization profiles of hydrogen lines. Authors: Casini, R.; Landi Degl'Innocenti, E. Bibcode: 1994A&A...291..668C Altcode: In this article, we investigate some noteworthy properties of the first-order moments of the polarization profiles of hydrogen lines in the presence of external electric and magnetic fields. These properties are useful in testing the applicability of the centers-of-gravity method for the estimate of magnetic fields, whenever electric fields are also present. A criticism is also raised about the effective Lande factor in hydrogen lines as previously calculated by different authors. In addition, we achieve a better insight into the problem of the numerical precision of the software package which has been developed for the calculation of the polarization properties of hydrogen lines, a problem already approached in a previous paper. Title: Complete determination of the magnetic field vector and of the electron density in 14 prominences from linear polarizaton measurements in the HeI D3 and Hα lines Authors: Bommier, Veronique; Landi Degl'Innocenti, Egidio; Leroy, Jean-Louis; Sahal-Brechot, Sylvie Bibcode: 1994SoPh..154..231B Altcode: The present paper is devoted to the interpretation of linear polarization data obtained in 14 quiescent prominences with the Pic-du-Midi coronagraph-polarimeter by J. L. Leroy, in the two lines HeI D3 andHα quasi-simultaneously. The linear polarization of the lines is due to scattering of the anisotropic photospheric radiation, modified by the Hanle effect due to the local magnetic field. The interpretation of the polarization data in the two lines is able to provide the 3 components of the magnetic field vector, and one extra parameter, namely the electron density, because the linear polarization of Hα is also sensitive to the depolarizing effect of collisions with the electrons and protons of the medium. Moreover, by using two lines with different optical thicknesses, namely HeI D3, which is optically thin, and Hα, which is optically thick (τ = 1), it is possible to solve the fundamental ambiguity, each line providing two field vector solutions that are symmetrical in direction with respect to the line of sight in the case of the optically thin line, and which have a different symmetry in the case of the optically thick line. Title: (Erratum) The polarized spectrum of hydrogen in the presence of electric and magnetic fields Authors: Casini, R.; Landi Degl'Innocenti, E. Bibcode: 1994A&A...287..692C Altcode: Erratum to Astron. Astrophys. 276, 289-302 (1993) Title: A long period model for the magnetic star γ Equulei. Authors: Leroy, J. L.; Bagnulo, S.; Landolfi, M.; Landi Degl'Innocenti, E. Bibcode: 1994A&A...284..174L Altcode: Linear polarimetry has enabled us to observe the rotation of the magnetic axis of the star γ Equ (nearly 15deg over the period 1990-1993). Thus, the very long rotation period of more than 70 years, suggested by previous authors, is now confirmed in a straightforward way. We propose numerical values for the various parameters which enter the oblique rotator model and we show that they are consistent with all the available data on the magnetism of γ Equ. Title: Resonance line polarization for arbitrary magnetic fields in optically thick media. III. A generalization of the ɛ^1/2^-law. Authors: Landi Degl'Innocenti, E.; Bommier, V. Bibcode: 1994A&A...284..865L Altcode: The well-known "ɛ^1/2^-law" - one of the few exact analytical results in the theory of radiative transfer - is generalized to the case of an isothermnal, plane-parallel atmosphere in the presence of a magnetic field vector of arbitrary intensity and direction and in the presence of depolarizing collisions. A compact expression is found, relating the squares of the surface value of the upper level components of the atomic density matrix in the representation of the irreducible spherical tensors to the value of the constant Planck function. By taking the appropriate limits, the usual ɛ^1/2^-law for unpolarized radiation, and its generalization to resonance scattering polarization in a non-magnetic atmosphere (Ivanov 1990), are recovered as particular cases. Title: Recipes for solar polarimetry Authors: Landi Degl'Innocenti, E. Bibcode: 1994ASIC..433...29L Altcode: No abstract at ADS Title: High resolution solar observations: Spectropolarimetry with THEMIS Authors: Landi Degl'Innocenti, E.; Rayrole, J.; Mein, P. Bibcode: 1994LNP...432..315L Altcode: 1994LNPM...11..315L Solar observations now require many capabilities: high resolution to detect fine flux tubes, polarization-free optics to measure the vector magnetic field, spectral range including many lines to disentangle thermodynamic from magnetic signatures. The site of Canary Islands, the active optics, the Cassegrain telescope, the long spectrographs and the universal filter of THEMIS fulfill many conditions for major advances in the near future of solar physics. Title: The polarized spectrum of hydrogen in the presence of electric and magnetic fields Authors: Casini, R.; Landi Degl'Innocenti, E. Bibcode: 1993A&A...276..289C Altcode: The polarization properties of a beam of radiation interacting with a hydrogen atom subject to simultaneous stationary electric and magnetic fields are investigated, assuming no constraints on the direction of the two fields. The problem of determining the energy eigenstates is solved within the theory of Rayleigh-Schroedinger for the stationary perturbations (the contributions of the fine and hyperfine structure of the energy spectrum are also accounted for). Then the polarized transition rates (for absorption, spontaneous emission and stimulated emission) are evaluated according to the methods of non-relativistic quantum electrodynamics, adopting the density matrix formalism which allows one to deal with partially polarized states of the atomic and the radiation field systems. Typical results are then shown. Title: A Spectroscopic Method for the Solution of the 180 degrees Azimuth Ambiguity in Magnetograms Authors: Landi Degl'Innocenti, Egidio; Bommier, Veronique Bibcode: 1993ApJ...411L..49L Altcode: A spectroscopic method is proposed for removing the azimuth ambiguity intrinsically present in vector magnetograms. The method is based on the idea that the polarization observed in resonance lines (typically formed at the chromospheric level) depends not only on the magnetic field vector, but also on the anisotropy of the radiation field that is illuminating the scattering atoms. An observational scheme is proposed. Title: Linear polarimetry of AP stars. 1. A simple canonical model Authors: Landolfi, M.; Landi Degl'Innocenti, E.; Landi Degl'Innocenti, M.; Leroy, J. L. Bibcode: 1993A&A...272..285L Altcode: The present knowledge of the magnetism of Ap stars derives essentially from the analysis of the longitudinal Zeeman effect. The transverse Zeeman effect is more difficult to observe but it contains important information on the angular parameters which describe the `oblique rotator'. This effect can be conveniently studied via broadband polarization measurements: among the previously published results, the Kemp & Wolstencroft (1974) contribution has revealed to be particularly interesting, especially after a theoretical interpretation has been given for the time variation of linear polarization (Landi Degl'Innocenti et al. 1981). This example remained however an isolated one and we have decided to tackle again the same type of investigation with the help of the Pic du Midi 2-meter telescope.

Although the general theory of the phenomenon is now quite clear, we have considered useful to analyze in some detail an inversion procedure allowing to determine the parameters of the magnetic field from the observed polarization. To this aim we have developed a canonical model which provides simple analytical solutions to the inversion problem. These solutions are shown to give a close approximation to the broadband polarization obtained through more rigorous calculations.

The present work is limited to the classical schemes of the dipolar and quadrupolar magnetic structure, although in principle it could be extended to more complex configurations. Title: Linear polarimetry of AP stars. II. New observations with a reappraisal of former ones. Authors: Leroy, J. L.; Landolfi, M.; Landi Degl'Innocenti, E. Bibcode: 1993A&A...270..335L Altcode: We have presented, in a previous paper, a canonical model which helps one to understand the intrinsic linear polarization measured in the light of magnetic Ap stars. This linear polarization, which provides a tracer of the magnetic field component perpendicular to the line of sight, can be observed in broad spectral regions, and it has been actually observed in several stars. Such measurements can provide useful information on the magnetism of Ap stars only when they sample correctly the whole rotation period of the object under study. Up to now, this condition had been fulfilled only in the case of HD 65339; in other cases, a more limited amount of data was available. Adding our new observations has enabled a first detailed analysis of HD 137909, HD 7 1866 and HD 115708; in particular, we can decide which of the angle i (between the line of sight and the rotation axis) and beta (between the rotation axis and the magnetic axis) is larger. Altogether, this paper contains a general review on all existing measurements and a comprehensive investigation on the linear polarization of four Ap stars based on previous observations and on our new measurements. The comparison of this observational material with the previously established model shows the capabilities and the limits of this method of study of Ap stars. Title: Broadband Measurements of the Transverse Magnetic Field of Cool Ap-Stars Authors: Leroy, J. L.; Landstreet, J. D.; Landi Degl'Innocenti, E.; Landolfi, M. Bibcode: 1993ASPC...44..274L Altcode: 1993IAUCo.138..274L; 1993pvnp.conf..274L No abstract at ADS Title: Atomic orientation in chromospheric lines. Authors: Trujillo Bueno, J.; Martínez Pillet, V.; Sánchez Almeida, J.; Landi Degl'Innocenti, E. Bibcode: 1993ASPC...46..526T Altcode: 1993ASPC...46..526B; 1993mvfs.conf..526T; 1993IAUCo.141..526T Observations of the Stokes I and V profiles of the Ca II H and K lines in solar magnetic regions are presented. Least-squares fits of dI/dλ to V are obtained and the wavelength variation of the residuals, i.e. V-kdI/dλ, calculated. The authors find significant symmetric residuals in umbrae, which are in agreement with the effect on the V profiles due to atomic orientation, i.e. with the existence of an unequal population of the Zeeman sublevels with M > 0 with respect to those with M < 0. Title: Broadband Linear Polarization in Ap-Stars Authors: Landolfi, M.; Landi Degl'Innocenti, E.; Landi Degl'Innocenti, M.; Leroy, J. L.; Bagnulo, S. Bibcode: 1993ASPC...44..305L Altcode: 1993pvnp.conf..305L; 1993IAUCo.138..305L No abstract at ADS Title: Electron Impact Polarization of Atomic Spectral Lines. I. A General Theoretical Scheme Authors: Fineschi, Silvano; Landi Degl'Innocenti, Egidio Bibcode: 1992ApJ...392..337F Altcode: A suitable theoretical scheme able to describe, in a wide variety of astrophysical situations, the phenomenon of atomic line polarization by electron impact is developed. Starting from the general principles of quantum mechanics and assuming the Born approximation, the rate equations for the density matrix elements of a multilevel atomic system, interacting with a nonrelativistic electron beam having any kind of angular distribution, are derived in full generality. The resulting theory generalizes the previous ones by accounting for the collisional rates and the cross sections concerning both inelastic and superelastic collisions (in any geometrical situation), and, moreover, by taking into account the coherences among Zeeman sublevels split by a magnetic field. As an example of particular relevance, the general formulas derived in the first sections of the paper are subsequently particularized to the case of the electric dipole interaction. Title: Magnetic field measurements. Authors: Landi Degl'Innocenti, Egidio Bibcode: 1992soti.book...71L Altcode: 1992soti.book...71D Contents: (1) Description of polarized radiation. (2) A prototype polarimeter: setting of various devices at fixed angles; measurements with rotating wave plates; measurements with variable retarders. (3) Physical components of polarimeters: polarizers; retarders. (4) Generalities on polarization phenomena in spectral lines: Zeeman effect; impact and resonance polarization; resonance polarization and the Hanle effect; the role of collisions in resonance polarization; a classification scheme for polarimetric observations. (5) Radiative transfer for polarized radiation. (6) Line formation in a magnetic field. (7) Transfer equations for the Stokes parameters in a magnetized atmosphere. (8) Solutions of the transfer equations and magnetic field measurements: weak field solution; solution for a Milne-Eddington atmosphere; more general analytical solutions; numerical solutions; particular solutions. (9) Magnetic field measurements in unresolved structures: the line ratio technique. (19) Magnetic field measurements in prominences. Title: Resonance line polarization and the Hanle effect in optically thick media. II - Case of a plane-parallel atmosphere Authors: Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Brechot, S. Bibcode: 1991A&A...244..383B Altcode: The results of computations of resonance polarization and the Hanle effect (weak magnetic field) for a two-level atom in a plane-parallel optically thick atmosphere and numerical methods for solving them are presented. The findings are compared with results yielded by other methods, of the differential method type, in zero magnetic field and under the hypothesis of complete frequency redistribution, and a good agreement is obtained. The novel computation method, called the 'global' method, is applied to test the validity of the results obtained by the iterative method. The result of the computations are finally presented in the form of Hanle diagrams for some magnetic field and line-of-sight geometries. Title: Resonance line polarization for arbitrary magnetic fields in optically thick media. I - Basic formalism for a 3-dimensional medium. Authors: Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S. Bibcode: 1991A&A...244..391L Altcode: We present in this paper a general formalism to describe resonance line polarization for a two-level atom in an optically thick three-dimensional medium embedded in a magnetic field of arbitrary strength and irradiated by an arbitrary radiation field. The results contained in the present paper generalize those derived in a previous paper (Landi Degl'Innocenti et al. 1990) that were restricted to weak magnetic fields (νL ≪ ΔνD, with νL the Larmor frequency and ΔνD the Doppler broadening of the line). Here the restriction νL ≪ ΔνD is released, which makes the present formulation capable of describing, in a unified framework, resonance polarization, the Hanle effect and the Zeeman effect. Analogously to our previous paper, neglecting atomic polarization in the lower level and stimulated emission, we derive an integral equation for the multipole moments of the density matrix of the upper level by coupling the statistical equilibrium equations for the density matrix with the radiative transfer equations for polarized radiation. The final equation accounts for the effect of the magnetic field and for the role of inelastic and elastic (or depolarizing) collisions. Obviously, in the limiting case of weak magnetic fields (νL ≪ ΔνD), the results of our previous paper are recovered. Title: Resonance Line Polarization for Arbitrary Magnetic Fields in Optically Thick Media - Part Two - Case of a Plane-Parallel Atmosphere and Absence of Zeeman Coherences Authors: Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S. Bibcode: 1991A&A...244..401L Altcode: The general problem of resonance scattering for a two-level atom in a magnetized plane-parallel atmosphere is formulated by using the irreducible tensor representation of the atomic density matrix. A more general formalism presented in a previous paper (Paper I), convenient for taking into account arbitrary magnetic field effects (Zeeman effect as well as Hanle effect), is particularized in the present paper to the case of a "strong" magnetic field (Zeeman splitting much larger than the natural width of the upper level), and to the case of a unidimensional medium. A system of coupled integral equations, relating the density matrix elements at different depths in the atmosphere, is derived, and the properties of the relative kernels are discussed. It is shown that, in the limiting case of weak magnetic fields (VL ≪ ΔνD), the presence of atomic polarization induces a breakdown in the usual formula V(ν) = -gνL(dI/dν), that is commonly used for measuring magnetic fields from magnetograph-type observations. Title: High resolution spectropolarimetry of an active region. Authors: Bonaccini, D.; Landi Degl'Innocenti, E.; Smaldone, L. A.; Tamblyn, P. Bibcode: 1991sopo.work..251B Altcode: Some spectropolarimetric observations at moderately high spatial resolution are presented. The observations, obtained through a Fabry-Perot interferometer in cascade of an Universal Birefringent Filter, show the high potentiality of this spectroscopic technique for the detailed analysis of solar active regions. Title: Diagnostic of the magnetic field vector using the atomic density matrix formalism. Authors: Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Bréchot, S. Bibcode: 1991sopo.work..434B Altcode: The authors present the work which has been done and which is being done using the atomic density matrix formalism, for the interpretation of linear polarization measurements, leading to the magnetic field diagnostic in astrophysical media. This formalism has been used for interpreting polarization data from solar prominences, leading to original results on the prominence magnetic field obtained through the Hanle effect. An attempt is made to solve the coupled problem of polarized radiative transfer and statistical equilibrium in the case of weak, intermediate and strong magnetic fields, using a method of the integral method type; the advantages of this method, with respect to other methods, of the differential method type, are briefly discussed. Title: Velocities and Magnetic Fields Observed in a Sunspot Authors: Arena, P.; Landi Degl'Innocenti, E.; Noci, G. Bibcode: 1990SoPh..129..259A Altcode: A diagnostic method for the determination of the vector magnetic field through the interpretation of spectropolarimetric profiles observed in solar active regions is presented. An inversion routine, that is based on the analytical solution of the radiative transfer equation for polarized radiation given by Unno and Rachkowsky, is described; the routine performs a comparison among theoretical profiles depending on eight parameters and the observed profiles by means of a non linear least square fit. The routine has been applied to the interpretation of the spectropolarimetric profiles observed on 15 September, 1980 in a sunspot with the spectropolarimeter (Stokes II) of the High Altitude Observatory, National Center for Atmospheric Research*. One of the eight parameters (the line center) gives information on the plasma motions. The significance of these motions inside the sunspot is discussed. Title: Resonance line polarization and the Hanle effect in optically thick media. Authors: Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S. Bibcode: 1990A&A...235..459L Altcode: A general formalism is presented to describe resonance line polarization for a two-level atom in an optically thick, three-dimensional medium embedded in an arbitrary varying magnetic field and irradiated by an arbitrary radiation field. The magnetic field is supposed sufficiently small to induce a Zeeman splitting much smaller than the typical line width. By neglecting atomic polarization in the lower level and stimulated emission, an integral equation is derived for the multipole moments of the density matrix of the upper level. This equation shows how the multipole moments at any assigned point of the medium are coupled to the multipole moments relative at a different point as a consequence of the propagation of polarized radiation between the two points. The equation also accounts for the effect of the magnetic field, described by a kernel locally connecting multipole moments of the same rank, and for the role of inelastic and elastic (or depolarizing) collisions. After having given its formal derivation for the general case, the integral equation is particularized to the one-dimensional and two-dimensional cases. For the one-dimensional case of a plane parallel atmosphere, neglecting both the magnetic field and depolarizing collisions, the equation here derived reduces to a previous one given by Rees (1978). Title: Diagnostic of Prominence Magnetic Fields Authors: Landi Degl'Innocenti, Egidio Bibcode: 1990LNP...363..206L Altcode: 1990doqp.coll..206L; 1990IAUCo.117..206L An updated review on theoretical research on the role of magnetic fields in prominences is presented. It is concluded that the theory of the Hanle effect has reached a sufficient degree of sophistication and provides a reliable method for measuring the vector magnetic field. For optically thin lines, insensitive to depolarizing collisions, the theory provides a 'model independent' diagnostic method. The He I D3 line is considered to be particularly suitable for the diagnostics of magnetic fields in prominences, due to the negligibility of optical thickness and its insensitivity to depolarizing collisions. Optically thick lines provide the unique possibility of determining the magnetic field vector from disk observations. Linear polarization observations in H-alpha filaments using new spectropolarimetric instrumentation will make it possible to obtain important information on the magnetic configuration in the higher layers of prominences. Title: A diagnostic method for vector magnetic field and plasma velocity measurement in sunspots through the analysis of spectropolarimetric profiles. Authors: Arena, P.; Landi Degl'Innocenti, E.; Noci, G. Bibcode: 1990PDHO....7..116A Altcode: 1990dysu.conf..116A No abstract at ADS Title: Linear Polarization of Hydrogen Hα Line in Filaments - Method and Results of Computation Authors: Bommiier, V.; Landi Degl'Innocenti, E.; Sahal-Bréchot, S. Bibcode: 1990LNP...363..281B Altcode: 1990IAUCo.117..281B; 1990doqp.coll..281B No abstract at ADS Title: Some comments on the methods for measuring magnetic fields in late-type stars Authors: Landolfi, M.; Landi Degl'Innocenti, M.; Landi Degl'Innocenti, E. Bibcode: 1989A&A...216..113L Altcode: Various method for measuring magnetic field strengths and filling factors in active late-type stars are considered. The method of Saar (1988) consists of fitting analytical expressions for the intensity profiles of magnetic lines to the observed profiles. An analysis of synthetic line profiles illustrates how simplifying assumptions employed in this method affect the deduced magnetic field and filling factor values. It is pointed out that the line polarization profiles expected from a uniformly magnetized star could in principle be used as an additional diagnostic tool for the magnetic fields of late-type stars. Title: Polarization properties of a `Zeiss-type' coelostat: The case of the solar tower in Arcetri Authors: Capitani, C.; Landi Degl'Innocenti, E.; Cavallini, F.; Ceppatelli, G.; Landi Degl'Innocenti, M.; Landolfi, M.; Righini, A. Bibcode: 1989SoPh..120..173C Altcode: A theoretical model of the polarization properties of a `Zeiss-type' coelostat is presented and discussed in detail. The Muller matrix describing the modification of the Stokes vector of the incident radiation as a result of the multiple reflections on the coelostat mirrors is derived as a function of the solar coordinates, the geometrical configuration of the coelostat, and the parameters defining the optical properties of the mirrors. These parameters, or more particularly, the index of refraction n and the extinction coefficient k, have been evaluated by means of laboratory measurements performed on a series of specimens having characteristics similar to those of the coelostat mirrors. The geometry of the coelostat configuration is described in full detail. The theoretical model has been then particularized to the case of the Donati Solar Tower in Arcetri, and some experimental measurements have been performed to check the correctness of the model. These measurements show the basic adequacy of the mathematical model, although some offset terms are found in the Stokes parameters U and V. Title: Linear polarization of the hydrogen H-alpha line in filaments. I - Theoretical investigation Authors: Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Brechot, S. Bibcode: 1989A&A...211..230B Altcode: Results are presented of theoretical calculations of the expected linear polarization in H-alpha from a filament observed at different positions over the solar disk. The geometry of the filament is represented by an infinite cylinder with an elliptical cross section, standing horizontally over the solar surface. The calculation results indicate a clear effect of a magnetic field; it was found that the polarization degrees in the presence of a magnetic field can reach values of the order of 2 percent. In addition, there was an optical thickness effect on the polarization degree and direction. These results suggest that it is possible to use the observations of the H-alpha line from filaments to determine the magnetic field vector. Title: Linear Polarization of Hydrogen H-alpha Line in Filaments: Method and Results of Computation Authors: Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Brechot, S. Bibcode: 1989HvaOB..13..339B Altcode: No abstract at ADS Title: Expected linear polarization during the eclipsing phase of detached binaries Authors: Landi Degl'Innocenti, E.; Landi Degl'Innocenti, M.; Landolfi, M. Bibcode: 1988A&A...204..133L Altcode: Simple analytical expressions are derived to describe the variable polarization to be expected, during the eclipsing phase of a detached binary system, due to stellar limb polarization. Such expressions are discussed with particular emphasis on their symmetry properties. Some polarization diagrams for typical cases are presented and the diagnostic content of polarimetric observations of eclipsing binaries is briefly discussed. Title: An analytical expression for the Hanle-effect scattering phase matrix Authors: Landi Degl'Innocenti, M.; Landi Degl'Innocenti, E. Bibcode: 1988A&A...192..374L Altcode: The authors have derived analytical expressions for the matrix elements of the scattering phase-matrix in the presence of a magnetic field (Hanle effect). These expressions have been obtained for the most general geometry, where the directions of the incident and scattered beams and of the magnetic field vector are specified with respect to an arbitrary direction. The relative formulae for a turbulent distribution of the magnetic field directions are also presented. Title: Linear polarization of hydrogen Balmer lines in optically thick prominences: theoretical investigation. Authors: Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Bréchot, S. Bibcode: 1988dssp.conf...41B Altcode: The expected linear polarization in Hα for a filament observed at different positions over the solar disk is investigated from a theoretical point of view. The filament is schematized as an infinite cylinder with an elliptical cross-section standing horizontally on the solar surface. The emerging linear polarization is calculated according to a perturbative scheme introduced in a preceding paper (Landi Degl'Innocenti et al., 1987). The role of depolarizing collisions and the influence of local magnetic fields (Hanle effect) is fully accounted for. Typical results are presented for the expected Hα polarization across filaments observed at various positions and skew angles over the solar disk. Title: Linear polarization of hydrogen Balmer lines in optically thick quiescent prominences Authors: Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S. Bibcode: 1987A&A...186..335L Altcode: The linear polarization of H-alpha and H-beta in quiescent prominences having a nonnegligible optical thickness in H-alpha is theoretically deduced, starting from a zero-order self-consistent model obtained by solving the conventional non-LTE problem in prominences. The results show that the fractional linear polarization in zero magnetic field decreases with increasing optical thickness of the prominence and is rotated a small angle with respect to the solar limb when the prominence is seen at a sharp angle with respect to its plane. They also show that the polarization diagrams have a less symmetrical shape with respect to the analogous diagrams obtained for the limiting case of negligible optical thickness. Title: Resonance scattering of Lyman-alpha in the presence of an electrostatic field Authors: Favati, B.; Landi Degl'Innocenti, E.; Landolfi, M. Bibcode: 1987A&A...179..329F Altcode: The influence of an electrostatic field on the polarization of the scattered radiation in Lyα is investigated. The incident radiation is supposed to be in the form of a unidirectional, unpolarized pencil of radiation, while the scattering atom is schematized as a two-level atom, devoid of hyperfine structure, with no atomic polarization in its ground level. The atom is described in the formalism of the density matrix operator and the statistical equilibrium equations for the density matrix are derived. The results are given in terms of linear and circular polarization as a function of the electric field intensity and direction, and they are interpreted through convenient analogies with the Hanle effect and through a semiclassical model based on the electromagnetic equations of a damped oscillator in an electric field. Title: Transfer of Polarized Radiation, using 4 x 4 Matrices Authors: Landi Degl'Innocenti, E. Bibcode: 1987nrt..book..265L Altcode: No abstract at ADS Title: Linear Polarization of Hydrogen Balmer Lines in Optically Thick Prominences - Theoretical Investigation Authors: Bommier, V.; Landi degl'Innocenti, E.; Sahal-Brechot, S. Bibcode: 1987dssp.work...41B Altcode: 1987ASSL..150...41B No abstract at ADS Title: Measurements of magnetic fields in solar prominences. Authors: Landi Degl'Innocenti, Egidio Bibcode: 1986NASCP2442..203L Altcode: 1986copp.nasa..203L Magnetic fields can be measured, in solar prominences, by means of two different basic mechanisms that are responsible for the introduction (or the reduction) of a given amount of polarization in spectral lines: these are the Zeeman effect and the Hanle effect. Through the splitting of the magnetic components of a spectral line, the Zeeman effect is capable of introducing a certain amount of circular polarization across the line profile. The Hanle effect consist of a modification of the linear polarization that is induced in spectral lines by the anisotropic illumination of the prominence plasma by the photospheric radiation field. These two effects are briefly discussed. Title: Resonance scattering and the diagnostic of very weak magnetic fields in diffuse media Authors: Landolfi, M.; Landi Degl'Innocenti, E. Bibcode: 1986A&A...167..200L Altcode: Resonance scattering in a two-level atom is affected by the presence of very weak magnetic fields when the Zeeman splitting is comparable with the radiative broadening of the lower level due to absorption. This phenomenon, called here the "lower level Hanle effect", is analyzed in some detail for several atomic transitions and the corresponding polarization diagrams are drawn. It is suggested that this effect could be used in practice for the diagnostic of very weak magnetic fields in diffuse media by the measurement of the polarization of the scattered radiation in resonance lines. Title: Polarization in spectral lines. IV: Resonance polarization in the Hanle effect, collisionless regime. Authors: Landi Degl'Innocenti, E. Bibcode: 1985SoPh..102....1L Altcode: 1985SoPh..102....1D The general formalism presented in a previous paper of this series (Landi Degl'Innocenti, 1983a) is particularized to deduce the radiative transfer equations for polarized radiation and the statistical equilibrium equations for a multi-level atom in the Hanle effect, collisionless regime. The formulae are developed both in the standard representation and in the representation of the statistical tensors. For resonance scattering in a two-level atom in the presence of a weak magnetic field, in the limiting case of complete depolarization of the ground level, we recover the classical results of the Hanle effect and we derive the expression of the phase matrix in terms of ordinary rotation matrices. A magnetic kernel is introduced in the formalism and its main properties are analyzed. In particular, an expression for the magnetic kernel is derived for a turbulent magnetic field and the corresponding phase matrix is evaluated. Finally, the law of scattering is generalized to take properly into account the influence of the anisotropy of the radiation field on the atomic polarization of the ground level (depopulation pumping in the Hanle effect). Title: Radiative Transfer in Smallscale Magnetic Structures Authors: Landi Degl'Innocenti, E. Bibcode: 1985tphr.conf..162L Altcode: No abstract at ADS Title: The Zeeman pattern of magnetic lines and their statistical propertiesin the Fe I solar spectrum. Authors: Landi Degl'Innocenti, E. Bibcode: 1985SoPh...99....1L Altcode: 1985SoPh...99....1D The Zeeman patterns of magnetic lines are characterized by their first, second, and third order moments and a `minimal equivalent' representation is suggested for each line. The statistical properties of the Zeeman patterns of the Fe I lines in the solar optical spectrum are analyzed in detail and the various patterns are classified in three different types according to the relative position of the σ-components having larger strength. Title: Polarization of the Sodium D-Lines in Prominences Authors: Landolfi, M.; Landi Degl'Innocenti, E. Bibcode: 1985SoPh...98...53L Altcode: The expected polarization of the sodium D lines from solar prominences is computed as a function of the local magnetic field vector. To this aim, the formulation of the Hanle effect in terms of the statistical tensors developed by Landi Degl'Innocenti (1982) is employed, with minor changes connected to hyperfine structure. The sodium atoms are described in the incomplete Paschen-Back regime so that the validity of the results is not limited to `weak' magnetic fields. The polarization diagrams obtained are discussed and compared with the corresponding diagrams for the helium D3 line. Title: On the solution of the radiative transfer equations for polarized radiation Authors: Landi Degl'Innocenti, E.; Landi Degl'Innocenti, M. Bibcode: 1985SoPh...97..239L Altcode: 1985SoPh...97..239D Radiative transfer equations for polarized radiation are derived, assuming the Mueller matrix of the Stokes parameters is constant along the ray-path. The analytical solution to the radiative transfer equations is obtained within the framework of a general formalism. Results are given in the form of an analytical approximation of the Stokes parameter profiles for a typical chromospheric line having an optical depth dependence of the source function of the form S(tau) = (epsilon + delta)exp 1/2(1 + tau)exp 1/2. Title: Generation and transfer of polarized radiation in the solar atmosphere: Physical mechanisms and magnetic-field diagnostics Authors: Landi Degl'Innocenti, E. Bibcode: 1985svmf.nasa..279L Altcode: 1985svmf.nasa..279D The main physical mechanisms responsible for the generation and transfer of polarized radiation in the solar atmosphere can be classified in a suitable bidimensional diagram with an indicator of the magnetic field strength on its vertical axis and an indicator of the radiation field anisotropy on its horizontal axis. The various polarimetric observations performed on solar spectral lines are interpreted with different theoretical schemes according to their classification in the diagram and to the optical depths involved. These theoretical schemes, and the associated diagnostic tools for inferring the magnetic field vector from observations are reviewed. In particular, the role of magneto-optical effects in determining the direction of the observed linear polarization in active regions is discussed in some detail. Title: Effect of polarized radiative transfer on the Hanle magnetic field determination in prominences: Analysis of hydrogen H alpha line observations at Pic-du-Midi Authors: Bommier, V.; Landi Degl'Innocenti, E.; Leroy, J. L.; Sahal-Brechot, S. Bibcode: 1985svmf.nasa..335B Altcode: The linear polarization of the Hydrogen H alpha line of prominences has been computed, taking into account the effect of a magnetic field (Hanle effect), of the radiative transfer in the prominence, and of the depolarization due to collisions with the surrounding electrons and protons. The corresponding formalisms are developed in a forthcoming series of papers. In this paper, the main features of the computation method are summarized. The results of computation have been used for interpretation in terms of magnetic field vector measurements from H alpha polarimetric observations in prominences performed at Pic-du-Midi coronagraph-polarimeter. Simultaneous observations in one optically thin line (He I D(3)) and one optically thick line (H alpha) give an opportunity for solving the ambiguity on the field vector determination. Title: Vector Magnetic Fields in Prominences - Part Two Hei d3 Stokes Profiles Analysis for Two Quiescent Prominences Authors: Querfeld, C. W.; Smartt, R. N.; Bommier, V.; Landi Degl'Innocenti, E.; House, L. L. Bibcode: 1985SoPh...96..277Q Altcode: The Stokes components of He I D3 emission in two quiescent prominences, using full spectral profile measurements, are analyzed to derive vector magnetic fields. Two independently developed schemes, based on the Hanle effect, are used for interpretation. They involve solutions of the statistical equilibrium equations for the He I D3 multiplet, including the effect of coherency and full level crossing, which predict the magnetic field dependence of the observed polarization. Derived magnetic field vector solutions for each pair of linear polarization Stokes profiles corresponding to an observational point in the prominence are, intrinsically, not uniquely determined, and a set of possible solutions is usually obtained. However, mutual consistency of these solutions with those independently predicted by the form of the circular polarized component, allow, in almost all cases, rejection of all solutions of a set except one symmetrical pair. Of such a pair, a unique solution can be determined with a high confidence level by reference to independent potential field information. Field vectors are found usually to be close to horizontal and normal to the prominence surface, but extreme exceptions are found. Field values range from 6 G to 60 G. The derived vectorfield configurations and their magnitudes are briefly discussed relative to these prominences and to different quiescent prominence models. Title: Effect of polarized radiative transfer on the Hanle magnetic field determination in prominences: analysis of hydrogen Hα line obervations at Pic-du-Midi. Authors: Bommier, V.; Landi Degl'Innocenti, E.; Leroy, J. L.; Sahal-Bréchot, S. Bibcode: 1985NASCP2374..335B Altcode: The linear polarization of the hydrogen Hα line of prominences has been computed, taking into account the effect of a magnetic field (Hanle effect), of the radiative transfer in the prominence, and of the depolarization due to collisions with the surrounding electrons and protons. In this paper, the main features of the computation method are summarized. The results of computation have been used for interpretation in terms of magnetic field vector measurements from Hα polarimetric observations in prominences performed at Pic-du-Midi coronagraph-polarimeter (Leroy, 1981). Simultaneous observations in one optically thin line (He I D3) and one optically thick line (Hα) give an opportunity for solving the ambiguity on the field vector determination. Title: Radiative transfer in small-scale magnetic structures. Authors: Landi Degl'Innocenti, E. Bibcode: 1985MPARp.212..162L Altcode: For small scale magnetic structures the author presents an iterative scheme which has been followed with success for the non-LTE problem of polarized radiative transfer for hydrogen lines in prominences. Title: Generation and transfer of polarized radiation in the solar atmosphere: physical mechanisms and magnetic-field diagnostic. Authors: Landi Degl'Innocenti, E. Bibcode: 1985NASCP2374..279L Altcode: The main physical mechanisms responsible for the generation and transfer of polarized radiation in the solar atmosphere can be classified in a suitable bidimensional diagram with an indicator of the magnetic field strength on its vertical axis and an indicator of the radiation field anisotropy on its horizontal axis. The various polarimetric observations performed on solar spectral lines are interpreted with different theoretical schemes according to their classification in the diagram and to the optical depths involved. These theoretical schemes, and the associated diagnostic tools for inferring the magnetic field vector from observations are reviewed. Title: On the Diagnostic of Magnetic Fields in Sunspots Through the Interpretation of Stoke's Parameters Profiles Authors: Landolfi, M.; Landi Degl'Innocenti, E.; Arena, P. Bibcode: 1984SoPh...93..269L Altcode: The inversion routine proposed by Aueret al. (1977), for the determination of vector magnetic fields from Stokes profiles, has been generalized to include magneto-optical and damping effects. Synthetic profiles have then been generated from a sunspot model atmosphere accounting for the depth variation of the relevant physical parameters such as the magnetic field amplitude, inclination angle, etc...., each variation being considered one at a time. Alfvén waves and magnetic inhomogeneities over the field of view have also been considered. These synthetic profiles have been presented to the inversion routine. The results of the fits show that the magnetic field amplitude and direction are always recovered with good accuracy when these quantities are constant in the model atmosphere, and, in those cases where te magnetic field vector is supposed to vary monotonically with optical depth, the values recovered are always intermediate between the values corresponding to the top and bottom of the atmosphere. Moreover, we found that the differences between synthetic and best-fit profiles are able to characterize, in many cases, the particular physical situation considered. Title: Polarization in Spectral Lines - Part Three - Resonance Polarization in the Non-Magnetic Collisionless Regime Authors: Landi Degl'Innocenti, E. Bibcode: 1984SoPh...91....1L Altcode: The general formalism, presented in a previous paper of this series (Landi Degl'Innocenti, 1983a), is particularized to deduce the radiative transfer equations for polarized radiation and the statistical equilibrium equations for a multi-level atom in the zero-magnetic field, collisionless regime. The formulae are developed both in the standard representation and in the representation of the statistical tensors. For resonance scattering in a two-level atom, in the limiting case of complete depolarization of the ground level, we recover the classical results for Rayleigh scattering and we derive the expression of the phase matrix in terms of ordinary rotation matrices. The law of scattering is then generalized to take properly into account the influence of the anisotropy of the radiation field on the atomic polarization of the ground level (depopulation pumping). Title: Polarizzatori. Authors: Landi Degl'Innocenti, E. Bibcode: 1984GAst...10...29L Altcode: No abstract at ADS Title: Vector Magnetic Fields in Prominences - Part Three - Hei d3 Stokes Profile Analysis for Quiescent and Eruptive Prominences Authors: Athay, R. G.; Querfeld, C. W.; Smartt, R. N.; Landi Degl'Innocenti, E.; Bommier, V. Bibcode: 1983SoPh...89....3A Altcode: Observations of linear polarization in two resolved components of HeI D3 are interpreted using the Hanle effect to determine vector magnetic fields in thirteen prominences. As in all vector magnetic field measurements, there is a two-fold ambiguity in field direction that is symmetric to a 180° rotation about the line-of-sight. The polar angles of the fields show a pronounced preference to be close to 90° from the local solar radius, i.e., the field direction is close to horizontal. Azimuth angles show internal consistency from point to point in a given prominences, but because of the rotational symmetry, the fields may be interpreted, in most cases, as crossing the prominence either in the same sense as the underlying photospheric fields or in the opposite sense. Title: Erratum: Polarization in Spectral lines. I: A Unifying Theoretical Approach Authors: Landi Degl'Innocenti, E. Bibcode: 1983SoPh...88R.391L Altcode: No abstract at ADS Title: Erratum: Polarization in Spectral lines. II: A Classification Scheme for Solar Observatories Authors: Landi Degl'Innocenti, E. Bibcode: 1983SoPh...88S.391L Altcode: No abstract at ADS Title: Broadband linear polarization from magnetized stellar atmospheres. II - The influence of damping on net spectral line polarization Authors: Calamai, G.; Landi Degl'Innocenti, E. Bibcode: 1983A&AS...53..311C Altcode: The influence of broadening by damping on broadband linear polarization expected from a stellar atmosphere through the mechanism of magnetic intensification is investigated. Numerical tables are presented. Title: Asymmetries in stokes profiles of magnetic lines: A linear analysis in terms of velocity gradients Authors: Landi Degl'Innocenti, E.; Landolfi, M. Bibcode: 1983SoPh...87..221L Altcode: 1983SoPh...87..221D A linear analysis of the asymmetries in Stokes profiles of magnetic lines is performed. The asymmetries in the linear and circular polarization profiles are characterized by suitable quantities, δ tilde Q and δ tilde V, strictly related to observed profiles. The response functions of δ tilde Q and δ tilde V to velocity fields are introduced and computed for various configurations of the magnetic field vector in a Milne-Eddington atmosphere. Some conclusions are drawn as to the importance of the asymmetries in Stokes profiles for recovering the velocity gradients from observations. Title: Polarization in spectral lines Authors: Landi Degl'Innocenti, E. Bibcode: 1983SoPh...85....3L Altcode: 1983SoPh...85....3D A unifying theoretical approach is presented to derive from the general principles of Quantum Electrodynamics both the radiative transfer equations for polarized radiation and the statistical equilibrium equations for an atomic system interacting with a polarized radiation field. The radiation field is described by means of Stokes parameters while the atomic system is described in terms of its density-matrix operator. The non-diagonal terms of the density matrix are fully accounted for so that this formalism can be suitably employed to describe a wide variety of physical phenomena like resonance scattering, the Hanle effect and the Zeeman effect, either in optically thin or optically thick atmospheres, together with all the possible intermediate situations. The general formulae derived in the first sections of the paper are subsequently particularized introducing the dipole approximation in the relevant matrix elements describing the interaction between the atomic system and the radiation field. The final equations assume a quite compact expression by the introduction of suitable spherical tensors connected with the components of the polarization unit vectors associated with each direction of the radiation field. The general expressions and the main properties of these tensors are discussed in the Appendix. Title: Polarization in spectral lines Authors: Landi Degl'Innocenti, E. Bibcode: 1983SoPh...85...33L Altcode: 1983SoPh...85...33D A classification scheme is suggested for solar polarimetric observations in spectral lines originating both from magnetic and non-magnetic regions. A bidimensional diagram is introduced with an indicator of the magnetic field strength on its vertical axis and an indicator of the radiation field anisotropy on its horizontal axis. The diagram proves to be particularly suitable to sort out the relevant physical mechanisms playing an important role in the generation and transfer of polarized radiation for each single observation. Title: Meccanismi di emissione e assorbimento della radiazione in situazioniastrofisiche. Authors: Landi Degl'Innocenti, E.; Pallavicini, R. Bibcode: 1983GAst....9...25L Altcode: No abstract at ADS Title: Broadband linear polarization from magnetized stellar atmospheres - Numerical tables for the magnetic intensification mechanism Authors: Landi Degl'Innocenti, E.; Calamai, G. Bibcode: 1982A&AS...49..677L Altcode: Summary. - Some numerical tables are presented concerning the broadband linear polarization to be expected from a magnetized stellar atmosphere through the mechanism of magnetic intensificafion. Key words : Polarization - Stellar atmospheres - Magnetic field - Magnetic stars. Title: The determination of vector magnetic fields in prominences from the observations of the Stokes profiles in the D3 line of helium Authors: Landi Degl'Innocenti, E. Bibcode: 1982SoPh...79..291L Altcode: A method is presented to measure the magnetic field vector in prominences by means of the polarimetric observations in the D3 line of He obtained with the High Altitude Observatory Stokes polarimeter. The characteristics of the observed Stokes profiles are discussed. The theory of the Hanle effect is reformulated in the representation of the irreducible tensors of the density matrix, and is generalized to derive the circular polarization profiles across the spectral line in terms of the intensity and direction of the prominence magnetic field. The circular polarization profile so deduced can be employed to obtain useful information which adds to that carried by the linear polarization observations. A non-linear least-squares algorithm is proposed to derive the measurement of the magnetic field from the observations, and a consistency check is suggested to test the adequacy of the theoretical model to describe the physics of the He I atomic excitation in prominences. Title: Expected broadband linear polarization from cool stars with magnetic structures Authors: Landi Degl'Innocenti, E. Bibcode: 1982A&A...110...25L Altcode: A more detailed and quantitative investigation of the expected linear polarization in a rotating star having an assigned distribution of magnetic regions on its surface is presented. Expected polarization diagrams for magnetic regions of varying latitudes and inclination angles are depicted, and the concept of stochastic mean is introduced for the linear polarization to be expected from a random distribution of magnetic regions in two activity belts equidistant from the stellar equator. The relevance of linear polarization observations as a diagnostic tool to deduce the magnetic configuration of the star is discussed in some detail. Title: Magneto-Optical Effects and the Determination of Vector Magnetic Fields from Stokes Profiles Authors: Landolfi, M.; Landi Degl'Innocenti, E. Bibcode: 1982SoPh...78..355L Altcode: The analysis procedure proposed by Auer et al. (1977) for deducing magnetic field vectors from Stokes profiles has been tested to investigate the influence of magneto-optical effects on the deduced field parameters. The quality of the fit between synthetic profiles generated with the inclusion of magneto-optical effects and the profiles returned by the inversion routine is also investigated. The results show that magneto-optical effects should be included in the inversion routine especially to increase the accuracy of the deduced, azimuth of the magnetic field. Title: An atlas of theoretical Stokes profiles for solar disk observations Authors: Arena, P.; Landi Degl'Innocenti, E. Bibcode: 1982A&AS...48...81A Altcode: In order to express the range of polarimetric profiles which can be obtained in observations, depending on the intensity and direction of the magnetic field vector and on line strength, an atlas of theoretical Stokes profiles has been prepared for solar disk observations of magnetic regions. The approximations according to which the theoretical profiles have been computed include (1) unidirectional plane atmosphere with constant magnetic field, (2) linear behavior of the source function versus optical depth, (3) constant ratio between line and continuous absorption coefficients, and (4) normal Zeeman triplet with Gaussian profiles. Title: Thermodynamical Properties of Unresolved Magnetic Flux Tubes - Part One - a Diagnostic Method Based on Circular Polarization Ratios in Line Pairs Authors: Landi Degl'Innocenti, E.; Landolfi, M. Bibcode: 1982SoPh...77...13D Altcode: We propose a diagnostic method, based on the observation of circular polarization signals in line pairs, to derive the thermodynamical properties of unresolved magnetic elements in the solar atmosphere. The concept of response function for the ratio of circular polarization signals in two lines is introduced and its main properties are analyzed. Some detailed calculations for suitably selected line pairs are presented. Title: On the effective Landé factor of magnetic lines Authors: Landi Degl'Innocenti, Egidio Bibcode: 1982SoPh...77..285L Altcode: The effective Landé factor, g, of a magnetic sensitive line can be calculated by means of the experimental Landé factors of the lower and upper levels of the atomic transition. Values of g for several iron lines of the solar spectrum are calculated and compared with the approximate values based on the L-S coupling scheme. Simple formulae are also derived to express the variance of the distributions of the σ and π components of a Zeeman multiplet around the respective centers of gravity. Title: Measurements of solar magnetic fields through polarimetric observations Authors: Landi Degl'Innocenti, E. Bibcode: 1982MmSAI..53..841L Altcode: The limitations of the longitudinal magnetograph are detailed, noting that to make possible the measurement of vector magnetic fields at various levels in the chromosphere and the corona, different polarimeters have been developed during the past decade. The various results obtained by these instruments have stimulated a revival of interest in the generation and transfer of polarized radiation in the physical situation typical of the solar atmosphere. In discussing these, particular attention is given to the progress and problems in sunspots and active disk observations, resonance polarization at the limb, D3 observations in prominences, hydrogen line observations in prominences, Fe XIII and Fe XIV observations in the corona, and ultraviolet observations. Title: The magnetic intensification mechanism and its relevance for the study of stellar activity Authors: Landi Degl'Innocenti, E.; Calamai, G. Bibcode: 1982MmSAI..53..975L Altcode: The observation of the integral linear polarization over a wavelength interval covering one or several spectral lines is seen as particularly promising for analyzing the magnetic phenomena connected with stellar activity. The contributions made by Leroy (1962) in this area are summarized, as are those of Illing et al. (1974). As a result of their investigations of the spectra of sunspots, the role of the mechanism for magnetic intensification in broadband linear polarization observations is now well understood. It is pointed out, however, that in the calculations account must be taken of the variation in the magnetic field over the visible hemisphere of the star; here, an integration must be performed to deduce the value of the observed polarization from an assigned configuration of the magnetic field vector. Analogous calculations can also be carried out to deduce the value and the time variability of the broadband linear polarization expected from a rotating star covered by one or more magnetic regions. Also discussed is the technique now known as multislit photopolarimetry. Title: La composizione chimica del cosmo. Authors: Landi Degl'Innocenti, E. Bibcode: 1982GAst....8..337L Altcode: No abstract at ADS Title: Broad-band linear polarization and magnetic intensification in rotating magnetic stars. Authors: Landi Degl'Innocenti, M.; Calamai, G.; Landi Degl'Innocenti, E.; Patriarchi, P. Bibcode: 1981ApJ...249..228L Altcode: 1981ApJ...247..228L Magnetic intensification is proposed as a mechanism to explain the general features of the variable broad-band linear polarization emerging from rotating magnetic stars. This mechanism is studied in detail, and some efforts are made to investigate the wide variety of polarization diagrams that can result from it. Theoretical results are compared with direct observations of the variable magnetic star 53 Cam to determine its geometric and magnetic configuration. Title: Radiative transfer for polarized radiation - Symmetry properties and geometrical interpretation Authors: Landi Degl'Innocenti, E.; Landi Degl'Innocenti, M. Bibcode: 1981NCimB..62....1L Altcode: The general properties of the transfer equations for polarized radiation are discussed in detail and some relevant symmetries about the absorption matrix and the emission vector are deduced. A geometrical picture of the process of radiative transfer for polarized radiation is given by generalizing the model of the Poincare sphere. An electromagnetic analogy is achieved and it is then applied to the solution of some particular problems relevant in the process of line formation in a magnetic field. Title: Quiescent Prominence Vector Magnetic Fields Inferred from He I D3 Polarization Authors: Querfeld, C. W.; Smartt, R. N.; Bommier, V.; Landi Degl'Innocenti, E. Bibcode: 1980BAAS...12..792Q Altcode: No abstract at ADS Title: Vector Magnetic Fields Inferred from He I D3 Polarization in the August 5, 1980 Eruptive Prominence Authors: Querfeld, C. W.; Smartt, R. N.; Bommier, V.; Landi Degl'Innocenti, E. Bibcode: 1980BAAS...12..913Q Altcode: No abstract at ADS Title: Magneto-optical effects and the interpretation of linearly polarized intensity distributions observed with a vector magnetograph. Authors: Landi Degl'Innocenti, E. Bibcode: 1979SoPh...63..237L Altcode: Linearly polarized intensity distributions observed in sunspots with the Marshall Space Flight Center's (MSFC) vector magnetograph are interpreted taking into account magneto-optical effects. It is shown that these effects can be responsible for the observed spiral configuration in the pattern of linear polarization, even if a purely radial, conventional sunspot model is used. Title: Non-LTE transfer. An alternative derivation for sqrtepsilon . Authors: Landi Degl'Innocenti, E. Bibcode: 1979MNRAS.186..369L Altcode: 1979MNRAS.186..369D An important feature of the Wiener-Hopf integral equation is that the value of the source function at the surface of an isothermal atmosphere is given by the square root of the probability of collisional deexcitation (epsilon) times the Planck function (B), as long as a certain integral equation for the kernel (K) holds. In this paper, the Wiener-Hopf integral equation alone is used for an alternative derivation of the surface value of the source function in a semiinfinite isothermal atmosphere for a two-level atom with complete frequency redistribution. The same derivation is applied to determine upper and lower bounds to the surface value of the source function in exponential atmospheres. Title: Hyperfine structure and line formation in a magnetic field II. Numerical calculations of Zeeman components Authors: Landi Degl'Innocenti, E. Bibcode: 1978A&AS...33..157L Altcode: A FORTRAN code has been derived to calculate the strengths and the splittings of the Zeeman components of a spectral line with hyperfine structure. Key words: hyperfine structure magnetic fields - radiative transfer Title: Non-LTE line formation in a magnetic field. The two-level atom with a frequency independent source function. I. Formulation. Authors: Landi Degl'Innocenti, E. Bibcode: 1978A&A....66..119L Altcode: Non-LTE line formation in a plane-parallel semiinfinite atmosphere without macroscopic velocity fields but with a homogeneous magnetic field is considered for a two-level atom with the lower level having J = 0 and the upper level, J' = 1. The following simplifying assumptions are made: (1) the magnetic field is sufficiently strong that the separation among the Zeeman sublevels is much greater than their natural and collisional widths; (2) Doppler broadening and the line damping constant are independent of depth; (3) the continuum is formed in LTE; (4) there is complete frequency redistribution over each Zeeman sublevel; and (5) complete atomic-level depolarization occurs in the excited state. A system of coupled integral equations for the source functions of the Zeeman sublevels is obtained and solved, and the asymptotic behavior of the kernels is evaluated for Doppler as well as Lorentzian profiles. It is shown that the behavior of the kernels in the case of Doppler profiles is independent of both the amplitude and the inclination of the magnetic field and that the results obtained for Lorentzian profiles may be strongly modified by the inclusion of magnetooptical effects. Title: Response function for magnetic lines. Authors: Landi Degl'Innocenti, E.; Landi Degl'Innocenti, M. Bibcode: 1977A&A....56..111L Altcode: A perturbative solution to the equations of radiative transfer for polarized light is presented. This solution permits the evaluation of the influence of velocity fields and magnetic inhomogeneities on the Stokes-parameter profiles of magnetoactive Fraunhofer lines. The concept of a response function for polarized light is introduced. The frequency dependence of the response functions and their related symmetry properties are examined in some detail. Title: Non-LTE line formation in a magnetic field. The two-level atom with a frequency independent source function. I: Formulation. Authors: Landi Degl'Innocenti, E. Bibcode: 1977ROLun..12...35L Altcode: No abstract at ADS Title: Are there spots on magnetic white dwarfs? Authors: Landi Degl'Innocenti, E. Bibcode: 1976ApJ...209..208L Altcode: The temporal variation of the circular polarization observed in the magnetic white dwarf G195-19 is interpreted in terms of an oblique rotator model. The peculiar behavior observed in red light strongly suggests the presence of a spot on the surface of this star. A model based on this assumption is found to be consistent with observations. Subject headings: polarization - stars: magnetic - stars: white dwarfs Title: MALIP - a programme to calculate the Stokes parameters profiles of magnetoactive Fraunhofer lines Authors: Landi Degl'Innocenti, E. Bibcode: 1976A&AS...25..379L Altcode: A complete description of a programme to calculate the Stokes parameters profiles of magnetoactive Fraunhofer lines is given. The integration procedure is described in some detail as well as the influence of the various parameters on the accuracy of the results and on the computing time. The underlying Unno-Beckers theory of line formation in a magnetic field is summarized and generalized to take into account non-LTE effects in an empirical way. Key words: radiative transfer in magnetic fields - polarization - Stokes parameters Title: Statistical equilibrium equations in a polarized radiation field. Authors: Landi Degl'Innocenti, M.; Landolfi, M.; Landi Degl'Innocenti, E. Bibcode: 1976NCimB..35..117L Altcode: No abstract at ADS Title: Hyperfine structure and line formation in a magnetic field. Authors: Landi Degl'Innocenti, E. Bibcode: 1975A&A....45..269L Altcode: We derive the transfer equations of the Stokes parameters for a line with hyperfine structure in the presence of a magnetic field, both in LTE and NLTE. The effect of unresolved hyperfine structure on magnetographic determinations of solar magnetic fields is considered in the limiting case of small magnetic fields. An example is given on the determination of the Eu abundance in magnetic stars. It is shown that the combined effects of hyperfine structure and magnetic field may lower the measured abundance by as much as 2.5 dex. Title: Magnetic intensification as a mechanism for broad band linear polarization. Authors: Calamai, G.; Landi Degl'Innocenti, E.; Landi Degl'Innocenti, M. Bibcode: 1975A&A....45..297C Altcode: The solutions of the transfer equations for polarized light in a Milne-Eddington atmosphere are used to evaluate the importance of magnetic intensification as a possible mechanism for interpreting the net amount of linear polarization observed in broad-band measurements of magnetic regions. Magneto-optical effects are taken into account properly. Curves of growth for linear polarization are given for different values of the magnetic field vector. Theoretical results are compared with recent observations in sunspots. Title: A Perturbative Solution of the Transfer Equations for the Stokes Parameters in a Magnetic Field Authors: Landi Degl'Innocenti, Egidio; Landi Degl'Innocenti, Maurizio Bibcode: 1973SoPh...31..299L Altcode: 1973SoPh...31..299D The transfer equations for the Stokes parameters, as derived under the assumption of LTE and in the general case of anomalous Zeeman multiplet, are solved by a perturbative method that reduces the system of four coupled linear differential equations to an iterative series of well known linear differential equations. The perturbation parameter turns out to be of the order of magnitude of the ratio of the Larmor frequency to the line Doppler half-width, so that the method appears to be particularly suitable for small magnetic fields. Some qualitative results on the importance of Faraday rotation and the orders of magnitude of the line profiles of the Stokes parameters are obtained Title: A Search for Continuous Ultraviolet Opacity Sources in the Sun's Photosphere Authors: Landi Degl'Innocenti, Egidio; Noci, Giancarlo Bibcode: 1973SoPh...29..287L Altcode: 1973SoPh...29..287D Experimental results on limb darkening and specific intensities imply more ultraviolet continuous opacity than that predicted by theoretical calculations. Some atomic and molecular pro- cesses, not yet studied from this standpoint are investigated as to their importance on the continuous absorption coefficient. The negative results obtained suggest some arguments about the importance of iron as photo-absorber Title: Erratum: "Quantum theory of line formation in a magnetic field" [Sol. Phys., Vol. 27, p. 319 - 329 (1972)]. Authors: Landi Degl'Innocenti, E.; Landi Degl'Innocenti, M. Bibcode: 1973SoPh...29..528L Altcode: No abstract at ADS Title: Quantum Theory of Line Formation in a Magnetic Field Authors: Landi Degl'Innocenti, Egidio; Landi Degl'Innocenti, Maurizio Bibcode: 1972SoPh...27..319L Altcode: 1972SoPh...27..319D The transfer equations for the Stokes parameters in the presence of magnetic field and under the hypothesis of LTE are derived in an original way by the use of density matrix techniques. The results are substantially the same as those previously obtained by other authors. We finally compare our results to the previous ones in order to clarify some discrepancies still present in the literature