landi-deglinnocenti

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Author name code: landi-deglinnocenti
ADS astronomy entries on 2022-09-14
author:"Landi Degl'Innocenti, Egidio"

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Title: Forbidden Line Polarimetry to Detect the Evolution of the
Coronal Magnetic Field
Authors: Li, H.; Landi Degl'Innocenti, E.; Qu, Z. Q.
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.

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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.
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.

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Title: Relaxation Phenomena Due to Collisions with Neutral Perturbers
in Hyperfine Structure Multiplets
Authors: Landi Degl'Innocenti, E.; Belluzzi, L.
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.

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Title: Experimental Testing of Scattering Polarization Models
Authors: Li, W.; Casini, R.; Tomczyk, S.; Landi Degl'Innocenti, E.;
Marsell, B.
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.

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Title: Experimental testing of scattering polarization models
Authors: Li, Wenxian; Casini, Roberto; Tomczyk, Steven; Landi
Degl'Innocenti, Egidio; Marsell, Brandan
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.

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Title: The Physics and Diagnostic Potential of Ultraviolet
Spectropolarimetry
Authors: Trujillo Bueno, Javier; Landi Degl'Innocenti, Egidio;
Belluzzi, Luca
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 &amp; 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.

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Title: Polarization of Coronal Forbidden Lines
Authors: Li, Hao; Landi Degl'Innocenti, Egidio; Qu, Zhongquan
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.

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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
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.

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Title: The Physics of Polarization
Authors: Landi Degl'Innocenti, Egidio
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.

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Title: Isotropic Inelastic Collisions in a Multiterm Atom with
Hyperfine Structure
Authors: Belluzzi, Luca; Landi Degl'Innocenti, Egidio; Trujillo
Bueno, Javier
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.

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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.
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 <A
href="http://www.aanda.org/10.1051/0004-6361/201525887/olm">http://www.aanda.org</A>

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Title: Polarimetric shapes of spectral lines in solar observations
Authors: Landi Degl'Innocenti, Egidio
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.

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Title: Theoretical Schemes for the Interpretation of Solar
Polarimetric Observations: An Overview and Some New Ideas
Authors: Landi Degl'Innocenti, E.; Belluzzi, L.
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.

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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.
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.

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Title: Atomic Spectroscopy and Radiative Processes
Authors: Landi Degl'Innocenti, E.
2014asrp.book.....L Altcode:
No abstract at ADS

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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.
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.

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Title: Isotropic inelastic and superelastic collisional rates in a
multiterm atom
Authors: Belluzzi, L.; Landi Degl'Innocenti, E.; Trujillo Bueno, J.
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.

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Title: Spectropolarimetry with new generation solar telecopes
Authors: Landi Degl'Innocenti, E.
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.

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Title: Spectropolarimetric signatures of anisotropic velocity
distributions of optically thin coronal UV lines
Authors: Khan, A.; Landi Degl'Innocenti, E.
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.

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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.
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.

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Title: HAZEL: HAnle and ZEeman Light
Authors: Asensio Ramos, Andrés; Trujillo Bueno, Javier; Landi
Degl'Innocenti, E.
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.

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Title: Solar coronal magnetic field diagnostics through polarimetric
forward modelling of the Hanle effect
Authors: Khan, A.; Landi Degl'Innocenti, E.
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.

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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
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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” (<A
href="bib_query?2005ApJS...160..312S">ApJS, 160, 312 [2005]</A>)
Authors: Socas-Navarro, H.; Trujillo Bueno, J.; Landi Degl'Innocenti,
E.
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.
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.
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.
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.
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.
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.
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.
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 &amp;
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.
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.
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.
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.
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., &amp; 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 &amp; 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
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.
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.
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: <A href="https://www.springer.com/gb/book/9781402024146">
https://www.springer.com/gb/book/9781402024146</A>

---------------------------------------------------------
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.
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.
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.
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&amp;A 378, 627).

---------------------------------------------------------
Title: Theory of Polarization: What's Next?
Authors: Landi Degl'Innocenti, E.
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.
2003ASPC..307..425M Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Zeeman effect: applications to solar physics
Authors: Landi Degl'Innocenti, E.
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.
2003ASPC..307..241L Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Resonance Scattering Polarization in Molecular Lines
Authors: Landi Degl'Innocenti, E.
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.
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
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
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&gt;10 G and virtually zero
for B&gt;~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.
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
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.
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.
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.
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
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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
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.
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 &amp; 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.
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.
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.
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 &gt; 0 with respect
to those with M &lt; 0.

---------------------------------------------------------
Title: Broadband Linear Polarization in Ap-Stars
Authors: Landolfi, M.; Landi Degl'Innocenti, E.; Landi Degl'Innocenti,
M.; Leroy, J. L.; Bagnulo, S.
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
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
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
1987dssp.work...41B Altcode: 1987ASSL..150...41B
No abstract at ADS

---------------------------------------------------------
Title: Measurements of magnetic fields in solar prominences.
Authors: Landi Degl'Innocenti, Egidio
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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

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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.
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.

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Title: Response function for magnetic lines.
Authors: Landi Degl'Innocenti, E.; Landi Degl'Innocenti, M.
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.

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Title: Are there spots on magnetic white dwarfs?
Authors: Landi Degl'Innocenti, E.
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

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Title: MALIP - a programme to calculate the Stokes parameters profiles
of magnetoactive Fraunhofer lines
Authors: Landi Degl'Innocenti, E.
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

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Title: Statistical equilibrium equations in a polarized radiation
field.
Authors: Landi Degl'Innocenti, M.; Landolfi, M.; Landi Degl'Innocenti,
E.
1976NCimB..35..117L Altcode:
No abstract at ADS

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Title: Hyperfine structure and line formation in a magnetic field.
Authors: Landi Degl'Innocenti, E.
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.

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Title: Magnetic intensification as a mechanism for broad band linear
polarization.
Authors: Calamai, G.; Landi Degl'Innocenti, E.; Landi Degl'Innocenti,
M.
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.

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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
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

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Title: A Search for Continuous Ultraviolet Opacity Sources in the
Sun's Photosphere
Authors: Landi Degl'Innocenti, Egidio; Noci, Giancarlo
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

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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.
1973SoPh...29..528L Altcode:
No abstract at ADS

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Title: Quantum Theory of Line Formation in a Magnetic Field
Authors: Landi Degl'Innocenti, Egidio; Landi Degl'Innocenti, Maurizio
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