bommier

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Author name code: bommier
ADS astronomy entries on 2022-09-14
author:"Bommier, Veronique"

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Title: On Identifying and Mitigating Bias in Inferred Measurements
for Solar Vector Magnetic Field Data
Authors: Leka, K. D.; Wagner, Eric L.; Griñón-Marín, Ana Belén;
Bommier, Véronique; Higgins, Richard
2022arXiv220711572L Altcode:
The problem of bias, meaning over- or underestimation, of the component
perpendicular to the line-of-sight, Bperp, in vector magnetic field
maps is discussed. Previous works on this topic have illustrated that
the problem exists; here we perform novel investigations to quantify
the bias, fully understand its source(s), and provide mitigation
strategies. First, we develop quantitative metrics to measure the
Bperp bias and quantify the effect in both local (physical) and native
image-plane components. Second we test and evaluate different inversion
options and data sources, to systematically characterize the impacts of
choices, including explicitly accounting for the magnetic fill fraction
ff. Third we deploy a simple model to test how noise and different
models of the bias may manifest. From these three investigations we find
that while the bias is dominantly present in under-resolved structures,
it is also present in strong-field pixel-filling structures. Noise
in the magnetograms can exacerbate the problem, but it is not
the primary cause. We show that fitting ff explicitly provides
significant mitigation, but that other considerations such as choice
of chi^2 weights and optimization algorithms can impact the results
as well. Finally, we demonstrate a straightforward "quick fix" that
can be applied post-facto but prior to solving the 180deg ambiguity in
Bperp, and which may be useful when global-scale structures are, e.g.,
used for model boundary input. The conclusions of this work support
the deployment of inversion codes that explicitly fit ff or, as with
the new SyntHIA neural-net, that are trained on data that did so.

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Title: Mini solar flare and jet due to small scale surface motions
Authors: Joshi, Reetika; Vilmer, Nicole; Chandra, Ramesh; Heinzel,
Petr; Bommier, Veronique; Schmieder, Brigitte; Aulanier, Guillaume;
Tomin, James
2022cosp...44.2535J Altcode:
Here we present the study of the fine structure and dynamics of the
plasma at a jet base forming a mini-flare between two emerging magnetic
fluxes (EMFs) observed with Interface Region Imaging Spectrograph
(IRIS) and the Solar Dynamics Observatory instruments. This active
region is an outcome of the collapse of two EMFs overlaid by arch
filament systems. We observed that, before the jet an extension of
the flux rope was present and a part of it was detached and formed
a small bipole with a bald patch region, which dynamically became
an X-current sheet over the dome of one EMF where the reconnection
took place. At the time in the site of reconnection, the IRIS C II,
Si IV, and Mg II line profiles present bi directional flows in a tiny
region. These types of spectra are typically associated with twist,
rotation, or the presence of plasma in helical structures. The tilt
observed in our spectra can be explained by the presence of a helical
structure at the jet base during the reconnection process due to a
transfer of the twist from a flux rope in the vicinity of the jet. We
also combined the observations of the Balmer continuum obtained with
the IRIS (spectra and SJIs 2832 Å). The calibrated Balmer continuum
was compared to non-local thermodynamic equilibrium radiative transfer
flare models and the radiated energy was estimated. Assuming thick
target HXR emission, we calculated the energy of the non thermal
electrons detected by the Fermi/GBM and compared it to the radiated
energy. The electron-beam flux estimated from Fermi/GBM between 10$
^{9}$ and 10$ ^{10}$ erg s$ ^{-1}$ cm$ ^{-2}$ is consistent with the
beam flux required in non-LTE radiative transfer models to obtain the
excess of Balmer continuum emission observed in this IRIS spectra. We
conclude that the bombardment of electrons could be in a region smaller
than the IRIS spatial resolution.

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Title: Electron thermal escape inside the Sun
Authors: Bommier, V.
2021sf2a.conf..181B Altcode:
No abstract at ADS

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Title: Empirical atmosphere model in a mini flare during magnetic
reconnection
Authors: Schmieder, Brigitte; Joshi, Reetika; Chandra, Ramesh;
Aulanier, Guillaume; Tei, Akiko; Heinzel, Petr; Tomin, James; Vilmer,
Nicole; Bommier, Veronique
2021arXiv211206790S Altcode:
A spatio-temporal analysis of IRIS spectra of MgII, CII, and SiIV ions
allows us to study the dynamics and the stratification of the flare
atmosphere along the line of sight during the magnetic reconnection
phase at the jet base. Strong asymmetric MgII and CII line profiles with
extended blue wings observed at the reconnection site are interpreted
by the presence of two chromospheric temperature clouds: one explosive
cloud with blueshifts at 290 km/s and one cloud with smaller Doppler
shift (around 36 km/s). Simultaneously at the same location a mini
flare was observed with strong emission in multi temperatures (AIA),
in several spectral IRIS lines (e.g. Oiv and Siiv, Mgii), absorption
of identified chromospheric lines in Siiv line profile, enhancement
of the Balmer continuum and X-ray emission by FERMI/GBM. With the
standard thick-target flare model we calculate the energy of non thermal
electrons observed by FERMI and compare it to the energy radiated by
the Balmer continuum emission. We show that the low energy input by
non thermal electrons above 20 keV was still sufficient to produce
the excess of Balmer continuum.

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Title: 24 synoptic maps of average magnetic field in 296 prominences
measured by the Hanle effect during the ascending phase of solar
cycle 21
Authors: Bommier, V.; Leroy, J. L.; Sahal-Bréchot, S.
2021A&A...647A..60B Altcode: 2020arXiv200708219B
 Aims: We present 24 synoptic maps of solar filaments, in which
the average unambiguous magnetic field vectors of 296 prominences were
determined with Pic-du-Midi observations between 1974 and 1982. This
was the ascending phase of cycle 21. Methods: The magnetic
field was determined by interpreting the Hanle effect, which is
observed in the He I D3 line. Previous results for the
prominence field polarity and prominence chirality were applied to
solve the fundamental ambiguity. The measurements were averaged in
each prominence for accuracy reasons. Results: The result is
twofold. First, alternating field directions can be observed from one
neutral line to the next. Second, a general field alignment is found
along a solar north-south field that is distorted by the differential
rotation effect. The 296 prominences solar coordinates and magnetic
field vector data are only available at the CDS via anonymous ftp to
<A href="http://cdsarc.u-strasbg.fr/">cdsarc.u-strasbg.fr</A>
(ftp://130.79.128.5) or via <A
href="http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/647/A60">http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/647/A60</A>

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Title: Electron thermal escape in the Sun
Authors: Bommier, V.
2021csss.confE...4B Altcode:
Magnetic field vector observations in the solar photosphere have
generally revealed a non-zero value of the divergence: the vertical
field component gradient is found on the order of 3 G/km when the
horizontal field component gradient is of 0.3 G/km only. This has
first to be assigned to the fact that the measured quantity is the
magnetic field H, which is related to the divergence-free magnetic
induction B by the law B=µ0(H+M), where M is the magnetization. In
plasmas like the solar photosphere, magnetization results from
plasma diamagnetism and spiral movement of charged particles about
the magnetic field. The usually admitted but very indirect electron
density leads to weak magnetization. However, it can be observed that
in the solar interior the electron thermal velocity is much larger than
the escape velocity. The attractive effect of the protons does not
completely prevent the electrons from escaping. A model of this will
be presented. The electrons escape from lower layers in a quasi-static
spreading, and accumulate in the photosphere. Therefore, the electron
density at surface is increased but decreases with height at surface,
which enables the observed values because divH = -divM. Such a structure
is probably at play in the solar-type stars.

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Title: Twist transfer to a solar jet from a big flux rope detected
in the HMI magnetogram
Authors: Joshi, Reetika; Schmieder, Brigitte; Aulanier, Guillaume;
Chandra, Ramesh; Bommier, Veronique
2021cosp...43E1752J Altcode:
Solar jets often have a helical structure containing both hot and
cool ejected plasma. Different mechanisms are proposed to trigger
jets by magnetic reconnection between the emergence of magnetic flux
and environment, or induced by twisted photospheric motions bringing
the system to instability. Multi-wavelength observations of a twisted
jet observed with the AIA and IRIS is presented to understand how the
twist was injected in the jet from a flux rope, fortunately, IRIS
spectrographic slit was just crossing the reconnection site. This
active region is a result of the collapse of two emerging magnetic
fluxes (EMFs) overlaid by arch filament systems. In the magnetic field
maps, we evidenced the pattern of a long sigmoidal flux rope along
the polarity inversion line between the two EMFs which is the site of
the reconnection. Before the jet, there was an extension of the flux
rope, and a part of it was detached and formed a small bipole with a
bald patch region which dynamically became an X-current sheet over the
dome of one EMF where the reconnection took place. At the time of the
reconnection, the Mg II spectra exhibited a strong extension of the
blue wing which is decreasing over a distance of 10 Mm (from -300 km/s
to a few km/s). This is the signature of the transfer of the twist to
the jet. Comparison with numerical magnetohydrodynamics simulations
confirmed the existence of the long flux rope in the neighborhood
of the jet. We conjecture that there is a transfer of twist to the
jet during the extension of the flux rope to the reconnection site
without the flux rope eruption. The reconnection would start in the
low atmosphere in the bald patch reconnection region and extend at an
X-point along the current sheet formed above.

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Title: VizieR Online Data Catalog: Prominence average magnetic fields
in cycle XXI (Bommier+, 2021)
Authors: Bommier, V.; Leroy, J. L.; Sahal-Brechot, S.
2021yCat..36470060B Altcode:
From our full sample of 3297 measurements achieved in 379 quiescent
prominences observed in HeI D3 at the Pic-du-Midi during the ascending
phase of Cycle XXI (1974-1982), we discarded those prominences for which
the identification of the neutral line is doubtful (64 prominences). As a result, we obtained unambiguous average horizontal magnetic
field vectors of 296 prominences each associated to a filament observed
eight days before (W limb) or after (E limb). (1 data file).

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Title: Master equation theory applied to the redistribution of
polarized radiation in the weak radiation field limit. VI. Application
to the second solar spectrum of the Na I D1 and D2 lines: convergence
Authors: Bommier, Véronique
2020A&A...644A..65B Altcode: 2020arXiv200708226B
Context. This paper presents a numerical application of a
self-consistent theory of partial redistribution in nonlocal
thermodynamical equilibrium conditions, developed in previous papers
of the series. Aims: The code was described in IV of this
series. However, in that previous paper, the numerical results were
unrealistic. The present paper presents an approximation able to restore
the reliability of the outgoing polarization profiles. Methods:
The convergence of the results is also proved. It is demonstrated
that the step increment decreases like 1/Nα, with α
&gt; 1. Results: Thanks to these additions, the results series
behaves like a Riemann series, which is absolutely convergent. However,
convergence is not fully reached in line wings within the allocated
computing time. Development of efficient acceleration methods would
be desirable for future work. Conclusions: Agreement between
the computed and observed linear polarization profiles remains
qualitative only. The discrepancy is assigned to the plane parallel
atmosphere model, which is insufficient to describe the chromosphere,
where these lines are formed. As all the integrals are numerical in
the code, it could probably be adapted to more realistic and higher
dimensional model atmospheres. However, this is time consuming for
lines with a hyperfine structure, as in the Na I D lines. The net
linear polarization observed in Na I D1 with the Zürich
Imaging Polarimeter ZIMPOL mounted on the McMath-Pierce telescope at
Kitt Peak is not confirmed by the present calculations and could be
an artefact of instrumental polarization. The presence of instrumental
polarization could be confirmed by the higher linear polarization degree
observed by this instrument in the Na I D2 line center with
respect to the present calculation result where the magnetic field is
not accounted for. At this precise point, the Hanle effect acts as a
depolarizing effect in the second solar spectrum. The observed linear
polarization excess is found to be of the same order of magnitude
in both line centers, namely 0.1%, which is also comparable to the
instrumental polarization compensation level of this experiment.

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Title: The role of small-scale surface motions in the transfer of
twist to a solar jet from a remote stable flux rope
Authors: Joshi, Reetika; Schmieder, Brigitte; Aulanier, Guillaume;
Bommier, Véronique; Chandra, Ramesh
2020A&A...642A.169J Altcode: 2020arXiv200806887J
Context. Jets often have a helical structure containing ejected plasma
that is both hot and also cooler and denser than the corona. Various
mechanisms have been proposed to explain how jets are triggered,
primarily attributed to a magnetic reconnection between the emergence
of magnetic flux and environment or that of twisted photospheric
motions that bring the system into a state of instability. 
Aims: Multi-wavelength observations of a twisted jet observed with
the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics
Observatory and the Interface Region Imaging Spectrograph (IRIS)
were used to understand how the twist was injected into the jet,
thanks to the IRIS spectrographic slit fortuitously crossing the
reconnection site at that time. Methods: We followed the
magnetic history of the active region based on the analysis of the
Helioseismic and Magnetic Imager vector magnetic field computed with
the UNNOFIT code. The nature and dynamics of the jet reconnection site
are characterised by the IRIS spectra. Results: This region
is the result of the collapse of two emerging magnetic fluxes (EMFs)
overlaid by arch filament systems that have been well-observed with AIA,
IRIS, and the New Vacuum Solar Telescope in Hα. In the magnetic field
maps, we found evidence of the pattern of a long sigmoidal flux rope
(FR) along the polarity inversion line between the two EMFs, which is
the site of the reconnection. Before the jet, an extension of the FR
was present and a part of it was detached and formed a small bipole
with a bald patch (BP) region, which dynamically became an X-current
sheet over the dome of one EMF where the reconnection took place. At
the time of the reconnection, the Mg II spectra exhibited a strong
extension of the blue wing that is decreasing over a distance of 10
Mm (from -300 km s-1 to a few km s-1). This
is the signature of the transfer of the twist to the jet. Conclusions: A comparison with numerical magnetohydrodynamics
simulations confirms the existence of the long FR. We conjecture that
there is a transfer of twist to the jet during the extension of the
FR to the reconnection site without FR eruption. The reconnection
would start in the low atmosphere in the BP reconnection region
and extend at an X-point along the current sheet formed above. Movies attached to Figs. 1, 3, 4, and 7 are available at <A
href="https://www.aanda.org/10.1051/0004-6361/202038562/olm">https://www.aanda.org</A>

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Title: Solar photosphere magnetization
Authors: Bommier, Véronique
2020A&A...634A..40B Altcode: 2019arXiv190706476B
Context. A recent review shows that observations performed with
different telescopes, spectral lines, and interpretation methods
all agree about a vertical magnetic field gradient in solar active
regions on the order of 3 G km-1, when a horizontal
magnetic field gradient of only 0.3 G km-1 is found. This
represents an inexplicable discrepancy with respect to the divB =
0 law. Aims: The objective of this paper is to explain these
observations through the law B = μ0(H + M) in magnetized
media. Methods: Magnetization is due to plasma diamagnetism,
which results from the spiral motion of free electrons or charges
about the magnetic field. Their usual photospheric densities lead
to very weak magnetization M, four orders of magnitude lower than
H. It is then assumed that electrons escape from the solar interior,
where their thermal velocity is much higher than the escape velocity,
in spite of the effect of protons. They escape from lower layers in a
quasi-static spreading, and accumulate in the photosphere. By evaluating
the magnetic energy of an elementary atom embedded in the magnetized
medium obeying the macroscopic law B = μ0(H + M), it is
shown that the Zeeman Hamiltonian is due to the effect of H. Thus, what
is measured is H. Results: The decrease in density with height
is responsible for non-zero divergence of M, which is compensated for
by the divergence of H, in order to ensure div B = 0. The behavior
of the observed quantities is recovered. Conclusions: The
problem of the divergence of the observed magnetic field in solar
active regions finally reveals evidence of electron accumulation in
the solar photosphere. This is not the case of the heavier protons,
which remain in lower layers. An electric field would thus be present
in the solar interior, but as the total charge remains negligible,
no electric field or effect would result outside the star.

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Title: Magnetic field vector ambiguity resolution in a quiescent
prominence observed on two consecutive days
Authors: Kalewicz, T.; Bommier, V.
2019A&A...629A.138K Altcode: 2019arXiv190401816K
Context. Magnetic field vector measurements are always ambiguous,
that is, two or more field vectors are solutions of the observed
polarisation. Aims: The aim of the present paper is to solve the
ambiguity by comparing the ambiguous field vectors obtained in the same
prominence observed on two consecutive days. The effect of the solar
rotation is to modify the scattering angle of the prominence radiation,
which modifies the symmetry of the ambiguous solutions. This method,
which is a kind of tomography, was successfully applied in the past
to the average magnetic field vector of 20 prominences observed at the
Pic du Midi. The aim of the present paper is to apply this method to a
prominence observed with spatial resolution at the THÉMIS telescope
(European site at Izaña, Tenerife Island). Methods: The
magnetic field vector is measured by interpretation of the Hanle effect
observed in the He I D3 5875.6 Å line, within the horizontal
field vector hypothesis for simplicity. The ambiguity is first solved
by comparing the two pairs of solutions obtained for a "big pixel"
determined by averaging the observed Stokes parameters in a large region
at the prominence centre. Each pixel is then disambiguated by selecting
the closest solution in a propagation from the prominence centre to the
prominence boundary. Results: The results previously obtained
on averaged prominences are all recovered. The polarity is found to be
inverse with a small angle of about -21° between the magnetic field
vector and the long axis of the filament. The magnetic field strength
of about 6 G is found to slightly increase with height, as previously
observed. The new result is the observed decrease with height, of
the absolute value of the angle between the magnetic field vector and
the long axis of the filament. Conclusions: This result is in
excellent agreement with prominence magnetohydrodynamical models.

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Title: Self-consistent Multilevel PRD
Authors: Bommier, Véronique
2019ASPC..519...39B Altcode:
After having recalled what are the physical components of frequency
partial redistribution (PRD), this paper presents a new multilevel
theoretical formalism based on non-markovian master equation theory for
describing the atom-radiation interaction. As an application, this paper
present final results of a modeling, based on this theory, of the second
solar spectrum of the Na I D lines, which is the spectrum of the linear
polarisation formed by scattering and observed close to the solar limb.

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Title: Collisional Line Broadening and Collisional Depolarization
of Spectral Lines: Similarities and Differences
Authors: Sahal-Bréchot1, S.; Bommier, V.
2019ASPC..526...35S Altcode:
The collisional width of a spectral line takes part in the frequency
redistribution of the scattered radiation in the line. Within the
impact approximation, collisional line broadening parameters (widths
and shifts), depolarization and polarization transfer rates seem
very similar: both include the effect of collisional transitions
between the Zeeman sublevels of a given level, or between fine
or hyperfine structure levels of a given term. However, there are
important differences. On the one hand, for line broadening, the
two levels connected by the radiative transition contribute to the
broadening. There is also an interference term between the two levels
of the line, which can be very important for collisions with neutral
hydrogen. On the other hand, only one level or two close levels are
concerned in the depolarization. Another difference lies in the fact
that elastic cross-sections of the two levels contribute to the line
broadening, whereas they do not contribute to the depolarization. The
possibility to find some theoretical relationships concerning
depolarization versus collisional broadening will be shown to be
impossible. The perturbation expansion of the collisional S matrix and
the Van der Waals interaction potential are recalled to be unsuitable,
since all the derived parameters are too small (by approximately a
factor 2). Finally, in the light of a very recent paper, numerical
relationships between line widths and level depolarization rates will
be quoted.

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Title: Non-Perturbative Theory of Radiative Scattering in the Weak
Radiation Field Limit: Resolution of Egidio Landi's "Paradox"
Authors: Bommier, V.
2019ASPC..526...17B Altcode:
No abstract at ADS

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Title: Interpretation of Hanle effect measurements in the Solar
Corona: promises and difficulties
Authors: Bommier, Veronique
2018cosp...42E.395B Altcode:
After having recalled the main features of the Hanle effect, and
of its application to coronal lines, the promises and difficulties
of the measurement interpretation in terms of magnetic field vector
diagnostics, will be investigated, based on Bommier, V., Leroy, J.L.,
and Sahal-Bréchot, S., 1981, A&amp;A, 100, 231, and in the light of
the new instrumentation presently available or in project, as well
as data-driven modeling present possibilities. The feasibility of
measuring the Coronal magnetic field by interpretation of the Zeeman
effect observed in the infrared, will also be investigated.

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Title: Disambiguated magnetic field measurements in a quiescent
prominence
Authors: Bommier, Veronique; Kalewicz, Thomas
2018cosp...42E.396B Altcode:
The magnetic field vector was measured in a prominence by interpretation
of the Hanle effect, following the method described in Bommier, V.,
Leroy, J.L., and Sahal-Bréchot, S., 1981, A&amp;A, 100, 231, but
with the difference that the measurements were spatially resolved
in the prominence body, because the prominence was observed with the
French THEMIS telescope (Izaña, Tenerife, Canarias). The prominence
was observed on two following days, and the measurement ambiguity was
resolved by selecting the closest pair in the ambiguous solutions,
whose symmetry changes along the days due to solar rotation. The method
successfully worked. The observed line was He I D3. The polarisation
was integrated along the line profile for accuracy purposes, and the two
line components were not resolved. The magnetic field was then assumed
to be horizontal, as shown by Athay et al. (1983, Solar Phys. 89,
3). The magnetic field strength and the α angle between the field
vector and the prominence long axis were unambiguously obtained for
nearly each pixel. A vertical gradient of +0.5e-4 G/km (increasing with
height) is found above h=34 Mm, in excellent agreement with Leroy et
al. (1983, Sol. Phys. 83, 135). The new result is that the α angle is
found to decrease with height, in accordance with the theoretical model
by Aulanier &amp; Démoulin (2003, A&amp;A, 402, 769). The second new
result is that measurements are now obtained close to the solar limb,
lower than 20 Mm. In these regions, the magnetic field strength gradient
is found negative -0.6e-4 G/km (decreasing with height), contrarily to
the model. In this region, the α angle is also found decreasing with
height, but in a quicker manner and with more scattered values. The
prominence is found of Inverse Polarity at all heights.

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Title: Ion traps at the Sun: observational evidence
Authors: Musset, Sophie; Fleishman, Gregory D.; Bommier, Veronique;
Glesener, Lindsay
2018tess.conf20955M Altcode:
Our understanding of thermal processes in the solar atmosphere relies
in particular on diagnostics of the plasma emission in ultraviolet and
extreme ultraviolet (EUV). These emissions are produced by heavy ions
in various ionization states and depend on the amount of these ions
and on the plasma temperature and density. Any non-uniformity of the
distribution of elements can therefore affect our thermal diagnostics of
the solar atmosphere. Using a simple model of ion propagation in current
carrying magnetic loops, we theoretically predicted a concentration
(depletion) of ions in regions of the solar atmosphere associated
with upward-directed (downward-directed) current densities. We present
here the data analysis that leads to observational evidence supporting
this prediction. We analyze the distribution of EUV emission from the
Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamic Observatory
(SDO) in regard to positive and negative vertical current densities
calculated at the photospheric level using the spectropolarimetric
data from the Helioseismic Magnetic Imager (SDO/HMI). A statistical
analysis of these distributions was performed for several active
regions and at several times, for several EUV wavelengths. We found
a significant excess in EUV brightness in the areas with positive
(i.e. upward) current densities rather than negative. We call such
areas of heavy ion concentrations the "ion traps". We will discuss
the implication of our result for the first ionization potential (FIP)
effect in particular, as well as the next theoretical and observational
developments foreseen to deepen our understanding of this effect in
the dynamic coronal environment during and between solar flares.

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Title: Ion Traps at the Sun: Implications for Elemental Fractionation
Authors: Fleishman, Gregory D.; Musset, Sophie; Bommier, Véronique;
Glesener, Lindsay
2018ApJ...857...85F Altcode: 2018arXiv180302851F
Why the tenuous solar outer atmosphere, or corona, is much hotter than
the underlying layers remains one of the greatest challenges for solar
modeling. Detailed diagnostics of the coronal thermal structure come
from extreme ultraviolet (EUV) emission. The EUV emission is produced
by heavy ions in various ionization states and depends on the amount
of these ions and on plasma temperature and density. Any nonuniformity
of the elemental distribution in space or variability in time affects
thermal diagnostics of the corona. Here we theoretically predict ionized
chemical element concentrations in some areas of the solar atmosphere,
where the electric current is directed upward. We then detect these
areas observationally, by comparing the electric current density with
the EUV brightness in an active region. We found a significant excess
in EUV brightness in the areas with positive current density rather
than negative. Therefore, we report the observational discovery of
substantial concentrations of heavy ions in current-carrying magnetic
flux tubes, which might have important implications for the elemental
fractionation in the solar corona known as the first ionization
potential effect. We call such areas of heavy ion concentration the
“ion traps.” These traps hold enhanced ion levels until they are
disrupted by a flare, whether large or small.

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Title: Master equation theory applied to the redistribution of
polarized radiation in the weak radiation field limit. V. The
two-term atom
Authors: Bommier, Véronique
2017A&A...607A..50B Altcode: 2017arXiv170805579B
Context. In previous papers of this series, we presented a formalism
able to account for both statistical equilibrium of a multilevel atom
and coherent and incoherent scatterings (partial redistribution). 
Aims: This paper provides theoretical expressions of the redistribution
function for the two-term atom. This redistribution function includes
both coherent (RII) and incoherent (RIII)
scattering contributions with their branching ratios. Methods:
The expressions were derived by applying the formalism outlined
above. The statistical equilibrium equation for the atomic density
matrix is first formally solved in the case of the two-term atom with
unpolarized and infinitely sharp lower levels. Then the redistribution
function is derived by substituting this solution for the expression
of the emissivity. Results: Expressions are provided for both
magnetic and non-magnetic cases. Atomic fine structure is taken into
account. Expressions are also separately provided under zero and
non-zero hyperfine structure. Conclusions: Redistribution
functions are widely used in radiative transfer codes. In our
formulation, collisional transitions between Zeeman sublevels within an
atomic level (depolarizing collisions effect) are taken into account
when possible (I.e., in the non-magnetic case). However, the need for
a formal solution of the statistical equilibrium as a preliminary step
prevents us from taking into account collisional transfers between the
levels of the upper term. Accounting for these collisional transfers
could be done via a numerical solution of the statistical equilibrium
equation system.

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Title: Interpretation of Hanle effect measurements in the Solar
Corona: promises and difficulties
Authors: Bommier, Veronique
2016cosp...41E.227B Altcode:
After having recalled the main features of the Hanle effect, and
of its application to coronal lines, the promises and difficulties
of the measurement interpretation in terms of magnetic field vector
diagnostics, will be investigated, based on Bommier, V., Leroy, J.L.,
and Sahal-Bréchot, S., 1981, A&amp;A, 100, 231, and in the light of
the new instrumentation presently available or in project, as well as
data-driven modeling present possibilities.

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Title: Enabling Solar Flare Forecasting at an Unprecedented Level:
the FLARECAST Project
Authors: Georgoulis, Manolis K.; Pariat, Etienne; Massone, Anna
Maria; Vilmer, Nicole; Jackson, David; Buchlin, Eric; Csillaghy,
Andre; Bommier, Veronique; Kontogiannis, Ioannis; Gallagher, Peter;
Gontikakis, Costis; Guennou, Chloé; Murray, Sophie; Bloomfield,
D. Shaun; Alingery, Pablo; Baudin, Frederic; Benvenuto, Federico;
Bruggisser, Florian; Florios, Konstantinos; Guerra, Jordan; Park,
Sung-Hong; Perasso, Annalisa; Piana, Michele; Sathiapal, Hanna;
Soldati, Marco; Von Stachelski, Samuel; Argoudelis, Vangelis;
Caminade, Stephane
2016cosp...41E.657G Altcode:
We attempt a brief but informative description of the Flare
Likelihood And Region Eruption Forecasting (FLARECAST) project,
European Commission's first large-scale investment to explore the
limits of reliability and accuracy for the forecasting of major solar
flares. The consortium, objectives, and first results of the project
- featuring an openly accessible, interactive flare forecasting
facility by the end of 2017 - will be outlined. In addition, we will
refer to the so-called "explorative research" element of project,
aiming to connect solar flares with coronal mass ejections (CMEs)
and possibly pave the way for CME, or eruptive flare, prediction. We
will also emphasize the FLARECAST modus operandi, namely the diversity
of expertise within the consortium that independently aims to science,
infrastructure development and dissemination, both to stakeholders and
to the general public. Concluding, we will underline that the FLARECAST
project responds squarely to the joint COSPAR - ILWS Global Roadmap
to shield society from the adversities of space weather, addressing
its primary goal and, in particular, its Research Recommendations
1, 2 and 4, Teaming Recommendations II and III, and Collaboration
Recommendations A, B, and D. The FLARECAST project has received funding
from the European Union's Horizon 2020 research and innovation programme
under grant agreement No. 640216.

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Title: Evolution of flare ribbons, electric currents, and
quasi-separatrix layers during an X-class flare
Authors: Janvier, M.; Savcheva, A.; Pariat, E.; Tassev, S.;
Millholland, S.; Bommier, V.; McCauley, P.; McKillop, S.; Dougan, F.
2016A&A...591A.141J Altcode: 2016arXiv160407241J
Context. The standard model for eruptive flares has been extended
to three dimensions (3D) in the past few years. This model predicts
typical J-shaped photospheric footprints of the coronal current
layer, forming at similar locations as the quasi-separatrix layers
(QSLs). Such a morphology is also found for flare ribbons observed in
the extreme ultraviolet (EUV) band, and in nonlinear force-free field
(NLFFF) magnetic field extrapolations and models. Aims: We
study the evolution of the photospheric traces of the current density
and flare ribbons, both obtained with the Solar Dynamics Observatory
instruments. We aim to compare their morphology and their time
evolution, before and during the flare, with the topological features
found in a NLFFF model. Methods: We investigated the photospheric
current evolution during the 06 September 2011 X-class flare
(SOL2011-09-06T22:20) occurring in NOAA AR 11283 from observational data
of the magnetic field obtained with the Helioseismic and Magnetic Imager
aboard the Solar Dynamics Observatory. We compared this evolution with
that of the flare ribbons observed in the EUV filters of the Atmospheric
Imager Assembly. We also compared the observed electric current density
and the flare ribbon morphology with that of the QSLs computed from
the flux rope insertion method-NLFFF model. Results: The NLFFF
model shows the presence of a fan-spine configuration of overlying
field lines, due to the presence of a parasitic polarity, embedding
an elongated flux rope that appears in the observations as two parts
of a filament. The QSL signatures of the fan configuration appear as
a circular flare ribbon that encircles the J-shaped ribbons related
to the filament ejection. The QSLs, evolved via a magnetofrictional
method, also show similar morphology and evolution as both the current
ribbons and the EUV flare ribbons obtained several times during the
flare. Conclusions: For the first time, we propose a combined
analysis of the photospheric traces of an eruptive flare, in a complex
topology, with direct measurements of electric currents and QSLs
from observational data and a magnetic field model. The results,
obtained by two different and independent approaches 1) confirm
previous results of current increase during the impulsive phase of the
flare and 2) show how NLFFF models can capture the essential physical
signatures of flares even in a complex magnetic field topology. A movie associated to Fig. 1 is available in electronic form at <A
href="http://www.aanda.org/10.1051/0004-6361/201628406/olm">http://www.aanda.org</A>

---------------------------------------------------------
Title: Energetic electrons and photospheric electric currents during
solar flares
Authors: Musset, Sophie; Vilmer, Nicole; Bommier, Veronique
2016cosp...41E1373M Altcode:
It is currently admitted that solar flares are powered by magnetic
energy previously stored in the coronal magnetic field. During
magnetic reconnection processes, this energy is transferred to particle
acceleration, plasma motion and plasma heating. Magnetic energy release
is likely to occur on coronal currents sheets along regions of strong
gradient of magnetic connectivity. These coronal current sheets can
be traced by their footprints at the surface on the Sun, i.e. by
photospheric current ribbons. We aim to study the relation between
these current ribbons observed at the photospheric level, tracing the
coronal current sheets, and the flare energetic electrons traced by
their X-ray emissions. The photospheric magnetic field and vertical
current density have been calculated from SDO/HMI spectropolarimetric
data with the UNNOFIT inversion and Metcalf disambiguation codes,
while the X-ray images and spectra have been reconstructed from RHESSI
data. In a first case, the GOES X2.2 flare of February 15, 2011, a
spatial correlation is observed between the photospheric current ribbons
and the coronal X-ray emissions from energetic electrons. Moreover,
a conjoint evolution of both the photospheric currents and the X-ray
emission is observed during the course of the flare. Both results are
interpreted as consequences of the magnetic reconnection in coronal
current sheets, and propagation of the reconnection sites to new
structures during the flare, leading to new X-ray emission and local
increase of the photospheric currents (Musset et al., 2015). We shall
discuss here similar results obtained for other X-class flares.

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Title: Evidence of flux rope and sigmoid in Active Regions prior
eruptions
Authors: Schmieder, Brigitte; Aulanier, Guillaume; Janvier, Miho;
Bommier, Veronique; Dudik, Jaroslav; Gilchrist, Stuart; Zhao, Jie
2016cosp...41E1750S Altcode:
In the solar corona, the magnetic field is dominant, and the current
density vector is nearly aligned with the magnetic field lines
for strong and stressed field regions. Stressed and highly twisted
flux ropes are at the origin of eruptive events such as flares and
coronal mass ejections, which inject material into the interplanetary
medium. The standard three dimensional (3D) flare model predicts
the complex evolution of flare loops and the flux rope before
the eruption. Flux ropes are not directly observed in the corona,
however it has started to be possible to detect their footprints
in the photosphere. Recent high spatial and temporal resolution
spectro-polarimeters have allowed us to compute the photospheric
electric currents and follow their evolution. Characteristics pattern
like J-shaped ribbons indicate the presence of a flux rope before
the flare. The results confirm the predictions of the 3D MHD standard
model of eruptive flares. It is interesting to compare the magnetic
helicity of the ejected flux rope with the in situ measurements of the
corresponding ICME at L1. We will show some examples (February 15 2011,
July 12 2012, Sept 10 2014).

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Title: Milne-Eddington inversion for unresolved magnetic structures
in the quiet Sun photosphere
Authors: Bommier, Véronique
2016JGRA..121.5025B Altcode:
This paper is first devoted to present our method for modeling
unresolved magnetic structures in the Milne-Eddington inversion of
spectropolarimetric data. The related definitions and other approaches
and different used inversion algorithms are recalled for comparison. In
a second part, we apply our method to quiet Sun data outside active
regions. We obtain the quiet Sun photospheric magnetic field as
composed of unresolved opening and connected magnetic flux tubes,
which form a loop carpet of field lines. We then analyze the spatial
correlation, which we also observed for the magnetic field vector,
in terms of flux tube diameter, distance, and field strength. We find
that different observations with the Zurich imaging polarimeter and
THEMIS polarimeter mounted on the THEMIS telescope give very close
results, and we add results also very close derived from HINODE/Solar
Optical Telescope/spectropolarimeter observations analyzed with the
same method. We obtain a mean flux tube diameter of 30 km, a mean flux
tube distance of 230 km, and a mean flux tube magnetic field of 1.3 kG.

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Title: Master equation theory applied to the redistribution of
polarized radiation in the weak radiation field limit. III. Theory
for the multilevel atom
Authors: Bommier, Véronique
2016A&A...591A..59B Altcode:
Context. We discuss the case of lines formed by scattering, which
comprises both coherent and incoherent scattering. Both processes
contribute to form the line profiles in the so-called second solar
spectrum, which is the spectrum of the linear polarization of such
lines observed close to the solar limb. However, most of the lines
cannot be simply modeled with a two-level or two-term atom model,
and we present a generalized formalism for this purpose. Aims:
The aim is to obtain a formalism that is able to describe scattering
in line centers (resonant scattering or incoherent scattering) and
in far wings (Rayleigh/Raman scattering or coherent scattering) for a
multilevel and multiline atom. Methods: The method is designed
to overcome the Markov approximation, which is often performed in the
atom-photon interaction description. The method was already presented
in the two first papers of this series, but the final equations of
those papers were for a two-level atom. Results: We present
here the final equations generalized for the multilevel and multiline
atom. We describe the main steps of the theoretical development, and,
in particular, how we performed the series development to overcome the
Markov approximation. Conclusions: The statistical equilibrium
equations for the atomic density matrix and the radiative transfer
equation coefficients are obtained with line profiles. The Doppler
redistribution is also taken into account because we show that the
statistical equilibrium equations must be solved for each atomic
velocity class.

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Title: Fast inversion of Zeeman line profiles using central
moments. II. Stokes V moments and determination of vector magnetic
fields
Authors: Mein, P.; Uitenbroek, H.; Mein, N.; Bommier, V.; Faurobert, M.
2016A&A...591A..64M Altcode:
Context. In the case of unresolved solar structures or stray light
contamination, inversion techniques using four Stokes parameters
of Zeeman profiles cannot disentangle the combined contributions of
magnetic and nonmagnetic areas to the observed Stokes I. Aims:
In the framework of a two-component model atmosphere with filling factor
f, we propose an inversion method restricting input data to Q , U, and
V profiles, thus overcoming ambiguities from stray light and spatial
mixing. Methods: The V-moments inversion (VMI) method uses
shifts SV derived from moments of V-profiles and integrals
of Q2, U2, and V2 to determine the
strength B and inclination ψ of a magnetic field vector through
least-squares polynomial fits and with very few iterations. Moment
calculations are optimized to reduce data noise effects. To specify the
model atmosphere of the magnetic component, an additional parameter
δ, deduced from the shape of V-profiles, is used to interpolate
between expansions corresponding to two basic models. Results:
We perform inversions of HINODE SOT/SP data for inclination ranges 0
&lt;ψ&lt; 60° and 120 &lt;ψ&lt; 180° for the 630.2 nm Fe I line. A
damping coefficient is fitted to take instrumental line broadening into
account. We estimate errors from data noise. Magnetic field strengths
and inclinations deduced from VMI inversion are compared with results
from the inversion codes UNNOFIT and MERLIN. Conclusions:
The VMI inversion method is insensitive to the dependence of Stokes I
profiles on the thermodynamic structure in nonmagnetic areas. In the
range of Bf products larger than 200 G, mean field strengths exceed
1000 G and there is not a very significant departure from the UNNOFIT
results because of differences between magnetic and nonmagnetic model
atmospheres. Further improvements might include additional parameters
deduced from the shape of Stokes V profiles and from large sets of
3D-MHD simulations, especially for unresolved magnetic flux tubes.

---------------------------------------------------------
Title: Master equation theory applied to the redistribution of
polarized radiation in the weak radiation field limit. IV. Application
to the second solar spectrum of the Na I D1 and D2 lines
Authors: Bommier, Véronique
2016A&A...591A..60B Altcode:
Context. The spectrum of the linear polarization, which is formed by
scattering and observed on the solar disk close to the limb, is very
different from the intensity spectrum and thus able to provide new
information, in particular about anisotropies in the solar surface
plasma and magnetic fields. In addition, a large number of lines show
far wing polarization structures assigned to partial redistribution
(PRD), which we prefer to denote as Rayleigh/Raman scattering. The
two-level or two-term atom approximation without any lower level
polarization is insufficient for many lines. Aims: In the
previous paper of this series, we presented our theory generalized
to the multilevel and multiline atom and comprised of statistical
equilibrium equations for the atomic density matrix elements
and radiative transfer equation for the polarized radiation. The
present paper is devoted to applying this theory to model the second
solar spectrum of the Na I D1 and D2 lines. Methods: The
solution method is iterative, of the lambda-iteration type. The usual
acceleration techniques were considered or even applied, but we found
these to be unsuccessful, in particular because of nonlinearity or large
number of quantities determining the radiation at each depth. 
Results: The observed spectrum is qualitatively reproduced in line
center, but the convergence is yet to be reached in the far wings
and the observed spectrum is not totally reproduced there. 
Conclusions: We need to investigate noniterative resolution methods. The
other limitation lies in the one-dimensional (1D) atmosphere model,
which is unable to reproduce the intermittent matter structure formed of
small loops or spicules in the chromosphere. This modeling is rough,
but the computing time in the presence of hyperfine structure and
PRD prevents us from envisaging a three-dimensional (3D) model at
this instant.

---------------------------------------------------------
Title: Energetic electrons and photospheric electric currents during
solar flares
Authors: Musset, S.; Vilmer, N.; Bommier, V.
2015AGUFMSH52A..06M Altcode:
Solar flares are among the most energetic events in the solar
system. Magnetic energy previously stored in the coronal magnetic
field is transferred to particle acceleration, plasma motion and
plasma heating. Magnetic energy release is likely to occur in coronal
currents sheets associated with regions of strong gradient of magnetic
connectivity. Coronal current sheets can be traced by their footprints
at the surface on the Sun, in e.g. photospheric current ribbons. We
aim to study the relationship between the current ribbons observed
at the photospheric level which trace coronal current sheets, and
the flare energetic electrons traced by their X-ray emissions. The
photospheric magnetic field and vertical current density are calculated
from SDO/HMI spectropolarimetric data using the UNNOFIT inversion and
Metcalf disambiguation codes, while the X-ray images and spectra are
reconstructed from RHESSI data. In a first case (the GOES X2.2 flare
of February 15, 2011), a spatial correlation is observed between
the photospheric current ribbons and the coronal X-ray emissions
from energetic electrons (Musset et al., 2015). Moreover, a conjoint
evolution of both the photospheric currents and the X-ray emission is
observed during the course of the flare. Both results are interpreted
as consequences of the magnetic reconnection in coronal current
sheets. Propagation of the reconnection sites to new structures during
the flare results in new X-ray emission sites and local increase of
the photospheric currents We will examine in this contribution whether
similar results are obtained for other X-class flares.

---------------------------------------------------------
Title: Solar Surface Anisotropy effect on the Magnetic Field
Authors: Bommier, Véronique
2015IAUS..305...28B Altcode:
Within the literature there are at least 15 references indicating that
the horizontal magnetic flux does not exactly balance vertical flux
in sunspots, leading to the surprising result that div B would depart
from zero. Intuitively, this has to be related to the stratification at
the surface of the star, due to which horizontal and vertical typical
lengths are different. This surface anisotropy results from gravity,
but how does gravity influence the magnetic field? To answer this
question, a scenario has been proposed in two recent publications,
based on anisotropic Debye shielding. The presentation reported in
this paper was devoted to investigate the possibility and causes of a
non-zero div B. A scaling law associated with the anisotropy is able
to reestablish the nullity of div B, which would lead to a renewed
MHD in the solar photosphere layer. An eventual observation in the
laboratory is also reported.

---------------------------------------------------------
Title: Hard X-ray emitting energetic electrons and photospheric
electric currents
Authors: Musset, S.; Vilmer, N.; Bommier, V.
2015A&A...580A.106M Altcode: 2015arXiv150602724M
Context. The energy released during solar flares is believed to be
stored in non-potential magnetic fields associated with electric
currents flowing in the corona. While no measurements of coronal
electric currents are presently available, maps of photospheric electric
currents can now be derived from SDO/HMI observations. Photospheric
electric currents have been shown to be the tracers of the coronal
electric currents. Particle acceleration can result from electric fields
associated with coronal electric currents. We revisit here some aspects
of the relationship between particle acceleration in solar flares
and electric currents in the active region. Aims: We study the
relation between the energetic electron interaction sites in the solar
atmosphere, and the magnitudes and changes of vertical electric current
densities measured at the photospheric level, during the X2.2 flare on
February 15, 2011, in AR NOAA 11158. Methods: X-ray images from
the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) are
overlaid on magnetic field and electric current density maps calculated
from the spectropolarimetric measurements of the Helioseismic and
Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) using
the UNNOFIT inversion and Metcalf disambiguation codes. X-ray images
are also compared with extreme ultraviolet (EUV) images from the SDO
Atmospheric Imaging Assembly (AIA) to complement the flare analysis. Results: Part of the elongated X-ray emissions from both thermal
and non-thermal electrons overlay the elongated narrow current ribbons
observed at the photospheric level. A new X-ray source at 50-100 keV
(produced by non-thermal electrons) is observed in the course of the
flare and is cospatial with a region in which new vertical photospheric
currents appeared during the same period (an increase of 15%). These
observational results are discussed in the context of the scenarios
in which magnetic reconnection (and subsequent plasma heating and
particle acceleration) occurs at current-carrying layers in the corona.

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Title: The auroral red line polarisation: modelling and measurements
Authors: Lilensten, Jean; Bommier, Véronique; Barthélemy, Mathieu;
Lamy, Hervé; Bernard, David; Idar Moen, Joran; Johnsen, Magnar
Gullikstad; Løvhaug, Unni Pia; Pitout, Frédéric
2015JSWSC...5A..26L Altcode:
In this work, we model the polarisation of the auroral red line
using the electron impact theory developed by &lt;xref ref-type="bibr"
rid="R5"&gt;Bommier et al. (2011)&lt;/xref&gt;. This theory enables the
computation of the distribution of the Degree of Linear Polarisation
(DoLP) as a function of height if the flux of precipitated electrons
is provided as input. An electron transport code is used to infer
the stationary electron flux at each altitude in the ionosphere as a
function of energy and pitch angle. Using adequate cross-sections,
the integral of this electron flux over energy and pitch angle
provides an anisotropy parameter from which the theoretical local
DoLP can be computed at each altitude. The modelled DoLP is then
derived by integrating along the line-of-sight. Depending on the
integration length, the modelled DoLP ranges between 0.6% for a
very long integration length and 1.8% for a very short integration
length localised around an altitude of 210 km. A parametric study
is performed to check how the characteristics of the local DoLP
(maximum value, altitude of the maximum, integrated height profile)
vary. It is found that the polarisation is highly sensitive to the
scattering function of the electrons, to the electron precipitation
and to the geomagnetic activity. We compare these values to measured
ones obtained during an observational campaign performed in February
2012 from Svalbard. The measured DoLP during the campaign was 1.9%
± 0.1%. The comparison between this value and the theoretical one
is discussed. Discrepancies may be due to the poor constraint of the
input parameters (thermosphere and ionosphere), to the fact that only
electron precipitation is considered in this approach (and not proton
precipitation for instance) and to the difficulty in constraining the
exact width of the emission layer in the thermosphere.

---------------------------------------------------------
Title: XTAT: A New Multilevel-Multiline Polarized Radiative Transfer
Code with PRD
Authors: Bommier, V.
2014ASPC..489..195B Altcode:
This work is intended to the interpretation of the so-called "Second
Solar Spectrum" (Stenflo 1996), which is the spectrum of the linear
polarization formed by scattering and observed close to the solar
internal limb. The lines are also optically thick, and the problem
is to solve in a coherent manner, the statistical equilibrium of the
atomic density matrix and the polarized radiative transfer in the
atmosphere. Following Belluzzi &amp; Landi Degl'Innocenti (2009), 30
% of the solar visible line linear polarization profiles display the
M-type shape typical of coherent scattering effect in the far wings. A
new theory including both coherent (Rayleigh) and resonant scatterings
was developed by Bommier (1997a,b). Raman scattering was later added
(Bommier 1999, SPW2). In this theory, which is straightly derived from
the Schrödinger equation for the atomic density matrix, the radiative
line broadening appears as a non-Markovian process of atom-photon
interaction. The collisional broadening is included. The Rayleigh
(Raman) scattering appears as an additional term in the emissivity
from the fourth order of the atom-photon interaction perturbation
development. The development is pursued and finally summed up, leading
to a non-perturbative final result. In this formalism, the use of
redistribution functions is avoided. The published formalism was
limited to the two-level atom without lower level alignment. But most
of the solar lines are more complex. We will present how the theory
has to be complemented for multi-level atom modeling, including lower
level alignment. The role of the collisions as balancing coherent and
resonant scatterings is fully taken into account. Progress report will
be given about the development of a new code for the numerical iterative
solution of the statistical equilibrium and polarized radiative transfer
equations, for multi-level atoms and their multi-line spectrum. Fine
and hyperfine structures, and Hanle, Kemp (Kemp et al. 1984), Zeeman,
incomplete Paschen-Back effects, are included. Doppler redistribution
is fully taken into account, by solving the statistical equilibrium for
each velocity class of the atoms. In the presentation, a particular
attention will be devoted to the depolarizing collisions and their
rate estimation.

---------------------------------------------------------
Title: Collisional line broadening versus collisional depolarization:
Similarities and differences
Authors: Sahal-Bréchot, S.; Bommier, V.
2014AdSpR..54.1164S Altcode:
Within the impact approximation, collisional line broadening parameters
and depolarizing and polarization transfer (population, orientation,
alignment transfer) rates are complementary: both include the effect
of collisional transitions between the Zeeman sublevels of a given
level, or between fine or hyperfine structure levels of a given
term. However, there are several differences: in line broadening,
the two levels connected by the radiative transition contribute to the
broadening, and there is also an interference term between these two
levels, whereas only one level or two close levels are concerned in
the depolarization. Another difference lies in the fact that purely
elastic collisions contribute also to the line broadening, whereas
they do not contribute to the depolarization. The nature of these two
kinds of coefficients are recalled. Then the possibility to find some
relationships or systematic trends concerning depolarization versus
collisional broadening is considered. This is to answer some current
questions which come from the polarization community.

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Title: Optical characterization of the breadboard narrowband
prefilters for Solar Orbiter PHI
Authors: Dominguez-Tagle, Carlos; Appourchaux, Thierry; Ruiz
de Galarreta, Claudia; Fourmond, Jean-Jacques; Philippon, Anne;
Le Clec'h, Jean-Christophe; Bouzit, Mehdi; Bommier, Véronique;
Le Cocguen, Regis; Crussaire, Daniel; Malherbe, Jean-Marie
2014SPIE.9143E..5GD Altcode:
The Polarimetric and Helioseismic Imager (PHI) on board of Solar
Orbiter will observe the Sun to measure the photospheric vector
magnetic field and the line-of-sight velocity. It will employ
a narrowband filtergraph (FG) to scan the FeI 6173 Å absorption
line. At different spectral positions, the polarization state of the
incoming light will be analyzed. The FG will provide a tuning range
to scan the line, the continuum, and to compensate for the spacecraft
radial velocity, as it will approach to the Sun down to 0.28 AU. The
FG includes a Fabry-Perot etalon and two narrowband prefilters. The
bandpass of the narrowest one has a nominal Full Width at Half Maximum
(FWHM) of 2.7 Å. The measurement of the prefilters characteristics is
essential for the instrument calibration. Here we present the results
of the breadboard prefilters characterization, which is an important
milestone in the development of the instrument.

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Title: Electric Currents in Flare Ribbons: Observations and
Three-dimensional Standard Model
Authors: Janvier, M.; Aulanier, G.; Bommier, V.; Schmieder, B.;
Démoulin, P.; Pariat, E.
2014ApJ...788...60J Altcode: 2014arXiv1402.2010J
We present for the first time the evolution of the photospheric electric
currents during an eruptive X-class flare, accurately predicted by the
standard three-dimensional (3D) flare model. We analyze this evolution
for the 2011 February 15 flare using Helioseismic and Magnetic
Imager/Solar Dynamics Observatory magnetic observations and find
that localized currents in J-shaped ribbons increase to double their
pre-flare intensity. Our 3D flare model, developed with the OHM code,
suggests that these current ribbons, which develop at the location of
extreme ultraviolet brightenings seen with Atmospheric Imaging Assembly
imagery, are driven by the collapse of the flare's coronal current
layer. These findings of increased currents restricted in localized
ribbons are consistent with the overall free energy decrease during a
flare, and the shapes of these ribbons also give an indication of how
twisted the erupting flux rope is. Finally, this study further enhances
the close correspondence obtained between the theoretical predictions
of the standard 3D model and flare observations, indicating that the
main key physical elements are incorporated in the model.

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Title: Possible measurements of the magnetic field in eruptive
prominences using the PROBA-3 coronagraph
Authors: Serge, Koutchmy; Zhukov, Andrei; Dolla, Laurent; Heinzel,
Petr; Lamy, Philippe; Bazin, Cyrille; Bommier, Veronique; Faurobert,
Marianne
2014cosp...40E2971S Altcode:
The PROBA-3 mission will fly a spacecraft put in the shadow of a
precisely occulting sister satellite orbiting “in formation” at a
distance of 150 m in front of it to make artificial total eclipses. The
region right above the solar limb will be studied for the first time
over a coronal background not polluted by any spurious light. Although
the priority will be the high-resolution fast imaging of the dynamic
white-light corona, the use of a narrow filter centered on a low
excitation D3 line of He I, is planned for imaging prominences. Adding
the linear polarization analysis would permit the measurements of the
magnetic field using the Hanle effect. We evaluate the possibility
offered during the eruptive phase of a CME with prominence material
inserted inside, for studying the associated magnetic field changes
related to both the heating process and the ejection of material. The
background highly polarized K-corona is taken into account. Sequences of
quasi- simultaneous white-light processed images at high resolution are
an additional feature of great interest for interpreting the overall
magnetic structure.

---------------------------------------------------------
Title: Relation between electric current densities and X-ray emissions
from particles accelerated during solar flares
Authors: Musset, Sophie; Vilmer, Nicole; Bommier, Veronique
2014cosp...40E2209M Altcode:
The energy released during solar flares is believed to be stored in
non-potential magnetic fields associated with electric currents. This
energy is partially transferred to particle acceleration. We studied for
several X-class flares located near the solar disk center the relation
between the location of the X-ray emissions produced by energetic
electrons accelerated in the corona and the magnetic field and vertical
component of the electric current density in the photosphere. The
study is based on X-ray images with data from the Reuven Ramaty High
Energy Solar Spectroscopic Imager (RHESSI) and magnetic field maps and
current density maps calculated with the UNNOFIT inversion and Metcalf
disambiguation codes from the spectropolarimetric measurements of the
Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory
(SDO). A comparison between X-ray and Extreme Ultraviolet (EUV) images
from the SDO Atmospheric Imaging Assembly (AIA) complete the study. We
shall present preliminary conclusions on the link between particle
acceleration and the presence of electric currents in the active region.

---------------------------------------------------------
Title: 24 synoptic maps 1974-1982 (ascending phase of cycle XXI)
of 323 prominence average magnetic fields measured by the Hanle effect
Authors: Bommier, Véronique
2014IAUS..300..397B Altcode:
The poster was made of 323 average prominence magnetic fields reported
on 24 synoptic maps. The paper first resumes the methods for the field
derivation, and the different results of the whole program of these
second generation Hanle effect observations. From their conclusions,
it was possible to derive a unique field vector for each of the 323
prominences. The maps put in evidence a large scale structure of the
prominence magnetic field, probably distorted by the differential
rotation, which leads to a systematically small angle (on the order
of 30°) between the field vector and the prominence long axis.

---------------------------------------------------------
Title: Reconciliating the Vertical and Horizontal Gradients of the
Sunspot Magnetic Field
Authors: Bommier, V.
2013PRI..2013E...1B Altcode: 2013PhyRI2013E...1B
In the literature, we found 15 references showing that the sunspot
photospheric magnetic field vertical gradient is on the order of 3-4
G/km, with field strength decreasing with height, whereas the horizontal
gradient is nine times weaker on the order of 0.4-0.5 G/km. This is
confirmed by our recent THEMIS observations. As a consequence, the
vanishing of divB is not realized. In other words, a loss of magnetic
flux is observed with increasing height, which is not compensated for
by an increase of the horizontal flux. We show that the lack of spatial
resolution, vertical as well as horizontal, cannot be held responsible
for the nonvanishing observed divB. The present paper is devoted to the
investigation of this problem. We investigate how the magnetic field
is influenced by the plasma anisotropy due to the stratification,
which is responsible for an "aspect ratio" between horizontal and
vertical typical lengths. On the example of our THEMIS observations,
made of two spectral lines formed at two different depths, which enables
the retrieval of the three components entering divB, it is shown that
once this aspect ratio is applied, the rescaled divB vanishes, which
suggests a new methodology for MHD modeling in the photosphere.

---------------------------------------------------------
Title: Polarisation of the auroral red line in the Earth's upper
atmosphere: a review (Invited)
Authors: Lamy, H.; Barthelemy, M.; Lilensten, J.; Bommier, V.; Simon
Wedlund, C.
2013AGUFM.P42B..03L Altcode:
Polarisation of light is a key observable to provide information
about asymmetry or anisotropy within a radiative source. Polarimetry
of auroral emission lines in the Earth's upper atmosphere has
been overlooked for decades. However, the bright red auroral
line (6300Å) produced by collisional impact with electrons
precipitating along magnetic field lines is a good candidate to
search for polarisation. This problem was investigated recently with
observations obtained by Lilensten et al (2008), Barthélemy et al
(2011) and Lilensten et al (2013) with a photopolarimeter. Analysis
of the data indicates that the red auroral emission line is polarised
at a level of a few percent. The results are compared to theoretical
predictions of Bommier et al (2011) that were obtained for a collimated
beam. The comparison suggests the existence of depolarization processes
whose origin will be discussed. A new dedicated spectropolarimeter
currently under development will also be presented. This instrument
will cover the optical spectrum from approximately 400 to 700 nm
providing simultaneously the polarisation of the red line and of other
interesting auroral emission lines such as N2+ 1NG (4278Å), other N2
bands, etc... The importance of these polarisation measurements in
the context of upper atmosphere modelling and geomagnetic activity
will be discussed. Lilensten, J. et al, Polarization in aurorae:
A new dimension for space environments studies, Geophys. Res. Lett.,
26, 269, 2008 Barthélemy M. et al, Polarisation in the auroral red
line during coordinated EISCAT Svalbard Radar/optical experiments,
Annales Geophysicae, Volume 29, Issue 6, 2011, 1101-1112, 2011. Bommier
V. et al, The Theoretical Impact Polarization of the O I 6300 Å Red
Line of Earth Auroræ, Annales Geophysicae, Volume 29, Issue 1, 2011,
71-79, 2011 Lilensten, J. et al, The thermospheric auroral red line
polarization: confirmation of detection and first quantitative analysis,
Journal of Space Weather and Space Climate, Volume 3, 12, 2013.

---------------------------------------------------------
Title: Longitudinal magnetic field and velocity gradients in the
photosphere inferred from THEMIS multiline observations
Authors: Molodij, G.; Bommier, V.; Rayrole, J.
2013A&A...552A..50M Altcode:
We present multiline observations taken with the French-Italian
telescope THEMIS operated by CNRS and CNR on the island of
Tenerife. Several spectral lines are observed simultaneously to study
magnetic phenomena at different altitudes of line formation, comprising
the Fe i 5250.65 Å, Cr i 5247.57 Å, Fe i 5250.22 Å, Fe i 6301.51
Å, Fe i 6302.50 Å, and Fe i 6151.62 Å lines. The observations were
analyzed using Milne-Eddington inversion algorithms modified to allow
for non-normal Zeeman triplet lines, and to take additionally into
account the vertical velocity gradient. We show the self-consistency
of the solutions found from the inversion and those obtained from
the quantitative bisector method. Results from the different lines
observed simultaneously yield the height dependence of the magnetic
field strength. From modeling the line formation heights applied on
selected points with a longitudinal magnetic field between 200 and 1000
G, we determine the gradient of the vertical component (absolute value)
of the magnetic field to be - 1.18 G/km.

---------------------------------------------------------
Title: Behavior of the vertical current during the X2 flare of 2011
February 15 observed by SDO/HMI, compared to a line-tied zero-beta
resistive MHD simulation
Authors: Bommier, Veronique; Aulanier, Guillaume
2013enss.confE..79B Altcode:
The level-1 data of SDO/HMI have been inverted with the UNNOFIT
inversion code (Bommier et al., 2007, A&amp;A, 464, 323), which differs
from VFISV about the magnetic filling factor modeling. More realistic
field inclinations are obtained outside the active region. The spatial
resolution seems to be also better. UNNOFIT is enabled for the taking
into account of gradients of radial velocity, responsible for asymmetry
of the Stokes profiles (Molodij et al., 2011, A&amp;A, 531, A139). The
ambiguity has been solved with the ME0 code of Metcalf, Leka, Barnes
&amp; Crouch. We present the movie of 4 hours of observation, the
flare occurring at middle. Two current ribbons of opposite polarity
are visible along the magnetic neutral line, in the vertical density
current map. The negative one strengthens and radially expands from
the flare center at the eruption moment. A similar current ribbon pair
is visible in a 3D line-tied zero-beta resistive MHD flare simulation
with the OHM code (Aulanier et al. , 2012, A&amp;A, 543, A110). The
two ribbons part from the flare center during the flare, similarly to
what observed on 2011 February 15 at 02:00 with SDO/HMI.

---------------------------------------------------------
Title: The thermospheric auroral red line polarization: confirmation
of detection and first quantitative analysis
Authors: Lilensten, Jean; Barthélémy, Mathieu; Amblard,
Pierre-Olivier; Lamy, Hervé; Simon Wedlund, Cyril; Bommier,
Véronique; Moen, Joran; Rothkaehl, Hanna; Eymard, Julien; Ribot,
Jocelyn
2013JSWSC...3A..01L Altcode:
The thermospheric atomic oxygen red line is among the brightest
in the auroral spectrum. Previous observations in Longyearbyen,
Svalbard, indicated that it may be intrinsically polarized, but
a possible contamination by light pollution could not be ruled
out. During the winter 2010/2011, the polarization of the red line
was measured for the first time at the Polish Hornsund polar base
without contamination. Two methods of data analysis are presented to
compute the degree of linear polarization (DoLP) and angle of linear
polarization (AoLP): one is based on averaging and the other one on
filtering. Results are compared and are in qualitative agreement. For
solar zenith angles (SZA) larger than 108° (with no contribution from
Rayleigh scattering), the DoLP ranges between 2 and 7%. The AoLP is
more or less aligned with the direction of the magnetic field line, in
agreement with the theoretical predictions of &lt;xref ref-type="bibr"
rid="R2"&gt;Bommier et al. (2010)&lt;/xref&gt;. However, the AoLP
values range between ±20° around this direction, depending on the
auroral conditions. Correlations between the polarization parameters
and the red line intensity I were considered. The DoLP decreases when
I increases, confirming a trend observed during the observations in
Longyearbyen. However, for small values of I, DoLP varies within a
large range of values, while for large values of I, DoLP is always
small. The AoLP also varies with the red line intensity, slightly
rotating around the magnetic field line.

---------------------------------------------------------
Title: Reconstruction of 3D Coronal Magnetic Structures from
THEMIS/MTR and Hinode/SOT Vector Maps
Authors: Schmieder, B.; Guo, Y.; Aulanier, G.; Démoulin, P.; Török,
T.; Bommier, V.; Wiegelmann, T.; Gosain, S.
2012ASPC..454..363S Altcode:
Coordinated campaigns using THEMIS, Hinode, and other instruments have
allowed us to study the magnetic fields of faculae, filaments, and
active regions. In a first case, we modelled the 3D magnetic field in a
flaring active region with a nonlinear force-free field extrapolation,
using magnetic vectors observed by THEMIS/MTR as boundary condition. In
order to construct a consistent bottom boundary for the model, we
first removed the 180 degree ambiguity of the transverse fields and
minimized the force and torque in the observed vector fields. We found
a twisted magnetic flux rope, well aligned with the polarity inversion
line and a part of an Hα filament, and located where a large flare is
initiated about two hours later. In a second case, Hinode/SOT allowed
us to detect fine flux concentrations in faculae, while MTR provided us
with magnetic information at different levels in the atmosphere. The
polarimetry analysis of the MTR and SOT data gave consistent results,
using both UNNOFIT and MELANIE inversion codes.

---------------------------------------------------------
Title: Inversion of Zeeman Line Profiles Using Central Moments
Authors: Mein, P.; Uitenbroek, H.; Mein, N.; Bommier, V.; Faurobert, M.
2012EAS....55...83M Altcode:
A new inversion method derived from central moments of Zeeman line
profiles (ICM), is used to determine magnetic field vectors (Mein et
al. 2011). Two quantities A1 and A2 combining
moments of profiles I ± S (S = Q,U,V) are nearly linear functions
of the longitudinal and transverse components and lead to the field
components through very fast iterations. Optimized exponents reduce
noise effects. The ICM inversion does not require Milne Eddington
approximation and can be used in a wide range of solar models.

---------------------------------------------------------
Title: Magnetic field distribution in the quiet and active photosphere
Authors: Bommier, V.
2012EAS....55...49B Altcode:
The presentation is intended to describe results obtained with the
UNNOFIT inversion of spectropolarimetric data. Quiet regions of the Sun
are studied on the one hand, where the structure of the magnetic field
remains unresolved and is approached via a magnetic filling factor. It
is got that the field is structured in thin flux tubes connected by
loops at any altitude in the solar atmosphere. The fluxtube diameter
size is evaluated. On the other hand, active regions are studied,
in particular sunspots where the magnetic field horizontal gradient
is found one order of magnitude weaker than the vertical gradient, as
in other observations reported in the literature. This is a difficulty
to ensure divB=0. Before entering the results, the particular features
of the UNNOFIT inversion are recalled, which concern essentially the
magnetic filling factor modeling.

---------------------------------------------------------
Title: Electric current density and related sigmoid in an active
region
Authors: Joulin, V.; Schmieder, B.; Aulanier, G.; Bommier, V.
2012EAS....55..143J Altcode:
Using THEMIS vector magnetograms we measured vertical electric current
density in the leading sunspot of NOAA 11127 active region during
its disk passage. The current structures evolve versus time. MHD
modelling allows us to explain the spiral pattern by torsion. We found
observational visible counterparts in the SDO/AIA 335 A images. The
field lines are visible as loops in the AIA images. When the torsion
is increasing, a sigmoid is observed. In the present event observed
on November 24th 2010, we find that reconnection is also necessary to
explain their sigmoidal shape.

---------------------------------------------------------
Title: Magnetic Field Structures in a Facular Region Derived from
THEMIS and Hinode Vector Magnetic Field
Authors: Guo, Y.; Schmieder, B.; Bommier, V.; Mein, P.
2012ASPC..456...55G Altcode:
In order to compare vector magnetic fields obtained by two spectral
polarimeters (THEMIS/MTR and Hinode SOT/SP) and two inversion codes
(UNNOFIT and MELANIE), we observed a facular region in the active region
NOAA 10996 on 2008 May 23. We found that they give consistent results
concerning the distributions of field strengths, azimuth and inclination
angles. SOT/SP could resolve small magnetic polarities with sizes of
1” to 2”, and detect convergence and divergence of the horizontal
components of magnetic fields in the facular cells. These findings
support the models suggesting the existence of flux tube bundles
in faculae. With this model and multi spectral line observations,
we could infer the relative formation heights of those spectral lines.

---------------------------------------------------------
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.

---------------------------------------------------------
Title: Hanle effect from a dipolar magnetic structure: the case of
the solar corona and the case of a star
Authors: Bommier, V.
2012A&A...539A.122B Altcode:
Context. The context is the magnetic field measurement in external
solar or stellar layers by interpreting line polarization measurements
and the Hanle effect. Aims: The aim is to model the Hanle
effect depolarization by integrating upon a star on the one hand,
and by integrating along a line-of-sight through the solar corona on
the other hand. Methods: The formalism of the atomic density
matrix is recalled. Particular attention was devoted to the four axis
rotations necessary to transform the magnetic field reference frame
into that of the line-of-sight. Results: In the stellar case, the
discrepancy between the results by López Ariste et al. (2011, A&amp;A,
527, A120) and the symmetry considerations by Ignace etal. (2011,
A&amp;A, 530, A82) is resolved. In the solar case, the computations of
the hydrogen Lyα polarization by Derouich et al. (2010, A&amp;A, 511,
A7) are revisited, owing to symmetry considerations. Conclusions:
In the stellar case, we confirm that the effect integrated on a star
leads to a non-vanishing magnetic depolarization due to the high
non-linearity of the Hanle effect. In the solar case, we find that the
Hanle sensitivity of hydrogen Lyβ and Lyγ could be better adapted
to the measurement of the coronal background magnetic field. They
form a pair of lines of different and complementary sensitivity,
which makes it possible to determine the full vector. Lyα would
be instead adapted to the coronal loop magnetic field measurement,
because this field is stronger and suited to the Lyα Hanle sensitivity.

---------------------------------------------------------
Title: Multi-wavelength observations to understand the solar magnetic
activity and its feedback on the interplanetary medium
Authors: Molodij, G.; Schmieder, B.; Bommier, V.
2012mfu3.conf...93M Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Polarisation of auroral emission lines in the Earth's upper
atmosphere : first results and perspectives
Authors: Lamy, H.; Barthelemy, M.; Simon Wedlund, C.; Lilensten, J.;
Bommier, V.
2011AGUFM.P14C..03L Altcode:
Polarisation of light is a key observable to provide information
about asymmetry or anisotropy within a radiative source. Following the
pioneering and controversial work of Duncan in 1959, the polarisation
of auroral emission lines in the Earth's upper atmosphere has been
overlooked for a long time, even though the red intense auroral line
(6300Å) produced by collisional impacts with electrons precipitating
along magnetic field lines is a good candidate to search for
polarisation. This problem was investigated again by Lilensten et
al (2006) and observations were obtained by Lilensten et al (2008)
confirming that the red auroral emission line is polarised. More recent
measurements obtained by Barthélemy et al (2011) are presented and
discussed. The results are compared to predictions of the theoretical
work of Bommier et al (2011) and are in good agreement. Following
these encouraging results, a new dedicated spectropolarimeter is
currently under construction between BIRA-IASB and IPAG to provide
simultaneously the polarisation of the red line and of other interesting
auroral emission lines such as N2+ 1NG (4278Å), other N2 bands,
etc... Perspectives regarding the theoretical polarisation of some of
these lines will be presented. The importance of these polarisation
measurements in the framework of atmospheric modeling and geomagnetic
activity will be discussed.

---------------------------------------------------------
Title: Fast inversion of Zeeman line profiles using central moments
Authors: Mein, P.; Uitenbroek, H.; Mein, N.; Bommier, V.; Faurobert, M.
2011A&A...535A..45M Altcode:
Context. Many inversion techniques derive vector magnetic fields and
other parameters of the solar atmosphere from Stokes profiles with an
iterative process. Aims: We propose a new inversion method, using
functions derived from central moments (ICM), to determine magnetic
field vectors with very few iterations. Methods: Two quantities
A1 and A2 that combine moments of profiles I ±
S (S = Q,U,V) are proposed. They are nearly linear functions of the
longitudinal and transverse components of the magnetic field, and lead
to estimates of the field components through a least-squares polynomial
fit. A third quantity AD can be used to interpolate between
expansions that correspond to two basic models. Exponents β1
and β2 in the moment expressions are adjusted to minimize
the sensitivity to data noise. Results: Inversion coefficients
are computed for magnetic fields up to 3000 G in the case of the 630.2
Fe i line by forward modeling in two selected 1D model atmospheres
(FALC and MALTM). After inversion of synthetic profiles computed with
four models at disk center (FALA, FALC, FALF, MALTM), the mean standard
deviations with respect to the input fields do not exceed 5 G for both
components over the full range 0-3000 G. A comparison of ICM results
with inversion by the UNNOFIT code of profiles observed with THEMIS/MTR
shows good agreement. The typical computing time for a solar map of 100
000 points is less than 30 s. Conclusions: The ICM inversions
are almost insensitive to thermodynamic properties and solve for vector
magnetic fields in a wide range of solar conditions, ranging from plage
to spot, with very little computational effort. They are, therefore,
extremely suitable for large data sets. Further improvements should
take into account instrumental profiles and effects of limited spatial
resolution by using filling factors. Extensions using more parameters
and models with large departures from the Milne Eddington approximation
could also be considered.

---------------------------------------------------------
Title: Observed difference between the vertical and horizontal
magnetic field gradients in sunspots
Authors: Bommier, Veronique
2011sdmi.confE...6B Altcode:
A difference (larger than the measurements uncertainties) was observed
between the vertical and horizontal gradients of the magnetic field
in sunspots. This difference was observed with multiline recordings
achieved with the THEMIS telescope and the HINODE/SOT/SP instrument. The
multiline feature corresponds to a depth probing. This difference
was already present in the literature, which will be discussed in
details. The method for interpreting the spectropolarimetric data in
terms of magnetic field will be also detailed.

---------------------------------------------------------
Title: A filament supported by different magnetic field configurations
Authors: Guo, Y.; Schmieder, B.; Démoulin, P.; Wiegelmann, T.;
Aulanier, G.; Török, T.; Bommier, V.
2011IAUS..273..328G Altcode:
A nonlinear force-free magnetic field extrapolation of vector
magnetogram data obtained by THEMIS/MTR on 2005 May 27 suggests the
simultaneous existence of different magnetic configurations within
one active region filament: one part of the filament is supported by
field line dips within a flux rope, while the other part is located
in dips within an arcade structure. Although the axial field chirality
(dextral) and the magnetic helicity (negative) are the same along the
whole filament, the chiralities of the filament barbs at different
sections are opposite, i.e., right-bearing in the flux rope part and
left-bearing in the arcade part. This argues against past suggestions
that different barb chiralities imply different signs of helicity of
the underlying magnetic field. This new finding about the chirality of
filaments will be useful to associate eruptive filaments and magnetic
cloud using the helicity parameter in the Space Weather Science.

---------------------------------------------------------
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: Network velocity gradients in the photosphere. I. Modeling
Authors: Molodij, G.; Bommier, V.; Rayrole, J.
2011A&A...531A.139M Altcode:
We present an extension of the Unno-Rachkovsky solution that provides
the theoretical profiles coming out of a Milne-Eddington atmosphere
imbedded in a magnetic field, and that then takes a vertical velocity
gradient into account. Thus, the theoretical profiles may display
asymmetries as do the observed profiles, which facilitates the inversion
based on the Unno-Rachkovsky theory, and leads to the additional
determination of the vertical velocity gradient. We present UNNOFIT
inversion on synthetic data and spectropolarimetric observations
performed on an active region of the Sun with the French-Italian
telescope THEMIS operated by CNRS and CNR on the island of Tenerife.

---------------------------------------------------------
Title: Inclusion of velocity gradients in the Unno solution for
magnetic field diagnostic from spectropolarimetric data
Authors: Molodij, Guillaume; Bommier, Véronique
2011IAUS..274..291M Altcode:
We present an extension of the Unno-Rachkovsky solution that provides
the theoretical profiles coming out of a Milne-Eddington atmosphere
imbedded in a magnetic field, to the additional taking into account
of a vertical velocity gradient. Thus, the theoretical profiles may
display asymmetries as do the observed profiles, which facilitates
the inversion based on the Unno-Rachkovsky theory, and leads to the
additional determination of the vertical velocity gradient. We present
UNNOFIT inversion on spectropolarimetric data performed on an active
region of the Sun with the french-italian telescope THEMIS operated
by CNRS and CNR on the island of Tenerife.

---------------------------------------------------------
Title: The quiet Sun magnetic field: statistical description from
THEMIS observations
Authors: Bommier, V.
2011A&A...530A..51B Altcode:
Context. The pioneer interpretation of Hanle-effect depolarization
observed at the limb was the one of a turbulent nature for the solar
internetwork photospheric magnetic field. In the present paper, we
propose an alternative interpretation of these measurements, which
are now complemented with Zeeman-effect observations to allow one to
conclude on the properties of weak fields. Aims: In a previous
paper, we presented an internetwork field diagnostic from data obtained
with the ZIMPOL II polarimeter mounted on the THEMIS telescope. In
the present paper, we present the results obtained with the THEMIS
polarimeter with ten times more pixels. The agreement between the
results obtained with the two polarimeters confirm the goodness of
both the THEMIS polarimeter measurements and our data treatment. Methods: The Zeeman-effect measurements are interpreted via a
2-component model, which has a field-free component and a magnetized
one, filling a fraction of the analyzed pixel equal to 1 - α and α,
respectively. We determine this α parameter independently of the
magnetic inversion. We already applied these methods to the previous
interpretation of the ZIMPOL/THEMIS data. Results: The magnetic
field strength and magnetic field inclination are not independent,
because the strongest fields are more vertical and the weakest fields
are more horizontal, both in ZIMPOL/THEMIS and THEMIS/THEMIS data. Conclusions: This suggests that the photospheric internetwork
field has the structure of scattered narrow fluxtubes consisting in a
vertical field, which weakens in opening - widening with individual
field line bending - with height. The weakest fields then have a 2D
horizontal structure, instead of the usually admitted 3D turbulent
one. This does not contradict the previous Hanle-effect observations,
because it is insensitive to vertical fields. The number of fluxtubes
inside each pixel (which was 0.21 arcsec for the THEMIS/THEMIS and 0.53
arcsec for the ZIMPOL/THEMIS data) should, however, remain small. We
could make a conclusion about this after observing a non-zero spatial
correlation of the magnetic field orientation, with an estimated
correlation length of 250 km. 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: The Quiet Sun Magnetic Field Structure Derived from a Full
Vector Determination
Authors: Bommier, V.
2011ASPC..437..471B Altcode:
The magnetic field vector of the quiet Sun has been first determined
by usual Milne-Eddington inversion of ZIMPOL/THEMIS data. But such
an inversion provides the local average field only, i.e. the product
of the field strength by the magnetic filling factor. To discriminate
between both quantities, an additional method has to be provided. We
proposed a direct but approached determination of the filling factor in
the spectropolarimetric data themselves. Then we were able to derive
the inhomogeneous magnetic field strength (i.e. disambiguated from
the filling factor). The methods and results from the ZIMPOL/THEMIS
data are now published (Bommier et al. 2009). The present paper is
intended to show that the THEMIS/THEMIS data, 10 times more numerous,
give the same results, validating thus the THEMIS polarimeter results
with the ZIMPOL ones. But the main new result is that finally the
inhomogeneous field strength is found clearly dependent on the field
inclination angle, thus ruling out the hypothesis of a turbulent
field. The corresponding field organization could be: thin scattered
vertical tubes of strong field opening and weakening with height
(in the photosphere). Thus the weak fields would be horizontally
(2D) distributed rather than following their generally admitted 3D
turbulent structure. This distribution is not incompatible with the
Hanle effect observations, because the Hanle effect is insensitive to
the vertical field. The distribution of the thin opening tubes remains
to be quantized, but spatial horizontal correlations were observed,
which suggests that their size would not be very small with respect
to the observation pixel size of 0.2-0.5 arcsec.

---------------------------------------------------------
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: The Theoretical Impact Polarization of the O I 6300 Å Red
Line of Earth Auroræ
Authors: Bommier, V.; Sahal-Bréchot, S.; Dubau, J.; Cornille, M.
2011ASPC..437...73B Altcode:
We present a semi-classical theory of the impact polarization due
to a quadrupolar electric excitation, well-suited to this forbidden
line. In addition, this line is also radiatively forbidden being
a triplet-singlet transition. This is overcome by scaling the
semi-classical result to a full quantum calculation at a single
energy value. The cross-section and impact polarization are thus
obtained as a function of energy (with good agreement with the quantum
calculated cross-section), and the behavior of the impact polarization
is found quite different of the usual one of the dipolar electric
interaction. Denoting as radial the polarization parallel to the
incident beam or magnetic field, and as tangential the perpendicular
polarization, the dipolar interaction (permitted lines) leads to radial
polarization at low energy, and tangential polarization at high energy,
the polarization vanishing at energy about twelve times the threshold
energy. In the case of the quadrupolar electric interaction, we get
a quite different behavior, the vanishing point being much closer to
the threshold energy. This leads to reanalyze the auroræ red line
polarization observation by Lilensten et al. (2008), and to conclude
that the line is only weakly radially polarized and only during the
auroral events. The weak polarization level leads to consider the
competing depolarization by collisions with the neighboring O atoms,
whose density could then be diagnosed with further measurements and
calculations.

---------------------------------------------------------
Title: Coexisting Flux Rope and Dipped Arcade Sections Along One
Solar Filament
Authors: Guo, Y.; Schmieder, B.; Démoulin, P.; Wiegelmann, T.;
Aulanier, G.; Török, T.; Bommier, V.
2010ApJ...714..343G Altcode:
We compute the three-dimensional magnetic field of an active
region in order to study the magnetic configuration of active region
filaments. The nonlinear force-free field model is adopted to compute
the magnetic field above the photosphere, where the vector magnetic
field was observed by THEMIS/MTR on 2005 May 27. We propose a new
method to remove the 180° ambiguity of the transverse field. Next, we
analyze the implications of the preprocessing of the data by minimizing
the total force and torque in the observed vector fields. This step
provides a consistent bottom boundary condition for the nonlinear
force-free field model. Then, using the optimization method to compute
the coronal field, we find a magnetic flux rope along the polarity
inversion line. The magnetic flux rope aligns well with part of an Hα
filament, while the total distribution of the magnetic dips coincides
with the whole Hα filament. This implies that the magnetic field
structure in one section of the filament is a flux rope, while the
other is a sheared arcade. The arcade induced a left-bearing filament
in the magnetic field of negative helicity, which is opposite to the
chirality of barbs that a flux rope would induce in a magnetic field
of the same helicity sign. The field strength in the center of the flux
rope is about 700 G, and the twist of the field lines is ~1.4 turns.

---------------------------------------------------------
Title: Magnetic Field Structures in a Facular Region Observed by
THEMIS and Hinode
Authors: Guo, Y.; Schmieder, B.; Bommier, V.; Gosain, S.
2010SoPh..262...35G Altcode: 2010SoPh..tmp...30G; 2010arXiv1002.4355G
The main objective of this paper is to build and compare vector
magnetic maps obtained by two spectral polarimeters, i.e. THEMIS/MTR and
Hinode SOT/SP, using two inversion codes (UNNOFIT and MELANIE) based
on the Milne - Eddington solar atmosphere model. To this end, we used
observations of a facular region within active region NOAA 10996 on 23
May 2008, and found consistent results concerning the field strength,
azimuth and inclination distributions. Because SOT/SP is free from the
seeing effect and has better spatial resolution, we were able to resolve
small magnetic polarities with sizes of 1″ to 2″, and we could
detect strong horizontal magnetic fields, which converge or diverge
in negative or positive facular polarities. These findings support
models which suggest the existence of small vertical flux tube bundles
in faculae. A new method is proposed to get the relative formation
heights of the multi-lines observed by MTR assuming the validity of
a flux tube model for the faculae. We found that the Fe I 6302.5 Å
line forms at a greater atmospheric height than the Fe I 5250.2 Å line.

---------------------------------------------------------
Title: Fast imaging spectroscopy with MSDP spectrometers. Vector
magnetic maps with THEMIS/MSDP
Authors: Mein, P.; Mein, N.; Bommier, V.
2009A&A...507..531M Altcode:
Context: Multichannel subtractive double pass (MSDP) spectrometers
produce 3D data cubes (x, y, λ) simultaneously across several line
profiles. They do not suffer from image convolution by any slit width,
and synchronous observations across all wavelengths avoid differential
seeing effects. They are very suitable for fast 2D spectroscopy. Aims: (1) We review specifications and capabilities of some existing
MSDP spectrometers with respect to high-cadence observations. (2)
THEMIS/MSDP is designed for the spectropolarimetry of strong lines. We
propose new data reductions also suitable for the spectropolarimetry of
photospheric lines. Methods: An off-line algorithm is described
as a way to increase the spectral resolution. Taking the opportunity
of 3D data, spatial interpolations are used around each solar point by
only assuming that intensity gradients partial I(x, y, λ)/partial x
are constant in the range (x± ɛ_x,λ ± ɛ_λ). The UNNOFIT inversion
is used to compare vector magnetic maps deduced from THEMIS/MSDP and
slit-spectropolarimetry THEMIS/MTR data. Results: Both results
are in good agreement. In active regions, the rms of the MSDP noise,
calculated over 1 arcsec^2, is less than 24 G for the LOS magnetic
field and less than 52 G for Bx and 32 G for B_y. The MSDP
scanning speed is 10 times the speed of slit-spectropolarimetry. Conclusions: THEMIS/MSDP can provide vector magnetic maps with typical
temporal resolutions that are less than 1 min for small fields-of-view
and 10 min for active regions. This allows addressing a number of fast
events. In the future, MSDP instruments should efficiently complement
single-slit spectroscopy and tunable filters. Their main capabilities
should be the multiline aspect and the high temporal and spatial
resolutions. New optical devices, such as image slicers, should
substantially increase the signal-to-noise ratio. For polarimetric
measurements, various compromises are possible between speed, spatial
resolution, and SNR. A-posteriori image restorations, either using wide
band proxies or bursts of multi-wavelength short exposures, should help
improving signal-to-noise ratio and spatial resolution. 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: 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: Non-LTE Modeling of the Ba II D2 Line Resonance Polarization
Authors: Faurobert, M.; Bommier, V.; Derouich, M.
2009ASPC..405...35F Altcode:
The Ba II resonance line at 455.4 nm is formed in the low solar
chromosphere. It shows significant linear polarization outside active
regions close to the solar limb. This so-called resonance polarization
is sensitive to the Hanle effect of weak magnetic fields. We report
on numerical simulations of the intensity and resonance polarization
center-to-limb variations in the line and in the adjacent continuum,
in a quiet solar atmosphere and we compare them to observations
performed at THEMIS in August 2007. In the simulations we take
into account non-LTE multilevel coupling, multiple scattering and
partial frequency redistribution, and we neglect the hyperfine
structure of the odd isotopes of Barium. As resonance polarization
and partial frequency redistribution effects are very sensitive to
elastic collisions with hydrogen atoms we use accurate depolarizing
collisional rates recently computed for this line by a semi-classical
method. Our radiative transfer calculations allow us to model the
central part of the line core and the wings quite well. We show that
the line polarization depends very much indeed on partial frequency
redistribution effects. Then we investigate its diagnostic potential
for weak unresolved magnetic fields in the low chromosphere. We
find that the observed polarization rates are in good agreement with
the simulations if we take into account the Hanle effect due to an
isotropic turbulent magnetic field of the order of 30 Gauss at the
altitude where the line core is formed, i.e. between 900 km and 1300
km above the basis of the photosphere.

---------------------------------------------------------
Title: The Height Dependence of the Magnetic Vector Field in Sunspots
Authors: Balthasar, H.; Bommier, V.
2009ASPC..405..229B Altcode:
A complex active region was observed simultaneously with the solar
telescopes VTT and THEMIS on Tenrife in May 2005. Spatial scans
across the sunspot group were performed at both telescopes. The
full Stokes-vector was recorded in several photospheric spectral
lines, i.~e. at the VTT in a group of iron and silicon lines in
the near infrared and at THEMIS in iron and chromium lines in the
visible. Inversions were carried out independently for the different
lines in order to derive the magnetic field strength, its inclination
and azimuth together with the temperature stratification. Thus we
obtained the three-dimensional structure of the magnetic field. Selected
locations in the penumbra and in light bridges were considered in
detail. We find a general tendency that the magnetic field is weaker
and less inclined in higher layers.

---------------------------------------------------------
Title: Atomic and Molecular Depolarizing Collision Rates
Authors: Bommier, V.
2009ASPC..405..335B Altcode:
This paper is divided in three parts: after having recalled the
different types of collisions with the different types of perturbers and
having provided rough orders of magnitude of the collision rates, three
cases are discussed. Although the most frequent type of depolarizing
collision is the one of the collisions with the surrounding Hydrogen
atoms, we discuss in the first part a particular case where the
depolarizing collision effect is due to collisions with electrons
and protons. This is the case of the Hydrogen lines observed in
solar prominences. We recall how the interpretation of polarization
observations in two lines has led to the joint determination of the
magnetic field vector and the electron and proton density, and we show
that this density determination gives results in agreement with the
densities determined by interpretation of the Stark effect, provided
that this last effect be evaluated in the impact approximation scheme
which is indeed more valid than the quasistatic approach at these
densities. In the second part, we describe a method that has been
recently developed for the computation of the depolarizing rates in
the case of collisions with the neutral Hydrogen atom. The case of
molecular lines is less favourable, because, even if depolarizing
collision rates computation may be soon expected and begin to be done
inside the ground level of the molecule, calculations inside the excited
states are far from the present ability. In the third part, we present
an example where the excited state depolarizing rates were evaluated
together with the magnetic field through the differential Hanle effect
interpretation, based on the fact that the molecule provides a series
of lines of different sensitivities that can be compared. This led to
an experimental/observational determination of these rates, waiting
for future theoretical computations for comparison.

---------------------------------------------------------
Title: Evidence for a Pre-Eruptive Twisted Flux Rope Using the Themis
Vector Magnetograph
Authors: Canou, A.; Amari, T.; Bommier, V.; Schmieder, B.; Aulanier,
G.; Li, H.
2009ApJ...693L..27C Altcode:
Although there is evidence that twisted structures form during
large-scale eruptive events, it is not yet clear whether these exist in
the pre-eruptive phase as twisted flux ropes (TFRs) in equilibrium. This
question has become a major issue since several theoretical mechanisms
can lead to the formation of TFRs. These models consider either the
evolution of a coronal configuration driven by photospheric changes or
the emergence of TFR from the convection zone. We consider as a target
for addressing this issue the active region NOAA AR 10808 known at
the origin of several large-scale eruptive phenomena, and associated
with the emergence of a δ-spot. Using the THEMIS vector magnetogram
as photospheric boundary conditions for our nonlinear force-free
reconstruction model of the low corona and without any other assumption,
we show that the resulting pre-eruptive configuration exhibits a TFR
above the neutral line of the emerging δ-spot. In addition, the free
magnetic energy of this configuration could even be large enough to
explain such resulting large-scale eruptive events.

---------------------------------------------------------
Title: The Solar Magnetic Field: Surface and Upper Layers, Network
and Internetwork Field
Authors: Bommier, V.
2009LNP...765..231B Altcode:
After having presented the magnetic field effects on the radiation
emitted in an atomic or molecular line (Zeeman effect, Hanle effect),
we present two applications: (i) the measurement of the magnetic
field vector in solar prominences during the ascending phase of Cycle
XXI. By transferring the results on synoptic maps of the filaments, a
general organization of the large-scale surface field becomes visible;
(ii) the measurements of the surface magnetic field made by recent
spectropolarimeters like THEMIS. The result is the division of the
surface magnetic field into two classes: (a) the network field, nearly
vertical and 100 G or more (local average value), located in active
regions and at the frontiers of supergranules; (b) the internetwork
field, turbulent in direction with an horizontal trend, with a local
average value of 20 Gauss or less.

---------------------------------------------------------
Title: Hanle effect in the solar Ba II D2 line: a diagnostic tool
for chromospheric weak magnetic fields
Authors: Faurobert, M.; Derouich, M.; Bommier, V.; Arnaud, J.
2009A&A...493..201F Altcode: 2008arXiv0811.1180F
Context: The physics of the solar chromosphere depends in a crucial way
on its magnetic structure. However there are presently very few direct
magnetic field diagnostics available for this region. Aims:
Here we investigate the diagnostic potential of the Hanle effect
on the Ba II D2 line resonance polarization for the determination
of weak chromospheric turbulent magnetic fields. Methods:
The line formation is described with a non-LTE polarized radiative
transfer model taking into account partial frequency redistribution
with an equivalent two-level atom approximation, in the presence of
depolarizing collisions and the Hanle effect. We investigate the line
sensitivity to temperature variations in the low chromosphere and
to elastic collision with hydrogen atoms. We compare center-to-limb
variations of the intensity and linear polarization profiles observed
at THEMIS in 2007 to our numerical results. Results: We show that
the line resonance polarization is very strongly affected by partial
frequency redistribution effects both in the line central peak and
in the wings. Complete frequency redistribution cannot reproduce the
polarization observed in the line wings. The line is weakly sensitive
to temperature differences between warm and cold components of the
chromosphere. The effects of elastic collisions with hydrogen atoms and
of alignment transfer due to multi-level coupling with the metastable
^2D{5/2} levels have been studied in a recent paper showing that they
depolarize the ^2P{3/2} level of the line. In the conditions where
the line is formed we estimate the amount of depolarization due to
this mechanism as a factor of 0.7 to 0.65. If we first neglect this
effect and determine the turbulent magnetic field strength required to
account for the observed line polarization, we obtain values between
20 G and 30 G. We show that this overestimates the magnetic strength
by a factor between 1.7 and 2. Applying these correction factors
to our previous estimates, we find that the turbulent magnetic field
strength is between 10 G and 18 G. Conclusions: Because of its low
sensitivity to temperature variations, the solar Ba II D2 line appears
as a very good candidate for the diagnosis of weak magnetic fields in
the low chromosphere (z ≥ 900 km) by means of the Hanle effect.

---------------------------------------------------------
Title: Photospheric flows around a quiescent filament at Large and
small scale and their ffects on filament destabilization
Authors: Roudier, Th.; Malherbe, J. M.; Švanda, M.; Molodij, G.;
Keil, S.; Sütterlin, P.; Schmieder, B.; Bommier, V.; Aulanier, G.;
Meunier, N.; Rieutord, M.; Rondi, S.
2008sf2a.conf..569R Altcode:
We study the influence of large and small scales photospheric
motions on the destabilization of an eruptive filament, observed
on October 6, 7, and 8, 2004 as part of an international observing
campaign (JOP 178). Large-scale horizontal flows are invetigated
from a series of MDI/SOHO full-disc Dopplergrams and magnetograms
from THEMIS. Small-scale horizontal flows were derived using local
correlation tracking on TRACE satellite, Dutch Open Telescope (DOT)
and The Dunn Solar telescope (DST) data. The topology of the flow field
changed significantly during the filament eruptive phase, suggesting
a possible coupling between the surface flow field and the coronal
magnetic field. We measured an increase of the shear below the point
where the eruption starts and a decrease in shear after the eruption. We
conclude that there is probably a link between changes in surface flow
and the disappearance of the eruptive filament.

---------------------------------------------------------
Title: Topological Departures from Translational Invariance along
a Filament Observed by THEMIS
Authors: Dudík, J.; Aulanier, G.; Schmieder, B.; Bommier, V.;
Roudier, T.
2008SoPh..248...29D Altcode: 2008SoPh..tmp...53D
We study the topology of the 3D magnetic field in a filament channel
to address the following questions: Is a filament always formed in a
single flux tube? How does the photospheric magnetic field lead to
filament interruptions and to feet formation? What is the relation
between feet-related field lines and the parasitic polarities? What
can topological analyses teach us about EUV filament channels? To do
so, we consider a filament observed on 6 October 2004 with THEMIS/MTR,
in Hα with the full line profile simultaneously and cospatially with
its photospheric vector magnetic field. The coronal magnetic field
was calculated from a "linear magnetohydrostatic" extrapolation of a
composite THEMIS-MDI magnetogram. Its free parameters were adjusted
to get the best match possible between the distribution of modeled
plasma-supporting dips and the Hα filament morphology. The model
results in moderate plasma β≤1 at low altitudes in the filament,
in conjunction with non-negligible departures from force-freeness
measured by various metrics. The filament here is formed by a split
flux tube. One part of the flux tube is rooted in the photosphere aside
an observed interruption in the filament. This splitted topology is
due to strong network polarities on the edge of the filament channel,
not to flux concentrations closer to the filament. We focus our study
to the northwest portion of the filament. The related flux tube is
highly fragmented at low altitudes. This fragmentation is due to small
flux concentrations of two types. First, some locally distort the
tube, leading to noticeable thickness variations along the filament
body. Second, parasitic polarities, associated with filament feet,
result in secondary dips above the related local inversion line. These
dips belong to long field lines that pass below the flux tube. Many
of these field lines are not rooted near the related foot. Finally,
the present model shows that the coronal void interpretation cannot
be ruled out to interpret the wideness of EUV filament channels.

---------------------------------------------------------
Title: Large-scale horizontal flows in the solar
photosphere. III. Effects on filament destabilization
Authors: Roudier, T.; Švanda, M.; Meunier, N.; Keil, S.; Rieutord,
M.; Malherbe, J. M.; Rondi, S.; Molodij, G.; Bommier, V.; Schmieder, B.
2008A&A...480..255R Altcode: 2007arXiv0711.3112R
Aims:We study the influence of large-scale photospheric motions on
the destabilization of an eruptive filament, observed on October 6,
7, and 8, 2004, as part of an international observing campaign (JOP
178). Methods: Large-scale horizontal flows were investigated
from a series of MDI full-disc Dopplergrams and magnetograms. From
the Dopplergrams, we tracked supergranular flow patterns using the
local correlation tracking (LCT) technique. We used both LCT and manual
tracking of isolated magnetic elements to obtain horizontal velocities
from magnetograms. Results: We find that the measured flow
fields obtained by the different methods are well-correlated on large
scales. The topology of the flow field changed significantly during
the filament eruptive phase, suggesting a possible coupling between
the surface flow field and the coronal magnetic field. We measured
an increase in the shear below the point where the eruption starts
and a decrease in shear after the eruption. We find a pattern in the
large-scale horizontal flows at the solar surface that interact with
differential rotation. Conclusions: We conclude that there is
probably a link between changes in surface flow and the disappearance
of the eruptive filament.

---------------------------------------------------------
Title: Magnetic Causes of the Eruption of a Quiescent Filament
Authors: Schmieder, B.; Bommier, V.; Kitai, R.; Matsumoto, T.; Ishii,
T. T.; Hagino, M.; Li, H.; Golub, L.
2008SoPh..247..321S Altcode: 2007SoPh..tmp..213S
During the JOP178 campaign in August 2006, we observed the
disappearance of our target, a large quiescent filament located at
S25°, after an observation time of three days (24 August to 26
August). Multi-wavelength instruments were operating: THEMIS/MTR
("MulTi-Raies") vector magnetograph, TRACE ("Transition Region and
Coronal Explorer") at 171 Å and 1600 Å and Hida Domeless Solar
telescope. Counter-streaming flows (+/−10 km s−1) in the
filament were detected more than 24 hours before its eruption. A slow
rise of the global structure started during this time period with a
velocity estimated to be of the order of 1 km s−1. During
the hour before the eruption (26 August around 09:00 UT) the velocity
reached 5 km s−1. The filament eruption is suspected to
be responsible for a slow CME observed by LASCO around 21:00 UT on 26
August. No brightening in Hα or in coronal lines, no new emerging
polarities in the filament channel, even with the high polarimetry
sensitivity of THEMIS, were detected. We measured a relatively large
decrease of the photospheric magnetic field strength of the network
(from 400 G to 100 G), whose downward magnetic tension provides
stability to the underlying stressed filament magnetic fields. According
to some MHD models based on turbulent photospheric diffusion, this
gentle decrease of magnetic strength (the tension) could act as the
destabilizing mechanism which first leads to the slow filament rise
and its fast eruption.

---------------------------------------------------------
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: Interaction of magnetic field systems leading to an X1.7
flare due to large-scale flux tube emergence
Authors: Li, H.; Schmieder, B.; Song, M. T.; Bommier, V.
2007A&A...475.1081L Altcode:
Aims:The aim of this paper is to understand the magnetic configuration
and evolution of an active region, which permitted an X1.7 flare to
be observed during the decaying phase of a long-duration X1.5 flare
on 2005 September 13. Methods: We performed a multi-wavelength
analysis using data from space-borne (Solar and Heliospheric Observatory
(SOHO), Transition Region and Coronal Explorer (TRACE), Reuven Ramaty
High-Energy Solar Spectroscopic Imager (RHESSI), GOES) and ground-based
(the French-Italian THEMIS telescope and the Huairou Video Vector
Magnetograph (HVVM)) instruments. We coaligned all the data in order to
study the origin of the flare by comparing the observed magnetic field
structures with the emissions detected by different instruments. Results: Reconstructed RHESSI images show three hard X-ray (HXR)
sources. In TRACE 195 Å images, two loops are seen: a short bright loop
and a longer one. Five ribbons are identified in Hα images, with two
of them remnant ribbons of the previous flare. We propose the following
scenario to explain the X1.7 flare. A reconnection occurs between the
short loop system and the longer loops (TRACE 195 Å). Two X-ray sources
could be the footpoints of the short loop, while the third one between
the two others is the site of the reconnection. The Hα ribbons are
the footprints in the chromosphere of the reconnected loops. During the
reconnection, the released energy is principally nonthermal according
to the RHESSI energy spectrum analysis (two orders of magnitude higher
than the maximum thermal energy). The proposed scenario is confirmed
by a nonlinear force-free field (NLFFF) extrapolation, which shows the
presence of short sheared magnetic field lines before the eruption
and less sheared ones after the reconnection, and the connectivity
of the field lines involved in the flaring activity is modified after
the reconnection process. The evolution of the photospheric magnetic
field over a few days shows the continuous emergence of a large-scale
magnetic flux tube, the tongue-shape of the two main polarities of
the active region being the signature of such an emergence. After the
previous X1.5 flare, the emergence of the tube continues and favors
new magnetic energy storage and the onset of the X1.7 flare.

---------------------------------------------------------
Title: Fast vector magnetographs: THEMIS/MSDP and EST project
Authors: Mein, P.; Bommier, V.; Mein, N.
2007sf2a.conf..601M Altcode:
Imaging spectro-polarimetry with Multichannel Subtractive Double
Pass (MSDP) is able to provide vector magnetic fields with high
temporal resolution. We present some results obtained with THEMIS and
reduced with the UNNOFIT code, as well as a new method to achieve
off-line the required spectral resolution. Performances of slit-
and imaging-spectroscopy are briefly compared, together with the high
capabilities expected from the EST project.

---------------------------------------------------------
Title: Photospheric flows around a quiescent filament
Authors: Rondi, S.; Roudier, Th.; Molodij, G.; Bommier, V.; Keil,
S.; Sütterlin, P.; Malherbe, J. M.; Meunier, N.; Schmieder, B.;
Maloney, P.
2007A&A...467.1289R Altcode:
Context: The horizontal photospheric flows below and around a
filament are one of the components in the formation and evolution of
filaments. Few studies exist because they require multiwalength time
sequences at high spatial resolution. Aims: Our objective
is to measure the horizontal photospheric flows associated
with the evolution and eruption of a filament. Methods:
We present observations obtained in 2004 during the international
JOP 178 campaign which involved eleven instruments both in space
and at ground based observatories. We use TRACE WL, DOT and DST
observation to derive flow maps which are then coaligned with
intensity images and with the vector magnetic field map obtained with
THEMIS/MTR. Results: Several supergranulation cells cross the
Polarity Inversion Line (PIL) and can transport magnetic flux through
the PIL, in particular parasitic polarities. We present a detailed
example of the formation of a secondary magnetic dip at the location
of a filament footpoint. Large-scale converging flows, which could
exist along the filament channel and contribute to its formation, are
not observed. Before the filament's eruptive phase, we observe both
parasitic and normal polarities being swept by a continuously diverging
horizontal flow located in the filament gap. The disappearance of the
filament initiates in this gap. Such purely horizontal motions could
lead to destabilization of the filament and could trigger the sudden
filament disappearance.

---------------------------------------------------------
Title: A generalized √ɛ-law. The role of unphysical source terms
in resonance line polarization transfer and its importance as an
additional test of NLTE radiative transfer codes
Authors: Stepán, J.; Bommier, V.
2007A&A...468..797S Altcode: 2007arXiv0704.1573S
Context: A derivation of a generalized √ɛ-law for nonthermal
collisional rates of excitation by charged perturbers is presented. Aims: Aim of this paper is to find a more general analytical
expression for a surface value of the source function which can be used
as an additional tool for verification of the non-LTE radiative transfer
codes. Methods: Under the impact approximation hypothesis,
static, one-dimensional, plane-parallel atmosphere, constant magnetic
field of arbitrary strength and direction, two-level atom model with
unpolarized lower level and stimulated emission neglected, we introduce
the unphysical terms into the equations of statistical equilibrium
and solve the appropriate non-LTE integral equations. Results:
We derive a new analytical condition for the surface values of the
source function components expressed on the basis of irreducible
spherical tensors.

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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.

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Title: Multipole rates for atomic polarization studies: the case
of complex atoms in non-spherically symmetric states colliding with
atomic hydrogen
Authors: Sahal-Bréchot, S.; Derouich, M.; Bommier, V.; Barklem, P. S.
2007A&A...465..667S Altcode:
Context: Interpretation of linearly polarized parameters of the lines of
complex atoms for the second solar spectrum needs a lot of collisional
coefficients which are often poorly known. Aims: We provide
general and simple formulae giving the coefficients of the atomic master
equation (depolarization, polarization transfer, population transfer,
and relaxation coefficients) for the case of any atomic level (but not
a spherically symmetric) that is perturbed by collisions with hydrogen
atoms. Methods: We use the theory of the density matrix and
the theory of atomic collisions with a few assumptions (frozen core
and spin neglected during the collision). We only study collisional
transitions between levels of the same configuration with no equivalent
electrons in the external shell, and with the rest of the configuration
(the core) frozen. We use the basis of the Tkq
irreducible spherical tensor operators. Results: The formulae
giving the depolarization and polarization transfer coefficients due to
collisions with neutral hydrogen for l ≠ 0 levels of complex atoms can
be expressed as a linear combination of the k-pole depolarization and
elastic collisional rate coefficients obtained for simple atoms. Conclusions: .It should be possible to apply this method for fast
calculation of multipole rates for any level having an external shell
l ≠ 0.

---------------------------------------------------------
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: Fast vector magnetic maps with imaging spectroscopy
Authors: Mein, P.; Mein, N.; Bommier, V.
2007MmSAI..78..160M Altcode:
We present a new observing mode of THEMIS / MSDP which can provide fast
vector magnetic maps of the solar photosphere in the 610.27 Ca line.

---------------------------------------------------------
Title: Simultaneous polarimetric observations with VTT and THEMIS
Authors: Balthasar, H.; Bommier, V.
2007msfa.conf..229B Altcode:
Spectro-polarimetric observations of sunspot groups have been performed
simultaneously with the VTT and with THEMIS. At the VTT we observed a
group of iron and silicon lines at 1078 nm with the Tenerife Infrared
Polarimeter, and at THEMIS we observed in five spectral channels
(MTRmode): Fe 630 nm, Na D, Hα, Fe 557.6 nm and alternatively Cr 578
nm or Fe 525 nm. The inversion of the Stokes-profiles was done with
the SIR-code for the infrared lines and for Fe 630 nm, for the other
spectral ranges the inversion is still pending. So far we derived that
the magnetic field strength decreases with height at most locations
inside the spots, in contrast to some recently published results of
other investigations.

---------------------------------------------------------
Title: Solar magnetism and dynamics and THEMIS users meeting
Authors: Bommier, V.; Sahal-Bréchot, S.
2007MmSAI..78....5B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Photospheric flows around a quiescent filament and CALAS
first results .
Authors: Rondi, S.; Roudier, Th.; Molodij, G.; Bommier, V.; Malherbe,
J. M.; Schmieder, B.; Meunier, N.; Rieutord, M.; Beigbeder., F.
2007MmSAI..78..114R Altcode:
The horizontal photospheric flows below and around a filament are one of
the components in the formation and evolution of filaments. Few studies
have been done so far because this requires multiwalength time sequences
with high spatial resolution. We present observations obtained in 2004
during the international JOP 178 campaign in which eleven instruments
were involved, from space and ground based observatories. Several
supergranulation cells are crossing the Polarity Inversion Line (PIL)
allowing the transport of magnetic flux through the PIL, in particular
the parasitic polarities. Before the filament eruptive phase, parasitic
and normal polarities are swept by a continuous diverging horizontal
flow located in the filament gap where the disappearance of the filament
starts. In the future, observations at high spatial resolution on a
large field-of-view would be very useful to study filaments, as they are
very large structures. We also present the first images obtained with
the use of our new 14 MPixel camera CALAS (CAmera for the LArge Scales
of the Solar Surface) (10 arcmin× 6.7 arcmin) . These are the first
large-scale and high-resolution images of the solar surface ever made.

---------------------------------------------------------
Title: Some THEMIS tip-tilt images .
Authors: Bommier, V.
2007MmSAI..78...23B Altcode:
In the MTR (`MulTiRaies', i.e. multiline spectropolarimetry) mode of
THEMIS, a map is the result of a reconstruction from a scan of the
solar image on the spectrograph entrance slit. The result of image
motion appears as zigzags along non-vertical lines or structures in
the map. As an image stabilization system, the new tip-tilt acts in
reducing such zigzags. A map is presented obtained with the tip-tilt
ON where nearly no zigzag is visible.

---------------------------------------------------------
Title: The granular magnetic field as observed with THEMIS
Authors: Bommier, V.; Molodij, G.; Meunier, N.
2007MmSAI..78...65B Altcode:
The search for correlation along the slit in THEMIS spectropolarimetric
observations of a quiet region shows a positive autocorrelation of the
magnetic field direction with a pixel size of 0.45 arcsec. Accordingly,
the magnetic field appears as partially resolved with such a pixel
size. Further spectropolarimetric observations have been performed by
scanning a quiet region with THEMIS tip-tilt ON, in order to investigate
a possible relationship between the granulation and the magnetic
field vector which is known in each pixel of this observation (pixel
size of 0.25 arcsec). As a result, we see a very clear correlation
between the granulation observed in the continuum and the longitudinal
velocity field observed via the Doppler effect, but the granulation
and the magnetic field vector (strength and direction) appear us as
uncorrelated, by looking at their respective maps. These quantities
(velocity and magnetic field) have been derived from spectropolarimetric
observations of the Fe I 6302.5 line, to which UNNOFIT inversion has
been applied to derive the magnetic field vector.

---------------------------------------------------------
Title: Second Spectrum of Na I D1 Observed with THEMIS
Authors: Bommier, V.; Molodij, G.
2006ASPC..358..231B Altcode:
The second solar spectrum (spectrum of the linear polarization
observed near the solar limb in a quiet region) of Na I D1
has always been found antisymmetrical when observed with THEMIS tep{b12
TB01,b12 BM02}. The same holds also for atlas of tet{b12 Ga00}. On the contrary, tet{b12 SK97} and tet{b12 St00} observed a
differently shaped profile, showing a central peak. We investigated
in depth our treatment of THEMIS data, in particular looking for
possible beam misalignments, by observing other unpolarized lines, but
we have failed to put in evidence any misalignment. We discuss these
complementary observations. In addition, we present a structure in the
V/I profile of Na I D1 and D2, which we have
repeatedly observed, and which we suggest be due to the Kemp effect
(the alignement-to-orientation transfer that occurs in the transition
from the Zeeman effect to the Paschen-Back effect).

---------------------------------------------------------
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: Semi-Classical Collision Formalism with Energy and Momentum
Transfer
Authors: Bommier, V.
2006ASPC..358..245B Altcode:
As expected, the semi-classical theory of atom-electron and atom-ion
collisions ( tealt{b11 Se62}; see also tealt{b11 SB96}) leads
to incorrect results when it is applied to impact polarization
computations. This is due to the fact that, near the threshold,
the Δ M=± 1 transitions between Zeeman sublevels remain open,
even though the momentum conservation law tep{b11 PS58} implies
that they should be forbidden at the exact threshold. An approximate
model of momentum transfer is proposed, which corrects this behavior,
leading to a fairly good agreement with observed impact polarization
for several target atoms. The agreement is improved also for the total
cross-section, because the Δ M=± 1 cross-sections were previously
overestimated. Comparison with experimental results are shown,
for electron-atom impact polarization and total cross-section. As a
second step, energy transfer is also taken into account, by splitting
the collision process in two halves: the first half is modeled within
the initial conditions, while the second half is modeled within the
final conditions.

---------------------------------------------------------
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: 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: 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: Predictions on the application of the Hanle effect to map
the surface magnetic field of Jupiter
Authors: Ben-Jaffel, L.; Harris, W.; Bommier, V.; Roesler, F.;
Ballester, G. E.; Jossang, J.
2005Icar..178..297B Altcode:
In this paper we evaluate the possibility of detecting, for the
first time, the surface magnetic field of Jupiter (∼1 bar level)
by observing the change of linear polarization induced by the Hanle
effect on the H Lyman-alpha (Ly α) emission line of the planet. We
find that, indeed, the Hanle effect, which results from the interaction
between a local magnetic field and the atomic polarization induced
by absorption of anisotropic radiation, is sensitive to relatively
weak values of the strength of the magnetic fields expected on
planets. First, we show that for the Ly α emission backscattered
by atomic H in the presence of a magnetic field, the Hanle effect is
polarizing. This new result is in total contrast to the depolarizing
effect predicted and observed for emission lines scattered at right
angles in solar prominences. Additionally, to estimate the polarization
rate for the case of Jupiter, we have considered three magnetic field
models: a dipole field for reference, an O based model [Connerney,
J.E.P., 1981. The magnetic field of Jupiter—A generalized inverse
approach. J. Geophys. Res. 86, 7679-7693], and finally, an O based model
[Khurana, K.K., 1997. Euler potential models of Jupiter's magnetospheric
field. J. Geophys. Res. 102, 11295-11306]. In all models, we show that
for the jovian backscattered Ly α line, the Hanle effect does enhance
the Ly α linear polarization; the polarization rate may exceed 2% at
specific regions of the jovian disc, making detection possible either
remotely or from an orbiter around Jupiter. In general, depending
on the instrumental sensitivity and the observing strategy used,
we show that accurate mapping of the linear polarization rate at the
planetary surface (thermosphere) or off-disc (corona) may provide a
rather accurate estimate of the jovian total magnetic field strength
on large area scales.

---------------------------------------------------------
Title: Vector magnetic field map at the photospheric level below
and around a solar filament (neutral line)
Authors: Bommier, V.; Rayrole, J.; Eff-Darwich, A.
2005A&A...435.1115B Altcode:
We present a vector magnetic field map obtained on 7 December 2003,
below and around a filament located not so far from the active
region NOAA 517, whose one spot is also found on the map of 240×
340 arcsec. This region was itself located near the disk center,
so that the longitudinal (resp. transverse) field is nearly the
vertical (resp. horizontal) one. The THEMIS telescope was used in
its spectropolarimetric multiline mode MTR ("MulTiRaies"). The noise
level is 5-10 Gauss in the longitudinal field and 50-100 Gauss in the
transverse field, while the pixel size is 0.45 arcsec. Fundamental
ambiguity is not solved, and the atmosphere is assumed to be
homogeneous. The magnetic field derivation method described in this
paper was validated on eight test points submitted to the UNNOFIT
inversion code, and the results are found in agreement within 14%
discrepancy. Two main results appear on the map: (i) a strong spatial
correlation between the longitudinal and transverse field resulting in
an inclined field vector (making a most probable angle of 60° or 120°
with the line-of-sight in the filament region); and (ii) homogeneity
of the field direction (inclination and azimuth) in the filament
region. Parasitic polarities were also detected: first those located
at the filament feet, as theoretically expected, on the one hand;
and then weak opposite polarity regular patterns that appear between
the network field (strong field at the frontiers of supergranules),
on the other. The exact superimposition of the magnetic field map
derived from the Fe I 6302.5 Å line and of the Hα map, which enabled
association of the parasitic polarities with the filament feet, was
possible because these two maps were simultaneously obtained, thanks
to a unique facility available in the multiline mode of THEMIS.

---------------------------------------------------------
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: 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: The Partial Redistribution in the Atomic Density Matrix
Formalism
Authors: Bommier, V.
2003ASPC..307..213B Altcode:
No abstract at ADS

---------------------------------------------------------
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: Theoretical Study of the Collisional Depolarization and of the
Hanle Effect in the Na I D2 Line Observed on the Solar Limb
Authors: Bommier, V.; Kerkeni, B.
2003ASPC..307..284B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Hanle effect observed in solar prominences: interpretation
of the 1974 1982 Pic-du-Midi observations, and new perspectives
Authors: Bommier, V.
2003EAS.....9..197B Altcode:
This paper is devoted to review the development and the results of
the program “solar prominences" that has been aimed to observe the
Hanle effect at the Pic-du-Midi during the ascending phase of Cycle
XXI (1974 1982). This aim had been defined and the observations have
been performed by Jean-Louis Leroy. The Hanle effect is the effect
of a weak magnetic field on the scattering linear polarization: its
main features are, for some field orientations, a depolarization and
eventually a rotation of the polarization direction. The magnetic
field diagnostic from polarization measurements requires a modelling
of the polarized line formation, that has been achieved in Meudon in
the well-adapted formalism of the atomic density matrix. It is shown
how the program has been developed to determine the 3components of
the field vector and the electron density, by setting multi-line
polarimetric observations. Particular attention has been devoted on
the solution of the 180degrees ambiguity, which has been solved by 3
independent methods. By using this solution, one unique average magnetic
field vector has been determined in each of 296 quiescent prominences,
leading to results on the field strength, direction, vertical gradient,
cyclic variations. The future perspective opened by the low scattered
light level of THEMIS and other spectropolarimeters is to increase
the spatial resolution of the measurements.

---------------------------------------------------------
Title: Theoretical study of the collisional depolarization and of the
Hanle effect in the Na I D2 line observed on the solar limb
Authors: Kerkeni, B.; Bommier, V.
2002A&A...394..707K Altcode:
In recent years, Landi Degl'Innocenti (\cite{Landi-98}, \cite{Landi-99})
has proposed a model of the polarization spectrum of the Na I D lines
observed near the solar limb, based on lower level polarization
effects. By so doing, he obtains a remarkable agreement between
his model and the observations, so that he comes to a conclusion
about a paradox, because the existence of lower level polarization
is incompatible with a magnetic field strength higher than 10 mGauss
(except vertical), and with possible depolarizing collision effects. In
the present paper, we investigate the depolarizing collision effects
(collisions with neutral hydrogen) by using the collisional rates
computed with ab-initio and quantum chemistry methods by Kerkeni
(\cite{Kerkeni-01}; see also Kerkeni et al. \cite{Kerkeni-etal-00},
and Kerkeni \cite{Kerkeni-02}). We solve the statistical equilibrium
equations for the atomic density matrix, taking into account these
depolarizing collisions. We investigate the effect of a weak magnetic
field (Hanle effect). Our results indicate that the lower levels should
be completely depolarized by the collisions at the depth where the
Na I D lines are formed. Furthermore, large values of the lower level
alignment such as those introduced by Landi Degl'Innocenti in his model
to get a good theoretical fit of the observations, seem to us unlikely,
as our computations confirm. Thus, as the agreement between the model
by Landi Degl'Innocenti and the observations is however very convincing,
the paradox is confirmed, reinforced and increased by our results.

---------------------------------------------------------
Title: Linear polarization of the O VI lambda 1031.92 coronal
line. I. Constraints on the solar wind velocity field vector in the
polar holes
Authors: Raouafi, N. -E.; Sahal-Bréchot, S.; Lemaire, P.; Bommier, V.
2002A&A...390..691R Altcode:
In the first part of the present work, we report on the determination
of the linear polarization parameters of the O VI lambda1031 .92
coronal line (hereafter O VI D2). Spectropolarimetric
observations done by the SUMER spectrometer on board the spacecraft
SoHO during minimum activity of the solar cycle (March, 1996) in the
south coronal hole were used to analyze the partial linear polarization
of the D2 resonance line scattered by the O {VI} coronal
ions. Widths of the O VI D2 and O VI 1037.61 (hereafter
O VI D1) lines and limb-brightening determined from data
observations of SUMER/SoHO are also presented. The second part of this
work is devoted to the interpretation of the determined polarization
parameters in terms of the macroscopic velocity field vector of the
O VI coronal ions that can be assimilated to the solar wind velocity
field. Numerical results of the linear polarization parameters of
the O VI D2 coronal line are presented. Constraints on the
strength and direction of the solar wind velocity vector are obtained
by comparing the numerical and the observational results of the O VI
D2 coronal line polarization parameters. In conclusion, the
effect of the macroscopic velocity field vector of the scattering ions
(Doppler redistribution) provides a first set of results compatible
with the observations. However, the inclination of the derived set
of compatible field vectors, with respect to the solar vertical, is
higher than expected in a coronal hole. The result will be improved
by the inclusion of the magnetic field effect (Hanle effect), which
will be treated in a further paper.

---------------------------------------------------------
Title: Theoretical study of the collisional depolarization and of
the Hanle effect in the line Na I D2 observed on the solar limb
Authors: Bommier, V.; Kerkeni, B.
2002sf2a.conf..125B Altcode:
Observations of the Na I D lines polarization in quiet regions near
the solar limb have been recently achieved, in particular with THEMIS
(Bommier V., Molodij G., 2002, AandA 381, 241). These observations
are in very good agreement with a theoretical model developed by Landi
Degl'Innocenti (1998, Nature 392, 256, and 1999, "Solar Polarization",
K.N. Nagendra and J.O. Stenflo (eds.), ASSL 243, 61). However, this
model, based on the existence of atomic polarization in the line
lower level, leads to the so-called "Sodium paradox": the existence
of this at omic polarization is incompatible with the existence of
a magnetic field stronger than 5 mG (except vertical), and also with
the existence of collisional depolarization. We have investigated this
last point, by using the collisional coefficients recently computed
by B. Kerkeni from a quantum chemistry model. We have solved the
statistical equilibrium equations for the atomic density matrix in
the last scattering approximation, in order to investigate the Na I D2
line polarization formation and destruction at the solar limb. We have
obtained that the atomic polarization in the lower level is completely
destroyed by the collisions with neutral hydrogen at the line formation
depth, which results in a "paradox in the paradox".

---------------------------------------------------------
Title: Some THEMIS-MTR observations of the second solar spectrum
(2000 campaign)
Authors: Bommier, V.; Molodij, G.
2002A&A...381..241B Altcode:
We report spectropolarimetric observations with the THEMIS telescope
multi-lines operating mode (MTR) during the 2000 observational
period from August 27th to September 1st. We measured the resonance
polarization at the limb of a series of lines: Sr I 460.7 nm,
Na I D1 589.6 nm and D2 589.0 nm, Ba Ii
D1 493.4 nm and D2 455.4 nm, C I 493.2 nm. The
data analysis method is mainly described in Bommier &amp; Rayrole
(\cite{Bommier-Rayrole-01}), and has been completed by using the beam
exchange facility as available in 2000 THEMIS, i.e., in a single Stokes
parameter. A so-called “generalized beam exchange” technique has
been settled on, for the full Stokes vector measurement under this
limitation. The observations have been devoted to the measurement of
the scattering polarization which is a linear polarization observed near
the limb of the Quiet Sun, eventually modified by a weak magnetic field
(the so-called Hanle effect). The entrance slit of the spectrograph has
been oriented parallel to the tangential direction of the solar limb,
and data have been averaged in time and along the spatial direction
of the slit in order to increase the polarimetric resolution. Two
different cameras have been used to record simultaneously the two
polarization states exiting the beam-splitter. The results of our
polarization measurements are in good agreement with those given in
the second spectrum solar atlas of Gandorfer (\cite{Gandorfer-00}),
based on 1999-2000 observations. Nevertheless, with regard to a
quantification of the polarization signal, we found that the signal
is systematically smaller than previous results obtained during the
1994-96 observational period and was also observed as decreasing during
the 1998 observational period, as if a 11-year cyclic variation of the
limb polarization occured. This signal variability obviously requires
further observational and interpretative investigations. We noticed
other differences to previous results, in particular, the linear
polarization shape of the Na I D1 line that also requires
further observational investigation. Based on observations made with
THEMIS operated on the island of Tenerife by CNRS-CNR in the Spanish
Observatorio del Teide of the Instituto de Astrofísica de Canarias.

---------------------------------------------------------
Title: Search for polarimetric sensitivity in the first observations
with THEMIS spectropolarimetric mode MTR (August 1998 campaign)
Authors: Bommier, V.; Rayrole, J.
2002A&A...381..227B Altcode:
The present paper is devoted to the search for the polarimetric
sensitivity level in observations of the Fe I 5576 Å line performed
with the THEMIS spectropolarimetric mode MTR on August 23 1998. This
line is insensitive to the Zeeman effect and the present work is
thus useful to calibration purposes. The upper level of the line
is unpolarizable (J=0) and insensitive to the Hanle effect, and the
observations have been performed at disk center to avoid any scattering
polarization of lower level atomic polarization origin. In the present
paper, we describe the steps of a method that is the basis of a data
reduction code implemented on systems at the Meudon Observatory for
the interpretation of observations where a large number ( ~ 150) of
images are averaged, and where the signal is in addition averaged
along the slit. First, we describe the numerical methods used to
determine the line position in the images, and to perform operations
on the profiles by FFT techniques (such as translation, dilation,
defocusing, apodization). Then, the preprocessing steps are described:
dark current subtraction, destretching and flat-field correction. The
polarization analysis is then performed, based on the idea that, as
the flat-field images are unpolarized, they can be used to correct
spurious polarization occuring in the observations. As a result,
the observed line is found to be unpolarized, and a sensitivity of
2-4x 10-4 is found for the polarization degree in the
neighboring continuum.

---------------------------------------------------------
Title: Polarization of the hydrogen Hα line in solar
flares. Contribution of the local polarized radiation field and
effect of the spectral index of the proton energy distribution
Authors: Vogt, E.; Sahal-Bréchot, S.; Bommier, V.
2001A&A...374.1127V Altcode:
Linear polarization of the hydrogen Hα line was observed during
solar flares. The polarization vector is directed towards disk center
and its degree is of the order of 5%. The best explanation for this
polarization is anisotropic collisional excitation of the n = 3 level
of hydrogen by vertical beams of protons with an energy greater than a
few keV. However, previous calculations gave an expected polarization
degree of 2.5% or less, a factor of two below the observations. In this
paper, the theoretical model for the formation of the line polarization
has been refined, including the effect of polarization in the local
radiation field that is created by hydrogen proton anisotropic
excitation. We have also increased the spectral index of the proton
energy distribution from 4 to 5, giving more weight to the low energy
protons which are the most efficient for impact polarization, without
ionizing the atmosphere too much. It is found that the inclusion of
the polarization of the local radiation field does not increase the
Hα polarization very significantly; however, going from a spectral
index of 4 to 5 results in an expected polarization degree of 4.5%,
compatible with the observations.

---------------------------------------------------------
Title: Full-Stokes spectropolarimetry of solar prominences
Authors: Paletou, F.; López Ariste, A.; Bommier, V.; Semel, M.
2001A&A...375L..39P Altcode:
We report on first spectropolarimetric observations of solar prominences
made at THEMIS. Hereafter we shall emphasis on the preliminary analysis
of He I D3 full-Stokes observations. Our measurements
clearly show manifestations of both the Hanle and Zeeman effects. More
generally, we demonstrate the very favourable performances of the THEMIS
multi-line spectropolarimetric mode for further new investigations of
the magnetic field in solar prominences. Based on observations made at
THEMIS, operated on the Island of Tenerife by CNRS-CNR in the Spanish
Observatorio del Teide of the Instituto de Astrofísica de Canarias.

---------------------------------------------------------
Title: Partial frequency redistribution with Hanle and Zeeman
effects. Non-perturbative classical theory
Authors: Bommier, V.; Stenflo, J. O.
1999A&A...350..327B Altcode:
A theory for the scattering of polarized radiation with partial
frequency redistribution and coherence effects in the presence of
magnetic fields of arbitrary strength and direction is developed within
a classical framework. The time-dependent equation for a classical
oscillator is solved. While the oscillator is being excited, it is
also damped by emission of radiation and subject to phase-destroying
collisions. Fourier transformation of the emitted wave train with
phase-scrambling collisions leads to the partial-redistribution
expressions for the relation between the polarization and frequencies
of the incident and scattered radiation. While previous treatments
of partial redistribution have been based on quantum perburbation
theory, the classical theory has the advantage of being fully
non-perturbative. It is therefore conceptually more transparent
and leads itself to direct physical interpretation. The classical
and quantum theories give identical results for a J=0-&gt; 1-&gt;
0 transition.

---------------------------------------------------------
Title: Doppler redistribution of resonance polarization of the O VI
103. 2 nm line observed above a polar hole
Authors: Raouafi, N. -E.; Sahal-Bréchot, S.; Lemaire, P.; Bommier, V.
1999ASSL..243..349R Altcode: 1999sopo.conf..349R
No abstract at ADS

---------------------------------------------------------
Title: The density matrix theory for polarized radiation
redistribution: Extensions for multilevel atom model and quantum
Doppler effect
Authors: Bommier, V.
1999ASSL..243...43B Altcode: 1999sopo.conf...43B
No abstract at ADS

---------------------------------------------------------
Title: Polarized radiation transfer in 2D geometry
Authors: Paletou, F.; Bommier, V.; Faurobert-Scholl, M.
1999ASSL..243..189P Altcode: 1999sopo.conf..189P
No abstract at ADS

---------------------------------------------------------
Title: Polarized redistribution matrix for Hanle effect: Numerical
tests
Authors: Faurobert-Scholl, M.; Paletou, F.; Bommier, V.
1999ASSL..243..115F Altcode: 1999sopo.conf..115F
No abstract at ADS

---------------------------------------------------------
Title: Doppler redistribution of anisotropic radiation and resonance
polarization in moving scattering media. I. Theory revisited in the
density matrix formalism
Authors: Sahal-Brechot, S.; Bommier, V.; Feautrier, N.
1998A&A...340..579S Altcode:
Under the light of recent developments of the theory of matter-radiation
interaction in the presence of magnetic field applied to non-LTE
spectropolarimetry in astrophysics, we have revisited the theory of
anisotropic resonance line scattering in moving media by means of the
density-matrix formulation. This has led us to present a theoretical
method of determination of the matter velocity field vector in the solar
wind acceleration region. The example of the O Vi 103.2 nm line has been
chosen for putting this theory into operation. It has been observed
by the ultraviolet spectrograph \textsc{Sumer} of \textsc{Soho} in
different regions of the solar wind acceleration region; it is partially
formed by resonance scattering of the incident underlying transition
region radiation which competes (and can predominate) with electron
collisional excitation at the low densities which prevail at these high
altitudes. The theory which is developed hereafter not only shows that
this line is shifted and its intensity dimmed by the Doppler effect,
due to the matter velocity field of the solar wind, but also predicts
that it is linearly polarized, owing to the anisotropy of the incident
radiation field; its two linear polarization parameters, degree and
direction of polarization, are sensitive to the matter velocity field
vector. Our results show that the interpretation of polarimetric data,
associated to the shift and the Doppler-dimming effect, may offer a
method of diagnostic of the complete velocity field vector, provided
that the partial anisotropy of the incident radiation field be taken
into account. In fact such a diagnostic is currently missing. Yet its
interest is crucial to understand various problems in astrophysics,
such as stellar winds, and especially the acceleration mechanisms
of the solar wind. It is also essential for a dynamical modelling of
solar structures.

---------------------------------------------------------
Title: Global Pattern of the Magnetic Field Vectors Above Neutral
Lines from 1974 to 1982: Pic-du-Midi Observations of Prominences
Authors: Bommier, V.; Leroy, J. L.
1998ASPC..150..434B Altcode: 1998npsp.conf..434B; 1998IAUCo.167..434B
No abstract at ADS

---------------------------------------------------------
Title: Master equation theory applied to the redistribution of
polarized radiation, in the weak radiation field limit. II. Arbitrary
magnetic field case
Authors: Bommier, V.
1997A&A...328..726B Altcode:
This paper addresses the problem of partial redistribution of polarized
radiation in the presence of a magnetic field of arbitrary strength. It
is the continuation of a previous paper (\cite{Paper I}) devoted to
the same problem, treated in the simpler case of vanishing magnetic
field. In the present paper, we give the results of the derivation
of the master equation for the atomic density matrix, and of the
coefficients of the radiative transfer equation, following the method
described in \cite{Paper I} (which makes use of the summation of the
perturbation series development for the atom-radiation interaction),
now applied to the case of a non-zero magnetic field of arbitrary
strength. The other hypotheses underlying the derivation of \cite{Paper
I} are maintained in the present paper, namely: (a) weak radiation field
(stimulated emission is neglected with respect to spontaneous emission);
(b) 2-level atom; (c) unpolarized lower level. The redistribution
matrix, that relates the frequency, polarization and direction of the
incident photon to those of the scattered photon, is derived in the
presence of a magnetic field of arbitrary strength. 3 successive levels
of approximation are proposed, in the case of a weak magnetic field,
in order to derive simpler expressions for the redistribution matrix
that might conveniently be used in radiative transfer calculations.

---------------------------------------------------------
Title: Master equation theory applied to the redistribution of
polarized radiation, in the weak radiation field limit. I. Zero
magnetic field case
Authors: Bommier, V.
1997A&A...328..706B Altcode:
This paper is devoted to describe the atom-radiation interaction in
the formalism of non-relativistic quantum electrodynamics by means
of a perturbative development extended to orders higher than 2. Atom
and radiation are treated quantum mechanically, through the density
matrix approach. Collision effects are also introduced, in the impact
approximation. Polarization is taken into account. The following
hypotheses are considered: (a) weak radiation field (stimulated
emission is neglected with respect to spontaneous emission); (b)
two-level atom; (c) unpolarized lower level; (d) atomic reference frame;
(e) zero magnetic field. The perturbation series development has been
summed. The result of the paper is twofold: (a) the profiles in the form
of delta -functions obtained in ordinary theories extended up to order
2 in the series development are now replaced by realistic profiles:
line-broadening is derived from the present formalism; (b) a new term
(Rayleigh scattering term) appears at order 4 in the emissivity. This
term is responsible for frequency coherence in scattering processes.

---------------------------------------------------------
Title: A Complex Diagnostic of Solar Prominences
Authors: Heinzel, P.; Bommier, V.; Vial, J. C.
1996SoPh..164..211H Altcode:
We use the polarimetric and intensity measurements of Hα and HeI
D3 lines in solar prominences to derive the true geometrical
thickness for several quiescent prominences. The electron densities,
derived from the collisional depolarization in Hα by Bommier et
al. (1994), are used to evaluate the thickness from the emission
measure. The emission measure was obtained from the theoretical
correlation with the Hα integrated intensity, according to Gouttebroze,
Heinzel, and Vial (1993). Theoretical electron densities obtained by
latter authors are also compared with those of Bommier et al. (1994) and
we find a very good agreement between them. The prominence geometrical
thickness exhibits a relatively large range of values from about 100 km
up to a few 104 km. The plasma densities vary by almost two
orders of magnitude in the observed structures, but the total column
mass in the direction perpendicular to the prominence sheet seems to
be fairly constant for the set of prominences studied.

---------------------------------------------------------
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: Atomic Coherences and Level-Crossings Physics
Authors: Bommier, Véronique
1996SoPh..164...29B Altcode:
A synthesis work about the interaction of matter with polarized
radiation, applied to solar magnetic field diagnostics, has recently
been done by Stenflo (1994). This synthesis uses the classical theory
of matter-radiation interaction - supplemented by the theory of partial
redistribution of Omont, Smith, and Cooper (1972), on the one hand,
and full quantum matter-radiation interaction theory, unable to take
into account the partial frequency redistribution effects, on the
other hand. The need of a full quantum approach taking into account
the partial frequency redistribution effects appears as a unifying
purpose; the present work, using the density matrix formalism, is a
first attempt in this direction.

---------------------------------------------------------
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: 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: 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: Stokes parameters of the O VI 103.2 nm line as a probe of the
matter velocity field vector in the solar wind acceleration region.
Authors: Sahal-Brechot, S.; Feautrier, N.; Bommier, V.; Dekertanguy, A.
1992ESASP.344...81S Altcode: 1992spai.rept...81S
The authors present a theoretical method of determination of the
matter velocity field vector in the solar wind acceleration region
that they have currently developed. The O VI 103.2 nm line should be
observed high in the corona in the solar wind acceleration region;
it would be formed by resonance scattering of the incident underlying
transition region radiation which competes (and can predominate) with
electron collisional excitation at these low densities which prevail
at these high altitudes. This line will not only be shifted and its
intensity dimmed by the Doppler effect but it will be also linearly
polarized, owing to the anisotropy of the incident radiation field;
its two polarization parameters, degree and direction of polarization,
should be sensitive to the matter velocity field vector. Preliminary
results show that the interpretation of polarimetric data, associated
to the shift and the Dopplerdimming effect, provided that the partial
anisotropy of the incident radiation field be taken into account, should
offer a method of diagnostic of the complete velocity field vector.

---------------------------------------------------------
Title: Derivation of the master equation for the atomic density
matrix for line polarization studies in the presence of magnetic
field and depolarizing collisions in astrophysics.
Authors: Bommier, V.; Sahal-Bréchot, S.
1991AnPh...16..555B Altcode:
The authors derive in a coherent manner the master equation for
the density matrix of an atom interacting with a bath of perturbers
and photons, in the presence of a weak magnetic field. This paper
has been inspired by astrophysical purposes: the interpretation of
line polarization induced by anisotropic excitation of the levels,
eventually modified by the local magnetic field (the Hanle effect);
the polarization can be due to scattering of the incident anisotropic
radiation, as in solar prominences, or to impact polarization, as
in solar flares. The physical conditions are then those of numerous
astrophysical media: any directions of polarization and magnetic
field, two-level atom approximation not valid, weak radiation field,
weak density of perturbers. The master equation for the atomic density
matrix has been derived in the framework of the impact approximation.

---------------------------------------------------------
Title: Derivation of the radiative transfer equation for line
polarization studies in the presence of magnetic field in
astrophysics.
Authors: Bommier, V.
1991AnPh...16..599B Altcode:
In the preceding paper (063.110), the master equation for the
atomic density matrix has been derived in the framework of the impact
approximation. In the present paper, the author obtains the spontaneous
emission 4-vector and absorption and stimulated emission 4×4 matrices
entering the transfer equation for polarized radiation, as functions
of the absorbed and emitted radiation polarization tensors, themselves
functions of the Zeeman coherences of the atomic density matrix. Line
profiles have been ignored.

---------------------------------------------------------
Title: Stark broadening of spectral lines of multicharged ions of
astrophysical interest. I - C IV lines. II - SI IV lines
Authors: Dimitrijevic, M. S.; Sahal-Brechot, S.; Bommier, V.
1991A&AS...89..581D Altcode:
Results are presented on calculations of the electron-, proton-, and
ionized helium-impact line widths and shifts for 31 C IV multiplets
and 40 Si IV multiplets. These data are compared with observations and
are used to investigate the Stark broadening parameter regularities
within the spectral series. For both the C IV and Si IV multiplets,
a gradual change of the Stark widths was obtained. The reason for this
is discussed.

---------------------------------------------------------
Title: Stark broadening parameter tables for spectral lines of
multicharged ions of astrophysical interest. II. Si IV lines.
Authors: Dimitrijević, M. S.; Sahal-Bréchot, S.; Bommier, V.
1991BOBeo.144...81D Altcode:
Using a semiclassical approach, the authors have calculated electron-,
proton-, and ionized helium-impact line widths and shifts for
39 Si IV multiplets as a function of temperature for perturber
densities 1015cm-3 and 1018-
1821cm-3.

---------------------------------------------------------
Title: Stark broadening parameter tables for spectral lines of
multicharged ions of astrophysical interest. I: C IV lines.
Authors: Dimitrijević, M. S.; Sahal-Bréchot, S.; Bommier, V.
1991BOBeo.144...65D Altcode:
Using a semiclassical approach, the authors have calculated electron-,
proton-, and ionized helium-impact line widths and shifts for
39 C IV multiplets as a function of temperature for perturber
densities 1015cm-3 and 1018-
1821cm-3.

---------------------------------------------------------
Title: Stark Broadening of Spectral Lines of Multicharged Ions of
Astrophysical Interest - Part Two - Si IV Lines
Authors: Dimitrijevic, M. S.; Sahal-Brechot, S.; Bommier, V.
1991A&AS...89..591D Altcode:
Using a semi-classical approach, we have calculated electron-,
proton-, and ionized helium-impact line widths and shifts for 40 Si IV
multiplets. The comprehensive set of obtained data has also been used
for investigation of Stark broadening parameter regularities within
spectral series.

---------------------------------------------------------
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: 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: 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: 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: 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: 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: Magnetic field vector and electron density diagnostics from
linear polarization measurements in 14 solar prominences.
Authors: Bommier, V.
1986NASCP2442..209B Altcode: 1986copp.nasa..209B
The Hanle effect is the modification of the linear polarization
parameters of a spectral line due to the effect of the magnetic
field. It has been successfully applied to the magnetic field vector
diagnostic in solar prominences. The magnetic field vector is determined
by comparing the measured polarization to the polarization computed,
taking into account all the polarizing and depolarizing processes in
line formation and the depolarizing effect of the magnetic field. The
method was applied to simultaneous polarization measurements in the
Helium D3 line and in the hydrogen beta line in 14 prominences. Four
polarization parameters are measured, which lead to the determination
of the three coordinates of the magnetic field vector and the electron
density, owing to the sensitivity of the hydrogen beta line to the
non-negligible effect of depolarizing collisions with electrons and
protons of the medium. A mean value of 1.3 x 10 to the 10th power
cu. cm. is derived in 14 prominences.

---------------------------------------------------------
Title: The polarization of the O VI 1032 Å line as a probe for
measuringthe coronal vector magnetic field via the Hanle effect.
Authors: Sahal-Brechot, S.; Malinovsky, M.; Bommier, V.
1986A&A...168..284S Altcode:
Recent works have shown the possibility of detecting resonance lines of
moderately ionized lithium-like ions (especially O VI 1032 Å) of the
chromosphere-corona transition region at high altitudes in the solar
corona (up to several solar radii). Since these lines would be partially
formed by resonance scattering of the anisotropic underlying transition
region radiation field, they are expected to be partially linearly
polarized; moreover this polarization should be modified by the local
magnetic field (e.g. the Hanle effect). The aim of the present paper is
to calculate the expected linear polarization and its modification by
the coronal local magnetic field and to provide analytical formulae,
in order to investigate the possibility of measuring coronal vector
magnetic fields via the interpretation of the Hanle effect.

---------------------------------------------------------
Title: The Linear Polarization of Hydrogen H-Beta Radiation and the
Joint Diagnostic of Magnetic Field Vector and Electron Density in
Quiescent Prominences - Part Two - the Electron Density
Authors: Bommier, V.; Leroy, J. L.; Sahal-Brechot, S.
1986A&A...156...90B Altcode:
Fourteen quiescent prominences of considerable height over the Solar
surface have been observed simultaneously in the helium D3
and hydrogen Hβ lines: the linear polarization measurements which have
been performed at the Pic-du-Midi Observatory have been interpreted by
means of the Hanle effect theory (modification of polarization by the
local magnetic field) and of the collisional depolarization theory. The
present paper is devoted to the analysis of the results concerning
the electron density Ne which have been obtained by this
new method of diagnostic. Firstly, a straightforward interpretation
of the measurements made by using the Hβ line polarization only has
provided an upper limit for Ne, which remains lower than 7
1010 cm-3 in all cases. Secondly, by taking into
account both the Hanle effect and the depolarization by collisions with
the electrons and the protons of the medium, the actual electron density
has been derived: it neighbours 1 1010 cm-3. As
physically expected, Ne decreases with increasing height in
prominences. Finally, our results have been compared to those obtained
quite recently by different methods, which shows an evident tendency
for Ne to get higher values in brighter prominences.

---------------------------------------------------------
Title: The linear polarization of hydrogen H-beta radiation and the
joint diagnostic of magnetic field vector and electron density in
quiescent prominences. I - The magnetic field. II - The electron
density
Authors: Bommier, V.; Sahal-Brechot, S.; Leroy, J. L.
1986A&A...156...79B Altcode:
Quasi-simultaneous measurements of the linear polarization of the
helium D3 and hydrogen Hβ lines have been achieved
at the Pic-du-Midi coronagraph-polarimeter for fourteen quiescent
prominences. Both lines are linearly polarized by resonant scattering
of the anisotropic photospheric and chromospheric radiation field, and
depolarized by the local magnetic field (i.e. the Hanle effect). The
measurements show that another depolarizing mechanism has to be taken
into account for the Hβ line: this is confirmed by the theory which
predicts that Hβ is also depolarized by collisions with the electrons
and protons of the medium. Therefore polarization measurements in
those two lines provide a method for determining both the magnetic
field B and the electron density Ne in prominences.

---------------------------------------------------------
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: Magnetic field-vector measurements in quiescent prominences
via the Hanle effect: Analysis of prominences observed at Pic-du-Midi
and at Sacramento Peak
Authors: Bommier, V.; Leroy, J. L.; Sahal-Brechot, S.
1985svmf.nasa..375B Altcode:
The Hanle effect method for magnetic field vector diagnostics has
now provided results on the magnetic field strength and direction
in quiescent prominences, from linear polarization measurements in
the He I E3 line, performed at the Pic-du-Midi and at
Sacramento Peak. However, there is an inescapable ambiguity in the
field vector determination: each polarization measurement provides two
field vector solutions symmetrical with respect to the line-of-sight. A
statistical analysis capable of solving this ambiguity was applied to
the large sample of prominences observed at the Pic-du-Midi (Leroy,
et al., 1984); the same method of analysis applied to the prominences
observed at Sacramento Peak (Athay, et al., 1983) provides results
in agreement on the most probable magnetic structure of prominences;
these results are detailed. The statistical results were confirmed on
favorable individual cases: for 15 prominences observed at Pic-du-Midi,
the two-field vectors are pointing on the same side of the prominence,
and the alpha angles are large enough with respect to the measurements
and interpretation inaccuracies, so that the field polarity is derived
without any ambiguity.

---------------------------------------------------------
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: Magnetic field-vector measurements in quiescent prominences
via the Hanle effect: analysis of prominences observed at Pic-du-Midi
and at Sacramento Peak.
Authors: Bommier, V.; Leroy, J. L.; Sahal-Bréchot, S.
1985NASCP2374..375B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: New data on the magnetic structure of quiescent prominences
Authors: Leroy, J. L.; Bommier, V.; Sahal-Brechot, S.
1984A&A...131...33L Altcode:
Hanle-effect vector-magnetic-field measurements in the unresolved
5876-A D3 line of He and simultaneous H-alpha or H-beta polarization
measurements obtained with the coronagraph polarimeter at Observatoire
du Pic du Midi during 1974-1982 are reported for 256 solar prominences
of medium and low latitude. The data are presented in graphs, tables,
diagrams, and photographs and analyzed statistically to resolve the
twofold ambiguity inherent in magnetic/polarimetric measurements of
this type. Prominences with maximum heights lower than 30,000 km are
found to have field-vector angles (alpha) about 20 deg and fields of
about 20 G; those above 30,000 km have alpha 25 deg and fields 5-10 G;
the structures correspond to the models proposed by Kippenhahn and
Schlueter (1957) and by Kuperus and Raadu (1974), respectively.

---------------------------------------------------------
Title: Vector Magnetic Field Measurements in Quiescent Prominences
via the Hanle Effect - Analysis of Prominences Observed at the Pic-Du
and at Sacramento-Peak
Authors: Bommier, V.; Leroy, J. L.; Sahal-Brechot, S.
1984apoa.conf...58B 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: The Magnetic Field in the Prominences of the Polar Crown
Authors: Leroy, J. L.; Bommier, V.; Sahal-Brechot, S.
1983SoPh...83..135L Altcode:
The Hanle effect method has been applied to the determination of the
magnetic field in 120 prominences of the polar crown observed during
the 1974-1980 period, which is the ascending phase of cycle XXI. The
average field strength which was about 6 G at the beginning of the
cycle reached twice this value just before the maximum. There is also a
clear trend for a increase of the prominence field with the altitude. We
confirm the fact that the magnetic vector makes a small angle (25 °)
with the long axis of the prominence. As to the field orientation,
we show that the most striking feature lies in the regular pattern
of the component which is parallel to the axis of the filament;
its direction seems to depend closely on the polarities of the high
latitude photospheric field.

---------------------------------------------------------
Title: The Hanle Effect of the Coronal L-Alpha Line of Hydrogen -
Theoretical Investigation
Authors: Bommier, V.; Sahal-Brechot, S.
1982SoPh...78..157B Altcode:
This paper is devoted to a computation of the effect of a magnetic field
on the linear polarization of the coronal Lα line of hydrogen. Recent
works (Gabriel et al., 1971) have shown that the linear polarization of
this line is due to resonant scattering of the incident chromospheric
Lα line. The Hanle effect is the modification of this linear
polarization, due to the magnetic field. After having briefly recalled
the main features of this effect and the conditions of the coronal Lα
line formation, we present the theoretical formalism to be used for
Hanle effect computations. The effect of the hyperfine structure of the
line is included. Then the results of our computations are given in
terms of linear polarization as a function of the magnetic field. We
get that the effect of the hyperfine structure on these results is
negligible, although this is not evident a priori. When the hyperfine
structure is neglected, the line structure is simplified and the Hanle
effect can be expressed with analytical formulae, which we give in the
last part of this paper. After integration along the line of sight,
these formulae could be used for magnetic field determination in
the solar corona from measurements of the linear polarization of the
Lα line.

---------------------------------------------------------
Title: Determination of the complete vector magnetic field in solar
prominences, using the Hanle effect
Authors: Bommier, V.; Sahal-Brechot, S.; Leroy, J. L.
1981A&A...100..231B Altcode:
Various methods which are liable to provide the three components of the
prominence magnetic field are investigated. It is noted that the methods
consist in adding information supplementary to that which results from
the Hanle effect analysis of linear polarization measurements of an
emission line. This supplementary information can be (1) the linear
polarization measurements of another line (which is thought to be
the most reliable method), (2) the projection of the field direction
onto the plane of the sky; or (3) the longitudinal field derived from
Zeeman effect measurements. It is noted that all these methods lead to
two magnetic field solutions. The way in which the varying scattering
geometry due to the sun's rotation makes it possible to choose between
them is described.

---------------------------------------------------------
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: Quantum theory of the Hanle effect. II - Effect of
level-crossings and anti-level-crossings on the polarization of the
D3 helium line of solar prominences
Authors: Bommier, V.
1980A&A....87..109B Altcode:
In this paper, we present a generalization of the quantum formalism
of the Hanle effect, including the case of level-crossings and
anti-level-crossings of the Zeeman sublevels. The transition from
the Zeeman effect to the Paschen-Back effect, which gives rise to
the anti-level-crossings, is explicitly taken into account. As an
application the calculation of the linear polarization parameters of
the Helium D3 line of solar quiescent prominences, in the presence
of a stationary magnetic field, has been performed. The results are
reported and the effect of the level-crossings is discussed. These
results extend our previous calculations which were valid only for
weak magnetic fields (B &lt; 10 G) because both the level-crossing
and anti-level-crossing effects were neglected.

---------------------------------------------------------
Title: The Hanle Effect and the Determination of Magnetic Fields.
Authors: Bommier, V.; Sahal-Brechot, S.
1979phsp.coll...87B Altcode: 1979IAUCo..44...87B; 1979phsp.conf...87B
The determination of prominence magnetic fields by interpreting the
two measured parameters that describe the linear polarization of
spectral lines (the Hanle method) is discussed. The possibility of
determining the three components of a prominence magnetic field
by using simultaneous observations in two different lines is
considered. Limitations on the Hanle method are summarized. It is
shown that a complete determination of a prominence magnetic field
may be possible with the Hanle method by observing the prominence of
interest during rotation of the sun.

---------------------------------------------------------
Title: Theory of the Hanle Effect; Application to the Linear
Polarization of the Helium Lines in Solar Prominences.
Authors: Bommier, V.
1979phsp.coll...93B Altcode: 1979IAUCo..44...93B; 1979phsp.conf...93B
No abstract at ADS

---------------------------------------------------------
Title: Quantum theory of the Hanle effect: calculations of the Stokes
parameters of the D3 helium line for quiescent prominences.
Authors: Bommier, V.; Sahal-Brechot, S.
1978A&A....69...57B Altcode:
A formalism of the quantum theory of the Hanle effect is developed to
obtain the Stokes parameters of the D3 line in quiescent prominences
in the presence of a stationary magnetic field. The aim is to develop
a method that can be used to determine the vector magnetic field in
prominences. The quantum description of an ensemble of atoms or photons
in terms of a density matrix is briefly recalled, and the evolution of
the time-dependent density matrix of the atom is treated by means of a
master equation in which the interaction between the scattering atom,
the incident photons, and the magnetic field appears. The approximations
leading to the master equation are discussed. The expression for the
density matrix of the reemitted photons is given as a function of the
atomic density matrix calculated for the steady state. The formalism
has been used for explicit calculations of the D3 polarization in an
earlier paper by Sahal-Brechot et al. (1977).

---------------------------------------------------------
Title: The Hanle effect and the determination of magnetic fields in
solar prominences.
Authors: Sahal-Brechot, S.; Bommier, V.; Leroy, J. L.
1977A&A....59..223S Altcode:
The object of this paper is to investigate whether the determination of
magnetic fields based on the interpretation of the linear polarization
modified by the Hanle effect of the He I D3 line in quiescent
prominences can be accurate and safe enough. It is shown that the
observed depolarization and rotation of the vector polarization
result only from magnetic effects. An account of the quantum theory
used (a more detailed account will be published separately) for the
calculations is given. The interpretation of the attached theoretical
polarization diagrams, their use for the determination of magnetic
fields, the limitations of the theory and the accuracy of the results
are discussed. From this it can be concluded that the present method
is very promising, especially for the weak magnetic fields (1-15 Gauss)
which are typical of most quiescent prominences.

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Title: The polarization of the D3 emission line in prominences.
Authors: Leroy, J. L.; Ratier, G.; Bommier, V.
1977A&A....54..811L Altcode:
Over 1,000 polarization measurements pertaining to about 90 distinct
solar prominences were taken on the D 3 triplet lines of helium at
5876 A. Most of the measurements were made on quiescent prominences
at the polar latitude. A typical D 3 polarization measurement in a
quiescent prominence yields a degree of polarization of about 0.020
and a polarization deviation of plus or minus 15 deg. Average height
variations of the degree of polarization and angular deviation of
polarization were also obtained. The observed polarizations fall
below the theoretical maximum, and it is believed that in some
cases one is dealing with prominence regions in which there is no
nonmagnetic depolarization or no magnetic depolarization. Several
possible nonmagnetic depolarization effects are likely to decrease
in the uppermost part of prominences, so that magnetic depolarization
must be larger at the top of quiescent prominences.

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Title: Quantum theory of the Hanle effect. Application to the
determination of magnetic fields in quiescent prominences.
Authors: Sahal-Brechot, S.; Bommier, V.
1977ROLun..12....5S Altcode:
No abstract at ADS