Modeling scattering polarization in molecular solar lines in spherical geometry

Milić, Ivan; Faurobert, M.

doi:10.1051/0004-6361/201117727

Cited by 8 publications

(10 citation statements)

References 16 publications

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“…This is in excellent agreement with the previous determination that we performed in Milić & Faurobert (2012), using observations presented in Gandorfer's Atlas (Gandorfer 2000) of the second solar spectrum, where we found α (2) ≈ 1.7 × 10 −9 cm 3 s −1 . We find that the microturbulent magnetic field strength shows a strong vertical gradient in the upper photosphere, where it decreases from ≈95 Gauss, at 200 km above the photosphere base, to ≈5 Gauss at the height of 400 km.…”

Section: Introductionsupporting

confidence: 93%

“…To self-consistently model the radiative transfer in the lines, we use the same approach as Milić & Faurobert (2012). We now briefly describe the method again.…”

Section: Methodsmentioning

confidence: 99%

“…For the second step we use an along-the-ray approach to perform a formal solution of the radiative transfer equation. Detailed equations are given in Milić & Faurobert (2012). We recall that the source function for the linear polarization Stokes parameter Q, depends on two factors, namely, the collisional depolarization parameter W c and the Hanle depolarization parameter W H in the following way:…”

Section: Polarized Radiative Transfermentioning

confidence: 99%

“…Furthermore, the C 2 and MgH lines we are considering are not optically thin lines, so implementing the differential Hanle effect method requires solving polarized radiative transfer equations for each of them using a prescribed atmospheric model. We also take sphericity effects into account, which play an important role in interpreting observations performed very close to the solar limb, typically closer than 5 arcsec (see Milić & Faurobert 2012). A&A 547, A38 (2012) THEMIS observations, presented in Faurobert & Arnaud (2003) provide us with measurements of the linear polarization in the wavelength range between 515.6 nm and 516.2 nm, containing two lines of MgH and six triplets of C 2 , at nine positions between 40 and 1 inside the solar limb.…”

Section: Introductionmentioning

confidence: 99%

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Hanle diagnostics of weak solar magnetic fields:

Milić

Faurobert

2012

A&A

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Context. The quiet Sun magnetism has been intensively investigated in recent years by various observational techniques. But several issues, such as the question of the isotropy and of the energy density spectrum of the mixed polarity turbulent magnetic fields, are still under debate. Aims. Here we present an inversion method that allows us to constrain the depth-dependence of the magnetic field strength. We use the center-to-limb variations of linear scattering polarization measured in molecular lines of C 2 and MgH molecules with different sensitivities to the Hanle effect. We consider six C 2 -triplets and one MgH line in the spectral range between 515.7 nm and 516.1 nm observed with the THEMIS Telescope. Methods. One of the delicate problems with Hanle diagnostics is to disentangle the effects of elastic depolarizing collisions from the depolarization due to the Hanle effect of the magnetic field. By making use of the different sensitivities of the molecular lines in our spectral range to microturbulent magnetic fields and, by using a non-LTE radiative transfer modeling of the line formation, we are able to determine both the depolarizing collision cross-section and the magnetic strength. We use a standard 1D quiet Sun atmospheric model and we invert the full set of center-to-limb polarization rates measured at line centers, with a depth-dependent magnetic field described by three free parameters. The depolarizing collision cross-section is also treated as a free parameter. A downhill simplex method is used to find the best-fitting values for the collisional and magnetic strength parameters. Results. For the elastic depolarizing collisions cross-section for the C 2 lines we obtain α (2) = 1.6 ± 0.4 × 10 −9 cm 3 s −1 , which is within an order of magnitude of the value previously obtained for MgH lines from a differential Hanle effect analysis. The observational constraints provided by the MgH and C 2 line polarization give access to the altitude range between z = 200 km and z = 400 km above the base of the photosphere. We find that the turbulent magnetic field strength decreases from 95 Gauss at the altitude z = 200 km to 5 Gauss at z = 400 km. Conclusions. The turbulent magnetic field strength that we derive from the Hanle effect shows a strong vertical gradient in the upper photosphere. We point out that this behavior may explain why very different turbulent magnetic field strengths have been inferred from the interpretation of Hanle depolarization when using different lines formed at different altitudes. We notice that the presence of a strong depth gradient is not compatible with the assumption of isotropy of the turbulent field.

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Section: Introductionsupporting

confidence: 93%

“…To self-consistently model the radiative transfer in the lines, we use the same approach as Milić & Faurobert (2012). We now briefly describe the method again.…”

Section: Methodsmentioning

confidence: 99%

Section: Polarized Radiative Transfermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hanle diagnostics of weak solar magnetic fields:

Milić

Faurobert

2012

A&A

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“…The magnetic fields probed in this application are typically a few kG. A second use of the paramagnetic properties of this band is the detection and analysis of Stokes Q spectra (i.e., the difference between the parallel and perpendicular linear polarized components of the spectral line; Rao & Rangarajan 1999;Faurobert & Arnaud 2002, 2003Stenflo et al 2002;Berdyugina & Fluri 2004;Bommier et al 2006;Shapiro et al 2007; Landi Degl 'Innocenti 2007;Milić & Faurobert 2012). The fields probed here are in the range of a few gauss and the spectra are due to the Hanle effect.…”

Section: Introductionmentioning

confidence: 99%

OPTICAL ZEEMAN SPECTROSCOPY OF THE (0, 0)A²Π-X²Σ⁺BAND SYSTEM OF MAGNESIUM HYDRIDE

Zhang

Steimle

2014

ApJ

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The Zeeman effect on lines in the (0, 0) A 2 Π-X 2 Σ + band system of a cold molecular beam sample of magnesium hydride, MgH, has been recorded at high resolution (FWHM ∼ =60 MHz) and analyzed. The lines associated with the lowest rotational levels are detected for the first time. The field-free spectrum was analyzed to produce spectroscopic parameters for the A 2 Π (v = 0) state. The experimentally observed magnetic tuning of the low-rotational spectral features at field strengths comparable to those found in sunspots is accurately modeled by assuming that the electronic spin and orbital magnetic g-factors, g S and g L , of the A 2 Π and X 2 Σ + states are 2.002 and 1.000, respectively, and g l is −0.0023 for the X 2 Σ + .

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One-dimensional, geometrically stratified semi-empirical models of the quiet-Sun photosphere and lower chromosphere

Borrero,

Milić,

Pastor Yabar

et al. 2024

A&A

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One-dimensional, semi-empirical models of the solar atmosphere are widely employed in numerous contexts within solar physics, ranging from the determination of element abundances and atomic parameters to studies of the solar irradiance and from Stokes inversions to coronal extrapolations. These models provide the physical parameters (i.e. temperature, gas pressure, etc.) in the solar atmosphere as a function of the continuum optical depth $ c $. The transformation to the geometrical $z$ scale (i.e. vertical coordinate) is provided via vertical hydrostatic equilibrium. Our aim is to provide updated, one-dimensional, semi-empirical models of the solar atmosphere as a function of $z,$ but employing the more general case of three-dimensional magneto-hydrostatic equilibrium (MHS) instead of vertical hydrostatic equilibrium (HE). We employed a recently developed Stokes inversion code that, along with non-local thermodynamic equilibrium effects, considers MHS instead of HE. This code is applied to spatially and temporally resolved spectropolarimetric observations of the quiet Sun obtained with the CRISP instrument attached to the Swedish Solar Telescope. We provide average models for granules, intergranules, dark magnetic elements, and overall quiet-Sun as a function of both $ c $ and $z$ from the photosphere to the lower chromosphere. We demonstrate that, in these quiet-Sun models, the effect of considering MHS instead of HE is negligible. However, employing MHS increases the consistency of the inversion results before averaging. We surmise that in regions with stronger magnetic fields (i.e. pores, sunspots, network) the benefits of employing the magneto-hydrostatic approximation will be much more palpable.

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Modeling scattering polarization in molecular solar lines in spherical geometry

Cited by 8 publications

References 16 publications

Hanle diagnostics of weak solar magnetic fields:

Hanle diagnostics of weak solar magnetic fields:

OPTICAL ZEEMAN SPECTROSCOPY OF THE (0, 0)A²Π-X²Σ⁺BAND SYSTEM OF MAGNESIUM HYDRIDE

One-dimensional, geometrically stratified semi-empirical models of the quiet-Sun photosphere and lower chromosphere

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Modeling scattering polarization in molecular solar lines in spherical geometry

Cited by 8 publications

References 16 publications

Hanle diagnostics of weak solar magnetic fields:

Hanle diagnostics of weak solar magnetic fields:

OPTICAL ZEEMAN SPECTROSCOPY OF THE (0, 0)A2Π-X2Σ+BAND SYSTEM OF MAGNESIUM HYDRIDE

One-dimensional, geometrically stratified semi-empirical models of the quiet-Sun photosphere and lower chromosphere

Contact Info

Product

Resources

About

OPTICAL ZEEMAN SPECTROSCOPY OF THE (0, 0)A²Π-X²Σ⁺BAND SYSTEM OF MAGNESIUM HYDRIDE