The molecular Zeeman effect and diagnostics of solar and stellar magnetic fields

Berdyugina, S. V.; Solanki, S. K.; Frutiger, C.

doi:10.1051/0004-6361:20031473

Cited by 93 publications

(127 citation statements)

References 43 publications

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“…As a consequence the CN concentration is more sensitive to temperature changes than the CH concentration (see e.g. the discussion of the chemical equilibrium calculations in Berdyugina et al 2003).…”

Section: Molecular Linesmentioning

confidence: 99%

The role of the Fraunhofer lines in solar brightness variability

Шапиро

Solanki

Krivova

et al. 2015

A&A

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Context. The solar brightness varies on timescales from minutes to decades. A clear identification of the physical processes behind such variations is needed for developing and improving physics-based models of solar brightness variability and reconstructing solar brightness in the past. This is, in turn, important for better understanding the solar-terrestrial and solar-stellar connections. Aims. We estimate the relative contributions of the continuum, molecular, and atomic lines to the solar brightness variations on different timescales. Methods. Our approach is based on the assumption that variability of the solar brightness on timescales greater than a day is driven by the evolution of the solar surface magnetic field. We calculated the solar brightness variations employing the solar disc area coverage of magnetic features deduced from the MDI/SOHO observations. The brightness contrasts of magnetic features relative to the quiet Sun were calculated with a non-LTE radiative transfer code as functions of disc position and wavelength. By consecutive elimination of molecular and atomic lines from the radiative transfer calculations, we assessed the role of these lines in producing solar brightness variability. Results. We show that the variations in Fraunhofer lines define the amplitude of the solar brightness variability on timescales greater than a day and even the phase of the total solar irradiance variability over the 11-year cycle. We also demonstrate that molecular lines make substantial contribution to solar brightness variability on the 11-year activity cycle and centennial timescales. In particular, our model indicates that roughly a quarter of the total solar irradiance variability over the 11-year cycle originates in molecular lines. The maximum of the absolute spectral brightness variability on timescales greater than a day is associated with the CN violet system between 380 and 390 nm.

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Section: Molecular Linesmentioning

confidence: 99%

The role of the Fraunhofer lines in solar brightness variability

Шапиро

Solanki

Krivova

et al. 2015

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“…The MgH line belongs to the Q band of the A 2 Π − X 2 Σ + (0, 0) transition, with J = 16 where J is the rotational lower level quantum number and the C 2 line belongs to the P3 band of the d 3 Π g −a 3 Π u transition with J = 26. The molecular number densities obey the equilibrium equation, given by, say Berdyugina et al (2003):…”

Section: Molecular Number Density and Line Absorption Coefficientmentioning

confidence: 99%

“…Convenient polynomial expressions for equilibrium constants and molecule partition functions are given by Sauval & Tatum (1984). In general, to obtain exact molecular number densities, one should take all molecules and all constituting atoms into account and solve a system of non-linear equations as explained by Berdyugina et al (2003). However, owing to the relatively high temperatures, molecular densities are low, so when computing the MgH density, we may approximate n(Mg) with the total number density of magnesium derived from its abundance relative to hydrogen.…”

Section: Molecular Number Density and Line Absorption Coefficientmentioning

confidence: 99%

Modeling scattering polarization in molecular solar lines in spherical geometry

Milić

Faurobert

2012

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Context. The atmosphere of the Sun is permeated by a vast amount of magnetic flux that remains invisible in magnetograms based on the Zeeman effect. A model-independent way of measuring weak hidden magnetic fields makes use of the differential Hanle effect on the scattering polarization of molecular lines with different sensitivities to magnetic fields. Aims. The observed line scattering polarization steeply increases at the solar limb. Here we are interested in interpreting observations performed at the solar limb, where plane-parallel semi-infinite geometry is not valid. The main reason is that the sphericity of the atmosphere means that the line-of-sight optical path intersects only a finite part of the solar atmosphere. In this paper we revisit the modeling of scattering polarization in two molecular lines of C 2 and MgH in the spectral range from 515.60 nm to 516.20 nm, where observations performed both inside and above the solar limb are available. Methods. The solar atmosphere is described by a one-dimensional, spherically symmetric medium following either the FALC or the FALX quiet Sun model. Both the line and background continuum scattering polarizations are computed by means of the "along-theray" approach. We assume a two-level atom formalism for the line source function, and we compute the molecule number densities and line opacities assuming LTE. We estimate the elastic and inelastic collision rates by fitting the line intensity and linear polarization in several couples of lines of the Second Solar Spectrum Atlas. Results. The limb variations of scattering polarization, both in the lines and in the continuum, are strongly modified when the sphericity of the solar atmosphere is accounted for. We show that the line polarization goes through a maximum at 0.4 above the limb, for both MgH and C 2 lines. The contribution of the line rapidly goes to zero at a larger limb distance, but continuum polarization keeps increasing. The maximum polarization rates have an amplitude of 2% to 2.5% when the FALC model is used, which agrees with previous observations, whereas the FALX model leads to much higher rates. We then investigate the Hanle effect of microturbulent magnetic fields on the C 2 line linear polarization. We show that polarization observed close to the limb would provide valuable diagnostics of weak magnetic fields in the region of the temperature minimum.

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“…To account for inhomogenities in the line forming regions, more sophisticated inversion codes, such as SPINOR (Frutiger et al 2000;Berdyugina et al 2003) or SIR (Ruiz Cobo & del Toro Iniesta 1992), introduce multiple model atmospheres resulting in a more complex line profile.…”

Section: Principles Of the Zcdmentioning

confidence: 99%

“…However, the validity to express the residual depth directly in terms of η λ does not depend on the actual values of a i , b i . They only affect R 0 , a parameter which we tabulate employing the code STOPRO (Solanki 1987;Frutiger et al 2000;Berdyugina et al 2003), solving the polarized radiative transfer equations for a large number of wavelengths, atmospheric models, elements and ions. Therefore, the only requirement for this model is that the source function is linear, whereas the actual behaviour (offset, steepness) is irrelevant.…”

Section: Blended Line Profile and Opacitymentioning

confidence: 99%

Zeeman component decomposition for recovering common profiles and magnetic fields

Sennhauser

Berdyugina

2010

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Context. High resolution spectropolarimetric data contain information about the region where atomic and/or molecular lines form. Existing multi-line techniques assuming similarities in shapes of line profiles can extract generalized Stokes signatures from noisy spectra. However, the interpretability of these signatures is limited by the commonly employed weak-field and weak-line approximations. On the other hand, inversion techniques based on realistic polarized radiative transfer can interpret complicated individual line profiles but still unable to handle the informative wealth of broad-band spectra.Aims. We present a new method, Zeeman component decomposition (ZCD), which combines the versatility of an unconstrained line profile resulting from a multi-line analysis with the radiative transfer physics implying that one profile constitutes all Stokes parameters. We show that the ZCD is capable of inferring a common Zeeman component profile as well as a reliable magnetic field vector from noisy broad-band spectra. Methods. We employ an analytic polarized radiative transfer solution describing formation of polarized line profiles in a MilneEddington atmosphere. The ZCD is built as a nonlinear inversion procedure with a number of free parameters, namely an unconstrained line profile, the line central depths, and the magnetic field parameters |B|, γ and χ. The procedure is applied to all Stokes parameters simultaneously. We carefully analyse blending of line profiles and Zeeman components and obtain practical analytical expressions. By comparing the anomalous Zeeman splitting with the commonly used triplet approximation, we obtain an estimate of the error, helping us to identify the cases where the simplification is not applicable. Results. We demonstrate the capabilities of the ZCD by applying it to simulated Stokes I, V, and full I, Q, U, V spectra. The first test shows that the ZCD outperforms standard multi-line techniques in finding common line profiles for noisy polarization spectra and, in addition, consistently recovers the line-of-sight magnetic field. Trials with I, Q, U, V spectra demonstrate the ability of the ZCD to work with noisy linear polarization spectra and recover the magnetic field parameters in realistic scenarios.

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The molecular Zeeman effect and diagnostics of solar and stellar magnetic fields

Cited by 93 publications

References 43 publications

The role of the Fraunhofer lines in solar brightness variability

The role of the Fraunhofer lines in solar brightness variability

Modeling scattering polarization in molecular solar lines in spherical geometry

Zeeman component decomposition for recovering common profiles and magnetic fields

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