Stokes profile analysis and vector magnetic fields. II - Formal numerical solutions of the Stokes transfer equations

Rees, D. E.; Durrant, C. J.; Murphy, G. A.

doi:10.1086/167364

Cited by 137 publications

(137 citation statements)

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“…The DELO method proposed by Rees et al (1989) can be considered a possible generalization of the scalar SC method to the radiative transfer problem of polarized radiation. That formal solver of the Stokes-vector transfer equation is, however, based on linear interpolation of the source function S eff between points M and O. Trujillo demonstrated that significantly more accurate solutions can be obtained by using instead a formal solver he calls DELOPAR, which is based on the choice in Eq.…”

Section: The Short Characteristics Methodsmentioning

confidence: 99%

PORTA: A three-dimensional multilevel radiative transfer code for modeling the intensity and polarization of spectral lines with massively parallel computers

Štěpán

Bueno

2013

A&A

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The interpretation of the intensity and polarization of the spectral line radiation produced in the atmosphere of the Sun and of other stars requires solving a radiative transfer problem that can be very complex, especially when the main interest lies in modeling the spectral line polarization produced by scattering processes and the Hanle and Zeeman effects. One of the difficulties is that the plasma of a stellar atmosphere can be highly inhomogeneous and dynamic, which implies the need to solve the non-equilibrium problem of the generation and transfer of polarized radiation in realistic three-dimensional (3D) stellar atmospheric models. Here we present PORTA, an efficient multilevel radiative transfer code we have developed for the simulation of the spectral line polarization caused by scattering processes and the Hanle and Zeeman effects in 3D models of stellar atmospheres. The numerical method of solution is based on the non-linear multigrid iterative method and on a novel short-characteristics formal solver of the Stokes-vector transfer equation which uses monotonic Bézier interpolation. Therefore, with PORTA the computing time needed to obtain at each spatial grid point the self-consistent values of the atomic density matrix (which quantifies the excitation state of the atomic system) scales linearly with the total number of grid points. Another crucial feature of PORTA is its parallelization strategy, which allows us to speed up the numerical solution of complicated 3D problems by several orders of magnitude with respect to sequential radiative transfer approaches, given its excellent linear scaling with the number of available processors. The PORTA code can also be conveniently applied to solve the simpler 3D radiative transfer problem of unpolarized radiation in multilevel systems.

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Section: The Short Characteristics Methodsmentioning

confidence: 99%

PORTA: A three-dimensional multilevel radiative transfer code for modeling the intensity and polarization of spectral lines with massively parallel computers

Štěpán

Bueno

2013

A&A

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“…This inversion software represents a further development of the Invers10 code ), previously applied for mapping magnetic geometries and chemical spots on Ap stars (Kochukhov et al 2004;Kochukhov & Wade 2010;Lüftinger et al 2010). Both codes incorporate full treatment of the polarised radiative transfer using a modified diagonal element lambda-operator (DELO) algorithm (Rees et al 1989;. All four Stokes parameters are calculated simultaneously and fully self-consistently, taking into account Zeeman broadening and splitting of spectral lines in the intensity spectra on the one hand, and attenuation of the polarised profiles due to temperature spots on the other hand.…”

Section: Zeeman Doppler Imaging Code Invers13mentioning

confidence: 99%

Magnetic field topology of the RS CVn star II Pegasi

Kochukhov

Mantere

Hackman

et al. 2013

A&A

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Context. The dynamo processes in cool active stars generate complex magnetic fields responsible for prominent surface stellar activity and variability at different time scales. For a small number of cool stars magnetic field topologies were reconstructed from the time series of spectropolarimetric observations using the Zeeman Doppler imaging (ZDI) method, often yielding surprising and controversial results. Aims. In this study we follow a long-term evolution of the magnetic field topology of the RS CVn binary star II Peg using a more self-consistent and physically more meaningful modelling approach compared to previous ZDI studies. Methods. We collected high-resolution circular polarisation observations of II Peg using the SOFIN spectropolarimeter at the Nordic Optical Telescope. These data cover 12 epochs spread over 7 years, comprising one of the most comprehensive spectropolarimetric data sets acquired for a cool active star. A multi-line diagnostic technique in combination with a new ZDI code is applied to interpret these observations. Results. We have succeeded in detecting clear magnetic field signatures in average Stokes V profiles for all 12 data sets. These profiles typically have complex shapes and amplitudes of ∼10 −3 of the unpolarised continuum, corresponding to mean longitudinal fields of 50-100 G. Magnetic inversions using these data reveals evolving magnetic fields with typical local strengths of 0.5-1.0 kG and complex topologies. Despite using a self-consistent magnetic and temperature mapping technique, we do not find a clear correlation between magnetic and temperature features in the ZDI maps. Neither do we confirm the presence of persistent azimuthal field rings found in other RS CVn stars. Reconstruction of the magnetic field topology of II Peg reveals significant evolution of both the surface magnetic field structure and the extended magnetospheric field geometry on the time scale covered by our observations. From 2004 to 2010 the total field energy drastically declined and the field became less axisymmetric. This also coincided with the transition from predominantly poloidal to mainly toroidal field topology. Conclusions. A qualitative comparison of the ZDI maps of II Peg with the prediction of dynamo theory suggests that the magnetic field in this star is produced mainly by the turbulent α 2 dynamo rather than the solar αΩ dynamo. Our results do not show a clear active longitude system, nor is there evidence of the presence of an azimuthal dynamo wave.

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“…The radiative transfer calculations were performed with an extended and improved version of the code STOPRO (Solanki et al 1992;Frutiger et al 2000), which solves the set of radiative transfer equations in the formulation given by Rees et al (1989). This code has been updated to enable computations of lines of diatomic molecules in the presence of a magnetic field, i.e.…”

Section: Line Synthesismentioning

confidence: 99%

Zeeman-split opposite-polarity OH lines in sunspot spectra: Resolution of a puzzle

Berdyugina

Solanki

2001

A&A

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Abstract. We present the first synthetic Zeeman-split Stokes I and V profiles of OH lines. They explain the puzzling observations reported by Harvey (1985) of two pairs of lines from the infrared (2, 0) band with Stokes V profiles exhibiting opposite polarities. Our new perturbation calculations of the Zeeman effect in diatomic molecules, which allow states of any multiplicity to be treated, resolve the puzzle. They reveal that the unusual behaviour of these lines stems from the fact that the two pairs have effective Landé factors of similar magnitude, but of opposite signs.

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Stokes profile analysis and vector magnetic fields. II - Formal numerical solutions of the Stokes transfer equations

Cited by 137 publications

References 0 publications

PORTA: A three-dimensional multilevel radiative transfer code for modeling the intensity and polarization of spectral lines with massively parallel computers

PORTA: A three-dimensional multilevel radiative transfer code for modeling the intensity and polarization of spectral lines with massively parallel computers

Magnetic field topology of the RS CVn star II Pegasi

Zeeman-split opposite-polarity OH lines in sunspot spectra: Resolution of a puzzle

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