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Numerical methods in polarized line formation theory

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dc.contributor.author Nagendra, K. N
dc.contributor.author Sampoorna, M
dc.date.accessioned 2009-09-16T10:32:30Z
dc.date.available 2009-09-16T10:32:30Z
dc.date.issued 2009-06
dc.identifier.citation Berdyugina, Svetlana V. Nagendra, K. N. and Ramelli, Renzo., eds., Solar Polarization 5: In Honor of Jan Stenflo Astronomical Society of the Pacific Conference Series, Vol. 405, proceedings of the conference held 17 - 21 September, 2007 at Centro Stefano Franscini-Monte Veritá, Ascona, Switzerland, pp. 261 – 274 en
dc.identifier.isbn 978-1-58381-690-5
dc.identifier.uri http://hdl.handle.net/2248/4825
dc.description Restricted Access
dc.description.abstract We review some numerical methods and provide benchmark solutions for the polarized line formation theory with partial redistribution (PRD) in the presence of magnetic fields. The transfer equation remains non-axisymmetric when written in the ‘Stokes vector basis’. It is relatively easier to develop numerical methods to solve the transfer equation for axisymmetric radiation fields. Therefore for non-axisymmetric problems it would be necessary to expand the azimuthal dependence of the scattering redistribution matrices in a Fourier series. The transfer equation in this so called ‘reduced form’ becomes axisymmetric in the Fourier domain in which it is solved, and the reduced intensity is then transformed into the Stokes vector basis in real space. The advantage is that the reduced problem lends itself to be solved by appropriately organized PALI (Polarized Approximate Lambda Iteration) methods. We first dwell upon a frequency by frequency method (PALI7) that uses non-domain based PRD for the Hanle scattering problem, and then compare it with a core-wing method (PALI6) that uses a domain based PRD. The PALI methods use operator perturbation and involve construction of a suitable procedure to evaluate an ‘iterated source vector correction’. Another important component of PALI methods is the ‘Formal Solver’ (for example Feautrier, short characteristic, DELOPAR etc.). The PALI methods are extremely fast on a computer and require very small memory. Finally, we present a simple perturbation method to solve the Hanle-Zeeman line formation problem in arbitrary strength magnetic fields. en
dc.language.iso en en
dc.publisher Astronomical Society of the Pacific en
dc.relation.ispartofseries Astronomical Society of the Pacific Conference Series; Vol. 405
dc.relation.uri http://aspbooks.org/custom/publications/paper/405-0261.html en
dc.rights © Astronomical Society of the Pacific en
dc.subject Numerical Methods en
dc.subject Polarized Line Formation Theory en
dc.subject Partial-Frequency-Redistribution en
dc.subject Operator Perturbation Method en
dc.subject Resonance Polarization en
dc.subject Spectral-Lines en
dc.subject Stellar Atmospheres en
dc.subject Radiative-Transfer en
dc.subject Collisionless Regime en
dc.subject Stokes Parameters en
dc.subject Classical-Theory en
dc.subject Weak Magnetic-Fields en
dc.title Numerical methods in polarized line formation theory en
dc.type Article en

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