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Title: | Numerical methods in polarized line formation theory |
Authors: | Nagendra, K. N Sampoorna, M |
Keywords: | Numerical Methods Polarized Line Formation Theory Partial-Frequency-Redistribution Operator Perturbation Method Resonance Polarization Spectral-Lines Stellar Atmospheres Radiative-Transfer Collisionless Regime Stokes Parameters Classical-Theory Weak Magnetic-Fields |
Issue Date: | Jun-2009 |
Publisher: | Astronomical Society of the Pacific |
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 |
Series/Report no.: | Astronomical Society of the Pacific Conference Series; Vol. 405 |
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. |
Description: | Restricted Access |
URI: | http://hdl.handle.net/2248/4825 |
ISBN: | 978-1-58381-690-5 |
Appears in Collections: | IIAP Publications |
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Numerical Methods in Polarized Line Formation Theory Restricted Access | Restricted Access | 250.09 kB | Adobe PDF | View/Open Request a copy |
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