Polarized Radiative Transfer in Discontinuous Media

Polarimetric observations of the Sun at high spatial resolution reveal an intermittent magnetic structuring of its atmosphere. Likewise, magnetohydrodynamic numerical simulations of the near surface layers of the Sun show shock fronts, contact discontinuities and steep gradients in their state variables. For the production and post-processing of numerical simulation data and for the interpretation of observed polarimetric maps, one needs to have access to radiative transfer codes that are able to deal with discontinuities and intermittent structuring. Here, we propose to apply well known concepts from computational fluid dynamics to the numerical simulation of radiative transfer. In particular, we plan to apply the concept of piecewise continuous reconstruction and slope-limiter methods to the source function and absorption matrix of the radiative transfer equation for polarized light. This novel idea contrasts with recent developments which focused on polynomial interpolations of ever higher order of accuracy and smoothness. We foresee application of the proposed method to radiation-magnetohydrodynamics codes and to the post-processing of the corresponding simulation data as well as to observed polarimetric data, all of which are developed, recorded, and collected at the Istituto Ricerche Solari Locarno (IRSOL). Beyond that, the field of potential application includes virtually all branches of astrophysics and from atmospheric and oceanographic science to techniques of remote sensing and computer graphics. The proposed research project is foreseen to be subject of a PhD-thesis carried out at the Seminar for Applied Mathematics (SAM) of the ETHZ under the supervision of Prof. Dr. Siddhartha Mishra and at IRSOL under the supervision of Dr. Oskar Steiner and Dr. Luca Belluzzi. We therefore apply for the financial support of one PhD-candidate position.