Radiative Transfer Problem in the Presence of Strong Magnetic Fields. Analytical and Numerical Treatment.

In this thesis we investigate analytical and numerical methods to find a solution of the radiative transfer equation in the presence of strong magnetic fields. My Ph.D research theme is focused on those astrophysical objects which presumably show an evidence of a strong magnetic field (B & 1012 G), with a particular emphasis on the physics of X-ray spectral formation in these objects. The radiative transfer equation which describes spectral formation is, in general, rather complicated because of its integro-differential nature. If we are interested in finding a solution, even numerically, we need to simplify the problem. For instance, we assume that stellar atmospheres can be represented, in first approximation, by a plane-parallel slab of fully ionized plasma of non-relativistic thermal electrons with an external uniform magnetic field. Since we are interested in modelling the high energy photon emission coming from the interaction with such medium, we assume also that the dominant radiative process which modifies the X-ray photon spectrum is multiple inverse Compton scattering. We propose two approaches to the study of this problem and we discuss the related solutions. In the first part of this thesis, we present an analytical and numerical study of the radiative transfer problem in the presence of a strong uniform magnetic field (B & 4:4 � 1013G) taking place in a medium filled by non-relativistic thermal electrons in plane-parallel geometry. Even after making some initial assumptions, the equation governing such system is still an integro-differential equation. Additional conditions are required to handle the radiative transfer equation the with separation of variable method. Then the radiative transfer problem can be reduced to the solution of the equation which has a diffusion operator for the energy variable and an integral operator for the space variable. Such an integro-differential equation was firstly derived and its solution was estimated in 1988 by Lyubarskii in [1],[2]. We have solved numerically the equation proposed by Lyubarskii and we have confirmed this solution using the analytical methods. The second part of the thesis is devoted to the description of a numerical algorithm that we implemented for the resolution of radiative transfer equation, when it reduces to a pure differential form. This is usually the case when the Fokker-Planck (diffusion) approximation is applicable. The algorithm is essentially based on relaxation methods and, generally, it solves all inhomogeneous second order elliptic partial differential equations with vanishing mixed derivatives. The numerical code gives a stable solution of the equation when the system has reached its steady-state equilibrium. We test the code solving the radiative transfer problem in the case of cylindrical accretion onto a magnetised neutron star, when a combined effect of bulk and thermal Comptonization takes place. Finally, we implemented the algorithm in the X-ray spectral fitting package XSPEC and we successfully fitted the X-ray spectra of the two Supergiant Fast X-ray Transients (SFXTs) XTE J1739-302 and IGR J17544-2619, observed with the Swift Gamma-ray Burst Telescope. Our model is then compared with other XSPEC models we used during the X-ray spectral fitting procedure and we briefly discuss possible implications on the geometry of these systems. I critically discuss and compare the results presented in the thesis in the conclusion section.