Simultaneous solution of Kompaneets equation and Radiative Transfer equation in the photon energy range 1 - 125 KeV

摘要

Radiative transfer equation in plane parallel geometry and Kompaneetsequation is solved simultaneously to obtain theoretical spectrum of 1-125 KeVphoton energy range. Diffuse radiation field is calculated usingtime-independent radiative transfer equation in plane parallel geometry, whichis developed using discrete space theory (DST) of radiative transfer in ahomogeneous medium for different optical depths. We assumed free-free emissionand absorption and emission due to electron gas to be operating in the medium.The three terms $n, n^2$ and $\displaystyle \bigg({\frac {\partial n}{\partialx_k}}\bigg)$ where $n$ is photon phase density and $\displaystyle x_k=\bigg({\frac {h \nu} {k T_e}} \bigg) $, in Kompaneets equation and those due tofree-free emission are utilized to calculate the change in the photon phasedensity in a hot electron gas. Two types of incident radiation are considered:(1) isotropic radiation with the modified black body radiation $I^{MB}$ [1] and(2) anisotropic radiation which is angle dependent. The emergent radiation at$\tau=0$ and reflected radiation $\tau=\tau_{max}$ are calculated by using thediffuse radiation from the medium. The emergent and reflected radiation containthe free-free emission and emission from the hot electron gas. Kompaneetsequation gives the changes in photon phase densities in different types ofmedia. Although the initial spectrum is angle dependent, the Kompaneetsequation gives a spectrum which is angle independent after several Comptonscattering times.