Relativistic effects on Radiative Transfer Equation: Order of Magnitude study

Abstract

We have analyzed how the high gas velocities which are observed in the objects such as the atmospheres of supergiant stars, novae, supernovae, accretion discs around high density objects (like black holes, neutron stars etc.) would change the co-efficient of different terms in the transfer equation which is solved in the commoving frame. Velocities as low as 5000 Km S-1 is enough to show the relativity effects in different terms in the transfer equation. We have considered the term of the order of V/C where V and C are the gas velocity and the velocity of the light respectively. We have neglected the terms containing V2/C2 and higher power of V/C. The commoving frame is adopted because it is convenient and natural to treat the photon transfer in a medium which is expanding at a very high radial velocity. The rest frame calculations would require a larger grid of angle-frequency radius which is not practicable in our calculations. We have in this investigation, considered the medium expanding in a steady state (time independent) conditions. Furthermore is velocity and density are set to change according to the equation of continuity given by 4πr^2ǷV=constant.