Diffusion Spectra of Ultrarelativistic Shell Radiation Depending on the Initial Energy Distribution in the Shell

Large-scale cosmic emissions of explosive energy that occur during the explosions of certain supernovae or the merger of compact objects are called gamma-ray bursts. The initial stage of a gamma-ray burst can be described by the diffusion of radiation in an ultrarelativistic shell obtained from the transport equation. Spectra were calculated using the solution of this equation, the Stefan–Boltzmann and Planck laws, as well as typical parameters of gammaray bursts. We consider various linear and parabolic initial energy distributions inside the shell. All obtained diffusion spectra contain Band components at low and high frequencies. The dependence of the diffusion spectrum on the number of terms taken into account in the formula for the effective temperature for the parametric initial energy distribution inside the shell is also considered.