GRBs Radiative Processes: Synchrotron and Synchrotron Self-Absorption From a Power Law Electrons Distribution with Finite Energy Range

摘要

Synchrotron emission behind relativistic magnetic internal-external shocks in gammaray bursts cosmological explosions is assumed to be the basic emission mechanism for prompt and afterglow emissions. Inverse Compton from relativistic electrons can also have appreciable effects by upscattering initial synchrotron or blackbody photons or other photons fields up to GeV-TeV energies. For extreme physical conditions such as high magnetic fields (e.g., B > 10~5 Gauss) selfabsorption is not negligible and can hardly affect spectra at least for the low energy range. In this paper we present calculations of the synchrotron power, P_v, and their asymptotic forms, generated by a power law relativistic electron distribution of type N_e(y)=Cy~(-p) with y_1 < y < y_2, especially for finite values of the higher limit y_2. For this aim we defined the dimensionless parametric function Z_p(x, η) with x = v/v_1 and η = y_2/y_1, so that P_v ∝ Z_p(v/v_1,η), with v_1 = (3/4π)y_1~2qBsinθ/mc (θ being the pitch angle). Asymptotic forms of this later are derived for three different frequency ranges, i.e., x 1, 1 xη~2 and x η~2. These results are then used to calculate the absorption coefficient, a_v, and the source function, S_v, together with their asymptotic forms through the dimensionless parametric functions H_p(x, η) and Y_p(x,η), respectively. Further calculation details are also presented and discussed.