Fast cooling synchrotron radiation in a decaying magnetic field and $\gamma$-ray burst emission mechanism

TL;DR

This paper investigates how a decreasing magnetic field in transient astrophysical sources like gamma-ray bursts affects synchrotron cooling, revealing a new regime where electrons have harder spectra and explaining observed GRB spectra.

Contribution

It introduces a novel physical regime of synchrotron cooling in decreasing magnetic fields, altering the expected electron energy distribution and GRB emission spectra.

Findings

Fast cooling electrons can have a harder energy spectrum in decreasing magnetic fields.

Standard $dN_e/d\,\gamma_e \propto \gamma_e^{-2}$ spectrum is only achieved in deep fast cooling.

GRB spectra with low-energy photon index around -1 can be explained by this regime.

Abstract

Synchrotron radiation of relativistic electrons is an important radiation mechanism in many astrophysical sources. In the sources where the synchrotron cooling time scale $t_c$ is shorter than the dynamical time scale $t_{dyn}$, electrons are cooled down below the minimum injection energy. It has been believed that such "fast cooling" electrons have an energy distribution $dN_e /d\gamma_e \propto \gamma_e^{-2}$, and their synchrotron radiation flux density has a spectral shape $F_\nu \propto \nu^{-1/2}$. On the other hand, in a transient expanding astrophysical source, such as a gamma-ray burst (GRB), the magnetic field strength in the emission region continuously decreases with radius. Here we study such a system, and find that in a certain parameter regime, the fast cooling electrons can have a harder energy spectrum, and the standard $d N_e / d \gamma_e \propto \gamma_e^{-2}$ spectrum is achieved only in the deep fast cooling regime when $t_c \ll t_{dyn}$. We apply this new physical regime to GRBs, and suggest that the GRB prompt emission spectra whose low-energy photon index $\alpha$ has a typical value -1 could be due to synchrotron radiation in this moderately fast cooling regime.