Gamma-Ray Burst Spectrum with Decaying Magnetic Field

Abstract

In the internal shock model for gamma-ray bursts (GRBs), the synchrotron spectrum from the fast cooling electrons in a homogeneous downstream magnetic field (MF) is too soft to produce the low-energy slope of GRB spectra. However the magnetic field may decay downstream with distance from the shock front. Here we show that the synchrotron spectrum becomes harder if electrons undergo synchrotron and inverse-Compton cooling in a decaying MF. To reconcile this with the typical GRB spectrum with low energy slope $\nu F_{\nu }\propto \nu$, it is required that the postshock MF decay time is comparable to the cooling time of the bulk electrons (corresponding to a MF decaying length typically of $\sim 10^5$ skin depths); that the inverse-Compton cooling should dominate synchrotron cooling after the MF decay time; and/or that the MF decays with comoving time roughly as $B\propto t^{-1.5}$. An internal shock synchrotron model with a decaying MF can account for the majority of GRBs with low energy slopes not harder than ${\nu }^{4/3}$.

Accepted for publication in ApJ

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