Inverse Compton cooling in Klein-Nishina regime and GRB prompt spectrum

TL;DR

This paper analytically investigates inverse Compton cooling in the Klein-Nishina regime to explain GRB spectra, finding it insufficient to account for observed spectral hardness without extreme parameter values.

Contribution

It provides an analytical assessment of inverse Compton cooling effects in the Klein-Nishina regime on GRB spectra, highlighting limitations of synchrotron models.

Findings

Inverse Compton cooling hardens the spectrum but not enough to match observations.

Achieving observed spectral indices requires extreme parameter values.

Synchrotron in internal shocks likely cannot explain GRB spectra with >-0.2.

Abstract

Synchrotron radiation mechanism, when electrons are accelerated in a relativistic shock, is known to have serious problems to explain the observed gamma-ray spectrum below the peak for most Gamma-Ray Bursts (GRBs); the synchrotron spectrum below the peak is much softer than observed spectra. Recently, the possibility that electrons responsible for the radiation cool via Inverse Compton, but in the Klein-Nishina regime, has been proposed as a solution to this problem. We provide an analytical study of this effect and show that it leads to a hardening of the low energy spectrum but not by enough to make it consistent with the observed spectra for most GRBs (this is assuming that electrons are injected continuously over a time scale comparable to the dynamical time scale, as is expected for internal shocks of GRBs). In particular, we find that it is not possible to obtain a spectrum with \alpha>-0.1 (f_{\nu} \propto \nu^{\alpha}) whereas the typical observed value is \alpha\sim0. Moreover, extreme values for a number of parameters are required in order that \alpha\sim-0.1: the energy fraction in magnetic field needs to be less than about 10^{-4}, the thermal Lorentz factor of electrons should be larger than 10^6, and the radius where gamma-rays are produced should be not too far away from the deceleration radius. These difficulties suggest that the synchrotron radiation mechanism in internal shocks does not provide a self-consistent solution when \alpha>-0.2.