Inverse-Compton cooling in Klein-Nishina regime and gamma-ray burst prompt spectrum

Synchrotron radiation mechanism, when electrons are accelerated in a relativistic shock, is known to have serious problems in explaining 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 KleinNishina 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 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 a > -0.1 (f? ? ?a), where the typical observed value is a similar to 0. Moreover, extreme values for a number of parameters are required in order that a similar to-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 106 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 a ? -0.2.