A shock emission model for gamma-ray bursts .2. Spectral properties

We discuss a simple model of high-energy emission for gamma-ray bursts (GRBs) based on synchrotron radiation of particles impulsively accelerated. The emission model assumes a source of magnetohydrodynamical outflow and efficient and fast particle acceleration (most likely mediated by a relativistic shock) in optically thin environments. The properties of the synchrotron shock emission can be derived under general conditions valid for both Galactic or cosmological interpretations of GRB sources. We show that the synchrotron shock model (SSM) predicts a specific shape of the GRB spectral continuum (broad maximum of the nu F-nu spectrum, low-energy continuum with characteristic curvature, high-energy power-law emission) in agreement with recently determined broadband GRB spectra. The calculated spectrum turns out to be a universal two-parameter function in the energy range similar to 30 keV-1 GeV. The peak photon energy E(p) of the GRB nu F-nu spectrum (power per logarithmic photon energy band) is interpreted as the relativistic synchrotron energy of impulsively accelerated particles. From the GRB properties, we obtain a crucial constraint relating the average Lorentz factor of preaccelerated particles gamma* and the strength of the local magnetic field B-ps at the GRB site (module possible Doppler and cosmological factors of order similar to 10(2) and an inverse Compton blueshift factor): 10(12) less than or similar to gamma*(2) B-ps less than or similar to 10(14) cgs. Hard-to-soft spectral evolution often observed in GRBs can be due to a variation of gamma* and B-ps as the synchrotron emission evolves within the burst. The burst emissivity depends on the strength of the average magnetic field at the acceleration site, and we derive general relations from among peak intensities, durations, and E(p)'s of elementary shock emission episodes. In general, a complex burst can be a superposition of different elementary shock emission episodes, and the durations of elementary shock emission episodes tau(e) can tentatively be identified with those of individual GRB pulses. We find that the pulse durations tau(e) have a simple physical meaning. On the contrary, the statistically defined durations T-90 and T-50 are not suitable for an accurate description of GRB physical processes. The SSM in its simplest realization predicts correlated spectral hardness and burst intensity and an anticorrelation between shock episode durations tau(e) and peak intensities. Both of these characteristics are qualitatively similar to GRB features expected in cosmological models. The determination of the GRB spectral continuum shapes as a function of time is particularly important for testing the shock model proposed here. Under general conditions of emission, the SSM predicts specific patterns of spectral evolution which can be tested. In this paper, we discuss the general properties of the shock emission model, and we leave open the issue of the ultimate origin of the relativistic MHD winds and nature of the outbursts.