Thermal synchrotron radiation and gamma-ray burst spectra

The standard classical expressions for the thermal synchrotron (TS) radiation from an optically thin thermal plasma are shown to be inapplicable at photon energies E≳kT since they neglect quantum effects. Quantum relationships are obtained for the TS spectral emissivity, opacity, and polarization. The quantum TS spectra are much softer at E≳kT than the classical ones. The TS radiation exhibits strong linear polarization in the classical domain, whereas the quantum effects reduce the polarization at high E. Expressions for the classical TS luminosity are obtained with quantum corrections which turn out to be significant for (B/B_c)(kT/mc²)≳10^-2(B_c=4.41×10¹³ G). Fitting the gamma-ray burst (GRB) spectra by the classical TS law (see, e.g., Liang et al., 1983) is incorrect in cases where kT is less than the maximum detected photon energy. The continua of the GRB spectra in the range E∼20 keV-2 MeV (Mazets et al., 1981a; Andreev et al., 1983) can be fitted satisfactorily by the quantum TS spectra. The results of this fitting may suggest the existence of temperatures much higher (up to ∼10 MeV), and of magnetic fields much lower (down to ∼10⁹ G) than those usually accepted. Under these conditions the thickness of the TS sources (∼10³-10⁴ cm) could be comparable with their transverse dimensions (in contrast to sources with ordinary temperatures and fields), if they lie within a few kpc. The quantum TS spectra are too soft to account for the hard components (up to tens of MeV) of the GRB spectra detected by the Solar Maximum Mission (Nolan et al., 1984), unless the temperatures are unreasonably high. A straightforward TS interpretation of the GRB spectra seems to be unrealistic. Most probably, the continuum radiation escapes from an optically thick, strongly magnetized, highly non-stationary, hot plasma near the surface of a neutron star.