Regulation of the spectral peak in gamma-ray bursts

Observations indicate that the peak of gamma-ray burst spectrum forms in the opaque region of an ultra-relativistic jet. Recent radiative transfer calculations support this picture and show that the spectral peak is inherited from initially thermal radiation, which is changed by heating into a broad photon distribution with a high-energy tail. We discuss the processes that regulate the observed position of the spectral peak E_pk. The opaque jet has three radial zones: (1) Planck zone r<R_P where a blackbody spectrum is enforced; this zone ends where Thomson optical depth decreases to tau10^5. (2) Wien zone R_P<r<R_W with Kompaneets parameter y»1 where radiation has a Bose-Einstein spectrum, and (3) Comptonization zone r>R_W where the radiation spectrum develops the high-energy tail. Besides the initial jet temperature, an important factor regulating E_pk is internal dissipation (of bulk motions and magnetic energy) at large distances from the central engine. Dissipation in the Planck zone reduces E_pk, and dissipation in the Wien zone increases E_pk. In jets with sub-dominant magnetic fields, the predicted E_pk varies around 1 MeV up to a maximum value of about 10 MeV. If the jet carries an energetically important magnetic field, E_pk can be additionally increased by dissipation of magnetic energy. This increase is hinted by observations, which show E_pk up to about 20 MeV. We also consider magnetically dominated jets; then a simple model of magnetic dissipation gives E_pk30 Gamma_W keV where Gamma_W is the jet Lorentz factor at the Wien radius R_W.