Regulation of the Spectral Peak in Gamma-Ray Bursts

Observations indicate that the peak of a gamma-ray burst spectrum forms in the opaque region of an ultrarelativistic 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) the Planck zone r < R P where a blackbody spectrum is enforced; this zone ends where the Thomson optical depth decreases to τ ≈ 10 5 , (2) the Wien zone R P < r < R W with a Kompaneets parameter y ≫ 1 where radiation has a Bose–Einstein spectrum, and (3) the Comptonization zone r > R W where the radiation spectrum develops a 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 can increase E pk . In jets with subdominant 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 suggested 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 pk ≈ 30 Γ W keV where Γ W is the jet Lorentz factor at the Wien radius R W .