Peak energy clustering and efficiency in compact objects

We study the properties of plasmas containing a low-energy thermal photon component at comoving temperatures of θ = kT¹/m _ec² ∼ 10^-5 to 10^-2 interacting with an energetic electron component characteristic of, e.g., the dissipation phase of relativistic outflows in gamma-ray bursts (GRBs), X-ray flashes, and blazars. We show that for scattering optical depths larger than a few, the balance between Compton and inverse Compton scattering leads to the accumulation of electrons at values of γβ ∼ 0.1-0.3. For optical depths larger than ∼ 100, this leads to a peak in the comoving photon spectrum at 1-10 keV that is very weakly dependent on the values of the free parameters. In particular, these results are applicable to the internal shock model of GRBs, as well as to slow dissipation models, e.g., as might be expected from reconnection, if the dissipation occurs at a subphotospheric radii. For GRB bulk Lorentz factors of ∼ 100, this results in observed spectral peaks clustering in the 0.1-1 MeV range, with conversion efficiencies of electrons into photon energy in the BATSE range of ∼30%.