The observable effect of a photospheric component on GRB's prompt emission spectrum: Peak energy clustering and flat spectra above the thermal peak

A thermal radiative component is likely to accompany the first stages of the prompt emission of Gamma-ray bursts (GRB's) and X-ray flashes (XRF's). We study the properties of plasmas containing a low energy thermal photon component at comoving temperature θ ≡ kT ′ / m_ec² ∼ 10^-5 - 10^-2 interacting with an energetic electron component. We show that, for scattering optical depths larger than a few, 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 and characteristic GRB bulk Lorentz factors of ∼ 100 this leads to a peak in the observed photon spectrum at 0.1 - 1 MeV, very weakly dependent on the values of the free parameters. For a wide range of the optical depths 0.03 ≲ τ_γe ≲ 100 and comparable energy densities in the thermal and the leptonic component, a nearly flat energy spectrum (vF_v ∝ v⁰) above the thermal peak at ≈ 10 - 100 keV and below 10 - 100 MeV is obtained, regardless of the details of the dissipation mechanism or the strength of the magnetic field. In particular, these results are applicable to the internal shock model of GRB, as well as to slow dissipation models, e.g. as might be expected from reconnection, if the dissipation occurs at a sub-photospheric radii. We conclude that dissipation near the thermal photosphere can naturally explain (a) clustering of the peak energy at sub-MeV energies at early times; (b) steep slopes observed at low energies; and (c) a flat spectrum above 10 keV at late times. Our model thus provides an alternative scenario to the optically thin synchrotron - SSC model.