GRB spectrum from gradual dissipation in a magnetized outflow

Abstract

ABSTRACT Modelling of many gamma-ray burst prompt emission spectra sometimes requires a (quasi) thermal spectral component in addition to the Band function that sometimes leads to a double-hump spectrum, the origin of which remains unclear. In photospheric emission models, a prominent thermal component broadened by sub-photospheric dissipation is expected to be released at the photospheric radius, $r_{\rm ph}\sim 10^{12}\,$ cm. We consider an ultra-relativistic strongly magnetized steady outflow with a striped-wind magnetic-field structure undergoing gradual and continuous magnetic energy dissipation at r < rs that heats and accelerates the flow to a bulk Lorentz factor Γ(r) = Γ∞min [1, (r/rs)1/3], where typically rph < rs. Similar dynamics and energy dissipation rates are also expected in highly variable magnetized outflows without stripes/field-reversals. Two modes of particle energy injection are considered: (a) power-law electrons, e.g. accelerated by magnetic reconnection, and (b) distributed heating of all electrons (and e±-pairs), e.g. due to magnetohydrodynamic instabilities. Steady-state spectra are obtained using a numerical code that evolves coupled kinetic equations for a photon-electron-positron plasma. We find that (i) the thermal component consistently peaks at $(1+z)E_{\rm pk}\sim 0.2-1\,$MeV, for a source at redshift z, and becomes sub-dominant if the total injected energy density exceeds the thermal one, (ii) power-law electrons cool mainly by synchrotron emission whereas mildly relativistic and almost monoenergetic electrons in the distributed heating scenario cool by Comptonization on thermal peak photons, (iii) both scenarios can yield a low-energy break, and (iv) the $\sim 0.5(1+z)^{-1}\,$ keV X-ray emission is suppressed in scenario (a), whereas it is expected in scenario (b). Energy-dependent linear polarization can differentiate between the two particle heating scenarios.