Low energy spectral index and Ep evolution of quasi-thermal photosphere emission of gamma-ray bursts

Abstract

Recent observations by the Fermi satellite suggest that a photosphere emission component is contributing to the observed spectrum of many gamma-ray bursts (GRBs). One important question is whether the photosphere component can interpret the typical "Band" function of GRBs with a typical low energy photon spectral index α ∼ -1. We perform a detailed study of the photosphere emission spectrum by progressively introducing several physical ingredients previously not fully incorporated, including the probability distribution of the location of a dynamically evolving photosphere, superposition of emission from an equal arrival time "volume" in a continuous wind, the evolution of optical depth of a wind with finite but evolving outer boundary, as well as the effect of different top-hat wind luminosity (L<inf>w</inf> ) profiles. By assuming a comoving blackbody spectrum emerging from the photosphere, we find that for an outflow with a constant or increasing L<inf>w</inf> , the low-energy spectrum below the peak energy (E <inf>p</inf> ), can be modified to F <inf>ν</inf> ∼ ν^1.5 (α ∼ +0.5). A softer (-1 < α < +0.5) or flat (α = -1) spectrum can be obtained during the L<inf>w</inf> decreasing phase or high-latitude-emission-dominated phase. We also study the evolution of E <inf>p</inf> as a function of wind and photosphere luminosity in this photosphere model. An E<inf>p-L</inf> tracking pattern can be reproduced if a certain positive dependence between the dimensionless entropy η and L <inf>w</inf> is introduced. However, the hard-to-soft evolution pattern cannot be reproduced unless a contrived condition is invoked. In order to interpret the Band spectrum, a more complicated photosphere model or a different energy dissipation and radiation mechanism is needed. © 2014. The American Astronomical Society. All rights reserved.