LOW ENERGY SPECTRAL INDEX AND Ep EVOLUTION OF QUASI-THERMAL PHOTOSPHERE EMISSION OF GAMMA-RAY BURSTS

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 alpha similar to -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-w) profiles. By assuming a comoving blackbody spectrum emerging from the photosphere, we find that for an outflow with a constant or increasing Lw, the low-energy spectrum below the peak energy (E-p), can be modified to F-v similar to v(1.5) (alpha similar to + 0.5). A softer (-1 < alpha < +0.5) or flat (alpha = -1) spectrum can be obtained during the Lw decreasing phase or high-latitude-emission-dominated phase. We also study the evolution of Ep as a function of wind and photosphere luminosity in this photosphere model. An E-p - L tracking pattern can be reproduced if a certain positive dependence between the dimensionless entropy. eta and L-w 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.