2011ApJ...732...26M

In this study, the light curves and spectrum of the photospheric thermal radiation from ultrarelativistic gamma-ray burst (GRB) jets are calculated using two-dimensional relativistic hydrodynamic simulations of jets from a collapsar. As the jet advances, the density around the head of the jet decreases, and its Lorentz factor reaches as high as 200 at the photosphere and 400 inside the photosphere. For an on-axis observer, the photosphere appears concave due to the low density and high beaming factor of the jet. The luminosity varies because of the abrupt change in the position of the photosphere due to the internal structure of the jet. Comparing our results with GRB 090902B, the flux level of the thermal-like component is similar to our model, although the peak energy appears slightly higher (but still within a factor of two). From the comparison, we estimate that the bulk Lorentz factor of GRB 090902B is Γ ∼ 2.4x10²(r/10¹² cm), where r is the radius of the photosphere. The spectrum for an on-axis observer is harder than that for an off-axis observer. There is a time lag of a few seconds for high energy bands in the light curve. This may be the reason for the delayed onset of GeV emission seen in GRB 080916C. The spectrum below the peak energy is a power law and the index is 2.3-2.6, which is softer than that of a single temperature Planck distribution but still harder than that of the typical value of the observed spectrum.