Recent observations by the Fermi satellite suggest that a photosphere emission component is contributing to the observed spectrum of many 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 \sim - 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 co-moving blackbody spectrum emerging from the photosphere , we find that for an outflow with a constant or increasing L _ { w } , the low-energy spectrum below the peak energy ( E _ { p } ) , can be modified to F _ { \nu } \sim \nu ^ { 1.5 } ( \alpha \sim + 0.5 ) .
A softer ( -1 < \alpha < +0.5 ) or flat ( \alpha = -1 ) spectrum can be obtained during the L _ { w } decreasing phase or high-latitude-emission-dominated phase .
We also study the evolution of E _ { p } 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 can not 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 are needed .