Low Energy Spectral Index and $E_{p}$ evolution of Quasi-thermal Photosphere Emission of Gamma-Ray Bursts

Wei Deng; Bing Zhang

doi:10.1088/0004-637X/785/2/112

paper

Low Energy Spectral Index and $E_{p}$ evolution of Quasi-thermal Photosphere Emission of Gamma-Ray Bursts

arXiv:1402.5364 · doi:10.1088/0004-637X/785/2/112

Abstract

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 $α \sim - 1$ . 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 $F_{ν} \sim ν^{1.5}$ ( $α \sim + 0.5$ ). A softer ( $- 1 < α < + 0.5$ ) or flat ( $α = - 1$ ) 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 $η$ 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 are needed.

Accepted by ApJ, 15 pages, 17 figures

Low Energy Spectral Index and $E_{p}$ evolution of Quasi-thermal Photosphere Emission of Gamma-Ray Bursts

Abstract

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Cited by in corpus (67)

Low Energy Spectral Index and Ep​ evolution of Quasi-thermal Photosphere Emission of Gamma-Ray Bursts

Abstract

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Cited by in corpus (67)

Low Energy Spectral Index and $E_{p}$ evolution of Quasi-thermal Photosphere Emission of Gamma-Ray Bursts