Transparency Parameters From Relativistically Expanding Outflows

Abstract

In many gamma-ray bursts a distinct blackbody spectral component is present, which is attributed to the emission from the photosphere of a relativistically expanding plasma. The properties of this component (temperature and flux) can be linked to the properties of the outflow and have been presented in the case where there is no subphotospheric dissipation and the photosphere is in coasting phase. First, we present the derivation of the properties of the outflow for finite winds, including when the photosphere is in the accelerating phase. Second, we study the effect of localized sub-photospheric dissipation on the estimation of the parameters. Finally, we apply our results to GRB 090902B. We find that during the first epoch of this burst the photosphere is most likely to be in the accelerating phase, leading to smaller values of the Lorentz factor than the ones previously estimated. For the second epoch, we find that the photosphere is likely to be in the coasting phase.

Spectropolarimetric analysis of prompt emission of GRB 160325A: jet with evolving environment of internal shocks

“…These detections also supported the idea that within the picture of classical fireball model, the thermal emission from the photosphere can be either subdominant or sometimes dominant depending on how much adiabatic cooling the outflow has undergone in the coasting phase before it reaches the photosphere. The spectral analysis of GRB 090902B showed that a narrow hard spectrum evolved into a broader one with time (Ryde et al 2010;Ryde et al 2011;Bromberg et al 2011;Bégué & Iyyani 2014). This pointed towards the possibility of subphotospheric dissipation, which when functional throughout the outflow till the photosphere, results in a significant broadening of the spectrum from that of a thermal emission and can resemble a typical Band function (Giannios 2008; Lazzati et al 2009;Beloborodov 2011;Beloborodov 2013;Bégué & Pe'er 2015).…”

Diffusive photospheres in gamma-ray bursts

“…Since the emitter radius for the photon thin outflows is the diffusion radius R = RD, from eqs. (8) and (15) one obtains, see also (Bégué & Iyyani 2014)…”

Photospheric emission in gamma-ray bursts

“…12). 88,[208][209][210] While in many works it is assumed that r 0 is ≈ few gravitational radii, in fact, there is no evidence for that in the data; the shortest variability time scale observed in GRBs, δt = r 0 /c > ∼ 10 ms, with average value of ≈ 500 ms. 211 These results are therefore consistent with the results obtained by analyzing the thermal data.…”