Liang 2009 Gamma_0-E_iso关系

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其实文章中还有其他很多统计，不过这个最有兴趣.
差不多 Gamma~E_iso^0.25

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Title:		Constraining GRB Initial Lorentz Factor with the Afterglow Onset Feature and Discovery of a Tight Gamma_0-E_iso Correlation
Authors:		Liang, En-Wei; Yi, Shuang-xi; Zhang, Jin; LV, Hou-Jun; Zhang, Bin-Bin; Zhang, Bing
Publication:		eprint arXiv:0912.4800
Publication Date:		12/2009
Origin:		ARXIV
Keywords:		Astrophysics - High Energy Astrophysical Phenomena, Astrophysics - Cosmology and Extragalactic Astrophysics
Comment:		15 pages, including 4 tables and 7 figures, Submitted to ApJ
Bibliographic Code:		2009arXiv0912.4800L

Abstract

The onset of GRB afterglow is characterized by a smooth bump in the early afterglow lightcurve. We make an extensive search for such a feature. Twenty optically selected GRBs and 12 X-ray selected GRBs are found, among which 17 optically selected GRBs and 2 X-ray-selected GRBs have redshift measurements. We fit the lightcurves with a smooth broken power-law and measure the temporal characteristic timescales of the bumps at FWHM. Strong mutual correlations among these timescales are found, and a dimmer and broader bump tends to peak at a later peak time. The ratio of rising to decaying timescales is almost universal among bursts, but the ratio of the rising time to the peak time varies from 0.3~1. The E_iso is tightly correlated with the peak luminosity and the peak time of the bump in the burst frame. Assuming that the bumps signal the deceleration of the GRB fireballs in a constant density medium, we calculate the initial Lorentz factor (Gamma_0) and the deceleration radius (R_dec) of the GRBs in the optical-selected sample. It is found that Gamma_0 are typically a few hundreds, and the typical deceleration radius is R_dec~10^{17} cm. More intriguingly, a tight correlation between the Gamma_0 and E_iso is found, namely Gamma_0 ~ 195 E_iso, 52}^{0.27} (satisfied for both the optical and X-ray z-known samples). It is helpful to understand GRB physics, and may serve as an indicator of Gamma_0. We find that the early bright X-rays are usually dominated by a different component from the external shock emission, but occasionally (for one case) an achromatic deceleration feature is observed. Components in X-rays would contribute to the diversity of the observed X-ray lightcurves (abridge).

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