Pe'er 2007 用火球热成份定伽玛暴初始大小和Lorentz因子 3

主要内容:
就是用简单的黑体辐射的公式，不过是相对论性的（加上观测温度是可以测定的），含有R和\Gamma，从而定出二者。

具体推导过程:


精彩摘抄:


文章信息:
A new method of determining the initial size and Lorentz factor of gamma-ray burst fireballs using a thermal emission component

Authors: Asaf Pe'er, Felix Ryde, Ralph A.M.J. Wijers, Peter Mészáros, Martin J. Rees

(Submitted on 28 Mar 2007)

Abstract: In recent years there is increasing evidence for a thermal component in the gamma- and X-ray spectrum of the prompt emission phase in gamma-ray bursts. The temperature and flux of the thermal component show a characteristic break in the temporal behavior after few seconds. We show here, that measurements of the temperature and flux of the thermal component at early times (before the break) allow the determination of the values of two of the least restricted fireball model parameters: the size at the base of the flow and the outflow bulk Lorentz factor. Relying on the thermal emission component only, this measurement is insensitive to the inherent uncertainties of previous estimates of the bulk motion Lorentz factor. We give specific examples of the use of this method: for GRB970828 at redshift z=0.9578, we show that the physical size at the base of the flow is r_0 = (3.3+-2.1)*10^8 cm and the Lorentz factor of the flow is \Gamma = 305+-28, and for GRB990510 at z=1.619, r_0=(1.9+-2.0)*10^8 cm and \Gamma=384+-71.

Comments:

4 pages, 1 figure; submitted to ApJ Letters

Subjects:

Astrophysics (astro-ph)

Cite as:

arXiv:astro-ph/0703734v1

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Title:		A New Method of Determining the Initial Size and Lorentz Factor of Gamma-Ray Burst Fireballs Using a Thermal Emission Component
Authors:		Pe'er, Asaf; Ryde, Felix; Wijers, Ralph A. M. J.; Mészáros, Peter; Rees, Martin J.
Affiliation:		AA(Astronomical Institute ``Anton Pannekoek,'' 1098SJ Amsterdam, Netherlands; apeer@science.uva.nl.), AB(Department of Physics, Royal Institute of Technology, AlbaNova, SE-106 91 Stockholm, Sweden.), AC(Astronomical Institute ``Anton Pannekoek,'' 1098SJ Amsterdam, Netherlands; apeer@science.uva.nl.), AD(Department of Astronomy and Astrophysics, Department of Physics, Pennsylvania State University, University Park, PA 16802.), AE(Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK.)
Publication:		The Astrophysical Journal, Volume 664, Issue 1, pp. L1-L4. (ApJ Homepage)
Publication Date:		07/2007
Origin:		UCP
ApJ Keywords:		Gamma Rays: Bursts, Gamma Rays: Theory, Plasmas, Radiation Mechanisms: Nonthermal, Radiation Mechanisms: Thermal
Abstract Copyright:		(c) 2007: The American Astronomical Society
DOI:		10.1086/520534
Bibliographic Code:		2007ApJ...664L...1P

Abstract

In recent years, increasing evidence has emerged for a thermal component in the γ- and X-ray spectrum of the prompt emission phase in gamma-ray bursts. The temperature and flux of the thermal component show a characteristic break in the temporal behavior after a few seconds. We show here that measurements of the temperature and flux of the thermal component at early times (before the break) allow the determination of the values of two of the least restricted fireball model parameters: the size at the base of the flow and the outflow bulk Lorentz factor. Relying on the thermal emission component only, this measurement is insensitive to the inherent uncertainties of previous estimates of the bulk motion Lorentz factor. We give specific examples of the use of this method: for GRB 970828 at redshift z=0.9578, we show that the physical size at the base of the flow is r₀=(2.9+/-1.8)×10⁸Y^-3/2₀ cm and the Lorentz factor of the flow is Γ=(305+/-28)Y^1/4₀, and for GRB 990510 at z=1.619, r₀=(1.7+/-1.7)×10⁸Y^-3/2₀ cm and Γ=(384+/-71)Y^1/4₀, where Y=1Y₀ is the ratio between the total fireball energy and the energy emitted in γ-rays.

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