Grimsrud, Ole M. 2009 相对论火球的演化的非平衡态

主要内容:
附录里提到了黑体的相对论谱, 结论是和温度为(\gamma T')相差很小, 为1/gamma的一阶小量.
所以想通过直接观测黑体谱型的变化来推测\gamma的大小的企图是不能实现的.

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Title:		Non-equilibrium effects in steady relativistic e^+e^-gamma winds
Authors:		Grimsrud, Ole M.; Wasserman, Ira
Affiliation:		AA(Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14853, USA), AB(Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14853, USA)
Publication:		Monthly Notices of the Royal Astronomical Society, Volume 300, Issue 4, pp. 1158-1180. (MNRAS Homepage)
Publication Date:		11/1998
Origin:		MNRAS
MNRAS Keywords:		HYDRODYNAMICS, RADIATIVE TRANSFER, GAMMA-RAYS: BURSTS
Abstract Copyright:		(c) 1998 The Royal Astronomical Society
DOI:		10.1046/j.1365-8711.1998.02004.x
Bibliographic Code:		1998MNRAS.300.1158G

Abstract

We consider an ultrarelativistic wind consisting of electron-positron pairs and photons with the principal goal of finding the asymptotic Lorentz factor gamma_∞ for zero baryon number. The wind is assumed to originate at radius r_i where it has a Lorentz factor gamma_i and a temperature T_i sufficiently high to maintain pair equilibrium. As r increases, T decreases and becomes less than the temperature corresponding to the electron mass m_e, after which non-equilibrium effects become important. The pairs, which carry only a small fraction of the total energy, may be accelerated by the photons until tau falls below ~2x10^-5gamma^3/4_i. Radiative transfer calculations show that only at this point do the radiation flux and pressure start to deviate significantly from their blackbody values. The acceleration of the pairs increases gamma by a factor ~45 compared with its value at the photosphere; it is shown to approach gamma_∞~1.4x10^3(r^6_i/10cm)^1/4gamma^{3/4}_iT_i/m_e. The limit of zero baryon number is a good approximation when the mass injection rate Msolar in the flow is below a critical value corresponding to (Esolar/MsolarM)_c,0~5x10^7(r^6_i/10cm)T_i/m_e for fixed energy injection rate E/E. For large baryon loading, (Esolar/Msolar<~Esolar/Msolar)_c,M~350(r_i/10^6cm)^1/4gamma^3/4_iT_i/ m_e, the asymptotic Lorentz factor is gamma_∞~Esolar/Msolar. Surprisingly, increasing Esolar/Msolar from (Esolar/Msolar)_c,M to ∞ only increases gamma_∞ by a factor ~(m_p/m_e)^1/4~6.5, less than an order of magnitude. As Esolar/Msolar increases, the fraction of the energy carried by pairs decreases, reaching ~10^-5gamma^3/4_i as Esolar/Msolar to ∞.