Gamma-ray burst afterglows: effects of radiative corrections and non-uniformity of the surrounding medium
Gamma-ray burst afterglows: effects of radiative corrections and non-uniformity of the surrounding medium
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DOI：
10.1046/j.1365-8711.1998.01681.x
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发表时间：
1998-06
影响因子：
4.8
通讯作者：
Z. Dai;T. Lu
中科院分区：
文献类型：
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作者：
Z. Dai;T. Lu
伽玛射线暴（GRB）的余辉通常被认为是周围介质中相对论膨胀的火球持续减速的结果。假设火球的膨胀是绝热的，介质的密度是激波半径的幂律函数，即n（ext）与R-k成正比，我们用解析方法研究了一阶辐射修正和介质的非均匀性对伽玛暴余辉的影响。本文首先导出了火球的观测时间、激波半径和洛仑兹因子之间的新关系式：t（ω）= R/4（4 - k）γ（2）c，并导出了火球的同动时间、激波半径和洛仑兹因子之间的新关系式：t（ω）= 2 R/（5 - k）γ c。接下来我们用Blandford & McKee的解析解研究火球的演化。辐射损失可能不会显著影响这种演变。我们进一步导出了新的X射线通量与观测时间之间以及光通量与观测时间之间的标度律。我们利用这些标度律讨论了GRB 970228和GRB 970616的余辉，发现如果电子分布的谱指数为p = 2.5，则GRB 970616的X射线余辉与K = 2的情况很好地拟合。
The afterglow of a gamma-ray burst (GRB) is commonly thought to be the result of continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, i.e. n(ext) proportional to R-k, we study the effects of the first-order radiative correction and the non-uniformity of the medium on a GRB afterglow analytically. We first derive a new relation among the observed time, the shock radius and the Lorentz factor of the fireball: t(+) = R/4(4 - k)gamma(2)c, and also derive a new relation among the comoving time, the shock radius and the Lorentz factor of the fireball: t(co) = 2R/(5 - k)gamma c. We next study the evolution of the fireball by using the analytic solution of Blandford & McKee. The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is p = 2.5, implied from the spectra of GRBs, the X-ray afterglow of GRB 970616 is well fitted by assuming k = 2.