主要内容:
以前的解析解认为在gamma=1/theta_j的时候就开始进入指数阶段，侧向膨胀很显著；但数值模拟发现不是这样的。Granot和Piran给出了新的解析解，得到了和数值解一致的结果。
结果是再共动系中侧向膨胀的速度 beta_theta ~ 1/(Gamma^2 delta_theta) ~ 1/(Gamma^2 theta)
精彩摘抄:
文章信息:
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- · arXiv e-print (arXiv:1109.6468)
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| Title: |
| On the lateral expansion of GRB jets |
| Authors: |
| Granot, Jonathan; Piran, Tsvi |
| Publication: |
| eprint arXiv:1109.6468 |
| Publication Date: |
| 09/2011 |
| Origin: |
| ARXIV |
| Keywords: |
| Astrophysics - High Energy Astrophysical Phenomena |
| Comment: |
| 33 pages, 11 figures, submitted to MNRAS |
| Bibliographic Code: |
| 2011arXiv1109.6468G |
Abstract
The dynamics of GRB jets during the afterglow phase have an important effect on the interpretation of their observations and for inferring key physical parameters such as their true energy and event rate. Semi-analytic models generally predict a fast lateral expansion, where the jet opening angle asymptotically grows exponentially with its radius. Numerical simulations, however, show a much more modest lateral expansion, where the jet retains memory of its initial opening angle for a very long time, and the flow remains non-spherical until it becomes sub-relativistic, and only then gradually approaches spherical symmetry. Here we suggest a new analytic model based on a new physically derived recipe for the lateral expansion. We also generalize the model by relaxing the common approximations of ultra-relativistic motion and a narrow jet opening angle. We find that the new analytic model fits much better the results of numerical simulations, mainly because it remains valid also in the mildly relativistic, quasi spherical regime. This model shows that for modest initial jet half-opening angles, \theta_0, the outflow is not sufficiently ultra-relativistic when its Lorentz factor reaches \Gamma = 1/\theta_0 and therefore the sideways expansion is rather slow, showing no rapid, exponential phase. On the other hand, we find that jets with a very narrow initial half-opening angle, \theta_0 << 1, which are still ultra-relativistic at \Gamma = 1/\theta_0, do show a phase of rapid, exponential lateral expansion. However, even such jets that expand sideways exponentially are still not spherical when they become sub-relativistic.
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