超大质量黑洞对恒星的破坏：光变曲线真的与$t^{-5/3}$成正比吗？
Stellar disruption by a supermassive black hole: is the light curve really proportional to $t^{-5/3}$?
摘要：
在本文中，我们重新讨论的论点的基础上的时间演变的耀斑预计出现时，恒星被破坏的超大质量黑洞。我们提出了一个简单的分析模型有关的光变曲线的内部密度结构的恒星。因此，我们表明，标准的光曲线比例$t^{-5/3}$只持有在后期的时间。在接近峰值光度时，光变曲线变浅，对于中心集中度更高的恒星（如太阳型），光变曲线偏离$t^{-5/3}$的程度更大。我们测试我们的模型数值模拟几个恒星模型，由简单的多变球指数$γ$的潮汐破裂。模拟同意与分析模型给出两个考虑。首先，恒星在到达近心点时有些膨胀，因为黑洞的潮汐场有效地减少了引力。这是很好地描述了同系膨胀的一个因素，成为较小的多变指数变得更大。第二，对于大多变指数的翅膀出现在尾部的能量分布，表明一些材料被推离抛物线轨道进一步的冲击潮汐尾巴。在我们所有的模拟中，$t^{-5/3}$光变曲线只在后期才能达到。特别是我们预测，对于太阳型恒星，这只发生在光度从峰值下降至少两个星等之后。我们讨论了我们的结果，在最近的观测耀斑，否则静止的星系，并注意到这些结果的依赖进一步的参数，如恒星/黑洞的质量比和恒星轨道。
英文摘要：
In this paper we revisit the arguments for the basis of the time evolution of the flares expected to arise when a star is disrupted by a supermassive black hole. We present a simple analytic model relating the lightcurve to the internal density structure of the star. We thus show that the standard lightcurve proportional to $t^{-5/3}$ only holds at late times. Close to the peak luminosity the lightcurve is shallower, deviating more strongly from $t^{-5/3}$ for more centrally concentrated (e.g. solar--type) stars. We test our model numerically by simulating the tidal disruption of several stellar models, described by simple polytropic spheres with index $γ$. The simulations agree with the analytical model given two considerations. First, the stars are somewhat inflated on reaching pericentre because of the effective reduction of gravity in the tidal field of the black hole. This is well described by a homologous expansion by a factor which becomes smaller as the polytropic index becomes larger. Second, for large polytropic indices wings appear in the tails of the energy distribution, indicating that some material is pushed further away from parabolic orbits by shocks in the tidal tails. In all our simulations, the $t^{-5/3}$ lightcurve is achieved only at late stages. In particular we predict that for solar type stars, this happens only after the luminosity has dropped by at least two magnitudes from the peak. We discuss our results in the light of recent observations of flares in otherwise quiescent galaxies and note the dependence of these results on further parameters, such as the star/hole mass ratio and the stellar orbit.
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