标题： 关于相对论引力对潮汐瓦解事件率的影响 显示英文标题

标题： On the impact of relativistic gravity on the rate of tidal disruption events

摘要： 由超大质量黑洞（SMBH）潮汐撕裂恒星探测相对论引力。 在未来十年内，观测到的潮汐瓦解事件（TDE）的数量将增加几个数量级，从而允许对SMBH和恒星群体的性质进行统计推断。 在这里，我们分析了在史瓦西几何中遇到SMBH的恒星近日点距离的概率分布函数，其中结果完全解析，并且考虑了克尔度规。 从这个分析中，我们计算了可观察到的TDE数量，定义为那些进入潮汐半径 $r_{\rm t}$ 但超出直接捕获半径的恒星（通常情况下，直接捕获半径大于视界半径）。 我们发现，相对论效应导致近日点距离为 $r_{\rm p} \lesssim 10\,r_{\rm g}$ 的恒星数量急剧下降，其中 $r_{\rm g} = GM/c^2$，并且对于最大自旋的SMBH，该距离处的 $r_{\rm p}$ 分布函数按 $f_{\rm r_{\rm p}}\propto r_{\rm p}^{4/3}$ 缩放，或者以 $\beta \equiv r_{\rm t}/r_{\rm p}$ 表示时按 $f_{\beta} \propto \beta^{-10/3}$ 缩放。 我们发现，自旋对潮 disruption 事件（TDE）比例的影响很小，直到极高质量端，在该端点处，发生率并非完全为零而是很小（相对论效应不存在时预期发生率的$\lesssim 1\%$）。如果 TDE 的前身天体反映了主要的低质量恒星群体，因此具有$\lesssim 1M_{\odot}$质量，则预计在$10^{7}M_{\odot}$以上，TDE 的发生率会大幅下降，且这种下降与自旋基本无关。 显示英文摘要

摘要： The tidal disruption of stars by supermassive black holes (SMBHs) probes relativistic gravity. In the coming decade, the number of observed tidal disruption events (TDEs) will grow by several orders of magnitude, allowing statistical inferences of the properties of the SMBH and stellar populations. Here we analyse the probability distribution functions of the pericentre distances of stars that encounter an SMBH in the Schwarzschild geometry, where the results are completely analytic, and the Kerr metric. From this analysis we calculate the number of observable TDEs, defined to be those that come within the tidal radius $r_{\rm t}$ but outside the direct capture radius (which is, in general, larger than the horizon radius). We find that relativistic effects result in a steep decline in the number of stars that have pericenter distances $r_{\rm p} \lesssim 10\,r_{\rm g}$, where $r_{\rm g} = GM/c^2$, and that for maximally spinning SMBHs the distribution function of $r_{\rm p}$ at such distances scales as $f_{\rm r_{\rm p}}\propto r_{\rm p}^{4/3}$, or in terms of $\beta \equiv r_{\rm t}/r_{\rm p}$ scales as $f_{\beta} \propto \beta^{-10/3}$. We find that spin has little effect on the TDE fraction until the very high-mass end, where instead of being identically zero the rate is small ($\lesssim 1\%$ of the expected rate in the absence of relativistic effects). Effectively independent of spin, if the progenitors of TDEs reflect the predominantly low-mass stellar population and thus have masses $\lesssim 1M_{\odot}$, we expect a substantial reduction in the rate of TDEs above $10^{7}M_{\odot}$.