论文标题
银河黑色孔的时空指标和环形波形被暗钉包围
Spacetime metrics and ringdown waveforms for galactic black holes surrounded by a dark matter spike
论文作者
论文摘要
理论模型表明，在星系核心的超级质量黑洞周围存在暗物质尖峰。人们认为，尖峰密度遵守了一个启动的幂定律，该法律从黑洞地平线半径范围内几次开始，并延伸至一千座的顺序，$ r_ \ text {sp} $。我们使用Tolman-Oppenheimer-Volkoff方程式来构建代表被这种暗物质尖峰包围的黑洞的时空度量。我们认为暗物质是一种完美的液体，但对其性质没有其他假设。假定的功率定律密度原则上提供了可以使用的三个参数：Power Law指数$γ_\ text {sp} $，外部半径$ r_ \ r_ \ text {sp} $和尖峰密度$ρ_\ text {dm}^\ text {dm}^\ text {sp}^sp {sp} $ at $ r_ \ r_ \ text sp sp {sp} $ {sp} $。这些反过来决定了尖峰的总质量。我们专注于射手座A*和M87，在尖峰参数上存在一些理论和观察性界限。使用这些边界与从Tolman-Oppenheemer-Volkoff方程获得的度量，我们研究了通过在黑洞扰动的Ringdown阶段发出的引力，检测到这些黑孔周围的暗物质尖峰的可能性。我们的结果表明，如果尖峰与黑洞的质量比大致恒定，那么更大的质量黑洞需要相对较小的尖峰密度才能产生可能可观察到的信号。我们发现，除非其质量大约比现有观测估计值大的数量级，否则通过Ringdown波形检测到M87中的尖峰。但是，鉴于信号随黑洞质量的增加而增加，在不太遥远的将来，可能会观察到更大的银河黑洞。
Theoretical models suggest the existence of a dark matter spike surrounding the supermassive black holes at the core of galaxies. The spike density is thought to obey a power law that starts at a few times the black hole horizon radius and extends to a distance, $R_\text{sp}$, of the order of a kiloparsec. We use the Tolman-Oppenheimer-Volkoff equations to construct the spacetime metric representing a black hole surrounded by such a dark matter spike. We consider the dark matter to be a perfect fluid, but make no other assumption about its nature. The assumed power law density provides in principle three parameters with which to work: the power law exponent $γ_\text{sp}$, the external radius $R_\text{sp}$, and the spike density $ρ_\text{DM}^\text{sp}$ at $R_\text{sp}$. These in turn determine the total mass of the spike. We focus on Sagittarius A* and M87 for which some theoretical and observational bounds exist on the spike parameters. Using these bounds in conjunction with the metric obtained from the Tolman-Oppenheimer-Volkoff equations, we investigate the possibility of detecting the dark matter spikes surrounding these black holes via the gravitational waves emitted at the ringdown phase of black hole perturbations. Our results suggest that if the spike to black hole mass ratio is roughly constant, greater mass black holes require relatively smaller spike densities to yield potentially observable signals. We find that is unlikely for the spike in M87 to be detected via the ringdown waveform with currently available techniques unless its mass is roughly an order of magnitude larger than existing observational estimates. However, given that the signal increases with black hole mass, spikes might be observable for more massive galactic black holes in the not too distant future.
