标题： 德赫宁黑洞在超微弱矮星系中的晕效应 显示英文标题

标题： Dehnen halo effect on a black hole in an ultra-faint dwarf galaxy

摘要： 在超暗弱矮星系的探测方面最近有了进展，由于其中一些几乎含有99$\%$的纯暗物质，它们可能成为暗物质探索的有用实验室。 这些星系中的大多数不包含居住其中的黑洞。 最近有报告称，一些矮星系可能内部存在黑洞。 在本研究中，我们构建了一个结合Dehnen暗物质晕轮廓的黑洞解，该轮廓常用于矮星系。 我们的目标是找出相对于标准黑洞特性是否存在偏差，这可能会帮助确定超暗弱矮星系中的暗物质轮廓是核心型还是尖峰型。 为了使模型更真实，我们应用了修正的Newman-Janis方法来获得旋转度规。 我们分析了黑洞的特性，如事件视界、能层、类时和零质点的测地线以及黑洞阴影。 利用这些可观测量，结果表明区分暗物质是核心型还是尖峰型存在困难。 为了找到一个能够潜在区分这两种轮廓的可观测量，我们还计算了弱偏转角，以检查Dehnen轮廓在有限距离和远距离近似下的影响。 我们的结果表明，使用弱偏转角在许多数量级上更能潜在地区分这些轮廓。 我们得出结论，尽管矮星系是暗物质主导的区域，但考虑到本文所用的方法，Dehnen轮廓的影响仍然取决于黑洞的质量。 显示英文摘要

摘要： There had been recent advancement toward the detection of ultra-faint dwarf galaxies, which may serve as a useful laboratory for dark matter exploration since some of them contains almost 99$\%$ of pure dark matter. The majority of these galaxies contain no black hole that inhabits them. Recently, there had been reports that some dwarf galaxies may have a black hole within. In this study, we construct a black hole solution combined with the Dehnen dark matter halo profile, which is commonly used for dwarf galaxies. We aim to find out whether there would be deviations relative to the standard black hole properties, which might allow determining whether the dark matter profile in an ultra-faint dwarf galaxy is cored or cuspy. To make the model more realistic, we applied the modified Newman-Janis prescription to obtain the rotating metric. We analyzed the black hole properties such as the event horizon, ergoregion, geodesics of time-like and null particles, and the black hole shadow. Using these observables, the results indicate the difficulty of distinguishing whether the dark matter is cored or cuspy. To find an observable that can potentially distinguish these two profiles, we also calculated the weak deflection angle to examine the effect of the Dehnen profile in finite distance and far approximation. Our results indicate that using the weak deflection angle is far better, in many orders of magnitude, in potentially differentiating these profiles. We conclude that although dwarf galaxies are dark matter-dominated places, the effect on the Dehnen profile is still dependent on the mass of the black hole, considering the method used herein.