嵌入暗物质晕中的黑洞的准正常模：Dehnen(1,4,5/2)与DC14密度剖面分析
Quasinormal Modes of Black Holes Embedded in Dark-Matter Halos: Analysis of Dehnen(1, 4, 5/2) and DC14 Density Profiles
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中文总结 AI 辅助
本文研究嵌入Dehnen(1,4,5/2)与DC14暗物质晕的黑洞的QNM谱，发现晕标度半径对其影响最大，Prony提取频率与六阶WKB结果吻合度高，为研究暗物质环境效应提供了数值框架。
中文摘要 AI 辅助
我们研究周围的暗物质晕如何在静态球对称黑洞的准正常模（QNM）谱上留下印记，考虑两种物理上不同的密度剖面：Dehnen (1,4,5/2)剖面和DC14剖面。两者均遵循双幂律形式，而DC14剖面的形状参数通过星系形成模拟校准，并随恒星与晕质量比$X=\log_{10}(M_*/M_{\rm halo})$变化，该参数控制暗物质晕的内部密度结构。针对两种剖面，我们计算了暗物质晕对度规函数的贡献，以及控制轴向引力（$s=2$）微扰的有效势，并提取了$\ell=2$多极的基态QNM频率。结果表明，在所研究的暗物质晕参数中，晕标度半径$r_s$对QNM谱的影响最大，它重塑了光环附近的有效势垒，并改变了QNM频率的实部与虚部。相比之下，密度归一化对Dehnen剖面的影响相对较小，但对DC14剖面更为重要，这反映了其随$X$值变化的不同内部结构。通过Prony方法提取的频率与六阶WKB结果吻合度极高，在所考虑的参数范围内相对差异始终低于0.04%。据我们所知，这是首次对嵌入DC14暗物质晕中的黑洞进行QNM分析。这些结果证明了QNM谱对周围暗物质环境的敏感性，并为研究此类环境效应提供了一致的数值框架。
英文摘要
We investigate how a surrounding dark-matter halo imprints itself on the QNM spectrum of a static, spherically symmetric black hole, considering two physically distinct density profiles: the Dehnen (1,4,5/2) and DC14 profiles. Both follow double-power-law forms, while the shape parameters of the DC14 profile are calibrated to galaxy-formation simulations and vary with the stellar-to-halo mass ratio $X=\log_{10}(M_*/M_{\rm halo})$, which controls the inner density structure of the halo. For both profiles, we compute the halo contribution to the metric function and the resulting effective potential governing axial gravitational ($s=2$) perturbations, and extract the fundamental QNM frequencies for the $\ell=2$ multipole. Our results show that the halo scale radius $r_s$ has the largest influence on the QNM spectrum among the halo parameters explored, reshaping the effective potential barrier near the light ring and shifting both the real and imaginary parts of the QNM frequencies. The density normalization, by contrast, plays a comparatively minor role for the Dehnen profile but is more consequential for DC14, reflecting the different inner structures associated with its varying $X$ values. The Prony-extracted frequencies show excellent agreement with the sixth-order WKB results, with relative differences remaining below $0.04\%$ across the parameter ranges considered. To our knowledge, this constitutes the first QNM analysis of a black hole embedded in a DC14 dark-matter halo. These results demonstrate the sensitivity of the QNM spectrum to the surrounding dark-matter environment and provide a consistent numerical framework for studying such environmental effects.
