AI 中文总结
该研究利用偏心极端质量比旋进源引力波，结合解析近似波形框架、贝叶斯推断与费舍尔矩阵分析，揭示暗物质尖峰的约束特性，为LISA探测黑洞周围暗物质分布提供理论依据。
AI 中文摘要
极端质量比旋进源（EMRIs）是探测大质量黑洞周围天体环境的灵敏探针。我们在解析近似（analytic-kludge）波形框架内，研究利用偏心EMRI引力波推断暗物质（DM）尖峰的问题，其中包含DM诱导的动力学摩擦与长期轨道演化中的吸积过程。我们采用马尔可夫链蒙特卡洛采样开展贝叶斯参数估计，并辅以费舍尔矩阵分析。研究发现，更陡峭的DM尖峰可产生更强的累积波形修正，能大幅提升对尖峰斜率α_DM的测量精度；更重要的是，约束结果对轨道偏心率呈现非单调依赖关系：中等偏心率下，高阶谐波可帮助打破e_LSO与α_DM之间的简并，而高偏心率系统中该关联仍可能存在或参数恢复效果会变差。这些结果表明，偏心EMRI的谐波结构可为未来LISA观测探测大质量黑洞周围的暗物质分布提供重要信息。
英文摘要
Extreme-mass-ratio inspirals (EMRIs) provide sensitive probes of the astrophysical environments surrounding massive black holes. We investigate the inference of dark-matter (DM) spikes with eccentric EMRI gravitational waves within the analytic-kludge waveform framework, including DM-induced dynamical friction and accretion in the secular orbital evolution. We perform Bayesian parameter estimation using Markov-chain Monte Carlo sampling, complemented by Fisher-matrix analyses. We find that steeper DM spikes produce stronger accumulated waveform modifications and substantially improve the measurement of the spike slope $α_{\rm DM}$. More importantly, the constraints exhibit a nonmonotonic dependence on orbital eccentricity. At moderate eccentricity, higher harmonics help break the degeneracy between $e_{\rm LSO}$ and $α_{\rm DM}$, whereas this correlation can persist or the parameter recovery can deteriorate for highly eccentric systems. These results demonstrate that the harmonic structure of eccentric EMRIs can provide valuable information for probing DM distributions around massive black holes with future LISA observations.
Comments20 pages, 10 figures
