AI 中文总结
本文利用GRAVITY对S2轨道的天体测量限制，得到银心0.02秒差距内黑洞尖峰的EMRI、EMRB率上限，其结果可扩展至宇宙学族群，且EMRI背景可被LISA探测，凸显了天体测量与引力波观测的互补性。
AI 中文摘要
银河系中心大质量黑洞周围的恒星轨道为探测银心致密天体族群及毫赫兹引力波源提供了独特的局部探针：近心点经过会产生极端质量比暴（EMRB），而成功捕获则会形成极端质量比旋近（EMRI）。本文利用GRAVITY观测站对恒星S2轨道扰动的最新天体测量限制，对约0.02秒差距内的恒星质量黑洞尖峰归一化设定上限。对于基于该数据的基准10倍太阳质量Bahcall-Wolf族群，我们得到EMRI率上限约为2.4×10²每十亿年，银河系可探测EMRB率上限约为0.2每年，这一结果处于以往理论估计的宽泛范围内。假设尖峰归一化与中心黑洞质量呈自相似标度关系，我们将该校准扩展至宇宙学族群，所得EMRI背景在所有考虑场景下均可被LISA探测，而更平缓的EMRB背景在低质量星系核中质量分异显著时可达到LISA灵敏度。我们的结果凸显了高精度恒星天体测量与毫赫兹引力波观测的互补性。
英文摘要
Stellar orbits around the massive black hole at the center of our galaxy provide a unique local probe of the compact-object population in the Galactic Centre and, consequently, of the sources of millihertz gravitational waves: periapse passages lead to extreme-mass-ratio bursts (EMRBs) while successful captures lead to extreme-mass ration inspirals (EMRIs). In this paper we use recent astrometric limits from the GRAVITY observatory on perturbations of the orbit of the star S2 to place upper limits on the normalisation of a stellar-mass black-hole cusp within ${\sim} \,0.02\,\mathrm{pc}$. For a benchmark $10\,M_\odot$ Bahcall--Wolf population anchored to this data, we obtain upper limits of ${\sim} \,2.4\times10^{2}\,\mathrm{Gyr}^{-1}$ on the EMRI rate and ${\sim} \, 0.2\,\mathrm{yr}^{-1}$ on the detectable EMRB rate in the Milky Way, which fall within the broad range of previous theoretical estimates. Assuming a self-similar scaling of the cusp normalisation with central black-hole mass, we extend this calibration to cosmological populations. The resulting EMRI background is detectable by LISA across all scenarios considered, whereas the flatter EMRB background can reach LISA sensitivity when mass segregation is efficient in low-mass galactic nuclei. Our results highlight the complementarity of precision stellar astrometry and millihertz gravitational-wave observations.
Comments22 pages, 10 figures; Claude Code-generated repository reproducing all results at https://github.com/andrea0292/s2-to-lisa
