[论文解读] Evolution of Galactic Nuclei. I. orbital evolution of IMBH

Tatsushi Matsubayashi, Junichiro Makino+1 more|CERN Bulletin|Nov 29, 2005

Astrophysical Phenomena and Observations被引用 45

一句话总结

本文研究了星系潮汐场破坏星团后，中等质量黑洞（IMBH）的轨道演化。通过大规模N体模拟，发现当IMBH到达约0.01 pc的半径时，其质量与周围恒星质量相等，导致动力摩擦停止，轨道偏心率显著增加。这促使IMBH通过引力波辐射迅速与中心超大质量黑洞（SMBH）合并，合并 timescale 缩短至100万年以内，使此类事件可被DECIGO（每年约50次）和LISA（每年5至50次）探测到。

ABSTRACT

Resent observations and theoretical interpretations suggest that IMBHs (intermediate-mass black hole) are formed in the centers of young and compact star clusters born close to the center of their parent galaxy. Such a star cluster would sink toward the center of the galaxy, and at the same time stars are stripped out of the cluster by the tidal field of the parent galaxy. We investigated the orbital evolution of the IMBH, after its parent cluster is completely disrupted by the tidal field of the parent galaxy, by means of large-scale N-body simulations. We constructed a model of the central region of our galaxy, with an SMBH (supermassive black hole) and Bahcall-Wolf stellar cusp, and placed an IMBH in a circular orbit of radius 0.086pc. The IMBH sinks toward the SMBH through dynamical friction, but dynamical friction becomes ineffective when the IMBH reached the radius inside which the initial stellar mass is comparable to the IMBH mass. This is because the IMBH kicks out the stars. This behavior is essentially the same as the loss-cone depletion observed in simulations of massive SMBH binaries. After the evolution through dynamical friction stalled, the eccentricity of the orbit of the IMBH goes up, resulting in the strong reduction in the merging timescale through gravitational wave radiation. Our result indicates that the IMBHs formed close to the galactic center can merge with the central SMBH in short time. The number of merging events detectable with DECIGO is estimated to be around 50 per year. Event rate for LISA would be similar or less, depending on the growth mode of IMBHs.

研究动机与目标

• 确定星团被星系潮汐场完全破坏后，IMBH的后破坏轨道演化。
• 评估IMBH通过引力波辐射与中心超大质量黑洞（SMBH）合并的timescale。
• 估算未来引力波探测器（如DECIGO和LISA）可探测到的IMBH-SMBH合并事件率。
• 研究损失锥耗尽和恒星散射在驱动IMBH轨道偏心率增长中的作用。

提出的方法

• 在银河系中心进行了包含SMBH和Bahcall-Wolf恒星晕的大规模N体模拟。
• 将IMBH置于距SMBH 0.086 pc的圆形轨道上，并在星团破坏后追踪其轨道演化。
• 使用动力摩擦timescale公式：$ t_{\text{fric}} \simeq \frac{2.38 \times 10^8}{\ln\Lambda} \left(\frac{r}{30~\text{pc}}\right)^2 \left(\frac{\sigma}{100~\text{km~s}^{-1}}\right) \left(\frac{10^5~M_\odot}{M_c}\right) $ yr。
• 使用Peters公式模拟引力波驱动的合并timescale：$ t_{\text{gr}} \simeq 6.3 \times 10^{13} F(e) \left(\frac{a}{0.01~\text{pc}}\right)^4 \left(\frac{M_S}{3 \times 10^6~M_\odot}\right)^{-2} \left(\frac{M_I}{3 \times 10^3~M_\odot}\right)^{-1} $ yr。
• 分析轨道偏心率的演化及其对引力波辐射效率的影响。

实验结果

研究问题

• RQ1 星团被星系潮汐场完全破坏后，IMBH的轨道演化将如何变化？
• RQ2 IMBH的动力摩擦在何处变得无效？原因是什么？
• RQ3 偏心率的增长如何影响IMBH-SMBH系统的引力波合并timescale？
• RQ4 DECIGO和LISA可探测到的IMBH-SMBH合并事件率预期是多少？其与SMBH生长模式的关系如何？

主要发现

• 当IMBH到达约0.01 pc的半径时，其质量与周围恒星质量相等，导致动力摩擦停止，阻止其进一步向内迁移。
• 在此半径处，IMBH开始驱逐周围恒星，引发损失锥耗尽，导致轨道偏心率显著增加。
• IMBH轨道的偏心率趋近于1，使引力波合并timescale缩短至100万年以内。
• 当偏心率趋近于1时，引力波驱动的合并timescale降至$<10^6$年，使IMBH能迅速与SMBH并合。
• 估算显示，DECIGO的事件率约为每年50次，而LISA的事件率在5至50次/年之间，具体取决于SMBH的生长模式。
• 该机制通过类似的恒星散射过程，解释了围绕Sgr A*观测到的高偏心率恒星（如S2，e ≈ 0.87）的成因。