宇宙黑洞的粗略估计最大质量
Crudely Estimated Maximum Mass for a Cosmological Black Hole
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中文总结 AI 辅助
该研究通过N体模拟结合引力辐射，估算出等质量超大质量黑洞双星的并合质量上限约为$1.4\times 10^{14} M_\bigodot$，推测这是当前宇宙黑洞质量的极粗略上限。
中文摘要 AI 辅助
M. Milosavljevic与D. Merritt的N体模拟表明，对于近圆轨道的超大质量黑洞双星，在引力波辐射占主导前，其并合率会使无量纲轨道相对速度平方$(v/c)^2$随时间近似线性增长，速率约为210 Gyr的倒数（约为当前宇宙年龄的15倍），且几乎与双星质量无关。仅靠该过程无法使黑洞在当前时间并合，但结合引力辐射后，等质量黑洞双星的并合质量上限约为$1.4\times 10^{14} M_\bigodot$，这可被视为当前宇宙黑洞质量的极粗略上限。该研究还指出，周期大于约10万年的并合超大质量黑洞双星的引力波应变会减小。
英文摘要
$N$-body simulations by M.~Milosavljevic and D.~Merritt \cite{Milosavljevic:2001vi} suggest that for supermassive black hole binaries in their expected nearly circular orbits, before gravitational wave emission dominates, the inspiral rate causes the dimensionless orbital relative velocity squared, $(v/c)^2$, to increase nearly linearly with time at a rate that is approximately the inverse of 210 Gyr (about 15 times the present age of the universe), nearly independently of the mass of the binary. This by itself would not lead to coalescence by the present time, but when it is augmented by gravitational radiation, it can lead to coalescence for equal-mass black hole binaries up to about $1.4\times 10^{14} M_\odot$, which might then be conjectured to be a very crude upper limit to the mass of black holes in our universe at the present time. This also suggests that the gravitational wave strain from coalescing supermassive black hole binaries should decrease for wave periods greater than about 100\,000 years.
