MOCCA-SURVEY数据库I：评估球状星团中BH-BH合并的GW反冲保留分数
MOCCA-SURVEY Database I: Assessing GW kick retention fractions for BH-BH mergers in globular clusters
摘要：
引力波发射的各向异性导致黑洞合并产物获得净动量，反冲速度可达$\sim10^3\text{ km s}^{-1}$，这可能将黑洞从球状星团中踢出。我们估计GW踢保留分数的合并产品假设不同的模型BH自旋大小和方向（MS 0-随机，MS 1-自旋作为质量和金属度的函数，MS 2-恒定值的$0.5$）。我们检查它们如何依赖于BH-BH合并时间和集群的属性。我们分析了GW踢保留分数的影响，中间大规模BH（IMBH）形成的重复合并在GC。我们还计算了合并产物的最终自旋，并研究了它与二元有效自旋的关系。我们利用MOCCA（Monte Carlo Cluster simulAtor）GC模拟的数据得到了一个真实的BH-BH合并样本，根据所研究的模型赋予每个BH自旋值，并根据最新的理论公式计算了反冲速度和最终自旋。我们发现，对于物理驱动的模型，GW反冲保留分数约为$30\%$，并显示对自旋假设的小依赖，但更倾向于集群属性。特别是，我们发现了一个强大的依赖GW踢保留分数集群密度。我们还表明，GW踢保留分数是高的，在最后的生命阶段的集群，但在开始低。最后，我们导出了原始双星的最终自旋与有效自旋之间的关系式，以及动力学双星的最大有效自旋与最终自旋之间的关系式。
英文摘要：
Anisotropy of gravitational wave (GW) emission results in a net momentum gained by the black hole (BH) merger product, leading to a recoil velocity up to $\sim10^3\text{ km s}^{-1}$, which may kick it out of a globular cluster (GC). We estimate GW kick retention fractions of merger products assuming different models for BH spin magnitude and orientation (MS0 - random, MS1 - spin as a function of mass and metalicity, MS2 - constant value of $0.5$). We check how they depend on BH-BH merger time and properties of the cluster. We analyze the implications of GW kick retention fractions on intermediate massive BH (IMBH) formation by repeated mergers in a GC. We also calculate final spin of the merger product, and investigate how it correlates with effective spin of the binary. We used data from MOCCA (MOnte Carlo Cluster simulAtor) GC simulations to get a realistic sample of BH-BH mergers, assigned each BH spin value according to a studied model, and calculated recoil velocity and final spin based on most recent theoretical formulas. We discovered that for physically motivated models, GW kick retention fractions are about $30\%$ and display small dependence on assumptions about spin, but are much more prone to cluster properties. In particular, we discovered a strong dependence of GW kick retention fractions on cluster density. We also show that GW kick retention fractions are high in final life stages of the cluster, but low at the beginning. Finally, we derive formulas connecting final spin with effective spin for primordial binaries, and with maximal effective spin for dynamical binaries.
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