论文标题
重力布朗运动作为不均匀扩散：球状簇中的黑洞种群
Gravitational Brownian motion as inhomogeneous diffusion: black hole populations in globular clusters
论文作者
论文摘要
观察性证据支持的最新理论和数值发展强烈表明，许多球状簇在其中心拥有黑洞（BH）人群。这与先前的长期信念相反，即BH子集群在核心崩溃并与集群中解耦后会蒸发。在这项工作中，我们提出，恒星重力场的波动产生的不均匀布朗运动可能充当一种机制，增加了BH人群的稳定压力。我们认为，在具有空间变化的扩散系数和温度的不均匀培养基中，布朗运动的扩散方程也最初是由van kampen发现的，也适用于自我散热系统。将固定相空间概率分布应用于沉浸在坠落的球状群集中的单个BH上，我们推断它可能会在$ \ sim 0.05，\，0.1，0.1，0.5 {\ rm pc} $中，质量为$ m _ {\ rm b} \ rm b} \ sim 10^3， M} _ \ odot $。此外，我们发现固定恒星平均重力场的波动足以稳定在Spitzer不稳定性阈值之上的BH种群。然而，我们确定了一个不稳定，其起源取决于Spitzer参数，$ s =（m _ {\ rm b}/m _ \ star）（m _ {\ rm b}/m_ \ star）/m _ \ star）^{3/2} {3/2}，$ and $ b = p =ρ_{\ rm b b} {\ rm b} {\ rm b}（\ rm b} 0） （4πr_c^3/m_b）（m_ \ star/m _ {\ rm b}）^{3/2} $，其中$ρ_{\ rm b}（0）$是布朗人总体中央密度。对于Plummer Sphere，不稳定发生在$（B，S）=（140,0.25）$。对于$ b> 140，$我们得到非常cuspy的BH子集群概况，仅支持波动就不稳定。对于$ s> 0.25，$没有证据表明基于不均匀扩散方程的BH人群的任何固定状态。
Recent theoretical and numerical developments supported by observational evidence strongly suggest that many globular clusters host a black hole (BH) population in their centers. This stands in contrast to the prior long-standing belief that a BH subcluster would evaporate after undergoing core collapse and decoupling from the cluster. In this work, we propose that the inhomogeneous Brownian motion generated by fluctuations of the stellar gravitational field may act as a mechanism adding a stabilizing pressure to a BH population. We argue that the diffusion equation for Brownian motion in an inhomogeneous medium with spatially varying diffusion coefficient and temperature, which was first discovered by Van Kampen, also applies to self-gravitating systems. Applying the stationary phase space probability distribution to a single BH immersed in a Plummer globular cluster, we infer that it may wander as far as $\sim 0.05,\,0.1,\,0.5{\rm pc}$ for a mass of $m_{\rm b} \sim 10^3,\,10^2,\,10{\rm M}_\odot$, respectively. Furthermore, we find that the fluctuations of a fixed stellar mean gravitational field are sufficient to stabilize a BH population above the Spitzer instability threshold. Nevertheless, we identify an instability whose onset depends on the Spitzer parameter, $S = (M_{\rm b}/M_\star) (m_{\rm b}/m_\star)^{3/2} ,$ and parameter $B = ρ_{\rm b}(0) (4πr_c^3/M_b)(m_\star/m_{\rm b})^{3/2} $, where $ρ_{\rm b}(0)$ is the Brownian population central density. For a Plummer sphere, the instability occurs at $(B,S) = (140,0.25)$. For $B > 140,$ we get very cuspy BH subcluster profiles that are unstable with regard to the support of fluctuations alone. For $S > 0.25,$ there is no evidence of any stationary states for the BH population based on the inhomogeneous diffusion equation.
