Gravitational Brownian motion as inhomogeneous diffusion: black hole populations in globular clusters

Abstract

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 $\sim 0.05,0.1,0.5\mathrm{pc}$ for a mass of $m_{\mathrm{b}}\sim 10^3,10^2,10{\mathrm{M}}_{\odot }$, 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, $S=(M_{\mathrm{b}}/M_{\star })(m_{\mathrm{b}}/m_{\star }{)}^{3/2},$ and parameter $B={\rho }_{\mathrm{b}}(0)(4\pi r_c^3/M_b)(m_{\star }/m_{\mathrm{b}}{)}^{3/2}$, where ${\rho }_{\mathrm{b}}(0)$ 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.

arXiv commentSimulation results included in revised version. Accepted in Astronomy & Astrophysics

References in corpus (49)

• The Gravitational Million-Body Problem
• Resonant Relaxation in Stellar Systems
• The Dynamical Evolution of Stellar Black Holes in Globular Clusters
• The DRAGON simulations: globular cluster evolution with a million stars
• Two stellar-mass black holes in the globular cluster M22
• A black hole in a globular cluster
• Multi-physics simulations using a hierarchical interchangeable software interface
• The Astrophysical Multipurpose Software Environment
• A detached stellar-mass black hole candidate in the globular cluster NGC 3201
• Dynamical evolution of black hole sub-systems in idealised star clusters
• A multiphysics and multiscale software environment for modeling astrophysical systems
• Black holes and core expansion in massive star clusters
• A Radio-Selected Black Hole X-ray Binary Candidate in the Milky Way Globular Cluster M62
• Retention of Stellar-Mass Black Holes in Globular Clusters
• Deep radio imaging of 47 Tuc identifies the peculiar X-ray source X9 as a new black hole candidate
• MOCCA-SURVEY Database I: Galactic Globular Clusters Harbouring a Black Hole Subsystem
• Core Formation by a Population of Massive Remnants
• Binary Black Holes in Dense Star Clusters: Exploring the Theoretical Uncertainties
• MOCCA-SURVEY Database I. Unravelling black hole subsystems in globular clusters
• How initial size governs core collapse in globular clusters
• The ultracompact nature of the black hole candidate X-ray binary 47 Tuc X9
• Dynamics of a Massive Black Hole at the Center of a Dense Stellar System
• Million-Body Star Cluster Simulations: Comparisons between Monte Carlo and Direct $N$-body
• Kinetic theory of long-range interacting systems with angle-action variables and collective effects
• How black holes shape globular clusters: Modeling NGC 3201
• Kinetic theory of spatially inhomogeneous stellar systems without collective effects
• Evidence for a Stellar Disruption by an IMBH in an Extragalactic Globular Cluster
• A Dynamical Survey of Stellar-Mass Black Holes in 50 Milky Way Globular Clusters
• A new Fokker-Planck approach for relaxation-driven evolution of galactic nuclei
• Brownian Motion of Black Holes in Dense Nuclei
• The Maveric Survey: a Red Straggler Binary with an Invisible Companion in the Galactic Globular Cluster M10
• Effects of Wandering on the Coalescence of Black Hole Binaries in Galactic Centers
• From cusps to cores: a stochastic model
• Predicting Stellar-Mass Black Hole Populations in Globular Clusters
• Brownian motion of massive black hole binaries and the final parsec problem
• On the formation of compact, massive sub-systems in stellar clusters and its relation with intermediate mass black holes
• Observational Evidence for a Dark Side to NGC5128's Globular Cluster System
• The effect of fluctuating fuzzy axion haloes on stellar dynamics: a stochastic model
• Brownian Motion in Gravitationally-Interacting Systems
• Isotropic-Nematic Phase Transitions in Gravitational Systems
• Relaxation in self-gravitating systems
• Evidence of non-luminous matter in the center of M62
• A variable ultraluminous X-ray source in a globular cluster in NGC 4649
• New XMM-Newton analysis of three bright X-ray sources in M31 globular clusters, including a new black hole candidate
• VVV Survey Observations of a Microlensing Stellar Mass Black Hole Candidate in the Field of the Globular Cluster NGC 6553
• A Note on Gravitational Brownian Motion
• Relaxation of spherical stellar systems
• Statistical Mechanics of Gravitational Systems with Regular Orbits: Rigid Body Model of Vector Resonant Relaxation
• Order-disorder phase transition in black-hole star clusters -- III. A mono-energetic cluster

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