Jacobi capture as a pathway to off-center massive black hole binaries in dwarf galaxies

TL;DR

The study addresses how off-center black holes in dwarf galaxies with cored dark matter haloes can still merge, despite long dynamical-friction timescales. It models two BHs on coplanar circular orbits in a simplified potential and scans a five-dimensional encounter space to assess Jacobi capture, then reduces the parameter space by placing BHs at core-stalling radii and drawing masses from SatGen merger trees. They find captures occur in about 13% of cases, producing highly eccentric binaries (typically $e>0.5$, many $e>0.9$) and exhibiting strong chaotic sensitivity to initial conditions. Without dissipation, captures are temporary, but could be stabilized in dense stellar environments like stripped nuclei or globular clusters, suggesting this is a non-negligible pathway for black hole growth and binary assembly across cosmic time.

Abstract

The recent detection of high-redshift supermassive black holes with JWST has renewed interest in the processes driving black hole growth. At the same time, both simulations and observations point to a widespread population of off-center intermediate-mass black holes in dwarf galaxies. Their ability to merge outside galactic centers may play a key role in shaping black hole mass assembly. Here, we investigate the dynamics of off-center black holes in dwarf galaxies hosting cored dark matter haloes, where long dynamical friction timescales and core stalling naturally arise. By embedding off-center black holes into an idealized galactic potential and scanning a wide range of orbital configurations, we assess the likelihood of close interactions through Jacobi capture. We find that captures occur in about 13% of cases. Such captures, possibly sustained within compact stellar systems like stripped nuclei or globular clusters, represent a crucial first step toward assembling massive black hole binaries beyond galactic centers.

Figures (4)

• Figure 1: Top: standard scenario of a black hole merger occurring at the galactic center. Bottom: new scenario of an off-center merger.
• Figure 2: Parameters defining the initial configuration: $r_i$ is the initial radius of the inner black hole, $\Delta r_i$ the radial separation between the two black holes, $\Delta \varphi_i$ their phase offset, and $M_1, M_2$ their respective masses.
• Figure 3: Examples of Jacobi captures with different numbers of close encounters ($N_\mathrm{e}$) between black holes. Top row: relative coordinates between black holes during the capture. The reference frame is centered on the most massive black hole and rotates with it. The binary influence radius is marked by the dotted circle. Bottom row: the black line represents the binding energy ($E_\mathrm{b}$) per unit mass of the binary ($M_\mathrm{tot}$), with negative values shown in the colored area. The blue curve represents the relative distance ($d_\mathrm{rel}$) between the black holes. The binary influence radius is indicated by a dashed blue horizontal line.
• Figure 4: Influence of the initial conditions on the number of close encounters ($N_\mathrm{e}$). We choose a reference capture involving five close encounters between the black holes and look at small variations of initial conditions. Central panel: variations of $N_\mathrm{e}$ as a function of the initial masses ($M_1, M_2$). The explored values of ($M_1, M_2$) differ by $\pm1\%$ from the reference configuration, ($M_1^0, M_2^0$). Right panel: variations of $N_\mathrm{e}$ with respect to the initial orbital parameters ($r_\mathrm{i}, \Delta r_\mathrm{i}$). Here, ($r_\mathrm{i}, \Delta r_\mathrm{i}$) are also varied within $\pm1\%$ of the reference values ($r_\mathrm{i}^0, \Delta r_\mathrm{i}^0$). In both panels, the reference case corresponds to the point ($0,0$). The strong variations of $N_\mathrm{e}$ with initial conditions is suggestive of chaotic motion.