Gravitational Encounters and the Evolution of Galactic Nuclei. IV. Captures Mediated by Gravitational-Wave Energy Loss

TL;DR

This paper uses numerical solutions of the Fokker-Planck equation, including relativistic effects, to study how compact objects are captured by supermassive black holes, revealing distinct regimes and distributions that differ from classical models.

Contribution

It extends previous work by incorporating higher-order post-Newtonian corrections and analyzing the impact on capture rates and orbital distributions in galactic centers.

Findings

Identification of two capture regimes: plunges and EMRIs.

Significant differences in orbital distributions compared to Bahcall-Wolf predictions.

Quantification of classical relaxation effects on the Schwarzschild barrier.

Abstract

Direct numerical integrations of the two-dimensional Fokker-Planck equation are carried out for compact objects orbiting a supermassive black hole (SBH) at the center of a galaxy. As in Papers I-III, the diffusion coefficients incorporate the effects of the lowest-order post-Newtonian corrections to the equations of motion. In addition, terms describing the loss of orbital energy and angular momentum due to the 5/2-order post-Newtonian terms are included. In the steady state, captures are found to occur in two regimes that are clearly differentiated in terms of energy, or semimajor axis; these two regimes are naturally characterized as "plunges" (low binding energy) and "EMRIs," or extreme-mass-ratio inspirals (high binding energy). The capture rate, and the distribution of orbital elements of the captured objects, are presented for two steady-state models based on the Milky Way: one with a relatively high density of remnants and one with a lower density. In both models, but particularly in the second, the steady-state energy distribution and the distribution of orbital elements of the captured objects are substantially different than if the Bahcall-Wolf energy distribution were assumed. The ability of classical relaxation to soften the blocking effects of the Schwarzschild barrier is quantified.These results, together with those of Papers I-III, suggest that a Fokker-Planck description can adequately represent the dynamics of collisional loss cones in the relativistic regime.