Relativistic dynamics of stars near a supermassive black hole

TL;DR

This paper introduces an efficient N-body simulation method incorporating relativistic effects to study star dynamics near supermassive black holes, revealing new relaxation regimes and refining the understanding of the Schwarzschild barrier.

Contribution

The paper develops a novel N-body algorithm that includes relativistic corrections and large star interactions, enabling detailed analysis of orbital evolution near black holes.

Findings

Identification of three distinct angular momentum regimes with different diffusion behaviors.

Discovery of a new 'anomalous relaxation' regime affecting star orbits.

Analytic expressions for diffusion coefficients across all regimes.

Abstract

General relativistic precession limits the ability of gravitational encounters to increase the eccentricity $e$ of orbits near a supermassive black hole (SBH). This "Schwarzschild barrier" (SB) has been shown to play an important role in the orbital evolution of stars like the galactic center S-stars. However, the evolution of orbits below the SB, $e>e_\mathrm{SB}$, is not well understood; the main current limitation is the computational complexity of detailed simulations. Here we present an $N$-body algorithm that allows us to efficiently integrate orbits of test stars around a SBH including general relativistic corrections to the equations of motion and interactions with a large ($\gtrsim 10^3$) number of field stars. We apply our algorithm to the S-stars and extract diffusion coefficients describing the evolution in angular momentum $L$. We identify three angular momentum regimes, in which the diffusion coefficients depend in functionally different ways on $L$. Regimes of lowest and highest $L$ are well-described in terms of non-resonant relaxation (NRR) and resonant relaxation (RR), respectively. In addition, we find a new regime of "anomalous relaxation" (AR). We present analytic expressions, in terms of physical parameters, that describe the diffusion coefficients in all three regimes, and propose a new, empirical criterion for the location of the SB in terms of the $L$-dependence of the diffusion coefficients. Subsequently we apply our results to obtain the steady-state distribution of angular momentum for orbits near a SBH.