Mass Segregation in the Galactic Centre

TL;DR

This paper investigates the formation and characteristics of stellar density cusps around massive black holes, emphasizing the effects of mass segregation and the implications for the Galactic Centre's observed stellar distribution.

Contribution

It provides a detailed analysis of mass segregation effects using Fokker-Planck models, highlighting how different stellar mass distributions influence cusp formation timescales.

Findings

Steady-state cusps form in less than a Hubble time.

Heavy stars can create steeper density profiles.

The absence of a visible cusp in the Galactic Centre challenges relaxation-based models.

Abstract

Two-body energy exchange between stars orbiting massive black holes (MBHs) leads to the formation of a power-law density distribution n(r)~r^(-a) that diverges towards the MBH. For a single mass population, a=7/4 and the flow of stars is much less than N(<r)/t_r (enclosed number of stars per relaxation time). This "zero-flow" solution is maintained for a multi-mass system for moderate mass ratios or systems where there are many heavy stars, and slopes of 3/2<a<2 are reached, with steeper slopes for the more massive stars. If the heavy stars are rare and massive however, the zero-flow limit breaks down and much steeper distributions are obtained. We discuss the physics driving mass-segregation with the use of Fokker-Planck calculations, and show that steady state is reached in 0.2-0.3 t_r. Since the relaxation time in the Galactic centre (GC) is t_r ~2-3 * 10^(10) yr, a cusp should form in less than a Hubble time. The absence of a visible cusp of old stars in the GC poses a challenge to these models, suggesting that processes other than two-body relaxation have played a role. We discuss astrophysical processes within the GC that depend crucially on the details of the stellar cusp.