Mass Segregation in the Galactic Centre

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.

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