Stellar relaxation processes near the Galactic massive black hole

Abstract

The massive black hole (MBH) in the Galactic Center and the stars around it form a unique stellar dynamics laboratory for studying how relaxation processes affect the distribution of stars and compact remnants and lead to close interactions between them and the MBH. Recent theoretical studies suggest that processes beyond "minimal" two-body relaxation may operate and even dominate relaxation and its consequences in the Galactic Center. I describe loss-cone refilling by massive perturbers, strong mass segregation and resonant relaxation; review observational evidence that these processes play a role in the Galactic Center; and discuss some cosmic implications for the rates of gravitational wave emission events from compact remnants inspiraling into MBHs, and the coalescence timescales of binary MBHs. † Invited talk.Milky Way is the archetype of the subset of galaxies with low-mass MBHs that are key targets for planned space-borne gravitational wave detectors, such as the Laser Interferometer Space Antenna (LISA). GC studies may help understand the effect of such relaxation processes on the open questions of the cosmic EMRI event rate and the EMRI orbital characteristics.Before turning to a discussion of the non-standard relaxation processes that are expected to operate in the GC, it is useful to briefly review the dynamics leading to close interactions with a MBH (loss-cone theory) and the dynamical conditions in the GC. Infall and inspiral into a MBHStars can fall into the MBH either by losing orbital energy, so that the orbit shrinks down to the size of the last stable circular orbit (r LSCO = 3r s for a non-rotating MBH, where the event horizon is at the Schwarzschild radius r s = 2GM • /c 2 ), or by losing orbital angular momentum so that the orbit becomes nearly radial and unstable (periapse r p < 2r s for a star with zero orbital energy falling into a non-rotating MBH) †. The timescale to lose energy by 2-body scattering, T E ≡ |E/Ė| is of the order of the relaxation time,where N ⋆ (< r) is the number of stars inside r, τ dyn (r) ∼ r 3 /GM • is the dynamical time and spherical symmetry and a Keplerian velocity dispersion are assumed, σ 2 ∼ GM • /r. The maximal angular momentum available for an orbit with energy E is that of a circular orbit, J c (E) = GM • / √ 2E (using here the stellar dynamical sign convention E ≡ −v 2 /2 − φ(r) > 0). The timescale for losing angular momentum, T J ≡ |J/J|, can be much shorter than T E when J < J c , sinceAs a consequence, almost all stars that reach the MBH, and are ultimately destroyed by a close interaction with it, do so by being scattered to low-J "loss-cone" orbits (near radial orbits with J < J lc ≃ √ 2GM • q, where q is the maximal periapse required for the close interaction of interest to occur. Frank & Rees 1976;Lightman & Shapiro 1977). The rate of close interaction events, Γ lc , is set by the replenishment rate of stars into the loss-cone. When the replenishment mechanism is diffusion in phase space by 2-body scattering, Γ lc ∝ T −1 R , which is typically a ver...

Extreme Mass Ratio Inspirals: Perspectives for Their Detection

“…which we want to rewrite later in the form [10]. We denote the SSCs (i), (ii) and (iii) as "T" and "F" and "w", and consider first the "T" condition, S ab p b = 0.…”

“…The characteristic time scale associated with resonant relaxation, t RR , is significantly smaller than t rlx and so this process can significantly boost the EMRI event rate. Resonant relaxation plays an important role for orbits with a CO ≤ a EM RI [7], [8], [9], [10]. However, for COs on eccentric orbits with small perhaps radii, the relativistic (GR) precession can be very high, which effectively destroys the resonant relaxation effect.…”

Formation and evolution of nuclear star clusters with in-situ star-formation: Nuclear cores and age segregation

“…It should be noted that younger stellar populations are more massive (higher turn-off mass), and therefore there could be a degeneracy between interpretation of observations as arising from mass segregation vs. age segregation. Indeed, there are clues for the existence of extreme masssegregation in the GC which could be difficult to explain in the context of mass-segregation processes Alexander (2007); age segregation processes may therefore help to better understand this issue.…”