Secular Stellar Dynamics near a Massive Black Hole

The Astrophysical Journal (Impact Factor: 5.99). 10/2010; 738(1). DOI: 10.1088/0004-637X/738/1/99
Source: arXiv


The angular momentum evolution of stars close to massive black holes (MBHs)
is driven by secular torques. In contrast to two-body relaxation, where
interactions between stars are incoherent, the resulting resonant relaxation
(RR) process is characterized by coherence times of hundreds of orbital
periods. In this paper, we show that all the statistical properties of RR can
be reproduced in an autoregressive moving average (ARMA) model. We use the ARMA
model, calibrated with extensive N-body simulations, to analyze the long-term
evolution of stellar systems around MBHs with Monte Carlo simulations.
We show that for a single-mass system in steady-state, a depression is carved
out near an MBH as a result of tidal disruptions. Using Galactic center
parameters, the extent of the depression is about 0.1 pc, of similar order to
but less than the size of the observed "hole" in the distribution of bright
late-type stars. We also find that the velocity vectors of stars around an MBH
are locally not isotropic. In a second application, we evolve the highly
eccentric orbits that result from the tidal disruption of binary stars, which
are considered to be plausible precursors of the "S-stars" in the Galactic
center. We find that RR predicts more highly eccentric (e > 0.9) S-star orbits
than have been observed to date.

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    • "Relativistic (GR) precession, or ultimately by their response to the resonant torques themselves. Resonant relaxation is the driving force behind many interesting physical phenomena, which include the emission of gravitational waves from compact objects that spiral into the MBH [2], the warping of circum-nuclear gaseous or stellar disks [3] [4], and the orbital evolution of tidally captured stars [5] [6] [7]. Resonant relaxation can also be a major obstacle for attempts to test GR by observation of stars very near MBHs [8] [9]. "
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    ABSTRACT: Stars around a massive black hole (MBH) move on nearly fixed Keplerian orbits, in a centrally-dominated potential. The random fluctuations of the discrete stellar background cause small potential perturbations, which accelerate the evolution of orbital angular momentum by resonant relaxation. This drives many phenomena near MBHs, such as extreme mass-ratio gravitational wave inspirals, the warping of accretion disks, and the formation of exotic stellar populations. We present here a formal statistical mechanics framework to analyze such systems, where the background potential is described as a correlated Gaussian noise. We derive the leading order, phase-averaged 3D stochastic Hamiltonian equations of motion, for evolving the orbital elements of a test star, and obtain the effective Fokker-Planck equation for a general correlated Gaussian noise, for evolving the stellar distribution function. We show that the evolution of angular momentum depends critically on the temporal smoothness of the background potential fluctuations. Smooth noise has a maximal variability frequency $\nu_{\max}$. We show that in the presence of such noise, the normalized angular momentum $j=\sqrt{1-e^{2}}$ of a relativistic test star, undergoing Schwarzschild (in-plane) General Relativistic precession with frequency $\nu_{GR}/j^{2}$, is exponentially suppressed for $j<j_{b}$, where $\nu_{GR}/j_{b}^{2}\sim\nu_{\max}$, due to the adiabatic invariance of the precession against the slowly varying random background torques. This results in an effective Schwarzschild precession-induced barrier in angular momentum. When $j_{b}$ is large enough, this barrier can have significant dynamical implications for processes near the MBH.
    Classical and Quantum Gravity 12/2014; 31(24):244003. DOI:10.1088/0264-9381/31/24/244003 · 3.17 Impact Factor
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    • "One is the incoherent (random) scattering between two stars (two-body relaxation [97]), and the other is the coherent torquing between the stars on near-Keplerian orbits, known as (scalar) resonant relaxation, or (scalar) " RR " [98] [99]. Numerical simulations including both processes showed that at least 20 − 25 Myr is needed to recover the observed eccentricity distribution if S-stars are injected continuously through binary separations [100] [101] [102] [103] [104]. If S-stars are produced by disk migration, a timescale longer than 100 Myr will be needed, since the near-circular orbits preferentially have larger angular momenta [102]. "
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    ABSTRACT: Observations of the innermost parsec surrounding Sgr A* ---the supermassive black hole in the center of our Galaxy--- have revealed a diversity of structures whose existence and characteristics apparently defy the fundamental principles of dynamics. In this article, we review the challenges to the dynamics theories that have been brought forth in the past two decades by the observations of the Galactic center (GC). We outline the theoretical framework that has been developed to reconcile the discrepancies between the theoretical predictions and the observational results. In particular, we highlight the role of the recently discovered sub-parsec stellar disk in determining the dynamics and resolving the inconsistencies. We also discuss the implications for the recent activity of Sgr A*.
    Classical and Quantum Gravity 10/2014; 32(6). DOI:10.1088/0264-9381/32/6/064001 · 3.17 Impact Factor
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    ABSTRACT: One of the most interesting sources of gravitational waves (GWs) for LISA is the inspiral of compact objects on to a massive black hole (MBH), commonly referred to as an "extreme-mass ratio inspiral" (EMRI). The small object, typically a stellar black hole (bh), emits significant amounts of GW along each orbit in the detector bandwidth. The slowly, adiabatic inspiral of these sources will allow us to map space-time around MBHs in detail, as well as to test our current conception of gravitation in the strong regime. The event rate of this kind of source has been addressed many times in the literature and the numbers reported fluctuate by orders of magnitude. On the other hand, recent observations of the Galactic center revealed a dearth of giant stars inside the inner parsec relative to the numbers theoretically expected for a fully relaxed stellar cusp. The possibility of unrelaxed nuclei (or, equivalently, with no or only a very shallow cusp) adds substantial uncertainty to the estimates. Having this timely question in mind, we run a significant number of direct-summation $N-$body simulations with up to half a million particles to calibrate a much faster orbit-averaged Fokker-Planck code. We then investigate the regime of strong mass segregation (SMS) for models with two different stellar mass components. We show that, under quite generic initial conditions, the time required for the growth of a relaxed, mass segregated stellar cusp is shorter than a Hubble time for MBHs with $M_\bullet \lesssim 5 \times 10^6 M_\odot$ (i.e. nuclei in the range of LISA). SMS has a significant impact boosting the EMRI rates by a factor of $\sim 10$ for our fiducial models of Milky Way type galactic nuclei.
    Classical and Quantum Gravity 10/2010; 28(9). DOI:10.1088/0264-9381/28/9/094017 · 3.17 Impact Factor
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