Secular Stellar Dynamics near a Massive Black Hole

The Astrophysical Journal (Impact Factor: 6.73). 10/2010; 738(1). DOI: 10.1088/0004-637X/738/1/99
Source: arXiv

ABSTRACT 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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    ABSTRACT: When a compact object on a highly eccentric orbit about a much more massive body passes through periapsis it emits a short gravitational wave signal known as an extreme-mass-ratio burst (EMRB). We consider stellar mass objects orbiting the massive black hole (MBH) found in the Galactic Centre. EMRBs provide a novel means of extracting information about the MBH; an EMRB from the Galactic MBH could be highly informative regarding the MBH's mass and spin if the orbital periapsis is small enough. However, to be a useful astronomical tool EMRBs must be both informative and sufficiently common to be detectable with a space-based interferometer. We construct a simple model to predict the event rate for Galactic EMRBs. We estimate there could be on average ~2 bursts in a two year mission lifetime for LISA. Stellar mass black holes dominate the event rate. Creating a sample of 100 mission realisations, we calculate what we could learn about the MBH. On average, we expect to be able to determine the MBH mass to ~1% and the spin to ~0.1 using EMRBs.
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    ABSTRACT: Massive black holes (MBHs) in galactic nuclei are believed to be surrounded by a high density stellar cluster, whose mass is mostly in hard-to-detect faint stars and compact remnants. Such dark cusps dominate the dynamics near the MBH: a dark cusp in the Galactic center (GC) of the Milky Way would strongly affect orbital tests of General Relativity there; on cosmic scales, dark cusps set the rates of gravitational wave emission events from compact remnants that spiral into MBHs, and they modify the rates of tidal disruption events, to list only some implications. A recently discovered long-period massive young binary (P_12 <~ 1 yr, M_12 ~ O(100 M_sun), T_12 ~ 6x10^6 yr), only ~0.1 pc from the Galactic MBH (Pfuhl et al 2013), sets a lower bound on the 2-body relaxation timescale there, min t_rlx ~ (P_12/M_12)^(2/3)T_12 ~ 10^7 yr, and correspondingly, an upper bound on the stellar number density, max n ~ few x 10^8/<M_star^2> 1/pc^3, based on the binary's survival against evaporation by the dark cusp. However, a conservative dynamical estimate, the drain limit, implies t_rlx > O(10^8) yr. Such massive binaries are thus too short-lived and tightly bound to constrain a dense relaxed dark cusp. We explore here in detail the use of longer-period, less massive and longer-lived binaries (P_12 ~ few yr, M_12 ~ 2-4 M_sun, T_12 ~ 10^8-10^10 yr), presently just below the detection threshold, for probing the dark cusp, and develop the framework for translating their future detections among the giants in the GC into dynamical constraints.
    The Astrophysical Journal 08/2013; 780(2). · 6.73 Impact Factor
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    ABSTRACT: We present 3D kinematic observations of stars within the central 0.5 pc of the Milky Way nuclear star cluster using adaptive optics imaging and spectroscopy from the Keck telescopes. Recent observations have shown that the cluster has a shallower surface density profile than expected for a dynamically relaxed cusp, leading to important implications for its formation and evolution. However, the true three dimensional profile of the cluster is unknown due to the difficulty in de-projecting the stellar number counts. Here, we use spherical Jeans modeling of individual proper motions and radial velocities to constrain for the first time, the de-projected spatial density profile, cluster velocity anisotropy, black hole mass ($M_\mathrm{BH}$), and distance to the Galactic center ($R_0$) simultaneously. We find that the inner stellar density profile of the late-type stars, $\rho(r)\propto r^{-\gamma}$ to have a power law slope $\gamma=0.05_{-0.60}^{+0.29}$, much more shallow than the frequently assumed Bahcall $\&$ Wolf slope of $\gamma=7/4$. The measured slope will significantly affect dynamical predictions involving the cluster, such as the dynamical friction time scale. The cluster core must be larger than 0.5 pc, which disfavors some scenarios for its origin. Our measurement of $M_\mathrm{BH}=5.76_{-1.26}^{+1.76}\times10^6$ $M_\odot$ and $R_0=8.92_{-0.55}^{+0.58}$ kpc is consistent with that derived from stellar orbits within 1$^{\prime\prime}$ of Sgr A*. When combined with the orbit of S0-2, the uncertainty on $R_0$ is reduced by 30% ($8.46_{-0.38}^{+0.42}$ kpc). We suggest that the MW NSC can be used in the future in combination with stellar orbits to significantly improve constraints on $R_0$.
    The Astrophysical Journal 11/2013; 779(1). · 6.73 Impact Factor


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