The Dynamics of Dense Stellar Systems with a Massive Black Hole
Gill, Michael Allen
Miller, M. Coleman
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In this work, we explore the dynamics of two similar types of dense stellar systems with a central black hole of mass much greater than a typical stellar object. In particular, we use numerical N-body simulations to examine the effects that the massive black hole (MBH) has on the surrounding stars and compact objects as they pertain to indirectly observable signals. The first systems we consider are the highly uncertain cusps likely comprised of primarily massive compact objects that surround the MBHs at the center of typical galaxies. The gradual inspiral of a compact object by emission of gravitational radiation, called an extreme mass-ratio inspiral (EMRI), will produce a signal that falls in the peak detection range of the space-bound laser interferometer space antenna (LISA). Despite a veritable gold mine of astrophysical data that could be gleaned from such a detection, previous investigations in the literature have left the predicted rate of these events uncertain by several orders of magnitude. We present direct N-body simulations of the innermost ≤ 100 objects with the inclusion of the first-order Post-Newtonian correction with the aim of reducing one of the key uncertainties in the dynamics of these systems - the efficiency of resonant relaxation. We find that relativistic pericenter precession prevents a significant enhancement of the EMRI rate; the rate we derive during this work is consistent with those derived in the literature from less direct methods. We do find, however, that our EMRI progenitors originate from much closer to the MBH than previous investigations have suggested was likely. Our second investigation delves into the possibility of finding intermediate-mass black holes (IMBHs), with masses ∼ 10<super>2−4</super> M<sub>sun</sub>, at the center of dense star clusters. Because of the substantial investment of telescope time needed to perform the multiyear proper motion studies that are likely needed to achieve a definitive detection, careful selection of candidate clusters is prudent. We provide a new observational signature of the presence of an IMBH in a dense star cluster - a quenching of mass segregation. Our ensemble of direct N-body simulations with N ≤ 32768 objects and highly varied initial conditions show that the existence of an IMBH with mass ∼ 1% of the total cluster mass limits the mass segregation in visible stars, as measured by the radial gradient in average stellar mass. This effect is consistently visible in systems that have had enough time to reach their equilibrium value of mass segregation, usually about 5 initial half-mass relaxation times. In practical terms, our method will apply to Galactic globular clusters that are fairly small, and that are unlikely to have lost a significant portion of their mass to Galactic tidal stripping. We apply this method to two of the ∼ 30 Galactic globular clusters that fit our conservative criteria for application of this method, NGC 2298 and NGC 6254(M10). Thanks to deep observations by the Hubble Space Telescope Advanced Camera for Surveys, data exist that are sufficient to allow a good comparison to our simulation data. We find that the degree of mass segregation we observe in NGC 2298 is clearly inconsistent with simulations harboring an IMBH at about the 3−σ level. In contrast, application of the method to NGC 6254 reveals a mass segregation profile that can only be explained by the presence of either an IMBH or a significant population of primordial binaries (≥ 5%). Unfortunately, a reliable measure of the binary fraction of NGC 6254 does not exist; however, NGC 6254 is a good candidate for follow-up proper motion studies.