Resonant Relaxation near a Massive Black Hole: The Stellar Distribution and Gravitational Wave Sources

By Clovis Hopman, T. Alexander. 2006

208 citations recorded by the source corpus.

Resonant relaxation (RR) of orbital angular momenta occurs near massive black holes (MBHs) where the potential is spherical and stellar orbits are nearly Keplerian and so do not precess significantly. The resulting coherent torques efficiently change the magnitude of the angular momenta and rotate the orbital inclination in all directions. As a result, many of the tightly bound stars very near the MBH are rapidly destroyed by falling into the MBH on low angular momentum orbits, while the orbits of the remaining stars are efficiently randomized. We solve numerically the Fokker-Planck equation in energy for the steady state distribution of a single-mass population with an RR sink term. We find that the steady state current of stars, which sustains the accelerated drainage close to the MBH, can be ≲10 larger than that due to noncoherent two-body relaxation alone. RR mostly affects tightly bound stars, and so it increases only moderately the total tidal disruption rate, which is dominated by stars originating from less bound orbits farther away. We show that the event rate of gravitational wave (GW) emission from inspiraling stars, originating much closer to the MBH, is dominated by RR dynamics. The GW event rate depends on the uncertain efficiency of RR. The efficiency indicated by the few available simulations implies rates ≲10 times higher than those predicted by two-body relaxation, which would improve the prospects of detecting such events by future GW detectors, such as LISA. However, a higher, but still plausible, RR efficiency can lead to the drainage of all tightly bound stars and strong suppression of GW events from inspiraling stars. We apply our results to the Galactic MBH and show that the observed dynamical properties of stars there are consistent with RR.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/31ec697b5f6fd0e60f915cc4f809d2fea4dfd5b4

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Citations in the corpus

SECULAR EVOLUTION OF COMPACT BINARIES NEAR MASSIVE BLACK HOLES: GRAVITATIONAL WAVE SOURCES AND OTHER EXOTICA (2012, methodology): “In a further set of integrations, the evaporation time-scale was computed from the combined density profile of stars and BHs corresponding to a mass segregated cusp near SgrA* (Hopman & Alexander 2006a): ρ(r) = ρ⋆(r) + ρBH ( r 1pc )−2 , (31) with ρBH = 1 × 104M⊙pc−3.”
Gravitational waves from scattering of stellar-mass black holes in galactic nuclei (2008, background): “We therefore conclude that the rates determined are rather robust to the depletion of BHs very close to the SMBH as may be caused by resonant relaxation (Rauch & Tremaine 1996; Rauch & Ingalls 1998; Hopman & Alexander 2006a) or our choice of the innermost radius for BHs.”
Rates of stellar tidal disruption as probes of the supermassive black hole mass function (2014, background): “Secular resonances in the vicinity of an SMBH may lead to “resonant relaxation” of angular momentum (Rauch & Tremaine 1996), although this is likely a subdominant contributor to the total TDE rate (Rauch & Ingalls 1998; Hopman & Alexander 2006; Madigan et al. 2011).”
A DISK OF YOUNG STARS AT THE GALACTIC CENTER AS DETERMINED BY INDIVIDUAL STELLAR ORBITS (2008, background): “This drop in the number of disk stars at small radii may be the result of resonant relaxation or other dynamical processes if the central arcsecond S-stars are a continuation of the disk population (Hopman & Alexander 2006).”
Doing Science with eLISA: Astrophysics and Cosmology in the Millihertz Regime (2012, background): “The problem of the presence of a dark cusp has been addressed, for the Galactic Centre, by different authors, from a semi-analytical and numerical standpoint (Freitag et al., 2006a,b, Hopman and Alexander, 2006a, Miralda-Escudé and Gould, 2000, Sigurdsson and Rees, 1997).”
Black Hole Mergers in Galactic Nuclei Induced by the Eccentric Kozai–Lidov Effect (2017, methodology): “On the other hand, the choice of uniform in ln(a2) initial distribution for the GC case results in a steeper distribution than the nominal Bahcall & Wolf (1976) density profile, with ∼ 57% of the systems remaining stable.”
Stellar Dynamics and Stellar Phenomena Near a Massive Black Hole (2017, background): “In particular, this effect allows stellar BHs to inspiral unperturbed into MBHs by the emission of GWs (Hopman & Alexander 2006; Bar-Or & Alexander 2016; Sec.”
Measuring Distance and Properties of the Milky Way’s Central Supermassive Black Hole with Stellar Orbits (2008, background): “Precession from general relativistic effects also influences the timescale for resonant relaxation processes close to the black hole (see, e.g., Rauch & Tremaine1996; Hopman & Alexander 2006).”
Greatly Enhanced Merger Rates of Compact-object Binaries in Non-spherical Nuclear Star Clusters (2017, background): “However, very near a MBH orbital angular momenta can evolve as a consequence of resonant relaxation (Rauch & Tremaine 1996; Hopman & Alexander 2006).”
HIGH ANGULAR RESOLUTION INTEGRAL-FIELD SPECTROSCOPY OF THE GALAXY'S NUCLEAR CLUSTER: A MISSING STELLAR CUSP? (2009, unknown): “In order to plausibly test stellar cusp formation theories, the stellar population used to trace the cusp profile must be older than the relaxation time, which is of order 1 Gyr within the sphere of influence of Sgr A* (e.g., Hopman & Alexander 2006).”
Massive Perturber-driven Interactions between Stars and a Massive Black Hole (2006, background): “…mass of captured stars does not exceed the dynamical constraints on the extended mass around the MBH (Mouawad et al. 2005), because 2-body relaxation and likely also resonant relaxation (Rauch & Tremaine 1996; Hopman & Alexander 2006a) scatters enough of them into the MBH or to wider orbits.”
Rapid and Bright Stellar-mass Binary Black Hole Mergers in Active Galactic Nuclei (2016, background): “Further out at the radius of influence, this timescale is of the order 107 M3/46 yr (Hopman & Alexander 2006).”
Merging Binaries in the Galactic Center: The eccentric Kozai-Lidov mechanism with stellar evolution (2016, methodology): “The associated timescale is shown in Figure 1 (e.g., Hopman & Alexander 2006; Kocsis & Tremaine 2011, 2015).”
STRONG MASS SEGREGATION AROUND A MASSIVE BLACK HOLE (2008, methodology): “Following the approach introduced by Bahcall & Wolf (1976, 1977) and its implementation by Hopman & Alexander (2006b), we calculate the approximate steady state DFs of a non-evolving stellar population in a spherical Keplerian system around a fixed MBH.”
Stellar Remnants in Galactic Nuclei: Mass Segregation (2006, background): “Recently Hopman & Alexander (2006) have considered, for the first time in the study of EMRIs, the role of ‘‘resonant relaxation,’’ i.e., of the random changes in eccentricity and orientation of the orbital planes due to the nonvanishing but fluctuating torque exerted on an orbit by the other…”
Quantifying the coexistence of massive black holes and dense nuclear star clusters (2009, result): “Due to the substantially higher density of stars in NCs, compared to the underlying host galaxy (see Figure 7.5), past estimates of LISA-detectable gravitational radiation events (e.g. Sigurdsson 1997; Freitag 2001; Gair et al. 2004; Hopman & Alexander 2005, 2006a,b) may need to be revised upwards.”
Starbursts near supermassive black holes: young stars in the Galactic Centre, and gravitational waves in LISA band (2006, background): “Here we argue that it is potentially important for the S-stars; this argument has also been made independently by Hopman and Alexander (2006)¶ The characteristic timescale for the eccentricity change due to RR is given by tRR ≃ (0.5/βs)2 ( M 4× 106M⊙ ) ( 16M⊙ ms ) (Porb/yr)×106yr,(37) where ms is…”