The Impact of Vector Resonant Relaxation on the Evolution of Binaries near a Massive Black Hole: Implications for Gravitational-wave Sources

Abstract

Binaries within the sphere of influence of a massive black hole (MBH) in galactic nuclei are susceptible to the Lidov-Kozai (LK) mechanism, which can drive orbits to high eccentricities and trigger strong interactions within the binary such as the emission of gravitational waves (GWs), and mergers of compact objects. These events are potential sources for GW detectors such as Advanced LIGO and VIRGO. The LK mechanism is only effective if the binary is highly inclined with respect to its orbit around the MBH (within a few degrees of 90 • ), implying low rates. However, close to an MBH, torques from the stellar cluster give rise to the process of vector resonant relaxation (VRR). VRR can bring a low-inclination binary into an 'active' LK regime in which high eccentricities and strong interactions are triggered in the binary. Here, we study the coupled LK-VRR dynamics, with implications for LIGO and VIRGO GW sources. We carry out Monte Carlo simulations and find that the merger fraction enhancement due to LK-VRR dynamics is up to a factor of ∼ 10 for the lower end of assumed MBH masses (M • = 10 4 M ⊙ ), and decreases sharply with increasing M • . We find that, even in our most optimistic scenario, the baseline BH-BH merger rate is small, and the enhancement by LK-VRR coupling is not large enough to increase the rate to well above the LIGO/VIRGO lower limit, 12 Gpc −3 yr −1 . For the Galactic Center, the LK-VRR-enhanced rate is ∼ 100 times lower than the LIGO/VIRGO limit, and for M • = 10 4 M ⊙ , the rate barely reaches 12 Gpc −3 yr −1 .

Eccentric Black Hole Mergers in Dense Star Clusters: The Role of Binary–Binary Encounters

“…Other formation scenarios that may facilitate BBH inspirals with eccentricities accessible by current ground-based GW detectors have also been identified, including dynamical interactions with an intermediate-mass BH in a GC core (Leigh et al 2014;Fragione et al 2017, hyperbolic encounters between BHs in NSCs (O'leary et al 2009;Kocsis & Levin 2012), and through the evolution of three-and four-body hierarchical systems (e.g., Miller & Hamilton 2002;Antonini & Perets 2012;Antonini et al 2016;Silsbee & Tremaine 2017;Antonini et al 2017;Rodriguez & Antonini 2018;Hoang et al 2017;Liu & Lai 2017Randall & Xianyu 2018a,b;Hamers et al 2018;Arca-Sedda et al 2018), particularly when non-secular evolution is properly considered (Antonini et al 2014). Motivated by formation scenarios with this highly discriminating characteristic, efforts have been made to quantify the measurability of eccentric signals, and have placed limits on the amount of eccentricity needed in a signal to distinguish it from circular.…”

A period-dependent spatial scatter of Galactic black hole transients

“…Bartos et al 2017), in galactic nuclei (e.g. O'Leary et al 2009;Hamers et al 2018), and dynamical assembly in globular clusters (GCs; e.g. Rodriguez et al 2016).…”

Compact-object Mergers in the Galactic Center: Evolution in Triaxial Clusters

“…The dynamical evolution of binaries in these environments is a complex and multiscale process, ranging from impulsive-like close encounters with other stars to long-range tidal torques arising from the SMBH and the cluster. Despite this complexity, there has been significant recent progress in this field, mainly driven by the exciting possibility that a significant fraction of compact-object mergers detected by the LIGO-Virgo collaboration may arise dynamically in these extreme environments (e.g., Antonini & Perets 2012;VanLandingham et al 2016; Bartos et al 2017;Petrovich & Antonini 2017;Stone et al 2017;Hamers et al 2018;Hoang et al 2018;Leigh et al 2018;Randall & Xianyu 2018;Hamilton & Rafikov 2019a;Zhang et al 2019).…”