Defeating stochasticity: coalescence timescales of massive black holes in galaxy mergers

Abstract

The coalescence of massive black hole binaries (BHBs) in galactic mergers is the primary source of gravitational waves (GWs) at low frequencies. Current estimates of GW detection rates for the Laser Interferometer Space Antenna and the Pulsar Timing Array vary by three orders of magnitude. To understand this variation, we simulate the merger of equal-mass, eccentric, galaxy pairs with central massive black holes and shallow inner density cusps. We model the formation and hardening of a central BHB using the Fast Multiple Method as a force solver, which features a $O(N)$ scaling with the number $N$ of particles and obtains results equivalent to direct-summation simulations. At $N\sim 5\times 10^5$, typical for contemporary studies, the eccentricity of the BHBs can vary significantly for different random realisations of the same initial condition, resulting in a substantial variation of the merger timescale. This scatter owes to the stochasticity of stellar encounters with the BHB and decreases with increasing $N$. We estimate that $N\sim 10^7$ within the stellar half-light radius suffices to reduce the scatter in the merger timescale to $\sim 10$\%. Our results suggest that at least some of the uncertainty in low-frequency GW rates owes to insufficient numerical resolution.

Submitted for publication in MNRAS

References in corpus (8)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Performance Analysis of Direct N-Body Algorithms on Special-Purpose Supercomputers
• Self consistent model for the evolution of eccentric massive black hole binaries in stellar environments: implications for gravitational wave observations
• Collisionless loss-cone refilling: there is no final parsec problem
• Long-Term Evolution of Massive Black Hole Binaries. III. Binary Evolution in Collisional Nuclei
• Inward Bound: The incredible journey of massive black holes as they pair and merge; I. The effect of mass ratio in flattened rotating galactic nuclei
• Ultramassive Black Hole Coalescence
• Eccentric Massive Black Hole Binaries in LISA I : The Detection Capabilities of Circular Templates

Cited by in corpus (20)

• EDGE: Two routes to dark matter core formation in ultra-faint dwarfs
• Eccentricity evolution of massive black hole binaries from formation to coalescence
• Formation of the largest galactic cores through binary scouring and gravitational wave recoil
• Signatures of the Many Supermassive Black Hole Mergers in a Cosmologically Forming Massive Early-Type Galaxy
• Formation of super-massive black holes in galactic nuclei I: delivering seed intermediate-mass black holes in massive stellar clusters
• Accretion-modified stellar-mass black hole distribution and milli-Hz gravitational wave backgrounds from galaxy centre
• Supermassive black hole fueling in IllustrisTNG: Impact of environment
• RABBITS -- I. The crucial role of nuclear star formation in driving the coalescence of supermassive black hole binaries
• Eccentricity effects on the supermassive black hole gravitational wave background
• NGC 6240 Supermassive Black Hole Binary dynamical evolution based on Chandra data
• Merging timescale for supermassive black hole binary in interacting galaxy NGC 6240
• RABBITS -- II. The impact of AGN feedback on coalescing supermassive black holes in disc and elliptical galaxy mergers
• Identifying supermassive black hole recoil in elliptical galaxies
• Evolution of Massive Black Hole Binaries in Collisionally Relaxed Nuclear Star Clusters -- Impact of Mass Segregation
• Realistic consecutive galaxy mergers form eccentric PTA sources
• Unravelling the formation of the first supermassive black holes with the SKA pulsar timing array
• Properties of loss cone stars in a cosmological galaxy merger remnant
• LeMMINGs. VI. Connecting nuclear activity to bulge properties of active and inactive galaxies: radio scaling relations and galaxy environment
• Formation of counter-rotating and highly eccentric massive black hole binaries in galaxy mergers
• Atacama Cosmology Telescope: Observations of supermassive black hole binary candidates. Strong sinusoidal variations at 95, 147 and 225 GHz in PKS 2131$-$021 and PKS J0805$-$0111