Interactions between multiple supermassive black holes in galactic nuclei: a solution to the final parsec problem

Abstract

Using few-body simulations, we investigate the evolution of supermassive black holes (SMBHs) in galaxies (M = 10 10 − 10 12 M at z = 0) at 0 < z < 4. Following galaxy merger trees from the Millennium simulation, we model BH mergers with two extreme binary decay scenarios for the 'hard binary' stage: a full or an empty loss cone. These two models should bracket the true evolution, and allow us to separately explore the role of dynamical friction and that of multi-body BH interactions on BH mergers. Using the computed merger rates, we infer the stochastic gravitational wave background (GWB). Our dynamical approach is a first attempt to study the dynamical evolution of multiple SMBHs in the host galaxies undergoing mergers with various mass ratios (10 −4 < q < 1). Our main result demonstrates that SMBH binaries are able to merge in both scenarios. In the empty loss cone case, we find that BHs merge via multi-body interactions, avoiding the 'final parsec' problem, and entering the PTA band with substantial orbital eccentricity. Our full loss cone treatment, albeit more approximate, suggests that the eccentricity becomes even higher when GWs become dominant, leading to rapid coalescences (binary lifetime 1 Gyr). Despite the lower merger rates in the empty loss cone case, due to their higher mass ratios and lower redshifts, the GWB in the full/empty loss cone models are comparable (0.70 × 10 −15 and 0.53 × 10 −15 at a frequency of 1 yr −1 , respectively). Finally, we compute the effects of high eccentricities on the GWB spectrum.

Constraining VLBI−optical offsets in high redshift galaxies using strong gravitational lensing

“…Such SMBH binaries are expected to merge, and produce outbursts of gravitational wave emission, whose detection can provide insights into galaxy merger rates and SMBH masses (Mingarelli 2019). However, the separation of SMBH binaries emitting gravitational waves must be smaller than 0.1 pc (Ryu et al 2018). For this reason, the study of binary (and, in general, multiple) SMBH coalescence is challenging due to the minimum angular resolution required spatially resolve and to monitor such systems (Ju et al 2013).…”

“…If the systems analyzed here were binary radio-loud AGN, as 0402+379, the lensing amplification would clearly separate the radio emission from the two AGN on parsec-scales. Thus, gravitational lensing is a promising tool to access the crucial scales needed to provide observational constraints to assess the final parsec problem (Ryu et al 2018).…”

Probing supermassive black hole binaries with pulsar timing

“…In the unlikely scenario where some fraction or all binaries stall, interactions between multiple SMBHs from subsequent galaxy mergers with mass ratios 10 −4 < * < 1 will allow the black holes to merge. This creates a floor to the GW background, albeit at a factor of a few lower than the amplitude of models with no stalling [11,12].…”

“…In 6 years, one may be able to determine if in fact supermassive black hole masses have really been overestimated [15]. Importantly, both [11] and [12] show that there is a floor to the GWB at around = 10 −16 . According to the results from [8], it should take PTAs another 10 years to reach this floor, Figure 2.…”

“…Ref [13] is the most optimistic model, and is in tension with current upper limits, while Ref [14] is starting to be in tension with upper limits. The amplitude of a GWB arising from a population of stalled binaries, eventually merging through many-body interactions, will be detectable in 5 years (Ref [11]), and if supermassive black hole masses are biased large (Ref [15]), the background will be detected in 6 years. In the worst-case scenario, explored by Ref [12], we will hit the floor of the GWB in 10 years from now.…”