Massive black hole binary mergers within subparsec scale gas discs

Abstract

We study the efficiency and dynamics of supermassive black hole binary mergers driven by angular momentum loss to small‐scale gas discs. Such binaries form after major galaxy mergers, but their fate is unclear since hardening through stellar scattering becomes very inefficient at subparsec distances. Gas discs may dominate binary dynamics on these scales, and promote mergers. Using numerical simulations, we investigate the evolution of the semimajor axis and eccentricity of binaries embedded within geometrically thin gas discs. Our simulations directly resolve angular momentum transport within the disc, which at the radii of interest is likely dominated by disc self‐gravity. We show that the binary decays at a rate which is in good agreement with analytical estimates, while the eccentricity grows. Saturation of eccentricity growth is not observed up to values e≳ 0.35. Accretion on to the black holes is variable, and is roughly modulated by the binary orbital frequency. Scaling our results, we analytically estimate the maximum rate of binary decay that is possible without fragmentation occurring within the surrounding gas disc, and compare that rate to an estimate of the stellar dynamical hardening rate. For binary masses in the range 105≲M≲ 108 M⊙ we find that decay due to gas discs may dominate for separations below a∼ 0.01–0.1 pc, in the regime where the disc is optically thick. The minimum merger time‐scale is shorter than the Hubble time for M≲ 107 M⊙. This implies that gas discs could commonly attend relatively low‐mass black hole mergers, and that a significant population of binaries might exist at separations of a few hundredths of a parsec, where the combined decay rate is slowest. For more massive binaries, where this mechanism fails to act quickly enough, we suggest that scattering of stars formed within a fragmenting gas disc could act as a significant additional sink of binary angular momentum.

Evolution of binary black holes in self gravitating discs

“…Additionally, it is still unclear how Nature bridges the gap between the two theoretically well understood stages of BHB evolution: (i) the dynamical friction driven stage, when the two BHs spiral in toward the centre of the merger remnant down to pc separations and (ii) the final inspiral driven by gravitational waves (GWs), which become efficient when the two BHs are at a separation < ∼ 10 −2 pc. Both dense stellar and gaseous environments have been shown to be effective in extracting the binary energy and angular momentum (see, e.g., Escala et al 2005;Dotti et al 2007;Cuadra et al 2009;Khan et al 2011;Preto et al 2011), likely driving the system to final coalescence (an extensive discussion on the fate of sub-parsec BHBs can be found in Dotti et al 2012). Scenarios involving cold gas are particular appealing not only A&A 545, A127 (2012) because they might produce distinctive observational signatures, but also because cold gas dominates the baryonic content in most galaxies at redshifts higher than one, providing a natural reservoir of energy and angular momentum to drive the BHB towards coalescence.…”

Misaligned accretion on to supermassive black hole binaries

“…This is a common outcome for simulations of self-gravitating discs which employ the β-cooling prescription (Equation 2) where β 5 (e.g. Gammie 2001;Rice et al 2003Rice et al , 2005Cuadra et al 2009). Figure 4 shows surface density renderings of the discs after t = 1000 t b : in both cases the disc structure is dominated by moderate-order (m ∼ 5-10) spiral density waves.…”

“…The code used was a modified version of gadget-2 (Springel 2005). Following the method of Cuadra et al (2009), we have removed the N-body particles from the gravitational tree, and instead compute their gravitational forces via direct summation. This is important as we must correctly resolve the dynamics of the binary in order to be sure our results are not purely numerical in origin.…”

“…However, dynamical friction typically stalls at ∼parsec separations, and loss-cone refilling due to stellar scattering (which has a typical time-scale of ∼ 10 9 years; Merritt & Wang 2005) occurs too slowly to drive the SMBHs to coalescence. For modest SMBH masses (∼ 10 6 − 10 7 M ) torques from a prograde circumbinary accretion disc can shrink the binary's orbit relatively rapidly (Armitage & Natarajan 2002;Cuadra et al 2009;Lodato et al 2009), but this E-mail: adunhill@astro.puc.cl † Einstein Fellow process is inefficient for higher binary masses, typically taking a Hubble time or longer (Cuadra et al 2009;Lodato et al 2009). However, observational evidence for binary or multiple SMBHs is scarce.…”

Resonances in retrograde circumbinary discs

“…Artymowicz & Lubow 1996;Escala et al 2005;Lodato et al 2009;Cuadra et al 2009;Roedig et al 2012;D'Orazio et al 2013). The simulations of Nixon et al (2012) and Nixon (2012) focussed on circular orbit binaries, with only a few simulations with e 0, in which the eccentricity was always small.…”