Black hole mergers: can gas discs solve the `final parsec problem?

📝 Abstract

We compute the effect of an orbiting gas disc in promoting the coalescence of a central supermassive black hole binary. Unlike earlier studies, we consider a finite mass of gas with explicit time dependence: we do not assume that the gas necessarily adopts a steady state or a spatially constant accretion rate, i.e. that the merging black hole was somehow inserted into a pre–existing accretion disc. We consider the tidal torque of the binary on the disc, and the binary’s gravitational radiation. We study the effects of star formation in the gas disc in a simple energy feedback framework. The disc spectrum differs in detail from that found before. In particular, tidal torques from the secondary black hole heat the edges of the gap, creating bright rims around the secondary. These rims do not in practice have uniform brightness either in azimuth or time, but can on average account for as much as 50 per cent of the integrated light from the disc. This may lead to detectable high–photon–energy variability on the relatively long orbital timescale of the secondary black hole, and thus offer a prospective signature of a coalescing black hole binary. We also find that the disc can drive the binary to merger on a reasonable timescale only if its mass is at least comparable with that of the secondary black hole, and if the initial binary separation is relatively small, i.e. $a_0 \lesssim 0.05$ pc. Star formation complicates the merger further by removing mass from the disc. In the feedback model we consider, this sets an effective limit to the disc mass. As a result, binary merging is unlikely unless the black hole mass ratio is $\la 0.001 $. Gas discs thus appear not to be an effective solution to the `last parsec’ problem for a significant class of mergers.

💡 Analysis

We compute the effect of an orbiting gas disc in promoting the coalescence of a central supermassive black hole binary. Unlike earlier studies, we consider a finite mass of gas with explicit time dependence: we do not assume that the gas necessarily adopts a steady state or a spatially constant accretion rate, i.e. that the merging black hole was somehow inserted into a pre–existing accretion disc. We consider the tidal torque of the binary on the disc, and the binary’s gravitational radiation. We study the effects of star formation in the gas disc in a simple energy feedback framework. The disc spectrum differs in detail from that found before. In particular, tidal torques from the secondary black hole heat the edges of the gap, creating bright rims around the secondary. These rims do not in practice have uniform brightness either in azimuth or time, but can on average account for as much as 50 per cent of the integrated light from the disc. This may lead to detectable high–photon–energy variability on the relatively long orbital timescale of the secondary black hole, and thus offer a prospective signature of a coalescing black hole binary. We also find that the disc can drive the binary to merger on a reasonable timescale only if its mass is at least comparable with that of the secondary black hole, and if the initial binary separation is relatively small, i.e. $a_0 \lesssim 0.05$ pc. Star formation complicates the merger further by removing mass from the disc. In the feedback model we consider, this sets an effective limit to the disc mass. As a result, binary merging is unlikely unless the black hole mass ratio is $\la 0.001 $. Gas discs thus appear not to be an effective solution to the `last parsec’ problem for a significant class of mergers.

📄 Content

arXiv:0906.0737v1 [astro-ph.CO] 3 Jun 2009 Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 11 June 2018 (MN LATEX style file v2.2) Black hole mergers: can gas discs solve the ‘final parsec’ problem? G. Lodato1,2, S. Nayakshin1, A.R. King1 & J. E. Pringle1,3 1Department of Physics & Astronomy, University of Leicester, Leicester, LE1 7RH, UK 2 Dipartimento di Fisica, Universit`a di Milano, Via Celoria, 16, Milano, I-20133, Italy 3 Institute of Astronomy, Madingley Road, Cambridge, CB1 0HA, UK 11 June 2018 ABSTRACT We compute the effect of an orbiting gas disc in promoting the coalescence of a central supermassive black hole binary. Unlike earlier studies, we consider a finite mass of gas with explicit time dependence: we do not assume that the gas necessarily adopts a steady state or a spatially constant accretion rate, i.e. that the merging black hole was somehow inserted into a pre–existing accretion disc. We consider the tidal torque of the binary on the disc, and the binary’s gravitational radiation. We study the effects of star formation in the gas disc in a simple energy feedback framework. The disc spectrum differs in detail from that found before. In particular, tidal torques from the secondary black hole heat the edges of the gap, creating bright rims around the secondary. These rims do not in practice have uniform brightness either in azimuth or time, but can on average account for as much as 50% of the integrated light from the disc. This may lead to detectable high–photon–energy variability on the relatively long orbital timescale of the secondary black hole, and thus offer a prospective signature of a coalescing black hole binary. We also find that the disc can drive the binary to merger on a reasonable timescale only if its mass is at least comparable with that of the secondary black hole, and if the initial binary separation is relatively small, i.e. a0 ≲0.05 pc. Star formation complicates the merger further by removing mass from the disc. In the feedback model we consider, this sets an effective limit to the disc mass. As a result, binary merging is unlikely unless the black hole mass ratio is ≲0.001. Gas discs thus appear not to be an effective solution to the ‘last parsec’ problem for a significant class of mergers. Key words: accretion, accretion discs – black hole physics – galaxies: formation – cosmol- ogy: theory – instabilities – hydrodynamics 1 INTRODUCTION In recent years, the process of shrinking a supermassive black hole (SMBH) binary by interaction with a circumbinary gaseous disc has been the topic of intense theoretical research. Initially this reflected attempts to overcome the ‘last parsec’ problem, i.e. the fact that dynamical friction with the stellar background is ineffective in shrinking the binary below separations smaller than 1pc (Begelman et al. 1980; Milosavljevi´c & Merritt 2001), to the point where gravitational radiation can complete the co- alescence of the two holes. More recently there has been in- terest in finding an electromagnetic counterpart to the grav- itational wave emission expected during the final stages of black hole coalescence (Ivanov et al. 1999; Armitage & Natarajan 2002; Milosavljevi´c & Phinney 2005; Dotti et al. 2006; Loeb 2007; Cuadra et al. 2009). In general most work on this subject has assumed driving by an accretion disc with constant mass inflow rate supplied from dis- tances far from the binary, and thus effectively assumed an infinite mass supply. However it is clear that in reality, where the gas is part of the galaxy merger producing the SMBH binary, the mass of gas ending up in the disc must be finite. Thus in general the disc does not settle to a steady state with a constant accretion rate, and its structure differs from a standard disc because it is affected by the tidal torque exerted by the binary. Moreover the rate or even the success of the shrinkage must depend on the total disc mass (as hinted by Cuadra et al, 2009). Here we investigate the problem by taking a disc of finite mass which is explicitly time–varying. We find significant differences from the results of assuming a steady– state accretion disc. We model the disc evolution in terms of a simple diffusion equation, including the effects of the tidal torques from the sec- ondary and calculating the binary orbit evolution self–consistently. Our initial condition is a finite disc mass concentrated at radii of the order of the initial binary separation. While still highly ide- alised, we regard this choice as more realistic than the assumption of a steady state, constant– ˙M disc, into which a second black hole has somehow been inserted. 2 Lodato et al The paper is organised as follows. In Section 2 we describe the general features of binary shrinkage by a gas disc. In Section 3 we describe our method for following both the binary and disc evolution. In Section 4 we describe the results. We constrain the disc mass required to bring the binary to coalescence and describe the expected appearanc

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