Formation of galactic nuclei with multiple supermassive black holes at high redshifts The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Kulkarni, Girish, and Abraham Loeb. 2012. “Formation of Galactic Nuclei with Multiple Supermassive Black Holes at High Redshifts.” Monthly Notices of the Royal Astronomical Society 422 (2): 1306–23. https://doi.org/10.1111/j.1365-2966.2012.20699.x. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:41412234 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Mon. Not. R. Astron. Soc. 422, 1306–1323 (2012) doi:10.1111/j.1365-2966.2012.20699.x Formation of galactic nuclei with multiple supermassive black holes at high redshifts Girish Kulkarni1,2 and Abraham Loeb1 1Institute for Theory and Computation, Harvard University, 60 Garden Street, Cambridge, MA 02138, USA 2Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019, India Downloaded from https://academic.oup.com/mnras/article-abstract/422/2/1306/1035079 by guest on 26 September 2019 Accepted 2012 February 6. Received 2011 November 24; in original form 2011 July 3 ABSTRACT We examine the formation of groups of multiple supermassive black holes (SMBHs) in gas- poor galactic nuclei due to high merger rate of galaxies at high redshifts. We calculate the relative likelihood of binary, triple and quadruple SMBH systems, by considering the time- scales for relevant processes and by combining merger trees with N-body simulations for the dynamics of stars and SMBHs in galactic nuclei. Typical haloes today with mass M0 ≈ 14 11 10 M have an average mass of Mz =6 = 5 × 10 M at z ∼ 6, while rare haloes with 15 12 current mass M0 10 M have an average mass of Mz =6 = 5 × 10 M at that redshift. These cluster-size haloes are expected to host single galaxies at z ∼ 6. We expect about 30 14 per cent galaxies within haloes with present-day mass M0 ≈ 10 M to contain more than 15 two SMBHs at redshifts 2 z 6. For larger present-day haloes, with M0 10 M, this fraction is almost 60 per cent. The existence of multiple SMBHs at high redshifts can potentially explain the mass deficiencies observed in cores of massive elliptical galaxies, which are up to five times the mass of their central BHs. Multiple SMBHs would also lead to an enhanced rate of tidal disruption of stars, modified gravitational wave signals compared to isolated BH binaries and slingshot ejection of SMBHs from galaxies at high speeds in excess of 2000 km s−1. Key words: black hole physics – galaxies: evolution – galaxies: high-redshift – galaxies: kinematics and dynamics – galaxies: nuclei. Volonteri, Haardt & Madau 2003; Hopkins et al. 2006; Tanaka & 1 INTRODUCTION Haiman 2009). Most local galaxies host supermassive black holes (SMBHs) at their Existing merger tree models are based on the assumption that centres (Richstone et al. 1998; Ferrarese & Ford 2005). The SMBH any binary BH system, which inevitably forms in a galaxy’s merger mass Mbh is correlated with properties of the spheroidal nucleus history, coalesces on a short time-scale. However, the evolution of of the host galaxy, such as velocity dispersion (Ferrarese & Merritt SMBH binaries is a complex open problem and it is unclear if a 2000; Gebhardt et al. 2000; Ferrarese 2002; Graham 2008; Hu 2008; binary can merge within a Hubble time (Merritt & Milosavljevic´ Gultekin¨ et al. 2009; Graham et al. 2011) and luminosity (Magorrian 2005). One expects that during a merger event of two galaxies, the et al. 1998; McLure & Dunlop 2002; Marconi & Hunt 2003; Graham dynamics of their constituent SMBHs would proceed in three stages 2007; Gultekin¨ et al. 2009). Detection of bright quasars at redshifts (Begelman, Blandford & Rees 1980). In the first stage, the SMBHs z 6 (Fan et al. 2001; Mortlock et al. 2011) suggests that SMBHs sink to the centre of the gravitational potential of the merger rem- with masses as high as ∼2 × 109 M already existed at z ∼ 7. nant by dynamical friction and form a gravitationally bound binary. In the standard cold dark matter (CDM) cosmological model, The newly formed binary continues to lose energy and angular mo- growth of galaxies is hierarchical and galaxy mergers are expected mentum through its global gravitational interaction with many stars to be particularly frequent at redshifts z ∼ 6–20. As galaxies merge, until the separation between the SMBHs reduces to a value at which their central SMBHs can grow through coalescence and accretion the dominant mechanism of energy loss is the three-body interaction of gas. It is commonly postulated that SMBHs at lower redshifts between the binary and individual stars. This is the second stage grew out of seed black holes (BHs) in the first galaxies (Loeb of the binary’s evolution, and is known as the ‘hard stage’. The & Rasio 1994; Eisenstein & Loeb 1995; Kauffmann & Haehnelt precise definition of a hard SMBH binary varies in the literature, 2000; Menou, Haiman & Narayanan 2001; Bromm & Loeb 2003; but it is commonly assumed that the binary becomes hard when its semimajor axis a reaches a value given by (Yu 2002) Gm m 200 km s−1 2 a ≈ a ≡ = 2.8 pc, (1) E-mail: [email protected] (GK); [email protected] (AL) h 4σ 2 108 M σ C 2012 The Authors Monthly Notices of the Royal Astronomical Society C 2012 RAS Multiple black holes 1307 where stars in the galactic nucleus are assumed to have a one- it was suggested that a third SMBH closely interacting with a hard dimensional velocity dispersion σ ,andm denotes the mass of the SMBH binary can reduce the binary separation to a small value lighter SMBH. Finally, once the SMBH separation decreases to a either due to the eccentricity oscillations induced in the binary via small enough value, gravitational wave (GW) emission becomes the Kozai–Lidov mechanism (Blaes, Lee & Socrates 2002) or due the dominant mode of energy loss and the SMBHs coalesce rapidly. to repopulation of the binary’s loss cone due to the perturbation in This is the third stage of the SMBH binary evolution. The value the large-scale potential caused by the third BH (Hoffman & Loeb of the semimajor axis a at which the coalescence time-scale due to 2007). Blaes et al. (2002) found that the merger time-scale of an GW emission alone is t is given by (Peters 1964; Loeb 2010) inner circular binary can be shortened by as much as an order of t 1/4 M 3/4 magnitude, and that general relativistic precession does not destroy a(t) ≡ a (t) = 4.3 × 10−3 pc, the Kozai–Lidov effect for hierarchical triples that are compact gw 105 yr 2 × 108 M (2) enough. Asphericity in the stellar distribution can also potentially overcome the final parsec problem due to availability of centrophilic Downloaded from https://academic.oup.com/mnras/article-abstract/422/2/1306/1035079 by guest on 26 September 2019 where M is the total mass of the binary, and we have considered orbits (Khan, Just & Merritt 2011). two SMBHs with mass 108 M each on a circular orbit. (Larger In summary, there is substantial uncertainty in the current under- orbital eccentricity results in a shorter coalescence time-scale.) GW standing of the evolution of binary SMBHs. Clearly, if the SMBH emission takes over as the dominant mode of energy loss when binary coalescence time is longer than the typical time between suc- a = a (t ), where t is the hardening time-scale. gw h h cessive major mergers of the galaxy, then more than two SMBHs Among these three stages of evolution of an SMBH binary, the may exist in the nucleus of a merger remnant. We study this pos- largest uncertainty in the binary’s lifetime originates from the hard sibility in this paper. We calculate the relative likelihood of bi- stage, which can be the slowest of the three stages since the binary nary, triple and quadruple SMBH systems, by considering the time- quickly ejects all low angular momentum stars in its vicinity, thus scales for relevant processes and combining galaxy merger trees cutting off its supply of stars. This is known as the ‘final parsec with direct-summation N-body simulations for the dynamics of problem’ (Milosavljevic´ & Merritt 2003b). For example, Yu (2002) stars and SMBHs in galactic nuclei. An obvious question regard- studied coalescence of SMBH binaries in a sample of galaxies ob- ing galactic nuclei with multiple SMBHs is whether such systems served by Faber et al. (1997) and found that spherical, axisymmetric can be long-lived. We consider this question here. Finally, systems or weakly triaxial galaxies can all have long-lived binary SMBHs with multiple SMBHs are likely to be interesting because of ob- that fail to coalesce. Similarly, Merritt & Milosavljevic´ (2005) found servational effects involving their effect on the properties of the that the time spent by a binary is less than 1010 years only for bi- host bulge, the enhancement in the rate of tidal disruption of stars, naries with very low-mass ratios (10−3).1 Furthermore, Merritt their associated GW and electromagnetic signals, and the slingshot & Milosavljevic´ (2005) showed that a binary may not be able to ejection of SMBHs at high speeds. We study some of these effects. interact with all the stars in its loss cone, thereby increasing the time In Section 2 we review previous results on galactic nuclei spent in the hard stage even further; they found that in a nucleus with more than two SMBHs.