The tidal disruption rate in dense galactic cusps containing a supermassive binary black hole

Abstract

We consider the problem of tidal disruption of stars in the centre of a galaxy containing a supermassive binary black hole with unequal masses. We assume that over the separation distance between the black holes, the gravitational potential is dominated by the more massive primary black hole. Also, we assume that the number density of stars is concentric with the primary black hole and has a power‐law cusp. We show that the bulk of stars with a small angular‐momentum component normal to the black hole binary orbit can reach a small value of total angular momentum through secular evolution in the gravitational field of the binary, and hence they can be tidally disrupted by the larger black hole. This effect is analogous to the so‐called Kozai effect well known in celestial mechanics. We develop an analytical theory for the secular evolution of the stellar orbits and calculate the rate of tidal disruption. We compare our analytical theory with a simple numerical model and find very good agreement. Our results show that for a primary black hole mass of ∼106–107 M⊙, the black hole mass‐ratio q > 10−2, cusp size ∼1 pc, the tidal disruption rate can be as large as ∼10−2–1 M⊙ yr−1. This is at least 102–104 times larger than estimated for the case of a single supermassive black hole. The duration of the phase of enhanced tidal disruption is determined by the dynamical‐friction time‐scale, and it is rather short: ∼105 yr. The dependence of the tidal disruption rate on the mass ratio, and on the size of the cusp, is also discussed.

An Enhanced Rate of Tidal Disruptions in the Centrally Overdense E+a Galaxy NGC 3156

“…If a galaxy merger creates a SMBH binary in the center of the merger product, a short-lived ( ) phase of greatly enhanced TDE rates will ensue, due partially to the Kozai effect (Ivanov et al 2005) but mostly to chaotic three-body orbits (Chen et al 2011). Arcavi et al (2014) hypothesized that if a major merger triggers the starburst, E +As may overproduce TDEs due to the presence of hardening SMBH binaries.…”

The Tidal Disruption of Stars by Supermassive Black Holes

“…Very large increases in tidal disruption rates have been discussed previously in the context of galaxy mergers, both as a prompt electromagnetic signal immediately following SMBH coalescence (Stone & Loeb 2011), and due to resonances or chaotic stellar orbits at the end of the dynamical friction phase of an SMBH binary (Ivanov et al 2005;Chen et al 2009;Wegg & Nate Bode 2011;Chen et al 2011). Neither of these mechanisms is capable of producing a tidal disruption flare with an observable spatial offset, as both can only occur in galactic nuclei.…”

“…Moreover, we find that SMBH recoil results in a sequence of TDEs over a timescale of decades and potentially years, with a rate that is ∼ 4 orders of magnitude higher than the typical TDE rate in normal galaxies (Donley et al 2002). The existence of TDEs accompanying SMBH mergers has been studied in the past only for long time delays (∼ 10 6 -10 9 yr) before (Ivanov et al 2005;Chen et al 2009) or after (Komossa & Merritt 2008) the binary coalescence event. While previous studies have focused on mechanisms to slowly feed stars into an empty loss cone, here we show that GW recoil will instantaneously shift the loss cone to a non-empty region of phase space.…”

“…The hardening of a SMBHB, or SMBH-IMBH binary, can accomplish this. At orbital separations comparable to the larger black hole's influence radius, the combination of Kozai effects (Ivanov et al 2005) and chaotic three-body interactions (Chen et al , 2011 can lead to a huge enhancement in the TDE rate, perhaps up to ∼ 10 −1 disruptions per year. This phase is short-lived, however, typically lasting ∼ 10 5 yr and ending once ejection and disruption of the available stars has led the SMBH binary system to stall its hardening (Chen et al 2011).…”

“…The most theoretically secure method of feeding stars into the loss cone is standard two-body relaxation, which sets a conservative lower limit onṄ TDE between 10 −4 and 10 −6 yr −1 (Frank & Rees 1976;Lightman & Shapiro 1977;Cohn & Kulsrud 1978;Magorrian & Tremaine 1999;Wang & Merritt 2004). Alternative mechanisms for enhancing the TDE rate include triaxiality in a galaxy's nuclear potential , encounters with massive perturbers (Perets et al 2007), the effect of an inspiraling secondary SMBH (Ivanov et al 2005;Chen et al 2009Chen et al , 2011Wegg & Nate Bode 2011), and gravitational wave recoil after the merger of a binary SMBH (Stone & Loeb 2011). …”