BH and NS mergers in GN: the role of triples

Black hole and neutron star mergers in Galactic Nuclei: the role of triples

Giacomo Fragione, Nathan W. C. Leigh, Rosalba Perna
Racah Institute for Physics, The Hebrew University, Jerusalem 91904, Israel
Departamento de Astronomía, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción, Chile
Department of Astrophysics, American Museum of Natural History, Central Park West and 79th Street, New York, NY 10024
Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA
Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA

Nuclear star clusters that surround supermassive black holes (SMBHs) in galactic nuclei are thought to contain large numbers of black holes (BHs) and neutron stars (NSs), a fraction of which form binaries and could merge by Kozai-Lidov oscillations (KL). Triple compact objects are likely to be present, given what is known about the multiplicity of massive stars, whose life ends either as a NS or a BH. In this paper, we present a new possible scenario for merging BHs and NSs in galactic nuclei. We study the evolution of a triple black hole (BH) or neutron star (NS) system orbiting an SMBH in a galactic nucleus by means of direct high-precision -body simulations, including Post-Newtonian terms. We find that the four-body dynamical interactions can increase the KL angle window for mergers compared to the binary case and make BH and NS binaries merge on shorter timescales. We show that the merger fraction can be up to times higher for triples than for binaries. Therefore, even if the triple fraction is only of the binary fraction, they could contribute to the merger events observed by LIGO/VIRGO in comparable numbers.

Galaxy: centre – Galaxy: kinematics and dynamics – stars: black holes – stars: kinematics and dynamics – galaxies: star clusters: general

1 Introduction

The LIGO-Virgo collaboration has recently released a catalogue of compact object (CO) mergers due to gravitational wave (GW) emission, comprised of ten merging black hole (BH-BH) binaries and one merging neutron star (NS-NS) binary (The LIGO Scientific Collaboration & the Virgo Collaboration, 2018). Studying the possible mechanisms that lead to BH and NS mergers is currently an active area of research. Several scenarios for their origins have been proposed. The possibilities include isolated binary evolution through a common envelope phase (Belczynski et al., 2016), chemically homogeneous evolution in short-period stellar binaries (Mandel & de Mink, 2016; Marchant et al., 2016), stellar triples (Antonini et al., 2017; Silsbee & Tremaine, 2017), quadruple systems (Fragione & Kocsis, 2019; Liu & Lai, 2019) and Kozai-Lidov (KL) mergers of binaries in galactic nuclei (Antonini & Perets, 2012; Hamers et al., 2018; Hoang et al., 2018; Fragione et al., 2018; Grishin et al., 2018). These mergers could either occur in active galactic nuclei (AGN) disks (e.g. McKernan et al., 2018; Secunda et al., 2018) or in star clusters (Askar et al., 2017; Banerjee, 2018; Fragione & Kocsis, 2018; Rodriguez et al., 2018). While these models typically predict roughly the same rates ( Gpc yr), their respective contributions could potentially be disentagled using the observed eccentricity, spin, mass and redshift distributions (see e.g. O’Leary et al., 2016; Samsing et al., 2018; Zevin et al., 2018; Perna et al., 2019).

The wide literature on dynamically-induced mergers has focused on GW signals generated from merging BH-BH binaries in open and globular clusters. However, galactic nuclei typically have total stellar masses comparable to the combined stellar masses of open cluster systems, and a significant fraction of globular clusters in a given galaxy (Böker et al., 2004; Côté et al., 2006). Thus, galactic nuclei represent a promising environment where CO binaries can form dynamically, then harden and finally merge due to the emission of GW radiation (O’Leary, Kocsis & Loeb, 2009; Antonini & Rasio, 2016; Petrovich & Antonini, 2017; Fragione, 2019; Rasskazov & Kocsis, 2019).

Compared to open and globular clusters, studies focused on galactic nuclei have generally either concentrated on how large-scale nuclear star cluster dynamics ( pc) can drive CO binaries to merge within a Hubble time (Antonini & Rasio, 2016; Petrovich & Antonini, 2017; Gondán et al., 2018), or on how these binaries merge due to eccentric KL oscillations imparted from the enormous SMBH potential ( pc; Antonini & Perets, 2012; Hoang et al., 2018; Fragione et al., 2018; Hamers et al., 2018).

Triple stars are likely not rare in open clusters and possibly even globular clusters, in particular for massive stars whose lives end either as a NS or a BH (Duquennoy & Mayor, 1991; Raghavan et al., 2010; Sana et al., 2013; Tokovinin, 2014a, b; Dunstall et al., 2015; Sana, 2017). Little attention has been devoted to the role of merging binary COs in triple systems in galactic nuclei, where they can orbit a central SMBH. Previous studies have primarily focused on determining the merger rates from isolated triple BHs (Antonini et al., 2017; Silsbee & Tremaine, 2017) or triple BHs in globular clusters (Antonini et al., 2016). Compared to binary systems, triples have an additional degree of freedom and KL oscillations can be imparted to the inner binary either by the SMBH or by the third companion (Lidov, 1962; Kozai, 1962). The interplay between these two KL mechanisms working together can give rise to a rich and complicated dynamical evolution for the inner binary (Grishin et al., 2018). This could potentially lead to a larger number of mergers due to, among other mechanisms, possible resonances (Hamers & Lai, 2017).

In this paper, we propose a new scenario for merging BHs and NSs in galactic nuclei. For the first time, we study the evolution of a triple composed of COs orbiting an SMBH in a galactic nucleus and compare it to the CO binary case (Fragione et al., 2018). We consider a four-body system consisting of a triple BH-BH-BH/NS-NS-NS and an SMBH (see Figure 1). We make a systematic and statistical study of these systems by means of direct high-precision -body simulations, including Post-Newtonian (PN) terms up to order PN2.5. Compared to secular evolution, our approach allows us to correctly follow the large eccentricity values attained by CO binaries via KL cycles (Antognini et al., 2014).

The paper is organized as follows. In Section 2, we discuss what is to date known about the multiplicity properties of BHs and NSs in galactic nuclei and star clusters. In Section 3, we discuss the relevant timescales for the systems considered in this paper. In Section 4, we present our numerical methods to determine the rate of BH and NS mergers in triples orbiting massive black holes, for which we discuss the results. Finally, in Section 5, we discuss the implications of our findings for future observations of mergers involving BHs and NSs, and draw our conclusions.

Figure 1: The four-body system studied in the present work. We denote the mass of the SMBH as , the masses of the components of the inner binary as and , and the mass of the third companion of the triple as . The semi-major axis and eccentricity of the outer orbit are denoted by and , respectively. For the triple, we denote with and the semi-major axis and eccentricity of the inner orbit. We further denote with and the semi-major axis and eccentricity of the outer orbit.

2 Multiplicity

In this section we briefly review what is known from the literature about multiplicity (i.e., binaries and triples) in the Galactic field, open clusters, globular clusters and nuclear star clusters.

2.1 The Galactic field

Raghavan et al. (2010) updated the seminal work of Duquennoy & Mayor (1991) by selecting from the Hipparcos catalogue a volume-limited sample of field solar-type primary stars in the solar neighbourhood. The authors find that the observed fractions of objects that are single, double, triple and higher-order systems are, respectively, 56 2, 33 2, 8 1 and 3 1 per cent. Subsequent work showed that most triples composed of low-mass stars tend to be approximately co-planar, whereas the inner and outer orbits of triples composed of massive stars tend to be more inclined relative to each other (e.g. Moe & Kratter, 2018).

2.2 Open clusters

The young star-forming region Taurus-Auriga has an exceedingly low density, such that dynamical interactions involving multiples should be very rare, if they occur at all. In fact, Taurus-Auriga is the only known open cluster with a triple fraction higher than that observed in the Galactic field (Raghavan et al., 2010; Leigh & Geller, 2013). Kraus et al. (2011) performed a high-resolution imaging study to characterize the multiple-star populations in Taurus-Auriga. They found that between of all targets are multiples composed of at least two stars. Thus, only of their objects are single stars.

More nearby open clusters (OCs) are also known to have comparably high multiplicity fractions (see Leigh & Geller (2013) for a more detailed review of the following studies). The Hyades (Patience et al., 1998), Pleiades (Mermilliod et al., 1992; Bouvier et al., 1997) and Praesepe (Mermilliod & Mayor, 1999; Bouvier et al., 2001) have binary fractions of, respectively, 35%, 34% and 40%, and triple fractions of, respectively, 6%, 3% and 6%.

Finally, old open clusters, with masses and densities typically higher than the above OCs, have also been observed to harbour high binary fractions. For example, for the old ( 4 Gyr) OC M67, Fan et al. (1996) observed a binary fraction of 45%. For comparison, the old ( 7 Gyr) OC NGC 188 has an observed multiplicity fraction of 27% (Geller et al., 2009). Following Leigh & Geller (2013), if we adopt the observed value for the ratio between the fractions of binaries and triples from Latham & Milone (1996), or / 0.1, we infer triple fractions for M67 and NGC 188 of, respectively, 5% and 2%.

2.3 Globular clusters

In globular clusters (GCs), the situation is quite different. Due to their much higher central densities compared to OCs, the multiple star populations in massive GCs can most efficiently be studied using photometry. The pioneering study of Milone et al. (2012) analyzed the main-sequence (MS) binary populations in a sample of 59 GCs. The authors find photometric binary fractions ranging from less than a percent to a few tens of percent, and a previously reported (Sollima et al., 2007) anticorrelation between the binary fraction and the total cluster mass. Sollima (2008) argued that this trend can arise assuming an universal initial binary fraction combined with the dynamical disruption of binaries by (mostly) interloping single stars. Here, the disruption of soft binaries in the cluster core generates the observed anticorrelation, combined with the evaporation of single stars from the cluster outskirts which serves to increase the binary fraction throughout the cluster in preferentially low-mass clusters evaporating at the fastest rates (e.g. Fregeau et al., 2009).

Other than identifying binaries photometrically above and/or to the red of the main sequence in the cluster colour-–magnitude diagram (e.g. Milone et al., 2012), binaries can also be found at higher energies as exotic objects like low-mass X-ray binaries (LMXBs; e.g. Hut et al., 1991), millisecond pulsars (MSPs; e.g. Verbunt et al., 1987) and cataclysmic variables (CVs; e.g. Pooley & Hut, 2006; Cohn et al., 2010). Blue straggler (BS) formation is also thought to involve binary or triple stars (e.g. Perets & Fabrycky, 2009; Knigge et al., 2009; Leigh & Sills, 2011). This can occur in several different ways, such as mass transfer within a binary, collisions during encounters involving binaries or even some triple-based mechanism (e.g. Leigh & Sills, 2011; Geller et al., 2013) such as KL-induced mergers (e.g. Perets & Fabrycky, 2009; Naoz & Fabrycky, 2014).

To date, only one triple star system is known to exist in the dense environments characteristic of GCs (e.g. Prodan & Murray, 2012). The system in question, called 4U 1820-30, lives near the centre of the GC NGC 6624. It consists of a low-mass X-ray binary with a NS primary and a WD secondary, in orbit with a period s. There is also a large luminosity variation for this system (a factor 2) with a period of 171 days. This longer period is thought to be due to the presence of a tertiary companion (Grindlay et al., 1988).

2.4 Nuclear clusters

Much less is known of the multiple star populations in nuclear star clusters (NSCs). Binaries can only be detected at home, in the Milky Way’s Galactic nucleus. But here, significant reddening intervenes along the relevant line of sight, rendering observations of the Galactic Centre challenging at most wavelengths.

There are at least 3 known stellar binaries within the central pc of the Galactic Centre (e.g. Naoz et al., 2018; Ott et al., 1999; Rafelski et al., 2007). What’s more, it is still possible that many of the observed S-stars are unresolved binaries (e.g. Naoz et al., 2018). Even S0-2, which has the closest pericentre passage to Sgr A* and has received relatively careful scrutiny in recent years, could still be an unresolved binary (Chu et al., 2018).

More recently, Hailey et al. (2018) discovered X-ray sources within pc from Sgr A*, at least in projection. The authors argue that the accretors must be BHs instead of NSs for the majority of their sample. This argument is based on attempting to relate the properties of the observed spectra to those of other NSs known to be present in the Galactic Centre. These authors argue that the new X-ray sources show, in this regard, unique spectral features relative to the other known NSs in the Galactic Centre.

As for triples, to the best of our knowledge, there are none yet known to exist in our Galactic Centre. If they do exist, they likely formed from a relatively recent episode of star formation, which there is plenty of observational evidence to support (Bartko et al., 2009). This is because in the high-density, high-velocity dispersion environment of the Galactic Centre, triples should be rapidly destroyed due to dynamical interactions with single stars (e.g. Leigh et al., 2018).

3 Timescales

Figure 2: KL timescales (Eqs. 4-5-6), 1+3 encounter timescale for triples (Eq. 7), and evaporation timescale (Eq. 9) as a function of distance from the SMBH for different parameters of the triple. The masses of the BHs are .

A triple system made up of an inner binary that is orbited by an outer companion undergoes KL oscillations in eccentricity whenever the initial mutual orbital inclination of the inner and outer orbit is in the window . The KL oscillations occur on a secular timescale (Antognini, 2015; Naoz, 2016)


where is the mass of the outer body, is the total mass of the triple system, and and are the orbital periods of the inner and outer binary, respectively. At the quadruple order of approximation, the maximal eccentricity is a function of the initial mutual inclination


The inner binary eccentricity approaches almost unity if . In the case of a CO binary, the large values reached by the eccentricity of the inner binary during the KL excursions make its merger time shorter since it efficiently dissipates energy when (e.g., see Antonini & Perets, 2012; Antognini, 2015). Tidal bulges and relativistic precession can suppress KL cycles (Naoz, 2016). In particular, for COs the relevant process is general relativistic precession that operates on a timescale


Thus, the KL oscillations of the orbital elements are damped by relativistic effects in the region of parameter space where .

For systems studied in this paper, there are three relevant KL timescales. The first can be calculated by considering the SMBH as a perturber of the inner binary of the CO triple. In this case and


The second KL timescale is obtained when considering the effect of the SMBH on the binary made up of the centre-of-mass of the inner binary and the third companion of the CO triple. Also in this case, and


where . Of course, . The last KL timescale refers to tidal perturbations of the third BH/NS on the inner binary of the CO triple (”internal” KL timescale of the triple)


Figure 2 shows these three relevant KL timescales as a function of distance from the SMBH, for different parameters of the triple. For reference, we fix . The internal KL timescale for the CO triple is mainly set by the (outer) semi-major axis . For the case AU and AU, is smaller than and when AU for (i.e. a Milky Way-like galaxy). For the same and AU, becomes the smallest only for AU– AU. On the other hand, if we reduce the inner semi-major axis of the triple to AU, the typical distance at which the internal triple KL mechanism operates on the shortest timescale increases by a factor of .

In Figure 2, we also plot two additional timescales relevant for triples in galactic nuclei. The first one is the typical encounter timescale for triples (Leigh & Sills, 2011),


where and are the fractions of binaries and triples in the galactic nucleus, is the central density in stars and is the velocity dispersion. The second timescale is the evaporation timescale due to dynamical interactions with field stars in the dense environment of a galactic nucleus. A triple can evaporate when


where is the internal orbital energy of the triple and . This process happens on an evaporation timescale (Binney & Tremaine, 1987)


where is the Coulomb logarithm. Both the encounter timescale and the evaporation timescale are of the order of Myr for a Milky Way-like galaxy.

In the case of a CO binary orbiting an SMBH, we expect most of the mergers due to the KL mechanism to happen when (Fragione et al., 2018). When a CO triple is present, the relative interplay among the three different KL mechanisms can bring the CO orbits into the relevant KL window, and hence induce mergers via GW emission because of a faster energy dissipation rate supplied by the increasing eccentricity. This is also favoured by the possible resonance between nodal precession and KL oscillations, whenever these two mechanisms operate on comparable timescales (Hamers & Lai, 2017; Grishin et al., 2018).

4 N-Body Simulations

In this section we quantify the physical properties of the merging triples with direct N-body simulations in order to compute their merger rates and assess whether they are enhanced with respect to the binary case.

Triple Type (AU)
BH uniform
BH uniform
BH uniform
BH thermal
BH uniform
BH uniform
BH uniform
BH uniform
NS - uniform
NS - uniform
NS - uniform
NS - thermal
NS - uniform
Table 1: Models: triple type, slope of the BH mass function (), slope of the outer semi-major axis distribution (), eccentricity distribution (), maximum outer semi-major axis of the triple (), merger fraction from the -body simulations ().

In our study, we consider an SMBH orbited by a triple CO, made up of either three BHs or three NSs. We assume an SMBH mass of for a Milky-Way like nucleus.

For the assumed distribution of BH masses, the initial mass function in triples is highly uncertain (and also likely to vary depending on the formation mechanism). Therefore we use a generic, parameterized form corresponding to a negative power-law distribution


in the mass range 111Note that pulsational pair instabilities may limit the maximum mass to (Belczynski et al., 2016)., and sample the three BH masses independently. To study how the results depend on our assumptions, we vary the slope of the BH mass function in the range , , , (O’Leary et al., 2016). For NSs, we fix the mass to (e.g. Lattimer & Prakash, 2005; Fragione, Pavlík & Banerjee, 2018).

The numbers and spatial profiles of BHs and NSs surrounding SMBHs are unconstrained from an observational point of view. Stars and COs tend to form a power-law density cusp () around an SMBH, where lighter and heavier objects develop shallower and steeper cusps, respectively (Bahcall & Wolf, 1976). Typically, stars tend to have , whereas BHs tend to have due to mass segregation (Alexander, 2017). We assume that the BH and NS number densities follow a cusp with , and we study the effects of the cusp slope, by considering a steeper cusp () for BHs, and a shallower cusp () for NSs. We take the maximum outer semi-major axis to be  pc (Hoang et al., 2018).

The triple (BH-BH-BH or NS-NS-NS) inner and outer semi-major axis and eccentricity distributions are not well known observationally. Apart from their initial distributions, it should be taken into account that the dense environments characteristic of galactic nuclei or star clusters could cause both distributions to change or diffuse over time (Hopman, 2009). We sample the triple inner and outer semi-major axis and , respectively, by adopting a log-uniform distribution. Given the uncertainties in the orbital parameters of the triples, we explore a wide range of values for the outer triple semi-major axis; in particular, we study models with AU– AU– AU.

The relative inclinations of the inner and outer orbits are also poorly constrained observationally. Observations have shown that inner and outer orbital planes of triples composed of massive stars tend to be inclined relative to each other (Moe & Kratter, 2018), which may hint at moderately high relative inclinations between the inner and outer orbital planes of the triple COs. For the sake of generality, we draw the mutual inclination angles between the inner binary orbit with respect to the SMBH orbit () and the third companion in the triple’s orbit () from an isotropic distribution.

After we sample from the relevant distributions, we check that the Mardling & Aarseth (2001) criterion, namely


is satisfied for each hierarchy in our four-body system in order to ensure orbital stability. In the previous equation, and are the total inner mass and the perturber mass, respectively, is the pericenter of the perturber, is the inner semi-major axis, and (either or in our system) is the relative orbital inclination (in radians).

Given the above sets of initial parameters, we integrate the system of differential equations of motion of the 3-bodies


with ,,,. The integrations are performed using the archain code (Mikkola & Merritt, 2006, 2008), a fully regularized code able to model the evolution of systems of arbitrary mass ratios and large eccentricities with extreme accuracy. archain includes PN corrections up to order PN2.5.

We fix the total integration time to Myr. As discussed in Fragione et al. (2018), this total integration time is smaller than the typical timescale for vector resonant relaxation to operate ( few Myr, see e.g. Kocsis & Tremaine, 2015), which reorients the binary centre-of-mass orbital plane with respect to the SMBH, thus affecting the relative inclination of the inner and outer orbital planes. This also affects the relative LK dynamics and renders the -body approximation insufficient. The in-plane precession induced by the nuclear cluster potential and departures from spherical symmetry in the galactic nucleus would make the CO center of mass orbit precess even faster than is quantified by vector resonant relaxation alone in a MW-like nucleus (Petrovich & Antonini, 2017). However, in the case of triples, the most relevant constraints most likely come from the encounter and evaporation timescales, both of which are of the order of Myr for a Milky Way-like galaxy.

Figure 3: Distributions of the initial orbital inclinations of the binaries that merge in our simulations with respect to the SMBH (, top panel) and the third companion in the triple (, bottom panel) in Models MW, for , and different assumptions for . Also shown is the distribution of initial inclinations for BH binary mergers (Fragione et al., 2018).
Figure 4: Top: mass distribution of merging BH-BH binaries in triples orbiting a SMBH in a Milky Way-like nucleus, for different values of , and . Bottom: Comparison of the total mass of merging BHs in binaries (Fragione et al., 2018) and triples, for different values of , , and AU.

4.1 Inclination distribution

We show in Fig. 3 the distribution of the initial orbital inclinations of the binaries that merge in our simulations with respect to the SMBH (top panel), for , and different . For the case of a binary CO orbiting an SMBH, most of the binaries that merge have initial inclinations with respect to the SMBH, where the enhancement of the maximum eccentricity is expected to be the largest due to KL oscillations whenever not suppressed by GR precession (Fragione et al., 2018). The distribution thus results in a sharp peak at and only a few mergers have larger or smaller initial inclinations. For a triple CO orbiting an SMBH, this distribution is no longer sharply peaked, but instead is almost isotropic.

Figure 5: Cumulative distribution functions of merger times for BH-BH and NS-NS binaries in triples orbiting an SMBH. Top: merger times of BH-BH mergers for different values of and (we fix ). Bottom: comparison to mergers in binaries (Fragione et al., 2018) for BH-BH mergers ( AU, ).

On the other hand, the distribution of the orbital inclination of the third companion with respect to the inner binary in the triple (bottom panel) is found to peak at , but with non-negligible tails. Isolated triples that merge due to the KL mechanism show a very pronounced peak at , with only a few mergers happening in low-inclination systems (Antonini et al., 2017). The reason for these deviations comes from the fact that a quadruple system presents a more complicated dynamical evolution (Grishin et al., 2018), with three different KL mechanisms competing. This, and possible resonances between nodal precession and KL oscillations, can arise. This could make even low-inclination systems merge (Hamers & Lai, 2017).

4.2 Mass distribution

Figure 4 (top panel) illustrates the distribution of the total mass of merging BH-BH-BH triples orbiting a SMBH in a Milky Way-like nucleus, for different values of , and . For binaries orbiting an SMBH (Fragione et al., 2018), the resulting total mass distribution is not significantly affected by the slope of the density profile around the SMBH, with a roughly constant shape in the range and a tail extending up to . Also, the extent of the triple does not influence the total mass distribution. The only parameter that sets the distribution properties is the slope of the BH mass function. As expected, we find that the shallower the slope of the BH mass function, the larger the typical total mass of merging BH-BH binaries. For , the distribution is peaked at a total mass of with a tail that extends up to . For larger values of , the tail gradually disappears and the distribution is peaked at . We find that of the mergers have total masses , , , and for , , , and , respectively.

In the bottom panel of Fig. 4, we show a comparison between the total mass of merging BHs in binaries (Fragione et al., 2018) and triples orbiting a SMBH, assuming and different values for the parameter (for triples we fix AU). We find that the total mass of merging binaries is nearly independent of the multiplicity of the system. Thus, the main parameter that governs the shape of the final distribution for the total mass of merged BHs is the slope of the BH mass function.

4.3 Merger times

Due to KL cycles, the eccentricity of the inner binary in the triple can approach almost unity when and the inner binary merger time becomes shorter due to efficient energy dissipation at pericentre via KL oscillations. In the top panel of Fig. 5, we show the cumulative distribution functions (CDFs) of merger times for BH-BH binaries in triples orbiting an SMBH of mass . Different values for the parameters , and do not affect the distribution of merger times.

In the bottom panel of Fig. 5, we compare the CDFs of BHs merging in binaries (Fragione et al., 2018) to those in triples orbiting a Milky Way-like SMBH, for different values of . BHs merge in triples on shorter timescales compared to BHs that merge in binaries, independent of the slope of the BH mass function ( AU, ). We find that of the mergers have typical merger timescales of yr and yr, respectively, for the binary and triple cases. The most likely reason for these deviations comes from a richer dynamical evolution combined with possible resonances that can arise in the case of triples orbiting an SMBH.

5 Discussion and conclusions

We have presented a new scenario for merging BHs and NSs in galactic nuclei. We have studied the mergers of binary BHs and NSs in triples orbiting an SMBH in a Milky Way-like galactic nucleus. By conducting a series of high-precision numerical integrations, we have quantified the relative differences with the case where the BHs and NSs are in binaries (Fragione et al., 2018). We find that, unlike the binary case in which the initial orbital inclination of the merging BHs/NSs is sharply peaked at , in the case of triples the distribution is significantly broader, due to the more complex dynamics of the triple-SMBH system and possible resonances between nodal precession and KL oscillations.

To accurately determine the global BH merger rate from this channel, we would need to quantify the population of triple BHs and NSs in galactic nuclei and star clusters, which is highly uncertain. For the binary case, this rate is thought to be of the order of (Antonini & Perets, 2012; Fragione et al., 2018; Hamers et al., 2018; Hoang et al., 2018). Nevertheless, the multiplicity fraction of high-mass main-sequence stars is large, with each star having two or more companions on average (Sana, 2017). We find that the merger fraction of triple BH and NS systems can be larger than the one for binaries, by up to a factor of (see the last column of Tab. 1). Our results thus suggest that dynamically-driven BH and NS mergers in this scenario may be important and contribute to the merger events observed by LIGO/VIRGO.

We caution, however, that there are a lot of uncertainties regarding the exact population of stars and CO triples, as well as their mass and orbital parameters distributions. In our simulations, we only consider triples made up of all BHs or all NSs, which implies that their progenitors had a mass ratio near unity. While this is the case for a subset of systems, additional simulations incorporating all possible compositions of the CO triples will be needed to precisely compute how the merger fraction depends on the specific composition of the triple. Importantly, the maximum outer semi-major axis of triples plays an important role in determining the relevant timescales. In particular, both the the 3+1 interaction timescale and the triple evaporation timescale depend crucially on it. As we show, these timescales can be as short as a few Myrs, such that that more compact triples will probably dominate the rate. This would in turn imply that CO triples in galactic nuclei need to be born more compact than in the field, if they were to contribute to the observed GW merger events.

What makes these events especially interesting for the GW community is the fact that they have enhanced chance of being detected also in the electromagnetic (EM) spectrum. For a binary NS merger, the intensity of the gamma-ray radiation, which primarily depends on the amount of mass available for accretion, is primarily determined by the properties (namely mass and equation of state) of the merging stars (Shibata et al., 2006; Rezzolla et al., 2010; Giacomazzo et al., 2013; Hotokezaka et al., 2013). However, if the merger event drives a relativistic jet as evinced by the observations of GW170817/GRB170817A (Abbott et al., 2017) and detailed broadband modeling (Lazzati et al., 2018), then the density of the medium in which the event occurs also plays an important role. In fact, the relativistic jet will produce bright radiation (known as an afterglow), spanning the full EM spectrum, from hard X-rays to the radio, and the peak of this emission scales as (Sari et al., 1998). The binary NS mergers from triples orbiting an SMBH studied here typically have short merger times, even shorter than those of isolated binaries alone, as studied by Fragione et al. (2018). As such, they are expected to merge in the innermost regions of a galaxy, where densities are at their highest. For gas densities of a few cm, the EM brightness would allow for their detection in multiple bands well beyond the LIGO horizon, as computed by Fragione et al. (2018). EM observations are a crucial element allowing for event localization, and hence to test the nuclear origins of these events.

Mergers of binaries made up of two BHs are more likely to be dark, lacking the natural reservoir of accretion matter provided by the tidal disruption of a NS immediately preceding the final coalescence. While some reservoir of material could still be found around one of the BHs as a dead disk remnant from the SN explosion (Perna et al., 2016), this may not be a common scenario. If the SMBH is surrounded by a dense disk as in active galactic nuclei then, if the binary BH merges within the disk, a temporary accretion of matter at high rates can ensue (Bartos et al., 2017), resulting in a possible EM counterpart. Nevertheless, for the case of a binary BH in a triple there is the additional possibility of producing electromagnetic radiation if the third object, instead of being a BH, is a main sequence star that fills its Roche lobe and generates a circumbinary disk around the inner binary BH (Chang & Murray, 2018). As the binary BH merges, the loss of energy via GWs along with a possible merger kick can result in orbital crossings of the disk particles, resulting in disk shocking. Alternatively (or additionally) the circumbinary disk will eventually accrete on a viscous timescale upon merger of the binary. All together, binary mergers from triples near SMBHs may constitute an especially important channel for combined GW/EM transients.


GF is supported by the Foreign Postdoctoral Fellowship Program of the Israel Academy of Sciences and Humanities. GF also acknowledges support from an Arskin postdoctoral fellowship. NL and RP acknowledge support by NSF award AST-1616157. GF thanks Seppo Mikkola for helpful discussions on the use of the code archain. Simulations were run on the Astric cluster at the Hebrew University of Jerusalem.


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