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N-Body Dynamics of Intermediate Mass-Ratio Inspirals in Star Clusters Haster, Carl-Johan; Antonini, Fabio; Kalogera, Vicky; Mandel, Ilya

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N-Body Dynamics of Intermediate Mass-Ratio Inspirals in Star Clusters Haster, Carl-Johan; Antonini, Fabio; Kalogera, Vicky; Mandel, Ilya University of Birmingham n-body dynamics of intermediate mass-ratio inspirals in star clusters Haster, Carl-Johan; Antonini, Fabio; Kalogera, Vicky; Mandel, Ilya DOI: 10.3847/0004-637X/832/2/192 License: None: All rights reserved Document Version Peer reviewed version Citation for published version (Harvard): Haster, C-J, Antonini, F, Kalogera, V & Mandel, I 2016, 'n-body dynamics of intermediate mass-ratio inspirals in star clusters', The Astrophysical Journal, vol. 832, no. 2. https://doi.org/10.3847/0004-637X/832/2/192 Link to publication on Research at Birmingham portal General rights Unless a licence is specified above, all rights (including copyright and moral rights) in this document are retained by the authors and/or the copyright holders. 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Oct. 2021 Draft version June 24, 2016 Preprint typeset using LATEX style emulateapj v. 01/23/15 N−BODY DYNAMICS OF INTERMEDIATE MASS-RATIO INSPIRALS IN GLOBULAR CLUSTERS Carl-Johan Haster School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom and Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) & Dept. of Physics and Astronomy, 2145 Sheridan Rd, Evanston, IL 60208, USA Fabio Antonini Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) & Dept. of Physics and Astronomy, 2145 Sheridan Rd, Evanston, IL 60208, USA Vicky Kalogera Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) & Dept. of Physics and Astronomy, 2145 Sheridan Rd, Evanston, IL 60208, USA Ilya Mandel School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom Draft version June 24, 2016 ABSTRACT The intermediate mass-ratio inspiral of a stellar compact remnant into an intermediate mass black hole (IMBH) can produce a gravitational wave (GW) signal that is potentially detectable by current ground-based GW detectors (e.g., Advanced LIGO) as well as by planned space-based interferome- ters (e.g., eLISA). Here, we present results from a direct integration of the post-Newtonian N-body equations of motion describing stellar clusters containing an IMBH and a population of stellar-mass black holes (BHs) and solar mass stars. We take particular care to simulate the dynamics closest to the IMBH, including post-Newtonian effects up to order 2.5. Our simulations show that the IMBH readily forms a binary with a BH companion. This binary is gradually hardened by transient 3-body or 4-body encounters, leading to frequent substitutions of the BH companion, while the binary’s eccen- tricity experiences large amplitude oscillations due to the Lidov-Kozai resonance. We also demonstrate suppression of these resonances by the relativistic precession of the binary orbit. We find an inter- mediate mass-ratio inspiral in one of the 12 cluster models we evolved for ∼ 100 Myr. This cluster hosts a 100M IMBH embedded in a population of 32 10M BH and 32,000 1M stars. At the end of the simulation, after ∼ 100 Myr of evolution, the IMBH merges with a BH companion. The IMBH–BH binary inspiral starts in the eLISA frequency window (& 1mHz) when the binary reaches an eccentricity 1 − e ' 10−3. After ' 105 years the binary moves into the LIGO frequency band with a negligible eccentricity. We comment on the implications for GW searches, with a possible detection within the next decade. 1. INTRODUCTION rell et al. 2009; Davis et al. 2011; Godet et al. 2014), Intermediate mass black holes (IMBHs) are conjec- but these dynamical measurements alone can not pro- tured to occupy the mass range between stellar-mass vide conclusive proof for the existence of IMBHs. If these lower-mass IMBHs reside in globular clusters, black holes (BHs), with masses . 100M , and super- 6 they will play an important role in cluster dynamics (e.g. massive black holes with masses & 10 M (see Miller & Colbert 2004, for a review). While the existence Trenti 2006; Umbreit & Rasio 2013; Konstantinidis et al. arXiv:1606.07097v1 [astro-ph.HE] 22 Jun 2016 of some IMBH candidates in dwarf spheroidal galaxies 2013; Leigh et al. 2014; MacLeod et al. 2016). Of particu- has been conjectured by extending the M–σ relation lar interest to our study is the likely tendency of IMBHs (Graham & Scott 2013) (but see Maccarone & Servillat to dynamically form compact binaries with other com- 2008), dynamical measurements of IMBHs in the few- pact remnants (e.g. Taniguchi et al. 2000; Miller 2002; hundred solar-mass range are extremely challenging (e.g., Miller & Hamilton 2002; Amaro-Seoane & Freitag 2006; Pasquato et al. 2016). The best evidence for such lower Brown et al. 2007; Mandel et al. 2008; Amaro-Seoane & Santamaría 2010; Mapelli et al. 2010; Mapelli 2016). mass IMBHs (with mass ∼ 100M ) could come from ul- traluminous X-ray sources (but see Berghea et al. 2008); Generally, these analyses find that the IMBH readily cap- for example, (Pasham et al. 2014) have claimed a mass of tures a binary companion. The binary is subsequently hardened through a sequence of 3-body and 4-body in- ∼ 400 M for M82 X-1 from quasi-periodic oscillations, 4 teractions, occasionally with substitutions which make a while a mass around 10 M has been suggested for the brightest ultraluminous X-ray source HLX-1 (e.g., Far- black hole (BH) of a few tens of solar masses the most likely IMBH companion, and possible Lidov-Kozai (LK) resonances (Lidov 1962; Kozai 1962) if hierarchical triples [email protected] 2 are formed. Eventually, the IMBH–BH binary merges The simulations were performed with the number of par- through the radiation of gravitational waves, emitting ticles N ⊂ {32768, 65536} and the mass of the IMBH, a signal that is potentially detectable by the Advanced M ⊂ {50, 100, 200} M and a cluster virial radius rv of LIGO ground-based GW detectors (Aasi et al. 2015; 3.5 pc. For N = 32768 and all three IMBH masses, sim- Abadie et al. 2010; Smith et al. 2013; Haster et al. 2016). ulations with rv ⊂ {0.35, 1.0} pc were also performed. Previous simulations of globular clusters with IMBH The inclusion of high-order pN terms fixes the physical coalescences have generally simplified the interactions in scale of the cluster, thus removing the conventional free- order to avoid excessive computational cost. For exam- dom for rescaling simulations in cluster size and density. ple, Gültekin et al.(2004) considered a series of individ- We observe the IMBH forming a binary with a BH ual Newtonian interactions interspersed with orbital evo- within . 20Myr in every simulated cluster. Only in one lution through GW emission. Mandel et al.(2008) car- cluster (N = 32768,M = 100M , rv = 3.5pc) we observe ried out analytical estimates of the hardening sequence a merger within the simulated time (' 100Myr). While to obtain the intermediate mass-ratio merger timescale. the result of the entire set of simulations will be pre- Leigh et al.(2014) simulated the entire cluster with a sented in a future paper, in what follows we will focus on mixture of analytical and numerical N-body analytical describing the detailed dynamics of the one cluster pro- calculations, while MacLeod et al.(2016) focused their ducing the merger event. We note in passing that as the N-body investigation on tidal disruptions of stars by the main focus of this study is the dynamical formation and IMBH as well as merger events. We note that in the evolution of binaries, and higher order N-tuples, with previous literature effects of pN terms are either not ac- the IMBH as the primary companion, all cluster parti- counted for (Leigh et al. 2014), or included only at the cles are solely characterized by their mass and no stellar 2.5pN level (Samsing et al. 2014; MacLeod et al. 2016). evolution is included in these simulations. In this paper we show a clear example in which lower order pN terms play a fundamental role in the dynamics. 3. RESULTS More specifically, an essential element that differs be- The simulated globular cluster was initialised with the tween the relativistic and non-relativistic dynamics turns IMBH at rest at the center while the remaining stars and out to be the 1pN precession of the periapsis. BHs follows a King model. Figure 1 shows the position We introduce our numerical method and the simula- of the IMBH and a subset of BH particles, and their tion setup in section 2. We describe our simulation re- subsequent movement within the cluster, relative to the sults in section 3.
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