Abstract
While most of the compact-binary mergers detected by LIGO and Virgo are expected to consist of first-generation black holes formed from the collapse of stars, others might instead be of second (or higher) generation, containing the remnants of previous black-hole mergers. We review theoretical findings, astrophysical modelling and current gravitational-wave evidence of hierarchical stellar-mass black-hole mergers. Such a subpopulation of hierarchically assembled black holes presents distinctive gravitational-wave signatures, namely higher masses, possibly within the pair-instability mass gap, and dimensionless spins clustered at the characteristic value of ~0.7. To produce hierarchical mergers, astrophysical environments need to overcome the relativistic recoils imparted to black-hole merger remnants, a condition that prefers hosts with escape speeds of ≳100 km s−1. Promising locations for efficient production of hierarchical mergers include nuclear star clusters and accretion disks surrounding active galactic nuclei, though environments that are less efficient at retaining merger products such as globular clusters may still contribute significantly to the detectable population of repeated mergers. While GW190521 is the single most promising hierarchical-merger candidate to date, constraints from large population analyses are becoming increasingly more powerful.
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References
Abbott, B. P. et al. Binary black hole mergers in the first advanced LIGO observing run. Phys. Rev. X 6, 041015 (2016).
Abbott, B. P. et al. GWTC-1: a gravitational-wave transient catalog of compact binary mergers observed by LIGO and Virgo during the first and second observing runs. Phys. Rev. X 9, 031040 (2019).
Abbott, R. et al. GWTC-2: compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run. Phys. Rev. X 11, 021053 (2021).
Venumadhav, T., Zackay, B., Roulet, J., Dai, L. & Zaldarriaga, M. New search pipeline for compact binary mergers: results for binary black holes in the first observing run of Advanced LIGO. Phys. Rev. D 100, 023011 (2019).
Venumadhav, T., Zackay, B., Roulet, J., Dai, L. & Zaldarriaga, M. New binary black hole mergers in the second observing run of Advanced LIGO and Advanced Virgo. Phys. Rev. D 101, 083030 (2020).
Nitz, A. H. et al. 1-OGC: the first open gravitational-wave catalog of binary mergers from analysis of public advanced LIGO data. Astrophys. J. 872, 195 (2019).
Nitz, A. H. et al. 2-OGC: open gravitational-wave catalog of binary mergers from analysis of public advanced LIGO and Virgo data. Astrophys. J. 891, 123 (2020).
Aasi, J. et al. Advanced LIGO. Class. Quantum Gravity 32, 074001 (2015).
Acernese, F. et al. Advanced Virgo: a second-generation interferometric gravitational wave detector. Class. Quantum Gravity 32, 024001 (2015).
Shapiro, S. L. & Teukolsky, S. A. Black Holes, White Dwarfs and Neutron Stars: the Physics of Compact Objects (Wiley, 1986).
Mandel, I. & Farmer, A. Merging stellar-mass binary black holes. Preprint at https://arxiv.org/abs/1806.05820 (2018).
Mapelli, M. Astrophysics of stellar black holes. Proc. Int. Sch. Phys. Fermi 200, 87–121 (2020).
Postnov, K. A. & Yungelson, L. R. The evolution of compact binary star systems. Living Rev. Relativ. 17, 3 (2014).
Paczynski, B. in Structure and Evolution of Close Binary Systems Vol. 73 (eds Eggleton, P. et al.) 75 (Springer, 1976).
van den Heuvel, E. P. J., Portegies Zwart, S. F. & de Mink, S. E. Forming short-period Wolf–Rayet X-ray binaries and double black holes through stable mass transfer. Mon. Not. R. Astron. Soc. 471, 4256–4264 (2017).
Mandel, I. & de Mink, S. E. Merging binary black holes formed through chemically homogeneous evolution in short-period stellar binaries. Mon. Not. R. Astron. Soc. 458, 2634–2647 (2016).
Marchant, P., Langer, N., Podsiadlowski, P., Tauris, T. M. & Moriya, T. J. A new route towards merging massive black holes. Astron. Astrophys. 588, A50 (2016).
Wen, L. On the eccentricity distribution of coalescing black hole binaries driven by the Kozai mechanism in globular clusters. Astrophys. J. 598, 419–430 (2003).
Antonini, F. & Perets, H. B. Secular evolution of compact binaries near massive black holes: gravitational wave sources and other exotica. Astrophys. J. 757, 27 (2012).
Benacquista, M. J. & Downing, J. M. B. Relativistic binaries in globular clusters. Living Rev. Relativ. 16, 4 (2013).
Bartos, I., Kocsis, B., Haiman, Z. & Márka, S. Rapid and bright stellar-mass binary black hole mergers in active galactic nuclei. Astrophys. J. 835, 165 (2017).
Ferrarese, L. & Merritt, D. A fundamental relation between supermassive black holes and their host galaxies. Astrophys. J. Lett. 539, L9–L12 (2000).
Begelman, M. C., Blandford, R. D. & Rees, M. J. Massive black hole binaries in active galactic nuclei. Nature 287, 307–309 (1980).
Volonteri, M. Formation of supermassive black holes. Astron. Astrophys. Rev. 18, 279–315 (2010).
Kormendy, J. & Ho, L. C. Coevolution (or not) of supermassive black holes and host galaxies. Annu. Rev. Astron. Astrophys. 51, 511–653 (2013).
Heckman, T. M. & Best, P. N. The coevolution of galaxies and supermassive black holes: insights from surveys of the contemporary universe. Annu. Rev. Astron. Astrophys. 52, 589–660 (2014).
Colpi, M. & Sesana, A. in An Overview of Gravitational Waves (ed. Auger, G.) 43–140 (World Scientific, 2017).
Inayoshi, K., Visbal, E. & Haiman, Z. The assembly of the first massive black holes. Annu. Rev. Astron. Astrophys. 58, 27–97 (2020).
Barausse, E. & Lapi, A. Massive black hole mergers. Preprint at https://arxiv.org/abs/2011.01994 (2020).
Pretorius, F. Evolution of binary black-hole spacetimes. Phys. Rev. Lett. 95, 121101 (2005).
Ossokine, S., Dietrich, T., Foley, E., Katebi, R. & Lovelace, G. Assessing the energetics of spinning binary black hole systems. Phys. Rev. D 98, 104057 (2018).
Heger, A., Fryer, C. L., Woosley, S. E., Langer, N. & Hartmann, D. H. How massive single stars end their life. Astrophys. J. 591, 288–300 (2003).
Woosley, S. E., Blinnikov, S. & Heger, A. Pulsational pair instability as an explanation for the most luminous supernovae. Nature 450, 390–392 (2007).
Woosley, S. E. The progenitor of GW150914. Astrophys. J. Lett. 824, L10 (2016).
Belczynski, K. et al. The effect of pair-instability mass loss on black-hole mergers. Astron. Astrophys. 594, A97 (2016).
Stevenson, S. et al. The impact of pair-instability mass loss on the binary black hole mass distribution. Astrophys. J. 882, 121 (2019).
Di Carlo, U. N. et al. Binary black holes in the pair instability mass gap. Mon. Not. R. Astron. Soc. 497, 1043–1049 (2020).
Mangiagli, A., Bonetti, M., Sesana, A. & Colpi, M. Merger rate of stellar black hole binaries above the pair-instability mass gap. Astrophys. J. Lett. 883, L27 (2019).
María Ezquiaga, J. & Holz, D. E. Jumping the gap: searching for LIGO’s biggest black holes. Astrophys. J. Lett. 909, L23 (2021).
Farmer, R., Renzo, M., de Mink, S. E., Marchant, P. & Justham, S. Mind the gap: the location of the lower edge of the pair-instability supernova black hole mass gap. Astrophys. J. 887, 53 (2019).
Farmer, R., Renzo, M., de Mink, S. E., Fishbach, M. & Justham, S. Constraints from gravitational-wave detections of binary black hole mergers on the 12C(α, γ)16O rate. Astrophys. J. Lett. 902, L36 (2020).
Renzo, M. et al. Sensitivity of the lower edge of the pair-instability black hole mass gap to the treatment of time-dependent convection. Mon. Not. R. Astron. Soc. 493, 4333–4341 (2020).
Marchant, P. & Moriya, T. J. The impact of stellar rotation on the black hole mass-gap from pair-instability supernovae. Astron. Astrophys. 640, L18 (2020).
Woosley, S. E. & Heger, A. The pair-instability mass gap for black holes. Astrophys. J. Lett. 912, L31 (2021).
Belczynski, K. et al. The formation of a 70 M⊙ black hole at high metallicity. Astrophys. J. 890, 113 (2020).
Vink, J. S., Higgins, E. R., Sander, A. A. C. & Sabhahit, G. N. Maximum black hole mass across cosmic time. Mon. Not. R. Astron. Soc. 504, 146–154 (2021).
Costa, G. et al. Formation of GW190521 from stellar evolution: the impact of the hydrogen-rich envelope, dredge-up, and 12C(α, γ)16O rate on the pair-instability black hole mass gap. Mon. Not. R. Astron. Soc. 501, 4514–4533 (2021).
Fishbach, M. & Holz, D. E. Where are LIGO’s big black holes? Astrophys. J. Lett. 851, L25 (2017).
Abbott, B. P. et al. Binary black hole population properties inferred from the first and second observing runs of advanced LIGO and advanced Virgo. Astrophys. J. Lett. 882, L24 (2019).
LIGO Scientific Collaboration et al. Population properties of compact objects from the second LIGO–Virgo gravitational-wave transient catalog. Astrophys. J. Lett. 913, L7 (2021).
Roulet, J., Venumadhav, T., Zackay, B., Dai, L. & Zaldarriaga, M. Binary black hole mergers from LIGO/Virgo O1 and O2: population inference combining confident and marginal events. Phys. Rev. D 102, 123022 (2020).
Tanikawa, A., Susa, H., Yoshida, T., Trani, A. A. & Kinugawa, T. Merger rate density of Population III binary black holes below, above, and in the pair-instability mass gap. Astrophys. J. 910, 30 (2021).
Farrell, E. et al. Is GW190521 the merger of black holes from the first stellar generations? Mon. Not. R. Astron. Soc. 502, L40–L44 (2021).
Kinugawa, T., Nakamura, T. & Nakano, H. Formation of binary black holes similar to GW190521 with a total mass of ~150 M⊙ from Population III binary star evolution. Mon. Not. R. Astron. Soc. 501, L49–L53 (2021).
Renzo, M., Cantiello, M., Metzger, B. D. & Jiang, Y. F. The stellar merger scenario for black holes in the pair-instability gap. Astrophys. J. Lett. 904, L13 (2020).
Kremer, K. et al. Populating the upper black hole mass gap through stellar collisions in young star clusters. Astrophys. J. 903, 45 (2020).
González, E. et al. Intermediate-mass black holes from high massive-star binary fractions in young star clusters. Astrophys. J. Lett. 908, L29 (2021).
Rice, J. R. & Zhang, B. Growth of stellar-mass black holes in dense molecular clouds and GW190521. Astrophys. J. 908, 59 (2021).
Safarzadeh, M. & Haiman, Z. Formation of GW190521 via gas accretion onto Population III stellar black hole remnants born in high-redshift minihalos. Astrophys. J. Lett. 903, L21 (2020).
Roupas, Z. & Kazanas, D. Generation of massive stellar black holes by rapid gas accretion in primordial dense clusters. Astron. Astrophys. 632, L8 (2019).
Natarajan, P. A new channel to form IMBHs throughout cosmic time. Mon. Not. R. Astron. Soc. 501, 1413–1425 (2021).
van Son, L. A. C. et al. Polluting the pair-instability mass gap for binary black holes through super-Eddington accretion in isolated binaries. Astrophys. J. 897, 100 (2020).
Scheel, M. A. et al. High-accuracy waveforms for binary black hole inspiral, merger, and ringdown. Phys. Rev. D 79, 024003 (2009).
Berti, E. & Volonteri, M. Cosmological black hole spin evolution by mergers and accretion. Astrophys. J. 684, 822–828 (2008).
Gerosa, D. & Berti, E. Are merging black holes born from stellar collapse or previous mergers? Phys. Rev. D 95, 124046 (2017).
Fishbach, M., Holz, D. E. & Farr, B. Are LIGO’s black holes made from smaller black holes? Astrophys. J. Lett. 840, L24 (2017).
Gálvez Ghersi, J. T. & Stein, L. C. A fixed point for black hole distributions. Class. Quantum Gravity 38, 045012 (2021).
Campanelli, M., Lousto, C. O. & Zlochower, Y. Spinning-black-hole binaries: the orbital hang-up. Phys. Rev. D 74, 041501 (2006).
Fuller, J. & Ma, L. Most black holes are born very slowly rotating. Astrophys. J. Lett. 881, L1 (2019).
Miller, S., Callister, T. A. & Farr, W. M. The low effective spin of binary black holes and implications for individual gravitational-wave events. Astrophys. J. 895, 128 (2020).
Vitale, S., Gerosa, D., Haster, C.-J., Chatziioannou, K. & Zimmerman, A. Impact of Bayesian priors on the characterization of binary black hole coalescences. Phys. Rev. Lett. 119, 251103 (2017).
Biscoveanu, S., Isi, M., Vitale, S. & Varma, V. A new spin on LIGO–Virgo binary black holes. Phys. Rev. Lett. 126, 171103 (2021).
Hut, P. Tidal evolution in close binary systems. Astron. Astrophys. 99, 126–140 (1981).
Qin, Y. et al. The spin of the second-born black hole in coalescing binary black holes. Astron. Astrophys. 616, A28 (2018).
Gerosa, D. et al. Spin orientations of merging black holes formed from the evolution of stellar binaries. Phys. Rev. D 98, 084036 (2018).
Zaldarriaga, M., Kushnir, D. & Kollmeier, J. A. The expected spins of gravitational wave sources with isolated field binary progenitors. Mon. Not. R. Astron. Soc. 473, 4174–4178 (2018).
Bavera, S. S. et al. The origin of spin in binary black holes. Predicting the distributions of the main observables of Advanced LIGO. Astron. Astrophys. 635, A97 (2020).
Steinle, N. & Kesden, M. Pathways for producing binary black holes with large misaligned spins in the isolated formation channel. Phys. Rev. D 103, 063032 (2021).
Safarzadeh, M., Farr, W. M. & Ramirez-Ruiz, E. A trend in the effective spin distribution of LIGO binary black holes with mass. Astrophys. J. 894, 129 (2020).
Baibhav, V. et al. The mass gap, the spin gap, and the origin of merging binary black holes. Phys. Rev. D 102, 043002 (2020).
Varma, V. et al. Surrogate models for precessing binary black hole simulations with unequal masses. Phys. Rev. Res. 1, 033015 (2019).
Varma, V., Gerosa, D., Stein, L. C., Hébert, F. & Zhang, H. High-accuracy mass, spin, and recoil predictions of generic black-hole merger remnants. Phys. Rev. Lett. 122, 011101 (2019).
Barausse, E., Morozova, V. & Rezzolla, L. On the mass radiated by coalescing black hole binaries. Astrophys. J. 758, 63 (2012).
Hofmann, F., Barausse, E. & Rezzolla, L. The final spin from binary black holes in quasi-circular orbits. Astrophys. J. Lett. 825, L19 (2016).
Gerosa, D. & Kesden, M. precession: dynamics of spinning black-hole binaries with Python. Phys. Rev. D 93, 124066 (2016).
Doctor, Z., Farr, B. & Holz, D. E. Black hole leftovers: the remnant population from binary black hole mergers. Astrophys. J. Lett. 914, L18 (2021).
Gerosa, D. & Berti, E. Escape speed of stellar clusters from multiple-generation black-hole mergers in the upper mass gap. Phys. Rev. D 100, 041301 (2019).
Boyle, L., Kesden, M. & Nissanke, S. Binary black-hole merger: symmetry and the spin expansion. Phys. Rev. Lett. 100, 151101 (2008).
Campanelli, M., Lousto, C. O., Zlochower, Y. & Merritt, D. Maximum gravitational recoil. Phys. Rev. Lett. 98, 231102 (2007).
González, J. A., Hannam, M., Sperhake, U., Brügmann, B. & Husa, S. Supermassive recoil velocities for binary black-hole mergers with antialigned spins. Phys. Rev. Lett. 98, 231101 (2007).
Lousto, C. O. & Zlochower, Y. Hangup kicks: still larger recoils by partial spin–orbit alignment of black-hole binaries. Phys. Rev. Lett. 107, 231102 (2011).
Schnittman, J. D. & Buonanno, A. The distribution of recoil velocities from merging black holes. Astrophys. J. Lett. 662, L63–L66 (2007).
Lousto, C. O., Zlochower, Y., Dotti, M. & Volonteri, M. Gravitational recoil from accretion-aligned black-hole binaries. Phys. Rev. D 85, 084015 (2012).
Gerosa, D., Hébert, F. & Stein, L. C. Black-hole kicks from numerical-relativity surrogate models. Phys. Rev. D 97, 104049 (2018).
Gnedin, O. Y. et al. The unique history of the globular cluster ω Centauri. Astrophys. J. Lett. 568, L23–L26 (2002).
Merritt, D., Milosavljević, M., Favata, M., Hughes, S. A. & Holz, D. E. Consequences of gravitational radiation recoil. Astrophys. J. Lett. 607, L9–L12 (2004).
Rodriguez, C. L. & Loeb, A. Redshift evolution of the black hole merger rate from globular clusters. Astrophys. J. Lett. 866, L5 (2018).
Fragione, G. & Kocsis, B. Black hole mergers from an evolving population of globular clusters. Phys. Rev. Lett. 121, 161103 (2018).
Miller, M. C. & Lauburg, V. M. Mergers of stellar-mass black holes in nuclear star clusters. Astrophys. J. 692, 917–923 (2009).
Antonini, F. & Rasio, F. A. Merging black hole binaries in galactic nuclei: implications for Advanced-LIGO detections. Astrophys. J. 831, 187 (2016).
Gröbner, M., Ishibashi, W., Tiwari, S., Haney, M. & Jetzer, P. Binary black hole mergers in AGN accretion discs: gravitational wave rate density estimates. Astron. Astrophys. 638, A119 (2020).
Tagawa, H., Haiman, Z. & Kocsis, B. Formation and evolution of compact-object binaries in AGN disks. Astrophys. J. 898, 25 (2020).
Sopuerta, C. F., Yunes, N. & Laguna, P. Gravitational recoil velocities from eccentric binary black hole mergers. Astrophys. J. Lett. 656, L9–L12 (2007).
Sperhake, U., Rosca-Mead, R., Gerosa, D. & Berti, E. Amplification of superkicks in black-hole binaries through orbital eccentricity. Phys. Rev. D 101, 024044 (2020).
Radia, M., Sperhake, U., Berti, E. & Croft, R. Anomalies in the gravitational recoil of eccentric black-hole mergers with unequal mass ratios. Phys. Rev. D 103, 104006 (2021).
Gondán, L., Kocsis, B., Raffai, P. & Frei, Z. Eccentric black hole gravitational-wave capture sources in galactic nuclei: distribution of binary parameters. Astrophys. J. 860, 5 (2018).
Samsing, J. Eccentric black hole mergers forming in globular clusters. Phys. Rev. D 97, 103014 (2018).
Zevin, M., Samsing, J., Rodriguez, C., Haster, C.-J. & Ramirez-Ruiz, E. Eccentric black hole mergers in dense star clusters: the role of binary–binary encounters. Astrophys. J. 871, 91 (2019).
Gondán, L. & Kocsis, B. High eccentricities and high masses characterize gravitational-wave captures in galactic nuclei as seen by Earth-based detectors. Preprint at https://arxiv.org/abs/2011.02507 (2020).
Quinlan, G. D. & Shapiro, S. L. Dynamical evolution of dense clusters of compact stars. Astrophys. J. 343, 725 (1989).
Lee, M. H. N-body evolution of dense clusters of compact stars. Astrophys. J. 418, 147 (1993).
Portegies Zwart, S. F., Makino, J., McMillan, S. L. W. & Hut, P. Star cluster ecology. III. Runaway collisions in young compact star clusters. Astron. Astrophys. 348, 117–126 (1999).
Ebisuzaki, T. et al. Missing link found? The ‘runaway’ path to supermassive black holes. Astrophys. J. Lett. 562, L19–L22 (2001).
Mouri, H. & Taniguchi, Y. Runaway merging of black holes: analytical constraint on the timescale. Astrophys. J. Lett. 566, L17–L20 (2002).
Miller, M. C. & Hamilton, D. P. Production of intermediate-mass black holes in globular clusters. Mon. Not. R. Astron. Soc. 330, 232–240 (2002).
Portegies Zwart, S. F. & McMillan, S. L. W. The runaway growth of intermediate-mass black holes in dense star clusters. Astrophys. J. 576, 899–907 (2002).
Gültekin, K., Miller, M. C. & Hamilton, D. P. Growth of intermediate-mass black holes in globular clusters. Astrophys. J. 616, 221–230 (2004).
Gültekin, K., Miller, M. C. & Hamilton, D. P. Three-body dynamics with gravitational wave emission. Astrophys. J. 640, 156–166 (2006).
Holley-Bockelmann, K., Gültekin, K., Shoemaker, D. & Yunes, N. Gravitational wave recoil and the retention of intermediate-mass black holes. Astrophys. J. 686, 829–837 (2008).
Giersz, M., Leigh, N., Hypki, A., Lützgendorf, N. & Askar, A. MOCCA code for star cluster simulations—IV. A new scenario for intermediate mass black hole formation in globular clusters. Mon. Not. R. Astron. Soc. 454, 3150–3165 (2015).
Mapelli, M. Massive black hole binaries from runaway collisions: the impact of metallicity. Mon. Not. R. Astron. Soc. 459, 3432–3446 (2016).
Fragione, G., Ginsburg, I. & Kocsis, B. Gravitational waves and intermediate-mass black hole retention in globular clusters. Astrophys. J. 856, 92 (2018).
Kovetz, E. D., Cholis, I., Kamionkowski, M. & Silk, J. Limits on runaway growth of intermediate mass black holes from Advanced LIGO. Phys. Rev. D 97, 123003 (2018).
Quinlan, G. D. & Shapiro, S. L. The collapse of dense star clusters to supermassive black holes: binaries and gravitational radiation. Astrophys. J. 321, 199 (1987).
Davies, M. B., Miller, M. C. & Bellovary, J. M. Supermassive black hole formation via gas accretion in nuclear stellar clusters. Astrophys. J. Lett. 740, L42 (2011).
Menou, K., Haiman, Z. & Narayanan, V. K. The merger history of supermassive black holes in galaxies. Astrophys. J. 558, 535–542 (2001).
Volonteri, M., Madau, P. & Haardt, F. The formation of galaxy stellar cores by the hierarchical merging of supermassive black holes. Astrophys. J. 593, 661–666 (2003).
Lupi, A., Colpi, M., Devecchi, B., Galanti, G. & Volonteri, M. Constraining the high-redshift formation of black hole seeds in nuclear star clusters with gas inflows. Mon. Not. R. Astron. Soc. 442, 3616–3626 (2014).
O’Leary, R. M., Meiron, Y. & Kocsis, B. Dynamical formation signatures of black hole binaries in the first detected mergers by LIGO. Astrophys. J. Lett. 824, L12 (2016).
Rodriguez, C. L., Amaro-Seoane, P., Chatterjee, S. & Rasio, F. A. Post-Newtonian dynamics in dense star clusters: highly eccentric, highly spinning, and repeated binary black hole mergers. Phys. Rev. Lett. 120, 151101 (2018).
Rodriguez, C. L. et al. Black holes: the next generation-repeated mergers in dense star clusters and their gravitational-wave properties. Phys. Rev. D 100, 043027 (2019).
Arca Sedda, M., Mapelli, M., Spera, M., Benacquista, M. & Giacobbo, N. Fingerprints of binary black hole formation channels encoded in the mass and spin of merger remnants. Astrophys. J. 894, 133 (2020).
Mapelli, M. et al. Hierarchical mergers in young, globular and nuclear star clusters: black hole masses and merger rates. Preprint at https://arxiv.org/abs/2007.15022 (2020).
Mapelli, M. et al. Hierarchical black hole mergers in young, globular and nuclear star clusters: the effect of metallicity, spin and cluster properties. Mon. Not. R. Astron. Soc. 505, 339–358 (2021).
Antonini, F., Gieles, M. & Gualandris, A. Black hole growth through hierarchical black hole mergers in dense star clusters: implications for gravitational wave detections. Mon. Not. R. Astron. Soc. 486, 5008–5021 (2019).
Morawski, J., Giersz, M., Askar, A. & Belczynski, K. MOCCA-SURVEY database I: assessing GW kick retention fractions for BH–BH mergers in globular clusters. Mon. Not. R. Astron. Soc. 481, 2168–2179 (2018).
Samsing, J. & Hotokezaka, K. Populating the black hole mass gaps in stellar clusters: general relations and upper limits. Preprint at https://arxiv.org/abs/2006.09744 (2020).
Liu, B. & Lai, D. Hierarchical black hole mergers in multiple systems: constrain the formation of GW190412-, GW190814-, and GW190521-like events. Mon. Not. R. Astron. Soc. 502, 2049–2064 (2021).
Fragione, G. & Silk, J. Repeated mergers and ejection of black holes within nuclear star clusters. Mon. Not. R. Astron. Soc. 498, 4591–4604 (2020).
O’Leary, R. M., Kocsis, B. & Loeb, A. Gravitational waves from scattering of stellar-mass black holes in galactic nuclei. Mon. Not. R. Astron. Soc. 395, 2127–2146 (2009).
Hong, J. & Lee, H. M. Black hole binaries in galactic nuclei and gravitational wave sources. Mon. Not. R. Astron. Soc. 448, 754–770 (2015).
Böker, T. in Star Clusters: Basic Galactic Building Blocks Throughout Time and Space Vol. 266 (eds de Grijs, R. & Lépine, J. R. D.) 58–63 (Cambridge Univ. Press, 2010).
Webb, J. J. & Leigh, N. W. C. Back to the future: estimating initial globular cluster masses from their present-day stellar mass functions. Mon. Not. R. Astron. Soc. 453, 3278–3287 (2015).
Banerjee, S., Baumgardt, H. & Kroupa, P. Stellar-mass black holes in star clusters: implications for gravitational wave radiation. Mon. Not. R. Astron. Soc. 402, 371–380 (2010).
Tanikawa, A. Dynamical evolution of stellar mass black holes in dense stellar clusters: estimate for merger rate of binary black holes originating from globular clusters. Mon. Not. R. Astron. Soc. 435, 1358–1375 (2013).
Rodriguez, C. L. et al. Binary black hole mergers from globular clusters: implications for Advanced LIGO. Phys. Rev. Lett. 115, 051101 (2015).
Rodriguez, C. L., Chatterjee, S. & Rasio, F. A. Binary black hole mergers from globular clusters: masses, merger rates, and the impact of stellar evolution. Phys. Rev. D 93, 084029 (2016).
Rodriguez, C. L., Haster, C.-J., Chatterjee, S., Kalogera, V. & Rasio, F. A. Dynamical formation of the GW150914 binary black hole. Astrophys. J. Lett. 824, L8 (2016).
Askar, A., Szkudlarek, M., Gondek-Rosińska, D., Giersz, M. & Bulik, T. MOCCA-SURVEY database—I. Coalescing binary black holes originating from globular clusters. Mon. Not. R. Astron. Soc. 464, L36–L40 (2017).
Park, D., Kim, C., Lee, H. M., Bae, Y.-B. & Belczynski, K. Black hole binaries dynamically formed in globular clusters. Mon. Not. R. Astron. Soc. 469, 4665–4674 (2017).
Antonini, F. & Gieles, M. Merger rate of black hole binaries from globular clusters: theoretical error bars and comparison to gravitational wave data from GWTC-2. Phys. Rev. D 102, 123016 (2020).
Fragione, G., Loeb, A. & Rasio, F. A. On the origin of GW190521-like events from repeated black hole mergers in star clusters. Astrophys. J. Lett. 902, L26 (2020).
Gupta, A. et al. Black holes in the low-mass gap: implications for gravitational-wave observations. Phys. Rev. D 101, 103036 (2020).
Safarzadeh, M., Hamers, A. S., Loeb, A. & Berger, E. Formation and merging of mass gap black holes in gravitational-wave merger events from wide hierarchical quadruple systems. Astrophys. J. Lett. 888, L3 (2020).
Lu, W., Beniamini, P. & Bonnerot, C. On the formation of GW190814. Mon. Not. R. Astron. Soc. 500, 1817–1832 (2021).
Vigna-Gómez, A. et al. Massive stellar triples leading to sequential binary black hole mergers in the field. Astrophys. J. Lett. 907, L19 (2021).
Hamers, A. S., Fragione, G., Neunteufel, P. & Kocsis, B. First and second-generation black hole and neutron star mergers in 2+2 quadruples: population statistics. Preprint at https://arxiv.org/abs/2103.03782 (2021).
Stone, N. C., Metzger, B. D. & Haiman, Z. Assisted inspirals of stellar mass black holes embedded in AGN discs: solving the ‘final au problem’. Mon. Not. R. Astron. Soc. 464, 946–954 (2017).
Leigh, N. W. C. et al. On the rate of black hole binary mergers in galactic nuclei due to dynamical hardening. Mon. Not. R. Astron. Soc. 474, 5672–5683 (2018).
McKernan, B. et al. Constraining stellar-mass black hole mergers in AGN disks detectable with LIGO. Astrophys. J. 866, 66 (2018).
Secunda, A. et al. Orbital migration of interacting stellar mass black holes in disks around supermassive black holes. Astrophys. J. 878, 85 (2019).
Armitage, P. J. Astrophysics of Planet Formation (Cambridge Univ. Press, 2013).
Bellovary, J. M., Mac Low, M.-M., McKernan, B. & Ford, K. E. S. Migration traps in disks around supermassive black holes. Astrophys. J. Lett. 819, L17 (2016).
Sirko, E. & Goodman, J. Spectral energy distributions of marginally self-gravitating quasi-stellar object discs. Mon. Not. R. Astron. Soc. 341, 501–508 (2003).
Thompson, T. A., Quataert, E. & Murray, N. Radiation pressure-supported starburst disks and active galactic nucleus fueling. Astrophys. J. 630, 167–185 (2005).
McKernan, B., Ford, K. E. S., Lyra, W. & Perets, H. B. Intermediate mass black holes in AGN discs—I. Production and growth. Mon. Not. R. Astron. Soc. 425, 460–469 (2012).
McKernan, B., Ford, K. E. S., Kocsis, B., Lyra, W. & Winter, L. M. Intermediate-mass black holes in AGN discs—II. Model predictions and observational constraints. Mon. Not. R. Astron. Soc. 441, 900–909 (2014).
McKernan, B., Ford, K. E. S., O’Shaugnessy, R. & Wysocki, D. Monte Carlo simulations of black hole mergers in AGN discs: low χeff mergers and predictions for LIGO. Mon. Not. R. Astron. Soc. 494, 1203–1216 (2020).
Yang, Y. et al. Hierarchical black hole mergers in active galactic nuclei. Phys. Rev. Lett. 123, 181101 (2019).
Bardeen, J. M. & Petterson, J. A. The Lense–Thirring effect and accretion disks around Kerr black holes. Astrophys. J. Lett. 195, L65 (1975).
Bogdanović, T., Reynolds, C. S. & Miller, M. C. Alignment of the spins of supermassive black holes prior to coalescence. Astrophys. J. Lett. 661, L147–L150 (2007).
Miller, M. C. & Krolik, J. H. Alignment of supermassive black hole binary orbits and spins. Astrophys. J. 774, 43 (2013).
Ragusa, E., Lodato, G. & Price, D. J. Suppression of the accretion rate in thin discs around binary black holes. Mon. Not. R. Astron. Soc. 460, 1243–1253 (2016).
Gerosa, D., Rosotti, G. & Barbieri, R. The Bardeen–Petterson effect in accreting supermassive black hole binaries: a systematic approach. Mon. Not. R. Astron. Soc. 496, 3060–3075 (2020).
Ryan, G. & MacFadyen, A. Minidisks in binary black hole accretion. Astrophys. J. 835, 199 (2017).
King, A. R., Lubow, S. H., Ogilvie, G. I. & Pringle, J. E. Aligning spinning black holes and accretion discs. Mon. Not. R. Astron. Soc. 363, 49–56 (2005).
Gerosa, D. et al. Precessional instability in binary black holes with aligned spins. Phys. Rev. Lett. 115, 141102 (2015).
Lousto, C. O. & Healy, J. Unstable flip–flopping spinning binary black holes. Phys. Rev. D 93, 124074 (2016).
Mould, M. & Gerosa, D. Endpoint of the up–down instability in precessing binary black holes. Phys. Rev. D 101, 124037 (2020).
Varma, V. et al. Up–down instability of binary black holes in numerical relativity. Phys. Rev. D 103, 064003 (2021).
McKernan, B. et al. Ram-pressure stripping of a kicked Hill sphere: prompt electromagnetic emission from the merger of stellar mass black holes in an AGN accretion disk. Astrophys. J. Lett. 884, L50 (2019).
Graham, M. J. et al. Candidate electromagnetic counterpart to the binary black hole merger gravitational-wave event S190521g*. Phys. Rev. Lett. 124, 251102 (2020).
Yi, S.-X. & Cheng, K. S. Where are the electromagnetic-wave counterparts of stellar-mass binary black hole mergers? Astrophys. J. Lett. 884, L12 (2019).
Bird, S. et al. Did LIGO detect dark matter? Phys. Rev. Lett. 116, 201301 (2016).
Korol, V., Mandel, I., Miller, M. C., Church, R. P. & Davies, M. B. Merger rates in primordial black hole clusters without initial binaries. Mon. Not. R. Astron. Soc. 496, 994–1000 (2020).
Hall, A., Gow, A. D. & Byrnes, C. T. Bayesian analysis of LIGO–Virgo mergers: primordial versus astrophysical black hole populations. Phys. Rev. D 102, 123524 (2020).
De Luca, V., Franciolini, G., Pani, P. & Riotto, A. Bayesian evidence for both astrophysical and primordial black holes: mapping the GWTC-2 catalog to third-generation detectors. J. Cosmol. Astropart. Phys. 5, 003 (2021).
Liu, L., Guo, Z.-K. & Cai, R.-G. Effects of the merger history on the merger rate density of primordial black hole binaries. Eur. Phys. J. C 79, 717 (2019).
Wu, Y. Merger history of primordial black-hole binaries. Phys. Rev. D 101, 083008 (2020).
De Luca, V., Franciolini, G., Pani, P. & Riotto, A. The evolution of primordial black holes and their final observable spins. J. Cosmol. Astropart. Phys. 2020, 052 (2020).
Clesse, S. & García-Bellido, J. Massive primordial black holes from hybrid inflation as dark matter and the seeds of galaxies. Phys. Rev. D 92, 023524 (2015).
Bianchi, E., Gupta, A., Haggard, H. M. & Sathyaprakash, B. S. Small spins of primordial black holes from random geometries: Bekenstein–Hawking entropy and gravitational wave observations. Preprint at https://arxiv.org/abs/1812.05127 (2018).
Chatziioannou, K. et al. On the properties of the massive binary black hole merger GW170729. Phys. Rev. D 100, 104015 (2019).
Doctor, Z., Wysocki, D., O’Shaughnessy, R., Holz, D. E. & Farr, B. Black hole coagulation: modeling hierarchical mergers in black hole populations. Astrophys. J. 893, 35 (2020).
Kimball, C., Berry, C. & Kalogera, V. What GW170729’s exceptional mass and spin tells us about its family tree. Res. Notes AAS 4, 2 (2020).
Kimball, C. et al. Black hole genealogy: identifying hierarchical mergers with gravitational waves. Astrophys. J. 900, 177 (2020).
Fishbach, M., Farr, W. M. & Holz, D. E. The most massive binary black hole detections and the identification of population outliers. Astrophys. J. Lett. 891, L31 (2020).
Zackay, B., Dai, L., Venumadhav, T., Roulet, J. & Zaldarriaga, M. Detecting gravitational waves with disparate detector responses: two new binary black hole mergers. Preprint at https://arxiv.org/abs/1910.09528 (2019).
Abbott, B. P. et al. Multi-messenger observations of a binary neutron star merger. Astrophys. J. Lett. 848, L12 (2017).
Pratten, G. & Vecchio, A. Assessing gravitational-wave binary black hole candidates with Bayesian odds. Preprint at https://arxiv.org/abs/2008.00509 (2020).
Gayathri, V. et al. GW170817A as a hierarchical black hole merger. Astrophys. J. Lett. 890, L20 (2020).
LIGO Scientific Collaboration et al. GW190412: observation of a binary-black-hole coalescence with asymmetric masses. Phys. Rev. D 102, 043015 (2020).
Fishbach, M. & Holz, D. E. Picky partners: the pairing of component masses in binary black hole mergers. Astrophys. J. Lett. 891, L27 (2020).
Damour, T. Coalescence of two spinning black holes: an effective one-body approach. Phys. Rev. D 64, 124013 (2001).
Racine, É. Analysis of spin precession in binary black hole systems including quadrupole–monopole interaction. Phys. Rev. D 78, 044021 (2008).
Schmidt, P., Ohme, F. & Hannam, M. Towards models of gravitational waveforms from generic binaries: II. Modelling precession effects with a single effective precession parameter. Phys. Rev. D 91, 024043 (2015).
Gerosa, D. et al. A generalized precession parameter χp to interpret gravitational-wave data. Phys. Rev. D 103, 064067 (2021).
Mandel, I. & Fragos, T. An alternative interpretation of GW190412 as a binary black hole merger with a rapidly spinning secondary. Astrophys. J. Lett. 895, L28 (2020).
Zevin, M., Berry, C. P. L., Coughlin, S., Chatziioannou, K. & Vitale, S. You can’t always get what you want: the impact of prior assumptions on interpreting GW190412. Astrophys. J. Lett. 899, L17 (2020).
Gerosa, D., Vitale, S. & Berti, E. Astrophysical implications of GW190412 as a remnant of a previous black-hole merger. Phys. Rev. Lett. 125, 101103 (2020).
Rodriguez, C. L. et al. GW190412 as a third-generation black hole merger from a super star cluster. Astrophys. J. Lett. 896, L10 (2020).
Tagawa, H., Haiman, Z., Bartos, I. & Kocsis, B. Spin evolution of stellar-mass black hole binaries in active galactic nuclei. Astrophys. J. 899, 26 (2020).
Tagawa, H. et al. Mass-gap mergers in active galactic nuclei. Astrophys. J. 908, 194 (2021).
Hamers, A. S. & Safarzadeh, M. Was GW190412 born from a hierarchical 3 + 1 quadruple configuration? Astrophys. J. 898, 99 (2020).
Kimball, C. et al. Evidence for hierarchical black hole mergers in the second LIGO–Virgo gravitational-wave catalog. Preprint at https://arxiv.org/abs/2011.05332 (2020).
Olejak, A. et al. The origin of inequality: isolated formation of a 30 + 10 M⊙ binary black hole merger. Astrophys. J. Lett. 901, L39 (2020).
Kalogera, V. Spin–orbit misalignment in close binaries with two compact objects. Astrophys. J. 541, 319–328 (2000).
Abbott, R. et al. GW190521: a binary black hole merger with a total mass of 150 M⊙. Phys. Rev. Lett. 125, 101102 (2020).
Abbott, R. et al. Properties and astrophysical implications of the 150 M⊙ binary black hole merger GW190521. Astrophys. J. Lett. 900, L13 (2020).
Romero-Shaw, I., Lasky, P. D., Thrane, E. & Calderón Bustillo, J. GW190521: orbital eccentricity and signatures of dynamical formation in a binary black hole merger signal. Astrophys. J. Lett. 903, L5 (2020).
Gayathri, V. et al. GW190521 as a highly eccentric black hole merger. Preprint at https://arxiv.org/abs/2009.05461 (2020).
Calderón Bustillo, J., Sanchis-Gual, N., Torres-Forné, A. & Font, J. A. Confusing head-on and precessing intermediate-mass binary black hole mergers. Phys. Rev. Lett. 126, 201101 (2020).
Anagnostou, O., Trenti, M. & Melatos, A. Hierarchical formation of an intermediate mass black hole via seven mergers: implications for GW190521. Preprint at https://arxiv.org/abs/2010.06161 (2020).
Bellm, E. C. et al. The Zwicky Transient Facility: system overview, performance, and first results. Publ. Astron. Soc. Pac. 131, 018002 (2019).
Chen, H.-Y., Haster, C.-J., Vitale, S., Farr, W. M. & Isi, M. A standard siren cosmological measurement from the potential GW190521 electromagnetic counterpart ZTF19abanrhr. Preprint at https://arxiv.org/abs/2009.14057 (2020).
Ashton, G., Ackley, K., Magaña Hernandez, I. & Piotrzkowski, B. Current observations are insufficient to confidently associate the binary black hole merger GW190521 with AGN J124942.3+344929. Preprint at https://arxiv.org/abs/2009.12346 (2020).
Palmese, A., Fishbach, M., Burke, C. J., Annis, J. T. & Liu, X. Do LIGO/Virgo black hole mergers produce AGN flares? The case of GW190521 and prospects for reaching a confident association. Astrophys. J. Lett. 914, L34 (2021).
Belczynski, K. The most ordinary formation of the most unusual double black hole merger. Astrophys. J. Lett. 905, L15 (2020).
Umeda, H., Yoshida, T., Nagele, C. & Takahashi, K. Pulsational pair-instability and the mass gap of Population III black holes: effects of overshooting. Astrophys. J. Lett. 905, L21 (2020).
Liu, B. & Bromm, V. The Population III origin of GW190521. Astrophys. J. Lett. 903, L40 (2020).
De Luca, V., Desjacques, V., Franciolini, G., Pani, P. & Riotto, A. GW190521 mass gap event and the primordial black hole scenario. Phys. Rev. Lett. 126, 051101 (2021).
Cruz-Osorio, A., Lora-Clavijo, F. D. & Herdeiro, C. GW190521 formation scenarios via relativistic accretion. Preprint at https://arxiv.org/abs/2101.01705 (2021).
Croon, D., McDermott, S. D. & Sakstein, J. Missing in action: new physics and the black hole mass gap. Phys. Rev. D 102, 115024 (2020).
Sakstein, J., Croon, D., McDermott, S. D., Straight, M. C. & Baxter, E. J. Beyond the standard model explanations of GW190521. Phys. Rev. Lett. 125, 261105 (2020).
Antoniou, I. Black hole or gravastar? The GW190521 case. Preprint at https://arxiv.org/abs/2010.05354 (2020).
Bustillo, J. C. et al. GW190521 as a merger of Proca stars: a potential new vector boson of 8.7 × 10−13 eV. Phys. Rev. Lett. 126, 081101 (2021).
Ziegler, J. & Freese, K. Filling the black hole mass gap: avoiding pair instability in massive stars through addition of non-nuclear energy. Preprint at https://arxiv.org/abs/2010.00254 (2020).
Fishbach, M. & Holz, D. E. Minding the gap: GW190521 as a straddling binary. Astrophys. J. Lett. 904, L26 (2020).
Nitz, A. H. & Capano, C. D. GW190521 may be an intermediate-mass ratio inspiral. Astrophys. J. Lett. 907, L9 (2021).
Abbott, R. et al. GW190814: gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object. Astrophys. J. Lett. 896, L44 (2020).
Bailyn, C. D., Jain, R. K., Coppi, P. & Orosz, J. A. The mass distribution of stellar black holes. Astrophys. J. 499, 367–374 (1998).
Özel, F., Psaltis, D., Narayan, R. & McClintock, J. E. The black hole mass distribution in the galaxy. Astrophys. J. 725, 1918–1927 (2010).
Tews, I. et al. On the nature of GW190814 and its impact on the understanding of supranuclear matter. Astrophys. J. Lett. 908, L1 (2021).
Dexheimer, V., Gomes, R. O., Klähn, T., Han, S. & Salinas, M. GW190814 as a massive rapidly rotating neutron star with exotic degrees of freedom. Phys. Rev. C 103, 025808 (2021).
Tsokaros, A., Ruiz, M. & Shapiro, S. L. GW190814: spin and equation of state of a neutron star companion. Astrophys. J. 905, 48 (2020).
Most, E. R., Papenfort, L. J., Weih, L. R. & Rezzolla, L. A lower bound on the maximum mass if the secondary in GW190814 was once a rapidly spinning neutron star. Mon. Not. R. Astron. Soc. 499, L82–L86 (2020).
Biswas, B., Nandi, R., Char, P., Bose, S. & Stergioulas, N. GW190814: on the properties of the secondary component of the binary. Mon. Not. R. Astron. Soc. 505, 1600–1606 (2021).
Fryer, C. L. et al. Compact remnant mass function: dependence on the explosion mechanism and metallicity. Astrophys. J. 749, 91 (2012).
Belczynski, K., Wiktorowicz, G., Fryer, C. L., Holz, D. E. & Kalogera, V. Missing black holes unveil the supernova explosion mechanism. Astrophys. J. 757, 91 (2012).
Farr, W. M. et al. The mass distribution of stellar-mass black holes. Astrophys. J. 741, 103 (2011).
Kreidberg, L., Bailyn, C. D., Farr, W. M. & Kalogera, V. Mass measurements of black holes in x-ray transients: is there a mass gap? Astrophys. J. 757, 36 (2012).
Ye, C. S. et al. On the rate of neutron star binary mergers from globular clusters. Astrophys. J. Lett. 888, L10 (2020).
Yang, Y. et al. Black hole formation in the lower mass gap through mergers and accretion in AGN disks. Astrophys. J. Lett. 901, L34 (2020).
Thrane, E. & Talbot, C. An introduction to Bayesian inference in gravitational-wave astronomy: parameter estimation, model selection, and hierarchical models. Publ. Astron. Soc. Aust. 36, e010 (2019).
Vitale, S., Gerosa, D., Farr, W. M. & Taylor, S. R. Inferring the properties of a population of compact binaries in presence of selection effects. Preprint at https://arxiv.org/abs/2007.05579 (2020).
Belczynski, K. et al. Evolutionary roads leading to low effective spins, high black hole masses, and O1/O2 rates for LIGO/Virgo binary black holes. Astron. Astrophys. 636, A104 (2020).
Tiwari, V. & Fairhurst, S. The emergence of structure in the binary black hole mass distribution. Astrophys. J. Lett. 913, L19 (2021).
Gerosa, D., Giacobbo, N. & Vecchio, A. High mass but low spin: an exclusion region to rule out hierarchical black-hole mergers as a mechanism to populate the pair-instability mass gap. Preprint at https://arxiv.org/abs/2104.11247 (2021).
Belczynski, K. & Banerjee, S. Formation of low-spinning 100 M⊙ black holes. Astron. Astrophys. 640, L20 (2020).
Tagawa, H., Haiman, Z., Bartos, I., Kocsis, B. & Omukai, K. Signatures of hierarchical mergers in black hole spin and mass distribution. Preprint at https://arxiv.org/abs/2104.09510 (2021).
Fishbach, M. et al. When are LIGO/Virgo’s big black-hole mergers? Astrophys. J. 912, 98 (2021).
Christian, P., Mocz, P. & Loeb, A. Evolution of the black hole mass function in star clusters from multiple mergers. Astrophys. J. Lett. 858, L8 (2018).
Flitter, J., Muñoz, J. B. & Kovetz, E. D. Outliers in the LIGO black hole mass function from coagulation in dense clusters. Preprint at https://arxiv.org/abs/2008.10389 (2020).
Baxter, E. J., Croon, D., McDermott, S. D. & Sakstein, J. Find the gap: black hole population analysis with an astrophysically motivated mass function. Preprint at https://arxiv.org/abs/2104.02685 (2021).
Veske, D. et al. Search for black hole merger families. Astrophys. J. Lett. 907, L48 (2021).
Taylor, S. R. & Gerosa, D. Mining gravitational-wave catalogs to understand binary stellar evolution: a new hierarchical Bayesian framework. Phys. Rev. D 98, 083017 (2018).
Wong, K. W. K., Breivik, K., Kremer, K. & Callister, T. Joint constraints on the field-cluster mixing fraction, common envelope efficiency, and globular cluster radii from a population of binary hole mergers via deep learning. Phys. Rev. D 103, 083021 (2021).
Zevin, M. et al. One channel to rule them all? Constraining the origins of binary black holes using multiple formation pathways. Astrophys. J. 910, 152 (2021).
Broekgaarden, F. S. et al. STROOPWAFEL: simulating rare outcomes from astrophysical populations, with application to gravitational-wave sources. Mon. Not. R. Astron. Soc. 490, 5228–5248 (2019).
Wong, K. W. K., Contardo, G. & Ho, S. Gravitational-wave population inference with deep flow-based generative network. Phys. Rev. D 101, 123005 (2020).
Abbott, B. P. et al. Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA. Living Rev. Relativ. 23, 3 (2020).
Acknowledgements
D.G. is supported by the European Union’s H2020 ERC Starting Grant 945155–GWmining, Leverhulme Trust Grant RPG-2019-350 and Royal Society Grant RGS-R2-202004. M.F. is supported by NASA through the NASA Hubble Fellowship Grant HST-HF2-51455.001-A awarded by the Space Telescope Science Institute. Computational work was performed on the University of Birmingham BlueBEAR cluster, the Athena cluster at HPC Midlands+ funded by EPSRC Grant EP/P020232/1, and the Maryland Advanced Research Computing Center (MARCC).
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Gerosa, D., Fishbach, M. Hierarchical mergers of stellar-mass black holes and their gravitational-wave signatures. Nat Astron 5, 749–760 (2021). https://doi.org/10.1038/s41550-021-01398-w
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