Abstract
The high rate of black hole (BH) mergers detected by LIGO/Virgo opened questions on their astrophysical origin. One possibility is the dynamical channel, in which binary formation and hardening is catalyzed by dynamical encounters in globular clusters (GCs). Previous studies have shown that the BH merger rate from the present day GC density in the Universe is lower than the observed rate. In this Letter, we study the BH merger rate by accounting for the first time for the evolution of GCs within their host galaxies. The mass in GCs was initially ∼8×higher, which decreased to its present value due to evaporation and tidal disruption. Many BH binaries that were ejected long before their merger originated in GCs that no longer exist. We find that the comoving merger rate in the dynamical channel from GCs varies between 18 to 35 Gpc-3 yr-1 between redshift z=0.5 to 2, and the total rate is 1, 5, 24 events per day within z=0.5, 1, and 2, respectively. The cosmic evolution and disruption of GCs systematically increases the present-day merger rate by a factor ∼2 relative to isolated clusters. Gravitational wave detector networks offer an unique observational probe of the initial number of GC populations and their subsequent evolution across cosmic time.
| Original language | English (US) |
|---|---|
| Article number | 161103 |
| Journal | Physical review letters |
| Volume | 121 |
| Issue number | 16 |
| DOIs | |
| State | Published - Oct 19 2018 |
Funding
In this Letter, we have determined the BH merger rate from dynamically formed binaries produced in GCs that coevolve with their host galaxies in the Universe. At redshift z = 0 , we have found a rate ∼ 4 – 60 Gpc - 3 yr - 1 , within the uncertainties of our model. We found that the expected merger rate ranges between R ∼ 18 Gpc - 3 yr - 1 to ∼ 35 Gpc - 3 yr - 1 for redshift between z = 0.5 to 2, and the total rate is 1, 5, and 24 events per day within z = 0.5 , 1, and 2, respectively. This corresponds to a factor ∼ 3 to a ∼ 2 higher rate from z = 0.5 to z = 2 with respect to the case neglecting the evolution of GCs in their host galaxies. If a significant fraction of mergers from GCs is from ejected binaries, the rate at low redshift z < 0.1 is ∼ 10 Gpc - 3 yr - 1 , a factor of ∼ 2 higher than previous estimates. For comparison, the current observational limit on the BH merger rate in the local Universe is R = 12 – 65 Gpc - 3 yr - 1 , assuming a log-uniform mass distribution, and R = 40 – 240 Gpc - 3 yr - 1 for a power-law BH mass distribution with d N / d m ∝ m - 2.35 . This result highlights the need for more detailed simulations of GCs tracking their evolution with their host galaxies. Our results were derived by scaling to Milky-Way type hosts. Future work is needed to study the discrepancy between the rates of evolving GC populations and isolated GCs for different host galaxies, whose GC population correlates with the dark matter masses [54] . Furthermore, the possible presence of an intermediate-mass black hole (IMBH) may significantly change the evolution of GCs and the distribution of merger rates [55,56] . At design sensitivity, LIGO-Virgo is expected to observe BH mergers up to z ∼ 1 [57] . Assuming that the LIGO-Virgo observational completeness is 1%–10% (i.e., the fraction of all mergers that LIGO-Virgo detects within this volume), our results suggest that one detection per day to ∼ 1 per week is expected from the dynamical channel. Recently, Fishbach et al. [58] suggested that with ∼ 100 – 300 LIGO-Virgo detections it will be possible to distinguish among different models of the merger rate evolution within the coming 2–5 years. Indeed, the redshift evolution of merger rate from the dynamical channel shown in Fig. 1 is distinct from other formation channels as it increases from z = 0 until the epoch of globular cluster formation with a particular shape as shown (see Refs. [4,58] and references therein, for the redshift evolution for other channels). The cosmic evolution and disruption of GCs increases the present-day merger rates by a factor ∼ 2 in comparison to isolated clusters (see Fig. 1 ). The redshift evolution of the merger rates carries information on the cosmic history of GCs. Thus, measuring the redshift evolution of the rates will represent an observation probe of GC formation, their initial numbers in the Universe and their evolution across cosmic time. With a sufficiently large sample of mergers the relative contribution of intergalactic GCs [59,60] may be distinguished from GCs evolving in galaxies. Future instruments such as the Voyager, Einstein Telescope, or Cosmic Explorer will make this endeavor more feasible [57,61] . We conclude that GW detectors have the potential to provide a view on the evolution of faint GCs, which are practically invisible to electromagnetic observatories. This may have far reaching implications in the theory of galaxy formation, possibly leading to the understanding of the theory of GC formation and the origin of the empirical correlations between the number of GCs, their host SMBH, and dark matter halos [62] . We thank Oleg Gnedin and Carl Rodriguez for useful discussions and comments and the anonymous referees for helpful suggestions. G. F. is supported by the Foreign Postdoctoral Fellowship Program of the Israel Academy of Sciences and Humanities. G. F. also acknowledges support from an Arskin postdoctoral fellowship and Lady Davis Fellowship Trust at the Hebrew University of Jerusalem. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme ERC-2014-STG under Grant Agreement No. 638435 (GalNUC) and from the Hungarian National Research, Development, and Innovation Office Grant No. NKFIH KH-125675 (to B. K.). [1] 1 https://www.ligo.caltech.edu/ . [2] 2 B. P. Abbott , R. Abbott , T. D. Abbott , M. R. Abernathy , F. Acernese , K. Ackley , C. Adams , T. Adams , P. Addesso , R. X. Adhikari , Phys. Rev. Lett. 116 , 061102 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.116.061102 [3] 3 B. P. Abbott , R. 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ASJC Scopus subject areas
- General Physics and Astronomy