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Register a new userThe Cosmic Evolution of Binary Black Holes in Young, Globular and Nuclear Star Clusters: Rates, Masses, Spins and Mixing Fractions
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The growing population of binary black holes (BBHs) observed by gravitational wave detectors is a potential Rosetta stone for understanding their formation channels. Here, we use an upgraded version of our semi-analytic codes FASTCLUSTER and COSMO$mathcal{R}$ATE to investigate the cosmic evolution of four different BBH populations: isolated BBHs and dynamically formed BBHs in nuclear star clusters (NSCs), globular clusters (GCs), and young star clusters (YSCs). We find that the merger rate density of BBHs in GCs and NSCs is barely affected by stellar metallicity ($Z$), while the rate of isolated BBHs changes wildly with $Z$. BBHs in YSCs behave in an intermediate way between isolated and GC/NSC BBHs. The local merger rate density of Nth-generation black holes (BHs), obtained by summing up hierarchical mergers in GCs, NSCs and YSCs, ranges from $sim{1}$ to $sim{4}$ Gpc$^{-3}$ yr$^{-1}$ and is mostly sensitive to the spin parameter. We find that the mass function of primary BHs evolves with redshift in GCs and NSCs, becoming more top-heavy at higher $z$. In contrast, the primary BH mass function almost does not change with redshift in YSCs and in the field. This signature of the BH mass function has relevant implications for Einstein Telescope and Cosmic Explorer. Finally, our analysis suggests that multiple channels contribute to the BBH population of the second gravitational-wave transient catalogue.
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Hierarchical mergers are one of the distinctive signatures of binary black hole (BBH) formation through dynamical evolution. Here, we present a fast semi-analytic approach to simulate hierarchical mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs). Hierarchical mergers are more common in NSCs than they are in both GCs and YSCs, because of the different escape velocity. The mass distribution of hierarchical BBHs strongly depends on the properties of first-generation BBHs, such as their progenitors metallicity. In our fiducial model, we form black holes (BHs) with masses up to $sim{}10^3$ M$_odot$ in NSCs and up to $sim{}10^2$ M$_odot$ in both GCs and YSCs. When escape velocities in excess of 100 km~s$^{-1}$ are considered, BHs with mass $>10^3$ M$_odot$ are allowed to form in NSCs. Hierarchical mergers lead to the formation of BHs in the pair instability mass gap and intermediate-mass BHs, but only in metal-poor environments. The local BBH merger rate in our models ranges from $sim{}10$ to $sim{} 60$ Gpc$^{-3}$ yr$^{-1}$; hierarchical BBHs in NSCs account for $sim{}10^{-2}- 0.2$ Gpc$^{-3}$ yr$^{-1}$, with a strong upper limit of $sim{}10$ Gpc$^{-3}$ yr$^{-1}$. When comparing our models with the second gravitational-wave transient catalog, we find that multiple formation channels are favored to reproduce the observed BBH population.
During the first three observing runs of the Advanced gravitational-wave detector network, the LIGO/Virgo collaboration detected several black hole binary (BHBH) mergers. As the population of detected BHBH mergers grows, it will become possible to constrain different channels for their formation. Here we consider the chemically homogeneous evolution (CHE) channel in close binaries, by performing population synthesis simulations that combine realistic binary models with detailed cosmological calculations of the chemical and star-formation history of the Universe. This allows us to constrain population properties, as well as cosmological and aLIGO/aVirgo detection rates of BHBH mergers formed through this pathway. We predict a BHBH merger rate at redshift zero of $5.8 , textrm{Gpc}^{-3} textrm{yr}^{-1}$ through the CHE channel, to be compared with aLIGO/aVirgos measured rate of ${53.2}_{-28.2}^{+55.8} , text{Gpc}^{-3} text{yr}^{-1}$, and find that eventual merger systems have BH masses in the range $17 - 43 , textrm{M}_{odot}$ below the pair-instability supernova (PISN) gap, and $>124 , textrm{M}_{odot}$ above the PISN gap. We investigate effects of momentum kicks during black hole formation, and calculate cosmological and magnitude limited PISN rates. We also study the effects of high-redshift deviations in the star formation rate. We find that momentum kicks tend to increase delay times of BHBH systems, and our magnitude limited PISN rate estimates indicate that current deep surveys should be able to detect such events. Lastly, we find that our cosmological merger rate estimates change by at most $sim 8%$ for mild deviations of the star formation rate in the early Universe, and by up to $sim 40%$ for extreme deviations.
Black holes formed in dense star clusters, where dynamical interactions are frequent, may have fundamentally different properties than those formed through isolated stellar evolution. Theoretical models for single star evolution predict a gap in the black hole mass spectrum from roughly $40-120,M_{odot}$ caused by (pulsational) pair-instability supernovae. Motivated by the recent LIGO/Virgo event GW190521, we investigate whether black holes with masses within or in excess of this upper-mass gap can be formed dynamically in young star clusters through strong interactions of massive stars in binaries. We perform a set of $N$-body simulations using the CMC cluster-dynamics code to study the effects of the high-mass binary fraction on the formation and collision histories of the most massive stars and their remnants. We find that typical young star clusters with low metallicities and high binary fractions in massive stars can form several black holes in the upper-mass gap and often form at least one intermediate-mass black hole. These results provide strong evidence that dynamical interactions in young star clusters naturally lead to the formation of more massive black hole remnants.
We investigate the evolution of supermassive binary black holes (BBHs) in galaxies with realistic property distributions and the gravitational-wave (GW) radiation from the cosmic population of these BBHs. We incorporate a comprehensive treatment of the dynamical interactions of the BBHs with their environments by including the effects of galaxy triaxial shapes and inner stellar distributions, and generate a large number of BBH evolution tracks. By combining these BBH evolution tracks, galaxy mass functions, galaxy merger rates, and supermassive black hole-host galaxy relations into our model, we obtain the statistical distributions of surviving BBHs, BBH coalescence rates, the strength of their GW radiation, and the stochastic GW background (GWB) contributed by the cosmic BBH population. About ~1%-3% (or ~10%) of supermassive BHs at nearby galactic centers are expected to be binaries with mass ratio >1/3 (or >1/100). The characteristic strain amplitude of the GWB at frequency 1/yr is estimated to be ~$2.0^{+1.4}_{-0.8}times 10^{-16}$, and the upper bound of its results obtained with the different BH-host galaxy relations can be up to $5.4times 10^{-16}$, which await testing by future experiments (e.g., the Square Kilometer Array, FAST, Next-Generation Very Large Array). The turnover frequency of the GWB spectrum is at ~0.25nHz. The uncertainties on the above estimates and prospects for detecting individual sources are also discussed. The application of the cosmic BBH population to the Laser Interferometer Space Antenna (LISA) band provides a lower limit to the detection rate of BBHs by LISA, ~0.9/yr.
We investigate properties of black hole (BH) binaries formed in globular clusters via dynamical processes, using direct N-body simulations. We pay attention to effects of BH mass function on the total mass and mass ratio distributions of BH binaries ejected from clusters. Firstly, we consider BH populations with two different masses in order to learn basic differences from models with single-mass BHs only. Secondly, we consider continuous BH mass functions adapted from recent studies on massive star evolution in a low metallicity environment, where globular clusters are formed. In this work, we consider only binaries that are formed by three-body processes and ignore stellar evolution and primordial binaries for simplicity. Our results imply that most BH binary mergers take place after they get ejected from the cluster. Also, mass ratios of dynamically formed binaries should be close to one or likely to be less than 2:1. Since the binary formation efficiency is larger for higher-mass BHs, it is likely that a BH mass function sampled by gravitational-wave observations would be weighed toward higher masses than the mass function of single BHs for a dynamically formed population. Applying conservative assumptions regarding globular cluster populations such as small BH mass fraction and no primordial binaries, the merger rate of BH binaries originated from globular clusters is estimated to be at least 6.5 per yr per Gpc^3. Actual rate can be up to more than several times of our conservative estimate.
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