Total Merger Rate Research Articles

Globular cluster formation histories, masses, and radii inferred from gravitational waves

ABSTRACT Globular clusters (GCs) are found in all types of galaxies and harbour some of the most extreme stellar systems, including black holes that may dynamically assemble into merging binary black holes (BBHs). Uncertain GC properties, including when they formed, their initial masses and sizes, affect their production rate of BBH mergers. Using the gravitational-wave transient catalogue (GWTC-3), we measure that dynamically assembled BBHs – those that are consistent with isotropic spin directions – make up ${61^{+29}_{-44}\%}$ of the total merger rate, with a local merger rate of ${10.9^{+16.8}_{-9.3}}$ Gpc−3 yr−1 rising to ${58.9^{+149.4}_{-46.0}}$ Gpc−3 yr−1 at z = 1. We assume that this inferred rate describes the contribution from GCs and compare it against the Cluster Monte Carlo (cmc) simulation catalogue to directly fit for the GC initial mass function, virial radius distribution, and formation history. We find that GC initial masses are consistent with a Schechter function with slope ${\beta _m = -1.9^{+0.8}_{-0.8}}$ . Assuming a mass function slope of βm = −2 and a mass range between 104–$10^8\, \mathrm{ M}_\odot$ , we infer a GC formation rate at z = 2 of ${5.0^{+9.4}_{-4.0}}$ Gpc−3 yr−1, or ${2.1^{+3.9}_{-1.7}}\times 10^6\, \mathrm{ M}_\odot$ Gpc−3 yr−1 in terms of mass density. We find that the GC formation rate probably rises more steeply than the global star formation rate between z = 0 and z = 3 (82 per cent credibility) and implies a local number density that is ${f_\mathrm{ev} = 22.6^{+29.9}_{-16.2}}$ times higher than the observed density of survived GCs. This is consistent with expectations for cluster evaporation, but may suggest that other environments contribute to the rate of BBH mergers with significantly tilted spins.

Constraining the merger history of primordial-black-hole binaries from GWTC-3

Primordial black holes (PBHs) can be not only cold dark matter candidates but also progenitors of binary black holes observed by LIGO-Virgo-KAGRA (LVK) Collaboration. The PBH mass can be shifted to the heavy distribution if multi-merger processes occur. In this work, we constrain the merger history of PBH binaries using the gravitational wave events from the third Gravitational-Wave Transient Catalog (GWTC-3). Considering four commonly used PBH mass functions, namely the log-normal, power-law, broken power-law, and critical collapse forms, we find that the multi-merger processes make a subdominant contribution to the total merger rate. Therefore, the effect of merger history can be safely ignored when estimating the merger rate of PBH binaries. We also find that GWTC-3 is best fitted by the log-normal form among the four PBH mass functions and confirm that the stellar-mass PBHs cannot dominate cold dark matter.

Testing time evolution of mass distribution of black hole mergers

The detection of gravitational-wave events revealed that there are numerous populations of black hole (BH) binaries that can merge within the age of the Universe. Although several formation channels of such binaries are known, considerable theoretical uncertainties associated with each channel defeat the robust prediction of how much each channel contributes to the total merger rate density. Given that the time evolution of the merger rate density in some channels is (exactly or nearly) independent of BH masses, clarifying this feature from observational data will shed some light on the nature of BH binaries. On the basis of this motivation, we formulate a methodology to perform a statistical test of whether the mass distribution of BH mergers evolves over time by hypothesis testing. Our statistical test requires neither a priori specification of the mass distribution, which is largely uncertain, nor that of the time dependence of merger rate. We then apply it to mock data for some concrete shapes of the merger rate density and show that the proposed method rejects/(does not reject) the null hypothesis correctly for a large sample size. After this verification, the method is applied to a catalog of the gravitational-wave events obtained during the LIGO-Virgo’s third observing run. We find that the selection bias degrades the effectiveness of our method for the O3 catalog owing to the reduction in the number of and the maximum redshifts of the merger events that we can explore. Within the range where the method can be applied, there is no indication of the time evolution of the mass distribution of merger rate density. This limitation will be eased in future observations containing more events, and our hypothesis testing will help determine whether the merger rate density evolves over time independently of BH masses.

Primordial black hole merger rate in self-interacting dark matter halo models

We study the merger rate of primordial black holes (PBHs) in self-interacting dark matter (SIDM) halo models. To explore a numerical description for the density profile of SIDM halo models, we use the result of a previously performed simulation for SIDM halo models with $\sigma/m=10~{\rm cm^{2}g^{-1}}$. We also propose a concentration-mass-time relation that can explain the evolution of the halo density profile related to SIDM models. Furthermore, we investigate the encounter condition of PBHs that may have been randomly distributed in the medium of dark matter halos. Under these assumptions, we calculate the merger rate of PBHs within each halo considering SIDM halo models and compare the results with that obtained for cold dark matter (CDM) halo models. To do this, we employ the definition of the time after halo virialization as a function of halo mass. We indicate that SIDM halo models for $f_{\rm PBH}>0.32$ can generate sufficient PBH mergers in such a way that those exceed the one resulted from CDM halo models. By considering the spherical-collapse halo mass function, we obtain similar results for the cumulative merger rate of PBHs. Moreover, we calculate the redshift evolution of the PBH total merger rate. To determine a constraint on the PBH abundance, we study the merger rate of PBHs in terms of their fraction and masses and compare those with the black hole merger rate estimated by the Advanced LIGO (aLIGO)-Advanced Virgo (aVirgo) detectors during the third observing run. The results demonstrate that within the context of SIDM halo models, the merger rate of $10~M_{\odot}-10~M_{\odot}$ events can potentially fall within the aLIGO-aVirgo window. We also estimate a relation between the fraction of PBHs and their masses, which is well consistent with our findings.

Primordial black hole merger rate in ellipsoidal-collapse dark matter halo models

We study the merger rate of primordial black holes (PBHs) in the ellipsoidal-collapse model of halo to explain the dark matter abundance by the PBH merger estimated from the gravitational waves detections via the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) detectors. We indicate that the PBH merger rate within each halo for the ellipsoidal models is more significant than for the spherical models. We specify that the PBH merger rate per unit time and per unit volume for the ellipsoidal-collapse halo models is about one order of magnitude higher than the corresponding spherical models. Moreover, we calculate the evolution of the PBH total merger rate as a function of redshift. The results indicate that the evolution for the ellipsoidal halo models is more sensitive than spherical halo models, as expected from the models. Finally, we present a constraint on the PBH abundance within the context of ellipsoidal and spherical models. By comparing the results with the aLIGO mergers during the third observing run, we show that the merger rate in the ellipsoidal-collapse halo models falls within the aLIGO window, while the same result is not valid for the spherical-collapse ones. Furthermore, we compare the total merger rate of PBHs in terms of their fraction in the ellipsoidal-collapse halo models for several masses of PBHs. The results suggest that the total merger rate of PBHs changes inversely with their masses. We also estimate the relation between the fraction of PBHs and their masses in the ellipsoidal-collapse halo model and show it for a narrow mass distribution of PBHs. The outcome shows that the constraint inferred from the PBH merger rate for the ellipsoidal-collapse halo models can be potentially stronger than the corresponding result obtained for the spherical-collapse ones.

Have hierarchical three-body mergers been detected by LIGO/Virgo?

ABSTRACT One of the proposed channels of binary black hole mergers involves dynamical interactions of three black holes. In such scenarios, it is possible that all three black holes merge in a so-called hierarchical merger chain, where two of the black holes merge first and then their remnant subsequently merges with the remaining single black hole. Depending on the dynamical environment, it is possible that both mergers will appear within the observable time window. Here, we perform a search for such merger pairs in the public available LIGO and Virgo data from the O1/O2 runs. Using a frequentist p-value assignment statistics, we do not find any significant merger pair candidates, the most significant being GW170809-GW151012 pair. Assuming no observed candidates in O3/O4, we derive upper limits on merger pairs to be ∼11–110 yr−1 Gpc−3, corresponding to a rate that relative to the total merger rate is ∼0.1−1.0. From this, we argue that both a detection and a non-detection within the next few years can be used to put useful constraints on some dynamical progenitor models.

Merger history of primordial black-hole binaries

As a candidate of dark matter, primordial black holes (PBHs) have attracted more and more attentions as they could be possible progenitors of the heavy binary black holes (BBHs) observed by LIGO/Virgo. Accurately estimating the merger rate of PBH binaries will be crucial to reconstruct the mass distribution of PBHs. It was pointed out the merger history of PBHs may shift the merger rate distribution depending on the mass function of PBHs. In this paper, we use 10 BBH events from LIGO/Virgo O1 and O2 observing runs to constrain the merger rate distribution of PBHs by accounting the effect of merger history. It is found that the second merger process makes subdominant contribution to the total merger rate, and hence the merger history effect can be safely neglected.

The Most Massive Binary Black Hole Detections and the Identification of Population Outliers

Abstract Advanced LIGO and Virgo detected 10 binary black holes (BBHs) in their first two observing runs (O1 and O2). Analysis of these events found evidence for a dearth of BBHs with component masses greater than ∼45 M ⊙, as would be expected from pair-instability supernovae. Meanwhile, a standalone analysis of the merger GW170729 found its primary mass to be , which appears to be in contradiction with the existence of a limit at ∼45 M ⊙. In this work, we argue that the masses of individual events can only be evaluated with reference to the full population. When GW170729 is analyzed jointly with the remaining detections, its inferred primary mass tightens considerably, to . In the presence of noise, apparent outliers in the detected distribution are inevitable. We discuss methods of distinguishing between statistical fluctuations and true population outliers using posterior predictive tests. Applying these tests to O1 and O2, we find that the 10 detections are consistent with even the simplest power-law plus maximum-mass model considered by the LIGO–Virgo Collaboration, supporting the claim that GW170729 is not a population outlier. We also provide non-parametric constraints on the rate of high-mass mergers and conservatively bound the rate of mergers with m 1 > 45 M ⊙ at of the total merger rate. After 100 detections like those of O1 and O2 from a population with a maximum primary mass of 45 M ⊙, it would be common for the most massive system to have an observed maximum-likelihood mass m 1 ≳ 70 M ⊙.

The Rate of Stellar Mass Black Hole Scattering in Galactic Nuclei

Abstract We consider a black hole (BH) density cusp in a nuclear star cluster (NSC) hosting a supermassive back hole (SMBH) at its center. Assuming the stars and BHs inside the SMBH sphere of influence are mass-segregated, we calculate the number of BHs that sink into this region under the influence of dynamical friction. We find that the total number of BHs increases significantly in this region due to this process for lower-mass SMBHs by up to a factor of 5, but there is no increase in the vicinity of the highest mass SMBHs. Due to the high BH number density in the NSC, BH–BH binaries form during close approaches due to gravitational wind (GW) emission. We update the previous estimate of O’Leary et al. for the rate of such GW capture events by estimating the parameter where n is the number density. We find a BH merger rate for this channel to be in the range . The total merger rate is dominated by the smallest galaxies hosting SMBHs, and the number of heaviest BHs in the NSC. It is also exponentially sensitive to the radial number density profile exponent, reaching when the BH mass function is or shallower, and the heaviest BH radial number density is close to . Even if the rate is much lower than the range constrained by the current LIGO detections, the GW captures around SMBHs can be distinguished by their high eccentricity in the LIGO band.

Black Hole Mergers in Galactic Nuclei Induced by the Eccentric Kozai–Lidov Effect

Abstract Nuclear star clusters around a central massive black hole (MBH) are expected to be abundant in stellar black hole (BH) remnants and BH–BH binaries. These binaries form a hierarchical triple system with the central MBH, and gravitational perturbations from the MBH can cause high-eccentricity excitation in the BH–BH binary orbit. During this process, the eccentricity may approach unity, and the pericenter distance may become sufficiently small so that gravitational-wave emission drives the BH–BH binary to merge. In this work, we construct a simple proof-of-concept model for this process, and specifically, we study the eccentric Kozai–Lidov mechanism in unequal-mass, soft BH–BH binaries. Our model is based on a set of Monte Carlo simulations for BH–BH binaries in galactic nuclei, taking into account quadrupole- and octupole-level secular perturbations, general relativistic precession, and gravitational-wave emission. For a typical steady-state number of BH–BH binaries, our model predicts a total merger rate of ∼1–3 −3 −1, depending on the assumed density profile in the nucleus. Thus, our mechanism could potentially compete with other dynamical formation processes for merging BH–BH binaries, such as the interactions of stellar BHs in globular clusters or in nuclear star clusters without an MBH.

The metallicity and star formation activity of long gamma-ray burst hosts for z < 3: insights from the Illustris simulation

We study non-parametric morphologies of mergers events in a cosmological context, using the Illustris project. We produce mock g-band images comparable to observational surveys from the publicly available Illustris simulation idealized mock images at $z=0$. We then measure non parametric indicators: asymmetry, Gini, $M_{20}$, clumpiness and concentration for a set of galaxies with $M_* >10^{10}$ M$_\odot$. We correlate these automatic statistics with the recent merger history of galaxies and with the presence of close companions. Our main contribution is to assess in a cosmological framework, the empirically derived non-parametric demarcation line and average time-scales used to determine the merger rate observationally. We found that 98 per cent of galaxies above the demarcation line have a close companion or have experienced a recent merger event. On average, merger signatures obtained from the $G-M_{20}$ criteria anticorrelate clearly with the elapsing time to the last merger event. We also find that the asymmetry correlates with galaxy pair separation and relative velocity, exhibiting the larger enhancements for those systems with pair separations $d < 50$ h$^{-1}$ kpc and relative velocities $V < 350$ km s$^{-1}$. We find that the $G-M_{20}$ is most sensitive to recent mergers ($\sim0.14$ Gyr) and to ongoing mergers with stellar mass ratios greater than 0.1. For this indicator, we compute a merger average observability time-scale of $\sim0.2$ Gyr, in agreement with previous results and demonstrate that the morphologically derived merger rate recovers the intrinsic total merger rate of the simulation and the merger rate as a function of stellar mass.

THE SPACE DENSITY EVOLUTION OF WET AND DRY MERGERS IN THE CANADA-FRANCE-HAWAII TELESCOPE LEGACY SURVEY

We analyze 1298 merging galaxies with redshifts up to z=0.7 from the Canada-France-Hawaii Telescope Legacy Survey, taken from the catalog presented in Bridge et al. (2010). By analyzing the internal colors of these systems, we show that so-called wet and dry mergers evolve in different senses, and quantify the space densities of these systems. The local space density of wet mergers is essentially dentical to the local space density of dry mergers. The evolution in the total merger rate is modest out to z ~ 0.7, although the wet and dry populations have different evolutionary trends. At higher redshifts dry mergers make a smaller contribution to the total merging galaxy population, but this is offset by a roughly equivalent increase in the contribution from wet mergers. By comparing the mass density function of early-type galaxies to the corresponding mass density function for merging systems, we show that not all the major mergers with the highest masses (M_stellar > 10^11 M_solar) will end up with the most massive early-type galaxies, unless the merging timescale is dramatically longer than that usually assumed. On the other hand, the usually-assumed merging timescale of ~ 0.5-1 Gyr is quite consistent with the data if we suppose that only less massive early-type galaxies form via mergers. Since low-intermediate mass ellipticals are 10 --100 times more common than their most massive counterparts, the hierarchical explanation for the origin of early-type galaxies may be correct for the vast majority of early-types, even if incorrect for the most massive ones.

The Total Merger Rate of Compact Object Binaries in the Local Universe

Using a population synthesis approach, we compute the total merger rate in the local universe for double neutron stars, double black holes, and black hole-neutron star binaries. These compact binaries are the prime source candidates for gravitational wave detection by LIGO and VIRGO. We account for mergers originating both from field populations and from dense stellar clusters, where dynamical interactions can significantly enhance the production of double compact objects. For both populations we use the same treatment of stellar evolution. Our results indicate that the merger rates of double neutron stars and black hole-neutron star binaries are strongly dominated by field populations, while merging black hole binaries are formed much more effectively in dense stellar clusters. The overall merger rate of double compact objects depends sensitively on the (largely unknown) initial mass fraction contained in dense clusters (fcl). For fcl 0.0001, the Advanced LIGO detection rate will be dominated by field populations of double neutron star mergers, with a small but significant number of detections, ~20 yr−1. However, for a higher mass fraction in clusters, fcl 0.001, the detection rate will be dominated by numerous mergers of double black holes originating from dense clusters, and it will be considerably higher, ~25-300 yr−1. In addition, we show that, once mergers of double black holes are detected, it is easy to differentiate between systems formed in the field and in dense clusters, since the chirp mass distributions are strikingly different. If significant field populations of double black hole mergers are detected, this will also place very strong constraints on common-envelope evolution in massive binaries. Finally, we point out that there may exist a population of merging black hole binaries in intergalactic space.