We have studied 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 LIGO (aLIGO) detectors. We have indicated that the PBH merger rate within each halo for the ellipsoidal models is more significant than for the spherical models. We have specified 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 have calculated 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 have presented 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 (O3), we have shown 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 have compared 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 have also estimated the relation between the fraction of PBHs and their masses in the ellipsoidal-collapse halo model and have shown 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.
We reinvestigate gravitational ellipsoidal collapse with special focus on its impact on primordial black-hole formation. For a generic model we demonstrate that the abundance and energy density of the produced primordial black holes will be significantly decreased when the non-sphericity of the overdensities is taken into account.
Primordial black holes (PBHs), as a potential macroscopic candidate for dark matter, can encounter other compact objects in dark matter halos because of their random distribution. Besides, the detection of gravitational waves (GWs) related to the stellar-mass black hole-neutron star (BH-NS) mergers raises the possibility that the BHs involved in such events may have a primordial origin. In this work, we calculate the merger rate of PBH-NS binaries within the framework of ellipsoidal-collapse dark matter halo models and compare it with the corresponding results derived from spherical-collapse d…
We have calculated the detectable merger rate of primordial black holes, as a function of the redshift, as well as the binary's mass ratio, total mass and chirp mass (observables that have not previously been explored in great detail for PBHs). We consider both the current and design sensitivity of LIGO and five different primordial black hole mass functions, as well as showing a comparison to a predicted astrophysical black hole merger rate. We show that the empirical preference for nearly equal-mass binaries in current LIGO/Virgo data can be consistent with a PBH hypothesis once observationa…
Recent Advanced LIGO detections of binary black hole mergers have prompted multiple studies investigating the possibility that the heavy GW150914 binary system was of primordial origin, and hence could be evidence for dark matter in the form of black holes. We compute the stochastic background arising from the incoherent superposition of such primordial binary black hole systems in the universe and compare it to the similar background spectrum due to binary black hole systems of stellar origin. We investigate the possibility of detecting this background with future gravitational wave detectors…
The properties of primordial curvature perturbations on small scales are still unknown while those on large scales have been well probed by the observations of the cosmic microwave background anisotropies and the large scale structure. In this paper, we propose the reconstruction method of primordial curvature perturbations on small scales through the merger rate of binary primordial black holes, which could form from large primordial curvature perturbation on small scales.
We develop a formalism to calculate the merger rate density of primordial black hole binaries with a general mass function, by taking into account the merger history of primordial black holes. We apply the formalism to three specific mass functions, monochromatic, power-law and log-normal cases. In the former case, the merger rate density is dominated by the single-merger events, while in the latter two cases, the contribution of the multiple-merger events on the merger rate density can not be ignored. The effects of the merger history on the merger rate density depend on the mass function.
We give an explanation for the signal detected by NANOGrav as the stochastic gravitational wave background from binary mergers of primordial "Stupendously Large Black Holes" (SLABs) of mass $M\sim(10^{11}-10^{12})M_{\odot}$, and corresponding to roughly $0.1\%$ of the dark matter. We show that the stringent bounds coming from $μ$ distortions of the CMB can be surpassed if the perturbations resulting in these BHs arise from the non-Gaussian distribution of fluctuations expected in single field models of inflation generating a spike in the power spectrum. While the tail of the stochastic backgro…
We develop an analytic formalism for computing the merger rate of primordial black hole binaries with a general mass function by taking into account the torques by the surrounding primordial black holes and linear density perturbations. We find that $α=-(m_{i}+m_{j})^2\partial^{2} \ln {\mathcal R}(m_{i},m_{j})/\partial m_{i} \partial m_{j}=36/37$ is independent of the mass function. Moreover, the ratio of the merger rate density of primordial black hole binaries by taking into account the torques by the surrounding primordial black holes to by the nearest primordial black hole is independent o…
A bulk acoustic wave cavity as high frequency gravitational wave antenna has recently detected two rare events at $5.5$MHz. Assuming that the detected events are due to gravitational waves, their characteristic strain amplitude lies at about $h_c\approx 2.5 \times 10^{-16}$. While a cosmological signal is out of the picture due to the large energy carried by the high frequency waves, the signal could be due to the merging of two planet mass primordial black holes ($\approx 4\times 10^{-4} M_\odot$) inside the Oort cloud at roughly $0.025$ pc ($5300$ AU) away. In this short note, we show that t…
It has been proposed that primordial black holes (PBHs) form binaries in the radiation dominated era. Once formed, some fraction of them may merge within the age of the Universe by gravitational radiation reaction. We investigate the merger rate of the PBH binaries when the PBHs have a distribution of masses around ${\cal O}(10) M_\odot$, which is a generalization of the previous studies where the PBHs are assumed to have the same mass. After deriving a formula for the merger time probability distribution in the PBH mass plane, we evaluate it under two different approximations. We identify a q…
In this work, we study the effect of a high-precision semianalytical mass function on the merger rate of primordial black holes (PBHs) in dark matter halos. For this purpose, we first explain a theoretical framework for dark matter halo models and introduce relevant quantities such as halo density profile, concentration parameter, and a high-precision semianalytical function namely Del Popolo (DP) mass function. In the following, we calculate the merger rate of PBHs in the framework of ellipsoidal-collapse dark matter halo models while considering the DP mass function, and compare it with our …
The merger rate of black hole binaries inferred from the detections in the first Advanced LIGO science run, implies that a stochastic background produced by a cosmological population of mergers will likely mask the primordial gravitational-wave background. Here we demonstrate that the next generation of ground-based detectors, such as the Einstein Telescope and Cosmic Explorer, will be able to observe binary black hole mergers throughout the universe with sufficient efficiency that the confusion background can potentially be subtracted to observe the primordial background at the level of $Ω_{\…
We propose a new scenario for the evolution of a binary of primordial black holes (PBHs). We consider a dynamical friction by ambient dark matter, scattering of dark matter particles with a highly eccentric orbit besides the standard two-body relaxation process to refill the loss cone, and interaction between the binary and a circumbinary disk, assuming that PBHs do not constitute the bulk of dark matter. Binary PBHs lose the energy and angular momentum by these processes, which could be sufficiently efficient for a typical configuration. Such a binary coalesces due to the gravitational wave e…
We consider gravitational radiation and electromagnetic radiation from point mass binary with electric charges in a Keplerian orbit, and calculate the merger rate distribution of primordial black hole binaries with charges and a general mass function by taking into account gravitational torque and electromagnetic torque by the nearest primordial black hole. We apply the formalism to the extremal charged case and find that $α=-(m_i+m_j)^2\partial^2 \ln {\cal R}(m_i,m_j)/\partial m_i \partial m_j=12/11$, which is independent of the mass function.
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 me…
Primordial black holes might comprise a significant fraction of the dark matter in the Universe and be responsible for the gravitational wave signals from black hole mergers observed by the LIGO/Virgo collaboration. The spatial clustering of primordial black holes might affect their merger rates and have a significant impact on the constraints on their masses and abundances. We provide some analytical treatment of the primordial black hole spatial clustering evolution, compare our results with some of the existing N-body numerical simulations and discuss the implications for the black hole mer…
We conduct a thorough Bayesian analysis of the possibility that the black hole merger events seen in gravitational waves are primordial black hole (PBH) mergers. Using the latest merger rate models for PBH binaries drawn from a lognormal mass function we compute posterior parameter constraints and Bayesian evidences using data from the first two observing runs of LIGO-Virgo. We account for theoretical uncertainty due to possible disruption of the binary by surrounding PBHs, which can suppress the merger rate significantly. We also consider simple astrophysically motivated models and find that …
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 $σ/m=10~{\rm cm^{2}g^{-1}}$. 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 ca…
If the primordial curvature perturbation followed a Gaussian distribution, primordial black holes (PBHs) will be Poisson distributed with no additional clustering. We consider local non-Gaussianity and its impact on the initial PBH clustering and mass function due to mode coupling between long and short wavelength modes. We show that even a small amount of non-Gaussianity results in a significant enhancement on the PBH initial clustering and subsequent merger rate and that the PBH mass function shifts to higher mass PBHs. However, as the clustering becomes strong, the local number density of P…
In this paper, the merger rate of black holes in a cluster of primordial black holes (PBHs) is investigated. The clusters have characteristics close to those of typical globular star clusters. A cluster that has a wide mass spectrum ranging from $10^{-2}$ to $10 \, M_{\odot}$ (Solar mass) and contains a massive central black hole of the mass $M_{\bullet} = 10^3 \, M_{\odot}$ is considered. It is shown that in the process of the evolution of cluster, the merger rate changed significantly, and by now, the PBH clusters have passed the stage of active merging of the black holes inside~them.
Mainly motivated by the recent GW190521 mass gap event which we take as a benchmark point, we critically assess if binaries made of a primordial black hole and a black hole of astrophysical origin may form, merge in stellar clusters and reproduce the LIGO/Virgo detection rate. While two previously studied mechanisms -- the direct capture and the three body induced -- seem to be inefficient, we propose a new "catalysis" channel based on the idea that a subsequent chain of single-binary and binary-binary exchanges may lead to the formation of a high mass binary pairs and show that it may explain…
The LIGO/Virgo collaboration has by now observed or constrained the gravitational merger rates of different classes of compact objects. We consider the possibility that the bulk of these mergers are primordial black hole (PBH) mergers of PBHs formed during the QCD epoch making up the entirety of the dark matter. Having shown in a companion paper that mergers due to the initial binary population formed in the early Universe are likely negligible, we compute current merger rates in PBH clusters in which the typical PBH resides. We consider two scenarios: (i) the PBH mass function dictated by the…
One of the crucial windows for distinguishing astrophysical black holes from primordial black holes is through the redshift evolution of their respective merger rates. The low redshift population of black holes of astrophysical origin is expected to follow the star formation rate. The corresponding peak in their merger rate peaks at a redshift smaller than that of the star formation rate peak ($z_p \approx 2$), depending on the time delay between the formation and mergers of black holes. Black holes of primordial origin are going to be present before the formation of the stars, and the merger …
We perform a hierarchical Bayesian analysis of the GWTC-2 catalog to investigate the mixed scenario in which the merger events are explained by black holes of both astrophysical and primordial origin. For the astrophysical scenario we adopt the phenomenological model used by the LIGO/Virgo collaboration and we include the correlation between different parameters inferred from data, the role of the spins in both the primordial and astrophysical scenarios, and the impact of accretion in the primordial scenario. Our best-fit mixed model has a strong statistical evidence relative to the single-pop…
Near-extremal primordial black holes stable over cosmological timescales may constitute a significant fraction of the dark matter. Due to their charge the coalescence rate of such black holes is enhanced inside clusters and the non-extremal merger remnants are prone to Hawking evaporation. We demonstrate that if these clusters of near-extremal holes contain a sufficient number of members to survive up to low redshift, the hard photons from continued evaporation begin to dominate the high energy diffuse background. We find that the diffuse photon flux can be observed for a monochromatic mass sp…
Merger rate of initially clustered primordial black holes for the two-body channel
Theory Center, Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK)（高能加速器研究机构粒子与核研究研究所理论中心）；ICRR, University of Tokyo（东京大学宇宙射线研究所）；Kavli IPMU (WPI), UTIAS, University of Tokyo（东京大学 Kavli 宇宙起源与物质研究所（世界顶尖学术研究中心）、宇宙前沿机构）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论与数学科学中心）；Department of Physics, Tohoku University（东北大学物理学系）
We develop a parameter-free analytic model to include the effects of mergers into the theoretical modelling of the X-ray temperature function of galaxy clusters. We include this description into our model for the cluster population based on fluctuations of the gravitational potential, which avoids any reference to mass. Comparisons with a numerical simulation reveal that the theoretical model is in good agreement with the simulation results. We show that building the model on the dynamics of spherical rather than ellipsoidal collapse yields better results if emission-weighted temperatures are …
The existence of primordial black holes (PBHs), which may form from the collapse of matter overdensities shortly after the Big Bang, is still under debate. Among the potential signatures of PBHs are gravitational waves (GWs) emitted from binary black hole (BBH) mergers at redshifts $z\gtrsim 30$, where the formation of astrophysical black holes is unlikely. Future ground-based GW detectors, Cosmic Explorer and Einstein Telescope, will be able to observe equal-mass BBH mergers with total mass of $\mathcal{O}(10-100)~M_{\odot}$ at such distances. In this work, we investigate whether the redshift…
Primordial black holes formed through the collapse of cosmological density fluctuations have been hypothesised as contributors to the dark matter content of the Universe. At the same time, their mergers could contribute to the recently observed population of gravitational-wave sources. We investigate the scenario in which primordial black holes form binaries at late times in the Universe. Specifically, we re-examine the mergers of primordial black holes in small clusters of ~30 objects in the absence of initial binaries. Binaries form dynamically through Newtonian gravitational interactions. T…
We derive a lower bound on the merger rate of primordial black hole (PBH) binaries by estimating the maximal fraction of binaries that were perturbed between formation in the early Universe and merger, and computing a conservative merger rate of perturbed binaries. This implies robust constraints on the PBH abundance in the range $1-100 M_\odot$. We further show that LIGO/Virgo design sensitivity has the potential to reach the PBH mass range of $10^{-2}-10^3 M_\odot$. The constraint from the merger rate of perturbed binaries is stronger if PBHs are initially spatially clustered.
We use path integrals in order to estimate merger rates of dark matter haloes using the Extended Press-Schechter approximation (EPS) for the Spherical Collapse (SC) and the Ellipsoidal Collapse (EC) models. Merger rates have been calculated for masses in the range $10^{10}M_{\odot}\mathrm{h}^{-1}$ to $10^{14}M_{\odot}\mathrm{h}^{-1}$ and for redshifts $z$ in the range 0 to 3. A detailed comparison between these models is presented. Path approach gives a better agreement with the exact solutions for constrained distributions than the approach of \cite{shto02}. Although this improvement seems no…
The possible existence of primordial black holes in the stellar mass window has received considerable attention because their mergers may contribute to current and future gravitational-wave detections. Primordial black hole mergers, together with mergers of black holes originating from Population~III stars, are expected to dominate at high redshifts ($z\gtrsim 10$). However the primordial black hole merger rate density is expected to rise monotonically with redshift, while Population~III mergers can only occur after the birth of the first stars. Next-generation gravitational-wave detectors suc…
Large-amplitude density perturbations may have collapsed during the radiation dominated epoch of the Universe to form primordial black holes (PBHs). There are several constraints to the abundance of PBHs that stem from evaporation or gravitational effects. Due to the connection between primordial perturbations and the formation of PBHs, constraints on the present-day abundance of PBHs can be translated into limits on the primordial curvature power spectrum. We introduce several new observational and forecasted constraints to the amplitude of the primordial power spectrum and incorporate in our…
The orbital evolution of a binary system consisting of two primordial black hole clusters is investigated. Such clusters are predicted in some theoretical models with broken symmetry in the inflation Lagrangian. A cluster consists of the most massive central black hole surrounded by many smaller black holes. Similar to single primordial black holes, clusters can form gravitationally bounded pairs and merge during their orbital evolution. The replacement of single black holes by such clusters significantly changes the entire merger process and the final rate of gravitational wave bursts in some…
We consider a cosmological model with dark matter in the form of $\sim10^{-12}M_\odot$ primordial black holes in dense weakly relativistic clusters with masses $18-560M_\odot$. It is shown that during the multiple collisions of the black holes the $\sim10$\% of the initial cluster mass can be transformed into gravitational waves in the time interval from recombination to the redshifts $z\geq 10$. At the recombination epoch, the density of matter was larger by $\sim10$\% and, accordingly, the universe expansion rate was higher. This leads to a shortening of the sound horizon scale, as is necess…
As a candidate bound for the Binary Black Hole (BBH) merger events detected by LIGO/Virgo, Primordial Black Holes (PBHs) provide a useful tool to investigate the primordial curvature perturbations on small scales. Using the GWTC-1 to GWTC-3 catalogs, under the scenario that PBHs originate from large primordial curvature perturbations on small scales during inflationary epoch, we for the first time reconstruct the power spectrum of primordial curvature perturbations on small scales. It is found that the value of the amplitude of the primordial power spectrum is enhanced to $\mathcal{O}(10^{-2})…
We study the merger history of primordial black holes (PBHs) in a scenario where they represent the dominant dark matter component of a typical dwarf galaxies' core. We investigate the possibility of a sequence of collisions resulting in a hierarchical merger of black holes and look at the final mass spectrum in such {\it clusters}, which initially present a monochromatic (single-mass) PBH population. Our study shows that the merging process results in the transfer of about $40\%$ of the total mass of the core to the merger products regardless of the initial mass of PBHs, with about $5\%$ of e…
It has been suggested that primordial black holes (PBHs) of roughly 30 solar masses could make up the dark matter and if so, might account for the recent detections by LIGO involving binary black holes in this mass range. It has also been argued that the super-massive black holes (SMBHs) that reside at galactic centers may be surrounded by extremely-dense dark-matter (DM) spikes. Here we show that the rate for PBH mergers in these spikes may well exceed the merger rate considered before in galactic dark-matter halos, depending on the magnitudes of two competing effects on the DM spikes: deplet…
Probing Primordial Black Hole Mergers in Clusters with Pulsar Timing Data
a Service de Physique Th\'eorique, Brussels Laboratory of the Universe BLU-ULB, Universit\'e Libre de Bruxelles, Boulevard du Triomphe, CP225, 1050 Brussels, Belgium
The Peters formula, which tells how the coalescence time of a binary system emitting gravitational radiation is determined by the initial size and shape of the elliptic orbit, is often used in estimating the merger rate of primordial black holes and the gravitational wave background from the mergers. Valid as it is in some interesting scenarios, such as the analysis of the LIGO-Virgo events, the Peters formula fails to describe the coalescence time if the orbital period of the binary exceeds the value given by the formula. This could underestimate the event rate of mergers that occur before th…
