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 the cosmic time $t\sim 10^{13}\ \text{s}$. As a result, the energy density spectrum of the gravitational wave background could develop a peak, which is from mergers occurring at either $t\sim 10^{13}\ \text{s}$ (for black holes with mass $M\gtrsim 10^8 M_\odot$) or $t\sim 10^{26}(M/M_\odot)^{-5/3}\ \text{s}$ (for $10^5 M_\odot \lesssim M\lesssim 10^8 M_\odot$). This can be used to constrain the fraction of dark matter in primordial black holes (denoted by $f$) if potential probes (such as SKA and U-DECIGO) do not discover such a background, with the result $f\lesssim 10^{-6}\text{-}10^{-4}$ for the mass range $10\text{-} 10^9M_\odot$. We then consider the effect of mass accretion onto primordial black holes at redshift $z\sim 10$, and find that the merger rate could drop significantly at low redshifts. The spectrum of the gravitational wave background thus gets suppressed at the high-frequency end. This feature might be captured by future detectors such as ET and CE for initial mass $M= \mathcal{O}(10\text{-}100) M_\odot$ with $f\gtrsim 10^{-4}$.
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…
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.
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）
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…
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 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.
Tight constraints on the abundance of primordial black holes can be deduced across a vast range of masses, with the exception of those light enough to fully evaporate before nucleosynthesis. This hypothetical population is almost entirely unconstrained, to the point where the early Universe could pass through a matter-dominated phase with primordial black holes as the primary component. The only obvious relic of this phase would be Hawking radiated gravitons which would constitute a stochastic gravitational wave background in the present-day Universe, albeit at frequencies far beyond the scope…
By performing Monte Carlo simulations of the evolution of binary primordial black hole (PBH) systems, we estimate the effect of distant encounters with single PBHs upon the coalescence time and merger rate of binary PBHs. We find that, for models where PBHs compose a large fraction of dark matter, $f_\mathrm{PBH}\sim 1$, the expected fractional change in coalescence time is negligible, of order $10^{-6}$ for most binaries. For models with significantly lower PBH abundances, $f_\mathrm{PBH}\ll 1$, we find that the average change in binary lifetime due to encounters can be as large as $\mathcal{…
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…
The PBHs clusters can be source of gravitational waves, and the merger rate depends on the spatial distribution of PBHs in the cluster which changes over time. It is well known that gravitational collisional systems experience the core collapse, that leads to significantly increase of the central density and shrinking of the core. After core collapse, the cluster expands almost self-similarly (i.e. density profile extends in size without changing its shape). These dynamic processes affect at the merger rate of PBHs. In this paper the dynamics of the PBH cluster is considered using the Fokker-P…
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…
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…
The measurement of gravitational waves produced by binary black-hole mergers at the Advanced LIGO has encouraged extensive studies on the stochastic gravitational wave background. Recent studies have focused on gravitational wave sources made of the same species, such as mergers from binary primordial black holes or those from binary astrophysical black holes. In this paper, we study a new possibility -- the stochastic gravitational wave background produced by mergers of one primordial black hole and one astrophysical black hole. Such systems are necessarily present if primordial black holes e…
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.
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…
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…
Primordial dark matter (DM) haloes are the smallest gravitationally bound DM structures from which the first stars, black holes, and galaxies form and grow in the early universe. However, their structures are sensitive to the free streaming scale of DM, which in turn depends on the nature of DM particles. In this work, we test the hypothesis that the slope of the central cusps in primordial DM haloes near the free streaming scale depends on the nature of merging process. By combining and analysing data from a cosmological simulation with the cutoff in the small-scale matter power spectrum as w…
We constrain the primordial gravitational waves from cosmic microwave background (CMB) and stochastic gravitational wave background (SGWB) observations. SGWB provides the latest way to explore the early universe and the cosmological evolution which can be reflected by primordial gravitational waves. We not only combine LIGO observations with CMB to measure primordial gravitational waves, but also forecast the potential abilities of the LISA detector and PTA projects. In the $Λ$CDM+$r$+$n_t$ model, the standard six parameters change slightly from SGWB observations. While the constraints on tens…
One of the seemingly strongest constraints on the fraction of dark matter in the form of primordial black holes (PBH) of ${\cal O}$(10)$\,M_\odot$ relies on the merger rate inferred from the binary BH merger events detected by LIGO/Virgo. The robustness of these bounds depends however on the accuracy with which the formation of PBH binaries in the early Universe can be described. We revisit the standard estimate of the merger rate, focusing on a couple of key ingredients: the spatial distribution of nearest neighbours and the initial clustering of PBHs associated to a given primordial power sp…
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…
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…
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.
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 study the production of primordial black hole (PBH) binaries and the resulting merger rate, accounting for an extended PBH mass function and the possibility of a clustered spatial distribution. Under the hypothesis that the gravitational wave events observed by LIGO were caused by PBH mergers, we show that it is possible to satisfy all present constraints on the PBH abundance, and find the viable parameter range for the lognormal PBH mass function. The non-observation of gravitational wave background allows us to derive constraints on the fraction of dark matter in PBHs, which are stronger …
The rate of gravitational wave bursts from the mergers of massive primordial black holes in clusters is calculated. Such clusters of black holes can be formed through phase transitions in the early Universe. The central black holes in clusters can serve as the seeds of supermassive black holes in galactic nuclei. The expected burst detection rate by the LISA gravitational wave detector is estimated.
We explore the effect of relic gravitational waves on the primordial phase change from the quark-gluon plasma into the low density hadron gas that occurred approximately $10^{-5}$s after the beginning. We show that the gravitational wave, through doing work on the fluid, modulates the local volumes, causing a pressure modulation which either suppresses or boosts the bubble cavitation rate. The boosted rate is significant, implying that the phase transition could have occurred earlier than if this interaction is not considered.
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…
We study the generation and evolution of second-order energy-density perturbations arising from primordial gravitational waves. Such "tensor-induced scalar modes" approximately evolve as standard linear matter perturbations and may leave observable signatures in the Large-Scale Structure of the Universe. We study the imprint on the matter power-spectrum of some primordial models which predict a large gravitational-wave signal at high frequencies. This novel mechanism in principle allows us to constrain or detect primordial gravitational waves by looking at specific features in the matter or ga…
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 formation of astrophysical and primordial black holes influences the distribution of dark matter surrounding them. Black holes are thus expected to carry a dark matter `dress' whose properties depend on their formation mechanism and on the properties of the environment. Here we carry out a numerical and analytical study of the merger of dressed black holes, and show that the distribution of dark matter around them dramatically affects the dynamical evolution of the binaries. Although the final impact on the merger rate of primordial black holes is rather small with respect to the case of `…
Primordial black hole (PBH) is a fascinating candidate for the origin of binary merger events observed by LIGO-Virgo collaboration. The spatial distribution of PBHs at formation is an important feature to estimate the merger rate. We investigate the clustering of PBHs formed by Affleck-Dine (AD) baryogenesis, where dense baryon bubbles collapse to form PBHs. We found that formed PBHs show a strong clustering due to the stochastic dynamics of the AD field. Including the clustering, we evaluate the merger rate and isocurvature perturbations of PBHs, which show significant deviations from those w…
We study the gravitational stability of gaseous streams in the complex environment of a galaxy merger, because mergers are known to be places of ongoing massive cluster formation and bursts of star formation. We find an analytic stability parameter for case of gaseous streams orbiting around the merger remnant. We test our stability criteria using hydrodynamical simulations of galaxy mergers, obtaining satisfactory results. We find that our criteria successfully predicts the streams that will be gravitationally unstable to fragment into clumps.
Primordial black holes (PBHs) from the early Universe constitute an attractive dark matter candidate. First detections of black hole-neutron star (BH-NS) candidate gravitational wave events by the LIGO/Virgo collaboration, GW200105 and GW200115, already prompted speculations about non-astrophysical origin. We analyze, for the first time, the total volumetric merger rates of PBH-NS binaries formed via two-body gravitational scattering, finding them to be subdominant to the astrophysical BH-NS rates. In contrast to binary black holes, a significant fraction of which can be of primordial origin, …
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_{\…
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 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…
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…
