Advanced Virgo Detectors Research Articles

Temperature Dependence of the Mechanical Dissipation of Gallium Bonds for Use in Gravitational Wave Detectors.

The mirror suspensions in gravitational wave detectors demand low mechanical loss jointing to ensure good enough detector performance and to enable the detection of gravitational waves. Hydroxide catalysis bonds have been used in the fused silica suspensions of the GEO600, Advanced LIGO, and Advanced Virgo detectors. Future detectors may use cryogenic cooling of the mirror suspensions and this leads to a potential change of mirror material and suspension design. Other bonding techniques that could replace or be used alongside hydroxide catalysis bonding are of interest. A design that incorporates repair scenarios is highly desirable. Indeed, the mirror suspensions in KAGRA, which is made from sapphire and operated at cryogenic temperatures, have used a combination of hydroxide catalysis bonding and gallium bonding. This Letter presents the first measurements of the mechanical loss of a gallium bond measured between 10K and 295K. It is shown that the loss, which decreases with temperature down to the level of (1.8±0.3)×10^{-4} at 10K, is comparable to that of a hydroxide catalysis bond.

Physics-inspired spatiotemporal-graph AI ensemble for the detection of higher order wave mode signals of spinning binary black hole mergers

We present a new class of AI models for the detection of quasi-circular, spinning, non-precessing binary black hole mergers whose waveforms include the higher order gravitational wave modes (ℓ,|m|)={(2,2),(2,1),(3,3),(3,2),(4,4)} , and mode mixing effects in the ℓ=3,|m|=2 harmonics. These AI models combine hybrid dilated convolution neural networks to accurately model both short- and long-range temporal sequential information of gravitational waves; and graph neural networks to capture spatial correlations among gravitational wave observatories to consistently describe and identify the presence of a signal in a three detector network encompassing the Advanced LIGO and Virgo detectors. We first trained these spatiotemporal-graph AI models using synthetic noise, using 1.2 million modeled waveforms to densely sample this signal manifold, within 1.7 h using 256 NVIDIA A100 GPUs in the Polaris supercomputer at the Argonne Leadership Computing Facility. This distributed training approach exhibited optimal classification performance, and strong scaling up to 512 NVIDIA A100 GPUs. With these AI ensembles we processed data from a three detector network, and found that an ensemble of 4 AI models achieves state-of-the-art performance for signal detection, and reports two misclassifications for every decade of searched data. We distributed AI inference over 128 GPUs in the Polaris supercomputer and 128 nodes in the Theta supercomputer, and completed the processing of a decade of gravitational wave data from a three detector network within 3.5 h. Finally, we fine-tuned these AI ensembles to process the entire month of February 2020, which is part of the O3b LIGO/Virgo observation run, and found 6 gravitational waves, concurrently identified in Advanced LIGO and Advanced Virgo data, and zero false positives. This analysis was completed in one hour using one NVIDIA A100 GPU.

Gravitational-wave Radiation from the Magnetar-driven Supernovae

Rapidly spinning magnetars are potential candidates for the energy source of supernovae (SNe) and gamma-ray bursts and the most promising sources for continuous gravitational waves (GWs) detected by ground-based GW detectors. Continuous GWs can be radiated from magnetars due to magnetic-induced deformation or fluid oscillations, compatible with magnetic dipole (MD) radiation for spin-down energy. In this paper, we investigate the diverse light curves of magnetar-driven SNe in the scenario that the spin-down is dominated by GW radiation and/or MD radiation. By simulating the light curves of SNe and employing the Markov Chain Monte Carlo method, we constrain the parameters of the magnetars and SN explosions and show that the signature of GW radiation may be indicated by the bolometric luminosity curves of SNe Ic-BL 2007ru and 2009bb. We find that the ellipticity of magnetars in the order of 10−3 can be induced by the magnetic field of ∼1016 G. If such continuous GWs associated with SNe can be detected in the future by the Advanced LIGO and Virgo detectors, this would be a smoking gun for a magnetar engine powering SNe.

A Joint Fermi-GBM and Swift-BAT Analysis of Gravitational-wave Candidates from the Third Gravitational-wave Observing Run

We present Fermi Gamma-ray Burst Monitor (Fermi-GBM) and Swift Burst Alert Telescope (Swift-BAT) searches for gamma-ray/X-ray counterparts to gravitational-wave (GW) candidate events identified during the third observing run of the Advanced LIGO and Advanced Virgo detectors. Using Fermi-GBM onboard triggers and subthreshold gamma-ray burst (GRB) candidates found in the Fermi-GBM ground analyses, the Targeted Search and the Untargeted Search, we investigate whether there are any coincident GRBs associated with the GWs. We also search the Swift-BAT rate data around the GW times to determine whether a GRB counterpart is present. No counterparts are found. Using both the Fermi-GBM Targeted Search and the Swift-BAT search, we calculate flux upper limits and present joint upper limits on the gamma-ray luminosity of each GW. Given these limits, we constrain theoretical models for the emission of gamma rays from binary black hole mergers.

On the merger rate of primordial black holes in cosmic voids

Cosmic voids are known as underdense substructures of the cosmic web that cover a large volume of the Universe. It is known that cosmic voids contain a small number of dark matter halos, so the existence of primordial black holes (PBHs) in these secluded regions of the Universe is not unlikely. In this work, we calculate the merger rate of PBHs in dark matter halos structured in cosmic voids and determine their contribution to gravitational wave events resulting from black hole mergers recorded by the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO)-Advanced Virgo (aVirgo) detectors. Relying on the PBH scenario, the results of our analysis indicate that about 3∼4 annual events of binary black hole mergers out of all those recorded by the aLIGO-aVirgo detectors should belong to cosmic voids. We also calculate the redshift evolution of the merger rate of PBHs in cosmic voids. The results show that the evolution of the merger rate of PBHs has minimum sensitivity to the redshift changes, which seems reasonable while considering the evolution of cosmic voids. Finally, we specify the behavior of the merger rate of PBHs as a function of their mass and fraction in cosmic voids and we estimate R(MPBH,fPBH) relation, which is well compatible with our findings.

A stochastic search for intermittent gravitational-wave backgrounds

A likely source of a gravitational-wave background (GWB) in the frequency band of the Advanced LIGO, Virgo, and KAGRA detectors is the superposition of signals from the population of unresolvable stellar-mass binary-black-hole (BBH) mergers throughout the Universe. Since the duration of a BBH merger in band ($\ensuremath{\sim}1\text{ }\text{ }\mathrm{s}$) is much shorter than the expected separation between neighboring mergers ($\ensuremath{\sim}{10}^{3}\text{ }\text{ }\mathrm{s}$), the observed signal will be ``popcornlike'' or intermittent with duty cycles of order ${10}^{\ensuremath{-}3}$. However, the standard cross-correlation search for stochastic GWBs currently performed by the LIGO-Virgo-KAGRA Collaboration is based on a continuous-Gaussian signal model, which does not take into account the intermittent nature of the background. The latter is better described by a Gaussian mixture model, which includes a duty cycle parameter that quantifies the degree of intermittence. Building on an earlier paper by Drasco and Flanagan [Detection methods for non-gaussian gravitational wave stochastic backgrounds, Phys. Rev. D 67, 082003 (2003).], we propose a stochastic-signal-based search for intermittent GWBs. For such signals, this search performs better than the standard continuous cross-correlation search. We present results of our stochastic-signal-based approach for intermittent GWBs applied to simulated data for some simple models, and we compare its performance to the other search methods, in terms of both detection and signal characterization. Additional testing on more realistic simulated datasets, e.g., consisting of astrophysically motivated BBH merger signals injected into colored detector noise containing noise transients, will be needed before this method can be applied with confidence on real gravitational-wave data.

IceCube Search for Neutrinos Coincident with Gravitational Wave Events from LIGO/Virgo Run O3

Using data from the IceCube Neutrino Observatory, we searched for high-energy neutrino emission from the gravitational-wave events detected by the advanced LIGO and Virgo detectors during their third observing run. We did a low-latency follow-up on the public candidate events released during the detectors’ third observing run and an archival search on the 80 confident events reported in the GWTC-2.1 and GWTC-3 catalogs. An extended search was also conducted for neutrino emission on longer timescales from neutron star containing mergers. Follow-up searches on the candidate optical counterpart of GW190521 were also conducted. We used two methods; an unbinned maximum likelihood analysis and a Bayesian analysis using astrophysical priors, both of which were previously used to search for high-energy neutrino emission from gravitational-wave events. No significant neutrino emission was observed by any analysis, and upper limits were placed on the time-integrated neutrino flux as well as the total isotropic equivalent energy emitted in high-energy neutrinos.

All-sky search for continuous gravitational waves from isolated neutron stars using Advanced LIGO and Advanced Virgo O3 data

We present results of an all-sky search for continuous gravitational waves which can be produced by spinning neutron stars with an asymmetry around their rotation axis, using data from the third observing run of the Advanced LIGO and Advanced Virgo detectors. Four different analysis methods are used to search in a gravitational-wave frequency band from 10 to 2048 Hz and a first frequency derivative from −10−8 to 10−9 Hz/s. No statistically significant periodic gravitational-wave signal is observed by any of the four searches. As a result, upper limits on the gravitational-wave strain amplitude h0 are calculated. The best upper limits are obtained in the frequency range of 100 to 200 Hz and they are ∼1.1×10−25 at 95% confidence level. The minimum upper limit of 1.10×10−25 is achieved at a frequency 111.5 Hz. We also place constraints on the rates and abundances of nearby planetary- and asteroid-mass primordial black holes that could give rise to continuous gravitational-wave signals.10 MoreReceived 3 January 2022Accepted 17 October 2022DOI:https://doi.org/10.1103/PhysRevD.106.102008© 2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGravitational wave sourcesPhysical SystemsNeutron stars & pulsarsTechniquesGravitational wave detectionGravitation, Cosmology & Astrophysics

Gravitational Wave Detection Based on Squeeze-and-excitation Shrinkage Networks and Multiple Detector Coherent SNR

Deep learning techniques have been applied to the detection of gravitational wave signals in the past few years. Most existing methods focus on the data obtained by a single detector. However, the signal-to-noise ratio (SNR) of gravitational wave signals in a single detector is pretty low, making it hard for deep neural networks to learn effective features. Therefore, how to use the observation signals obtained by multiple detectors in deep learning methods is a serious issue. We simulate binary neutron star signals from multiple detectors, including the Advanced LIGO and Virgo detectors. We calculate coherent SNR of multiple detectors using a fully coherent all-sky search method and obtain the coherent SNR data required for our proposed deep learning method. Inspired by the principle of attention network Squeeze-and-Excitation Networks (SENet) and the soft thresholding shrinkage function, we propose a novel Squeeze-and-Excitation Shrinkage (SES) module to better extract effective features. Then we use this module to establish a gravitational wave squeeze-and-excitation shrinkage network (GW-SESNet) detection model. We train and validate the performance of our model on the coherent SNR data set. Our model obtains satisfactory classification accuracy and can excellently complete the task of gravitational wave detection.

Prospects for reconstructing the gravitational-wave signals from core-collapse supernovae with Advanced LIGO-Virgo and the BayesWave algorithm

Our current understanding of the core-collapse supernova explosion mechanism is incomplete, with multiple viable models for how the initial shock wave might be energized enough to lead to a successful explosion. Detection of a gravitational-wave signal emitted in the initial few seconds after stellar core-collapse would provide unique and crucial insight into this process. With the Advanced LIGO and Advanced Virgo detectors expected to approach their design sensitivities soon, we could potentially detect this signal from a supernova within our galaxy. In anticipation of such a scenario, we study how well the BayesWave algorithm can recover the gravitational-wave signal from core-collapse supernova models in simulated advanced detector noise, and optimize its ability to accurately reconstruct the signal waveforms. We find that BayesWave can confidently reconstruct the signal from a range of supernova explosion models in Advanced LIGO-Virgo for network signal-to-noise ratios $\gtrsim 30$, reaching maximum reconstruction accuracies of $\sim 90\%$ at SNR $\sim 100$. For low SNR signals that are not confidently recovered, our optimization efforts result in gains in reconstruction accuracy of up to $20-40\%$, with typical gains of $\sim 10\%$.

Numerical relativity simulations of the neutron star merger GW190425: microphysics and mass ratio effects

ABSTRACT GW190425 was the second gravitational wave (GW) signal compatible with a binary neutron star (BNS) merger detected by the Advanced LIGO and Advanced Virgo detectors. Since no electromagnetic counterpart was identified, whether the associated kilonova was too dim or the localization area too broad is still an open question. We simulate 28 BNS mergers with the chirp mass of GW190425 and mass ratio 1 ≤ q ≤ 1.67, using numerical-relativity simulations with finite-temperature, composition dependent equations of state (EOS) and neutrino radiation. The energy emitted in GWs is $\lesssim 0.083\mathrm{\, M_\odot }c^2$ with peak luminosity of 1.1–$2.4\times ~10^{58}/(1+q)^2\, {\rm {erg \, s^{-1}}}$. Dynamical ejecta and disc mass range between 5 × 10−6–10−3 and 10−5–$0.1 \mathrm{\, M_\odot }$, respectively. Asymmetric mergers, especially with stiff EOSs, unbind more matter and form heavier discs compared to equal mass binaries. The angular momentum of the disc is 8–$10\mathrm{\, M_\odot }~GM_{\rm {disc}}/c$ over three orders of magnitude in Mdisc. While the nucleosynthesis shows no peculiarity, the simulated kilonovae are relatively dim compared with GW170817. For distances compatible with GW190425, AB magnitudes are always dimmer than ∼20 mag for the B, r, and K bands, with brighter kilonovae associated to more asymmetric binaries and stiffer EOSs. We suggest that, even assuming a good coverage of GW190425’s sky location, the kilonova could hardly have been detected by present wide-field surveys and no firm constraints on the binary parameters or EOS can be argued from the lack of the detection.

Constraining the Ellipticity of the Newborn Magnetar with the Observational Data of Long Gamma-Ray Bursts

The X-ray plateau emission observed in many long gamma-ray bursts (LGRBs) has been usually interpreted as the spin-down luminosity of a rapidly spinning, highly magnetized neutron star (millisecond magnetar). If this is true, then the magnetar may emit extended gravitational wave (GW) emission associated with the X-ray plateau due to nonaxisymmetric deformation or various stellar oscillations. The advanced LIGO and Virgo detectors have searched for long-duration GW transients for several years; no evidence of GWs from any magnetar has been found until now. In this work, we attempt to search for signatures of GW radiation in the electromagnetic observation of 30 LGRBs under the assumption of the magnetar model. We utilize the observations of the LGRB plateau to constrain the properties of the newborn magnetar, including the initial spin period P 0, dipole magnetic field strength B p , and the ellipticity ϵ. We find that there are some tight relations between magnetar parameters, e.g., and . In addition, we derive the GW strain for the magnetar sample via their spin-down processes, and find that the GWs from these objects may not be detectable by the aLIGO and Einstein Telescope (ET) detectors. For a rapidly spinning magnetar (P ∼ 1 ms, B ∼ 1015 G), the detection horizon for the advanced LIGO O5 detector is ∼180 Mpc. The detection of such a GW signal associated with the X-ray plateau would be a smoking gun that the central engine of a GRB is a magnetar.

Rapid source classification and distance estimation for compact binary mergers with PyCBC live

ABSTRACT During the third observing run (O3) of the advanced LIGO and advanced virgo detectors, dozens of candidate gravitational-wave (GW) events have been catalogued. A challenge of this observing run has been the rapid identification and public dissemination of compact binary coalescence (CBC) signals, a task carried out by low-latency searches such as PyCBC Live. During the later part of O3, we developed a method of classifying CBC sources via their probabilities of containing neutron star or black hole components within PyCBC Live in order to facilitate immediate follow-up observations by electromagnetic and neutrino observatories. This fast classification uses the chirp mass recovered by the search as input given the difficulty of measuring the mass ratio with high accuracy for lower mass binaries. We also use a distance estimate derived from the search output to correct for the bias in chirp mass due to the cosmological redshift. We present results for simulated signals, and for confirmed candidate events identified in low latency over O3.

Search for Short‐Duration Transient Gravitational Waves Emitted by Neutron Star Glitches

AbstractNeutron stars are known to show an accelerated spin‐up of their rotational frequency on a short time scale of around 40 s, called a “glitch” in the neutron star. These neutron star glitches can emit short‐duration transient gravitational wave signals as f‐mode oscillations at frequencies between 1.5 and 3 kHz and damping times of less than a few seconds. The observed rate of neutron star glitches are currently limited by their electromagnetic observations. There could be a population of the isolated neutron stars in the galaxy for which there is no electromagnetic observation, but they can produce gravitational wave signals. Here, the sensitivity of the generic all‐sky search for short‐duration transients towards neutron star glitches during the Advanced LIGO and Virgo's third observing run using the Coherent WaveBurst algorithm is presented. The prospects of detecting signals from such glitching neutron stars for the upcoming fourth and fifth observing runs of Advanced LIGO and Virgo detectors are also described.

All-sky, all-frequency directional search for persistent gravitational waves from Advanced LIGO’s and Advanced Virgo’s first three observing runs

We present the first results from an all-sky all-frequency (ASAF) search for an anisotropic stochastic gravitational-wave background using the data from the first three observing runs of the Advanced LIGO and Advanced Virgo detectors. Upper limit maps on broadband anisotropies of a persistent stochastic background were published for all observing runs of the LIGO-Virgo detectors. However, a broadband analysis is likely to miss narrowband signals as the signal-to-noise ratio of a narrowband signal can be significantly reduced when combined with detector output from other frequencies. Data folding and the computationally efficient analysis pipeline, PyStoch, enable us to perform the radiometer map-making at every frequency bin. We perform the search at 3072 HEALPix equal area pixels uniformly tiling the sky and in every frequency bin of width 1/32 Hz in the range 20–1726 Hz, except for bins that are likely to contain instrumental artefacts and hence are notched. We do not find any statistically significant evidence for the existence of narrowband gravitational-wave signals in the analyzed frequency bins. Therefore, we place 95% confidence upper limits on the gravitational-wave strain for each pixel-frequency pair, the limits are in the range (0.030−9.6)×10−24. In addition, we outline a method to identify candidate pixel-frequency pairs that could be followed up by a more sensitive (and potentially computationally expensive) search, e.g., a matched-filtering-based analysis, to look for fainter nearly monochromatic coherent signals. The ASAF analysis is inherently independent of models describing any spectral or spatial distribution of power. We demonstrate that the ASAF results can be appropriately combined over frequencies and sky directions to successfully recover the broadband directional and isotropic results.Received 25 October 2021Revised 22 February 2022Accepted 17 May 2022DOI:https://doi.org/10.1103/PhysRevD.105.122001© 2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGravitational wave detectionGravitational wavesGravitation, Cosmology & Astrophysics

Population inference of spin-induced quadrupole moments as a probe for nonblack hole compact binaries

Gravitational wave (GW) measurements of physical effects such as spin-induced quadrupole moments can distinguish binaries consisting of black holes from nonblack hole binaries. While these effects may be poorly constrained for single-event inferences with the second-generation detectors, combining information from multiple detections can help uncover features of nonblack hole binaries. The spin-induced quadrupole moment has specific predictions for different types of compact objects, and a generalized formalism must consider a population where different types of compact objects co-exist. In this study, we introduce a hierarchical mixture-likelihood formalism to estimate the fraction of nonbinary black holes in the population. We demonstrate the applicability of this method using simulated GW signals injected into Gaussian noise following the design sensitivities of the Advanced LIGO Advanced Virgo detectors. We compare the performance of this method with a traditionally-followed hierarchical inference approach. Both the methods are equally effective to hint at inhomogeneous populations, however, we find the mixture-likelihood approach to be more natural for mixture populations comprising compact objects of diverse classes. We also discuss the possible systematics in the mixture-likelihood approach, caused by several reasons, including the limited sensitivity of the second-generation detectors, specific features of the astrophysical population distributions, and the limitations posed by the waveform models employed. Finally, we apply this method to the LIGO-Virgo detections published in the second GW transient catalog (GWTC-2) and find them consistent with a binary black hole population with ${f}_{\mathrm{nbh}}$ estimated to be $\ensuremath{\le}0.29$ at 90% credibility.

Modified theories of gravity: Why, how and what?

General Relativity (GR) was proven via the direct detection of gravitational waves from the mergers of the binary black holes and binary neutron stars by the Advanced LIGO and Advanced Virgo detectors. These detections confirmed the prediction of GR and provided the first direct evidence of the existence of stellar-mass black holes (BHs). However, the occurrence of singularities at the centers of BHs suggests that GR is inapplicable because of the breakdown of the equivalence principle at the singularities. The fact that these singularities exist indicates that GR cannot be a universal theory of space-time. In the low-energy limit, the theoretical and observational challenges faced by the $\Lambda$CDM model also indicate that we might have to look beyond GR as the underlying theory of gravity. Unlike GR, whose field equations contain only up to second-order derivatives, the modified theories with higher derivative Ricci/Riemann tensor gravity models include higher derivatives. Therefore, one expects significant differences between GR and modified theories. Since there are many ways of modifying GR in the strong-gravity and cosmological distances, each model has unique features. This leads to the following crucial question: Are there a set of unique signatures that distinguish GR from modified gravity (MG) theories? This review discusses three aspects of MG theories: (1) Why do we need to consider MG theories? (2) How to modify GR? and (3) What are the observational consequences? The review is written in a pedagogical style with the expectation that it will serve as a useful reference for theorists and observers and those interested in bridging the divide between theory and observations.

High-accuracy simulations of highly spinning binary neutron star systems

With an increasing number of expected gravitational-wave detections of binary neutron star mergers, it is essential that gravitational-wave models employed for the analysis of observational data are able to describe generic compact binary systems. This includes systems in which the individual neutron stars are millisecond pulsars for which spin effects become essential. In this work, we perform numerical-relativity simulations of binary neutron stars with aligned and anti-aligned spins within a range of dimensionless spins of $\chi \sim [-0.28,0.58]$. The simulations are performed with multiple resolutions, show a clear convergence order and, consequently, can be used to test existing waveform approximants. We find that for very high spins gravitational-wave models that have been employed for the interpretation of GW170817 and GW190425 are not capable of describing our numerical-relativity dataset. We verify through a full parameter estimation study in which clear biases in the estimate of the tidal deformability and effective spin are present. We hope that in preparation of the next gravitational-wave observing run of the Advanced LIGO and Advanced Virgo detectors our new set of numerical-relativity data can be used to support future developments of new gravitational-wave models.

Understanding How Fast Black Holes Spin by Analyzing Data from the Second Gravitational-wave Catalogue

Abstract The Advanced LIGO and Virgo detectors have now observed approximately 50 black hole binary mergers, from which we can begin to infer how rapidly astrophysical black holes spin. The LIGO-Virgo Collaboration (LVC) analysis of detections up to the end of the first half of the third observing run (O3a) appeared to uncover a distribution of spin magnitudes that peaks at ∼0.2. This is surprising: is there a black hole formation mechanism that prefers a particular, nonzero spin magnitude, or could this be the cumulative effect of multiple formation processes? We perform an independent analysis of the most recent gravitational-wave (GW) catalog, and find that (a) the support for the LVC spin magnitude is tenuous; in particular, adding or removing just one signal from the catalog can remove the statistical preference for this distribution; and (b) we find potential evidence for two spin subpopulations in the observed black holes: one with extremely low spins and one with larger spin magnitudes. We make the connection that these spin subpopulations could be correlated with the mass of the binary, with more massive binaries preferring larger spin magnitudes, and argue that this may provide evidence for hierarchical mergers in the second GW catalog.

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.