Hierarchical Merging Research Articles

Hierarchical merger of primordial black holes in dwarf galaxies

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 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 energy radiated out in the form of gravitational waves. We find that, in the lighter mass limit, black holes up to eight times more massive than the original population can be formed within a Hubble time.

Limits on Hierarchical Black Hole Mergers from the Most Negative χ eff Systems

It has been proposed that some black holes (BHs) in binary black hole (BBH) systems are born from “hierarchical mergers” (HMs), i.e., earlier mergers of smaller BHs. These HM products have spin magnitudes χ ∼ 0.7, and, if they are dynamically assembled into BBH systems, their spin orientations will sometimes be antialigned with the binary orbital angular momentum. In fact, as Baibhav et al. showed, ∼16% of BBH systems that include HM products will have an effective inspiral spin parameter, χ eff < −0.3. Nevertheless, the LIGO–Virgo–KAGRA (LVK) gravitational-wave (GW) detectors have yet to observe a BBH system with χ eff ≲ −0.2, leading to upper limits on the fraction of HM products in the population. We fit the astrophysical mass and spin distribution of BBH systems and measure the fraction of BBH systems with χ eff < −0.3, which implies an upper limit on the HM fraction. We find that fewer than 26% of systems in the underlying BBH population include HM products (90% credibility). Even among BBH systems with primary masses m 1 = 60 M ⊙, the HM fraction is less than 69%, which may constrain the location of the pair-instability mass gap. With 300 GW events (to be expected in the LVK’s next observing run), if we fail to observe a BBH with χ eff < −0.3, we can conclude that the HM fraction is smaller than .

Avoiding a Cluster Catastrophe: Retention Efficiency and the Binary Black Hole Mass Spectrum

The population of binary black hole mergers identified through gravitational waves has uncovered unexpected features in the intrinsic properties of black holes in the universe. One particularly surprising and exciting result is the possible existence of black holes in the pair-instability mass gap, ∼50–120 M ⊙. Dense stellar environments can populate this region of mass space through hierarchical mergers, with the retention efficiency of black hole merger products strongly dependent on the escape velocity of the host environment. We use simple toy models to represent hierarchical merger scenarios in various dynamical environments. We find that hierarchical mergers in environments with high escape velocities (≳300 km s−1) are efficiently retained. If such environments dominate the binary black hole merger rate, this would lead to an abundance of high-mass mergers that is potentially incompatible with the empirical mass spectrum from the current catalog of binary black hole mergers. Models that efficiently generate hierarchical mergers, and contribute significantly to the observed population, must therefore be tuned to avoid a “cluster catastrophe” of overproducing binary black hole mergers within and above the pair-instability mass gap.

The Imprint of Superradiance on Hierarchical Black Hole Mergers

Ultralight bosons are a proposed solution to outstanding problems in cosmology and particle physics: they provide a dark-matter candidate while potentially explaining the strong charge-parity problem. If they exist, ultralight bosons can interact with black holes through the superradiant instability. In this work we explore the consequences of this instability on the evolution of hierarchical black holes within dense stellar clusters. By reducing the spin of individual black holes, superradiance reduces the recoil velocity of merging binary black holes, which, in turn, increases the retention fraction of hierarchical merger remnants. We show that the existence of ultralight bosons with mass 2 × 10−14 ≲ μ/eV ≲ 2 × 10−13 would lead to an increased rate of hierarchical black hole mergers in nuclear star clusters. An ultralight boson in this energy range would result in up to ≈60% more present-day nuclear star clusters supporting hierarchical growth. The presence of an ultralight boson can also double the rate of intermediate-mass black hole mergers to ≈0.08 Gpc−3 yr−1 in the local universe. These results imply that a select range of ultralight boson masses can have far-reaching consequences for the population of black holes in dense stellar environments. Future studies into black hole cluster populations and the spin distribution of hierarchically formed black holes will test this scenario.

Intra-pulse variability induced by plasmoid formation in pulsar magnetospheres

Context. Pulsars show irregularities in their pulsed radio emission that originate from propagation effects and the intrinsic activity of the source. Aims. In this work, we investigate the role played by magnetic reconnection and the formation of plasmoids in the pulsar wind current sheet as a possible source of intrinsic pulse-to-pulse variability in the incoherent, high-energy emission pattern. Methods. We used a two-dimensional particle-in-cell simulation of an orthogonal pulsar magnetosphere restricted to the plane perpendicular to the star spin axis. We evolved the solution for several tens of pulsar periods to gather a statistically significant sample of synthetic pulse profiles. Results. The formation of plasmoids leads to strong pulse-to-pulse variability in the form of multiple short, bright subpulses, which appear only on the leading edge of each main pulse. These secondary peaks of emission are dominated by the dozen plasmoids that can grow up to macroscopic scales. They emerge from the high end of the hierarchical merging process occurring along the wind current layer. The flux of the subpulses is correlated with their width in phase. Although the full-scale separation is not realistic, we argue that the simulation correctly captures the demographics and the properties of the largest plasmoids, and therefore of the brightest subpulses. Conclusions. The prediction of subpulses at specific pulse phases provides a new observational test of the magnetic reconnection scenario as the origin of the pulsed incoherent emission. High-time-resolution observations of the Crab pulsar in the optical range may be the most promising source to target for this purpose.

Scalable multi‐node multi‐GPU Louvain community detection algorithm for heterogeneous architectures

SummaryCommunity detection is an important problem that is widely applied for finding cluster patterns in brain, social, biological, and many other kinds of networks. In this work, we have developed a multi‐node multi‐GPU Louvain community detection algorithm, simultaneously harnessing the CPU and GPU cores of the devices. The algorithm partitions a given graph across multiple nodes and devices in the nodes and performs independent computations of Louvain algorithm on the parts on the devices. The independently formed communities in the devices are refined by identification of doubtful vertices and migrating them to the other processors. The communities are merged using a hierarchical merging algorithm that ensures that at any point the merged component can be accommodated within a processor. Our experiments show that our algorithm is highly scalable with increasing number of devices and provides large‐scale performance for BigData graphs.

Hot Circumsingle Disks Drive Binary Black Hole Mergers in Active Galactic Nucleus Disks

Abstract Binary black hole (BBH) mergers, particularly those with component masses in the pair-instability gap, may be produced by hierarchical mergers in the disks surrounding Active Galactic Nuclei (AGNs). While the interaction of an embedded BBH with an AGN disk is typically assumed to facilitate a merger, recent high-resolution hydrodynamical simulations challenge this assumption. However, these simulations often have simplified treatments for gas thermodynamics. In this work, we model the possible consequence of various feedback from an embedded BBH with a simple model that maintains an enhanced temperature profile around each binary component. We show that when the minidisks around each BH become hotter than the background by a factor of three, the BBH orbital evolution switches from expansion to contraction. By analyzing the gravitational torque profile, we find that this change in direction is driven by a weakening of the minidisk spirals and their positive torque on the binary. Our results highlight the important role of thermodynamics around BBHs and its effect on their orbital evolution, suggesting that AGN disks could be efficient factories for BBH mergers.

Time-dependent stellar-mass binary black hole mergers in AGN disks: Mass distribution of hierarchical mergers

There is much debate about the channels for astrophysical origins of the stellar-mass binary black hole (BBH) mergers detected by LIGO and Virgo. Active galactic nuclei (AGNs) are promising sites for the efficient formation and rapid mergers of BBHs due to migration traps in high-density gas disks within an inner radii. In this paper, we carry out Monte Carlo simulations to explore the mass properties of mergers over time and hierarchical mergers -- with one of the black holes (BHs) being the remnant of a previous merger. We find that the predicted merger rate is $\sim 27-37~{\rm Gpc^{-3}~yr^{-1}}$ and the detection rate of LIGO/Virgo accompanying with extreme mass-ratio mergers will increase in the late stage of AGNs. The fraction of hierarchical mergers is $\sim 24\%$, and its mass-ratio peak is $\sim 0.15-0.35$. Compared with the low-generation mergers in hierarchical mergers, the mass ratio of high-generation mergers has a flatter distribution around its peak. These reveal that the BBH mergers detected by LIGO/Virgo with the extreme mass ratio or heavy component masses can be well explained in AGN channel.

An Eccentric Binary Blackhole in Post-Newtonian Theory

Gravitational waves radiated during binary black hole coalescence are a perfect probe for studying the characteristics of strong gravity. Advanced techniques for creating numerical relativity substitute models for eccentric binary black hole systems are presumed to be crucial in existing and anticipated gravitational wave detectors. The imprint on the observation data of the gravitational wave emitted by the binary coalescence enhances two-body system studies. The aim of this study is to present an overview of the change in characteristic behaviors of hierarchical massive astrophysical objects merger, which are the databank of the early universe. We present results from numerical relativity simulations of an equal-mass and unequal mass nonspinning inspiral binary-black-hole system in the Post-Newtonian framework. We also consider the time evolution of eccentricity for an initial eccentric system. The eccentric Post-Newtonian equations are expanded in the form of the frequency related variable x=(Mω)2/3. The model is restricted to the (2, 2) spin-weighted spherical harmonic modes. We conclude that for higher eccentricity as well as mass ratio, there is higher oscillation in orbital radius and in eccentricity.

Prospects for Measuring Off-axis Spins of Binary Black Holes with Plus-era Gravitational-wave Detectors

Abstract The mass and spin properties of binary black holes (BBHs) inferred from their gravitational-wave signatures reveal important clues about how these systems form. BBHs originating from isolated binary evolution are expected to have spins preferentially aligned with their orbital angular momentum, whereas there is no such preference in binaries formed via dynamical assembly. The fidelity with which near-future gravitational-wave detectors can measure off-axis spins will have implications for the study of BBH formation channels. In this work, we examine the degree to which the Advanced LIGO Plus (A+) and Advanced Virgo Plus (AdV+) interferometric detectors can measure both aligned and misaligned spins. We compare spin resolution between the LIGO-Virgo network operating at either A+/AdV+ (“Plus”) sensitivity or Advanced-era design (“Design”) sensitivity using simulated BBH gravitational-wave signals injected into synthetic detector noise. The signals are distributed over the mass-spin parameter space of likely BBH systems, accounting for the effects of precession and higher-order modes. We find that the Plus upgrades yield significant improvements in spin estimation for systems with unequal masses and moderate or large spins. Using simulated signals modeled after different types of hierarchical BBH mergers, we also conclude that the Plus detector network will yield substantially improved spin estimates for 1G+2G binaries compared to the Design network.

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.

The cosmic evolution of binary black holes in young, globular, and nuclear star clusters: rates, masses, spins, and mixing fractions

ABSTRACT The growing population of binary black holes (BBHs) observed by gravitational wave (GW) detectors is a potential Rosetta stone for understanding their formation channels. Here, we use an upgraded version of our semi-analytical codes fastcluster and cosmo$\mathcal {R}$ate to investigate the cosmic evolution of four different BBH populations: isolated BBHs and dynamically formed BBHs in nuclear star clusters (NSCs), globular clusters (GCs), and young star clusters (YSCs). With our approach, we can study different channels assuming the same stellar and binary input physics. We find that the merger rate density of BBHs in GCs and NSCs is barely affected by stellar metallicity (Z), while the rate of isolated BBHs changes wildly with Z. BBHs in YSCs behave in an intermediate way between isolated and GC/NSC BBHs. The local merger rate density of Nth-generation black holes (BHs), obtained by summing up hierarchical mergers in GCs, NSCs, and YSCs, ranges from ∼1 to ∼4 Gpc−3 yr−1 and is mostly sensitive to the spin parameter. We find that the mass function of primary BHs evolves with redshift in GCs and NSCs, becoming more top-heavy at higher z. In contrast, the primary BH mass function almost does not change with redshift in YSCs and in the field. This signature of the BH mass function has relevant implications for Einstein Telescope and Cosmic Explorer. Finally, our analysis suggests that multiple channels contribute to the BBH population of the second GW transient catalogue.

Investigating the Baryon Cycle in Interacting Dwarfs with the Very Large Array and Pan-STARRS

Abstract We present resolved H i synthesis maps from the Very Large Array of three interacting dwarf systems: the NGC 3664 dwarf pair, the NGC 3264 dwarf pair, and the UGC 4638 dwarf triplet. All three dwarf systems are captured at various stages of interaction and span a range of environments. We detect clear hallmarks of tidal interactions through the presence of H i bridges and diffuse H i extensions that surround the dwarfs. We overlay the H i data on Pan-STARRS r-band images and find further evidence of tidal interactions through coincident distorted H i and tidal stellar features in NGC 3264 and UGC 4638, and an unwound spiral arm pointing toward its smaller companion in NGC 3264. In UGC 4638, both the gas and diffuse stars are extended to similar radii east of the primary, which could indicate that the smaller dwarf in the system has already completed one pass through the primary. We additionally find that our three systems, and those from the Local Volume TiNy Titans survey, are not H i deficient and thus the interaction has not resulted in a loss of gas from the systems. A comparison with noninteracting dwarf galaxies shows that the interactions have a significant impact on the kinematics of the systems. Our new resolved H i kinematics, combined with detailed stellar and H i morphologies, provide crucial constraints for future dynamical modeling of hierarchical mergers and the baryon cycle at the low-mass scale.

Local Scale-Guided Hierarchical Region Merging and Further Over- and Under-Segmentation Processing for Hybrid Remote Sensing Image Segmentation

With the development of medium- and high-resolution satellites, successfully segmenting differently sized geo-objects remains a challenging issue in the framework of geographic object-based image analysis (GEOBIA). The hybrid image segmentation method is a good alternative to produce good segmentation that best matched the different sizes of geo-objects. However, the existing methods almost use a certain scale or other segmentation parameters (SPs) to control the sizes and shapes of segments. This will lead to two issues: (1) one single scale is impossible to segment every geo-object well due to the land cover complexity within remote-sensing imageries; (2) over- and under-segmented regions still occur in the segmentation results, whatever using any advanced segmentation methods. To solve the above problems, this paper developed a hybrid image segmentation method with local scale-guided hierarchical region merging and further over- and under-segmentation processing. First, the primitive segmentation was produced and then stratified into layers with different land covers. Then, the local scale was calculated for a more objective merging process in the separating layers. Third, the over- and under-segmentation at separating layers was recognized and re-processed for achieving a fine segmentation. To validate the proposed method, it was applied to three test images of gaofen-1 satellite with different land cover types, and ten competing methods were compared. The visual and quantitative results indicated the advantage of our method in segmenting out different sizes of geo-objects, which can effectively reduce the over- and under-segmentation error.

Dynamic Cluster-Based Flow Management for Software Defined Networks

Software-defined network (SDN) allows traffic engineering and flow management by decoupling the control and data planes. SDN has attracted a lot of attention recently because of its centralized control, flow programmability and flexible resource management. However, to support centralized control, flow programmability and flexible resource management, most of the advanced SDN designs require per-flow management, which would easily make the flow table of a software switch overflow and incur undesired processing overhead when a network scales up. To overcome such huge traffic demands, we propose a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cluster-based macro-flow management</i> framework to balance the trade-off between customized services and management costs. The key idea of our design is to group similar flows into a cluster and replace per-flow management with per-cluster management. To achieve this goal, we cluster flows with consideration of the similarity of their traffic patterns. To adapt to varying traffic load, we further propose a hierarchical cluster merging scheme to dynamically merge clusters and make the best tradeoff between flow entry saving and routing performance guarantee. Our evaluation demonstrates that the proposed cluster-based flow management framework can significantly reduce the flow table usage, while producing minimum negative impact on routing performance.

Formation of giant plasmoids at the pulsar wind termination shock: A possible origin of the inner-ring knots in the Crab Nebula

Context. Nearby pulsar wind nebulae exhibit complex morphological features: jets, torus, arcs, and knots. These structures are well captured and understood in the scope of global magnetohydrodynamic models. However, the origin of knots in the inner radius of the Crab Nebula remains elusive. Aims. In this work, we investigate the dynamics of the shock front and downstream flow with a special emphasis on the reconnecting equatorial current sheet. We examine whether giant plasmoids produced in the reconnection process could be good candidates for the knots. Methods. To this end, we perform large semi-global three-dimensional particle-in-cell simulations in a spherical geometry. The hierarchical merging plasmoid model is used to extrapolate numerical results to pulsar wind nebula scales. Results. The shocked material collapses into the midplane, forming and feeding a large-scale, but thin, ring-like current layer. The sheet breaks up into a dynamical chain of merging plasmoids, reminiscent of three-dimensional reconnection. Plasmoids grow to a macroscopic size. The final number of plasmoids predicted is solely governed by the inverse of the dimensionless reconnection rate. Conclusions. The formation of giant plasmoids is a robust feature of pulsar wind termination shocks. They provide a natural explanation for the inner-ring knots in the Crab Nebula, provided that the nebula is highly magnetized.

Looking for the parents of LIGO’s black holes

Solutions to the two-body problem in general relativity allow us to predict the mass, spin and recoil velocity of a black-hole merger remnant given the masses and spins of its binary progenitors. In this paper we address the inverse problem: given a binary black-hole merger, can we use the parameters measured by gravitational-wave interferometers to tell if the binary components are of hierarchical origin, i.e. if they are themselves remnants of previous mergers? If so, can we determine at least some of the properties of their parents? This inverse problem is in general overdetermined. We show that hierarchical mergers occupy a characteristic region in the plane composed of the effective spin parameters $\chi_{\rm eff}$ and $\chi_{\rm p}$, and therefore a measurement of these parameters can add weight to the hierarchical-merger interpretation of some gravitational-wave events, including GW190521. If one of the binary components has hierarchical origin and its spin magnitude is well measured, we derive exclusion regions on the properties of its parents: for example we infer that the parents of GW190412 (if hierarchical) must have had unequal masses and low spins. Our formalism is quite general, and it can be used to infer constraints on the astrophysical environment producing hierarchical mergers.

Mass and Rate of Hierarchical Black Hole Mergers in Young, Globular and Nuclear Star Clusters

Hierarchical mergers are one of the distinctive signatures of binary black hole (BBH) formation through dynamical evolution. Here, we present a fast semi-analytic approach to simulate hierarchical mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs). Hierarchical mergers are more common in NSCs than they are in both GCs and YSCs because of the different escape velocity. The mass distribution of hierarchical BBHs strongly depends on the properties of first-generation BBHs, such as their progenitor’s metallicity. In our fiducial model, we form black holes (BHs) with masses up to ∼103 M⊙ in NSCs and up to ∼102 M⊙ in both GCs and YSCs. When escape velocities in excess of 100 km s−1 are considered, BHs with mass &gt;103 M⊙ are allowed to form in NSCs. Hierarchical mergers lead to the formation of BHs in the pair instability mass gap and intermediate-mass BHs, but only in metal-poor environments. The local BBH merger rate in our models ranges from ∼10 to ∼60 Gpc−3 yr−1; hierarchical BBHs in NSCs account for ∼10−2–0.2 Gpc−3 yr−1, with a strong upper limit of ∼10 Gpc−3 yr−1. When comparing our models with the second gravitational-wave transient catalog, we find that multiple formation channels are favored to reproduce the observed BBH population.

Remnant Black Hole Kicks and Implications for Hierarchical Mergers

Abstract When binary black holes merge in dense star clusters, their remnants can pair up with other black holes in the cluster, forming heavier and heavier black holes in a process called hierarchical merger. The most important condition for hierarchical merger to occur is that remnants formed by mergers are retained by the host star cluster. Using the publicly available gravitational-wave event database, we infer the magnitudes of kick velocities imparted to the remnant black holes due to anisotropic emission of gravitational waves and use that to quantify the retention probability of each event as a function of the escape speed of the star cluster. Among the second gravitational-wave transient catalog (GWTC-2) events, GW190814 provides the tightest constraint on the kick magnitude with V kick = 74 − 7 + 10 km s−1 at the 90% credible level. We find that star clusters with escape speeds of 200 km s−1 can retain about 50% of the events in the GWTC-2. Using the escape speed distributions of nuclear star clusters and globular clusters, we find that ∼17 (2) remnants of GWTC-2 may be retained by the host star cluster if all GWTC-2 events occurred in nuclear (globular) clusters. Our study demonstrates the importance of folding in kick velocity inferences in future studies of hierarchical mergers.

Signatures of hierarchical mergers in black hole spin and mass distribution

ABSTRACT Recent gravitational wave (GW) observations by LIGO/Virgo show evidence for hierarchical mergers, where the merging BHs are the remnants of previous BH merger events. These events may carry important clues about the astrophysical host environments of the GW sources. In this paper, we present the distributions of the effective spin parameter (χeff), the precession spin parameter (χp), and the chirp mass (mchirp) expected in hierarchical mergers. Under a wide range of assumptions, hierarchical mergers produce (i) a monotonic increase of the average of the typical total spin for merging binaries, which we characterize with $\scriptstyle{{\bar{\chi }}_\mathrm{typ}\equiv \overline{(\chi _\mathrm{eff}^2+\chi _\mathrm{p}^2)^{1/2}}}$, up to roughly the maximum mchirp among first-generation (1g) BHs, and (ii) a plateau at ${\bar{\chi }}_\mathrm{typ}\sim 0.6$ at higher mchirp. We suggest that the maximum mass and typical spin magnitudes for 1g BHs can be estimated from ${\bar{\chi }}_\mathrm{typ}$ as a function of mchirp. The GW data observed in LIGO/Virgo O1–O3a prefers an increase in ${\bar{\chi }}_\mathrm{typ}$ at low mchirp, which is consistent with the growth of the BH spin magnitude by hierarchical mergers at ∼2σ confidence. A Bayesian analysis using the χeff, χp, and mchirp distributions suggests that 1g BHs have the maximum mass of ∼15–$30\, {\rm M}_\odot$ if the majority of mergers are of high-generation BHs (not among 1g–1g BHs), which is consistent with mergers in active galactic nucleus discs and/or nuclear star clusters, while if mergers mainly originate from globular clusters, 1g BHs are favoured to have non-zero spin magnitudes of ∼0.3. We also forecast that signatures for hierarchical mergers in the ${\bar{\chi }}_\mathrm{typ}$ distribution can be confidently recovered once the number of GW events increases to ≳ O(100).