We review theoretical findings, astrophysical modeling, and current gravitational-wave evidence of hierarchical stellar-mass black-hole mergers. While most of the compact binary mergers detected by LIGO and Virgo are expected to consist of first-generation black holes formed from the collapse of stars, others might instead be of second (or higher) generation, containing the remnants of previous black-hole mergers. Such a subpopulation of hierarchically assembled black holes presents distinctive gravitational-wave signatures, namely higher masses, possibly within the pair-instability mass gap, and dimensionless spins clustered at the characteristic value of $\sim$0.7. In order to produce hierarchical mergers, astrophysical environments need to overcome the relativistic recoils imparted to black-hole merger remnants, a condition which prefers hosts with escape speeds $\gtrsim$ 100 km/s. Promising locations for efficient production of hierarchical mergers include nuclear star clusters and accretion disks surrounding active galactic nuclei, though environments that are less efficient at retaining merger products such as globular clusters may still contribute significantly to the detectable population of repeated mergers. While GW190521 is the single most promising hierarchical-merger candidate to date, constraints coming from large population analyses are becoming increasingly more powerful.
In dense stellar environments, the merger products of binary black hole mergers may undergo additional mergers. These hierarchical mergers are predicted to have higher masses than the first generation of black holes made from stars. The components of hierarchical mergers are expected to have significant characteristic spins $χ\sim 0.7$. However, since the population properties of first-generation black holes are uncertain, it is difficult to know if any given merger is first-generation or hierarchical. We use observations of gravitational waves to reconstruct the binary black hole mass and spi…
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 ho…
Most of the binary black hole (BBH) mergers detected by LIGO and Virgo could be explained by first-generation mergers formed from the collapse of stars, while others might come from second (or higher) generation mergers, namely hierarchical mergers, with at least one of the black holes (BHs) being the remnant of a previous merger. A primary condition for the occurrence of hierarchical mergers is that the remnant BHs can be retained by the host star cluster. We present a simple formula to estimate the hierarchical merger rate in star clusters. We find this latter to be proportional to the reten…
Despite the rapidly growing number of stellar-mass binary black hole mergers discovered through gravitational waves, the origin of these binaries is still not known. In galactic centers, black holes can be brought to each others' proximity by dynamical processes, resulting in mergers. It is also possible that black holes formed in previous mergers encounter new black holes, resulting in so-called hierarchical mergers. Hierarchical events carry signatures such as higher-than usual black hole mass and spin. Here we show that the recently reported gravitational-wave candidate, GW170817A, could be…
The occurrence of pair-instability supernovae is predicted to prevent the formation of black holes with masses $\gtrsim 50 M_\odot$. Recent gravitational-wave detections in this mass range require an explanation beyond that of standard stellar collapse. Current modeling strategies include the hierarchical assembly of previous generations of black-hole mergers as well as other mechanisms of astrophysical nature (lowered nuclear-reaction rates, envelope retention, stellar mergers, accretion, dredge-up episodes). In this paper, we point out the occurrence of an exclusion region that cannot be eas…
With better statistics and precision, eccentricity could prove to be a useful tool for understanding the origin and environment of binary black holes. Hierarchical triples in particular, which might be abundant in globular clusters and galactic nuclei, could generate observably large eccentricity at LIGO and future gravitational wave detectors. Measuring the eccentricity distribution accurately could help us probe the background and the formation of the mergers. In this paper we continue our previous investigation and improve our semi-analytical description of the eccentricity distribution of …
Data from the LIGO and Virgo detectors has confirmed that stellar-mass black holes can merge within a Hubble time, leaving behind massive remnant black holes. In some astrophysical environments such as globular clusters and AGN disks, it may be possible for these remnants to take part in further compact-object mergers, producing a population of hierarchically formed black holes. In this work, we present a parameterized framework for describing the population of binary black hole mergers, while self-consistently accounting for hierarchical mergers. The framework casts black holes as particles i…
The origins of the stellar-mass black hole mergers discovered by LIGO/Virgo are still unknown. Here we show that, if migration traps develop in the \add{accretion} disks of Active Galactic Nuclei (AGNs) and promote the mergers of their captive black holes, the majority of black holes within disks will undergo hierarchical mergers---with one of the black holes being the remnant of a previous merger. 40% of AGN-assisted mergers detected by LIGO/Virgo will include a black hole with mass $\gtrsim 50$ M$_\odot$, the mass limit from stellar core collapse. Hierarchical mergers at traps in AGNs will e…
A promising channel for producing binary black hole mergers is the Lidov-Kozai orbital resonance in hierarchical triple systems. While this mechanism has been studied in isolation, the distribution of such mergers in time and across star-forming environments is not well characterized. In this work, we explore Lidov-Kozai-induced black hole mergers in open clusters, combining semi-analytic and Monte Carlo methods to calculate merger rates and delay times for eight different population models. We predict a merger rate density of $\sim$1--10\,Gpc$^{-3}$\,yr$^{-1}$ for the Lidov-Kozai channel in t…
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 reduce the recoil velocity of merging binary black holes, which, in turn, increases the retention f…
While no consensus governs our understanding of the origin of low redshift radio galaxies, the possibility that mergers may trigger accretion from hot cluster halo gas has spurred a recent search for such signatures. Evidence for mergers is at best tenuous, however, and even when found, generates more questions than answers. With scant evidence for minor mergers, some connection to major mergers is found in isolated environments but not where one would expect, i.e. in clusters. We provide an explanation for these recent results by Gordon et al (2019) on the relevance of major mergers in low ex…
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…
We study the population properties of merging binary black holes in the second LIGO--Virgo Gravitational-Wave Transient Catalog assuming they were all formed dynamically in gravitationally bound clusters. Using a phenomenological population model, we infer the mass and spin distribution of first-generation black holes, while self-consistently accounting for hierarchical mergers. Considering a range of cluster masses, we see compelling evidence for hierarchical mergers in clusters with escape velocities $\gtrsim 100~\mathrm{km\,s^{-1}}$. For our most probable cluster mass, we find that the cata…
The gravitational wave event GW170817 associated with the short gamma-ray burst (GRB) 170817A confirms that binary neutron star (BNS) mergers are one of the origins of short GRBs. The associated kilonova emission, radioactively powered by nucleosynthesized heavy elements, was also detected. Black hole-neutron star (BH-NS) mergers have been argued to be another promising origin candidate of short GRBs and kilonovae. Numerical simulations show that the ejecta in BH-NS mergers is geometrically much more anisotropic than the BNS merger case. In this paper, we investigate observational signatures o…
Smoking-gun evidence for hierarchical black-hole mergers
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台暗物质与空间天文重点实验室）；Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江理工大学理论物理与宇宙学研究所）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）
Signatures of a subpopulation of hierarchical mergers in the GWTC-4 gravitational-wave dataset
LIGO Laboratory, Massachusetts Institute of Technology（麻省理工学院 LIGO 实验室）；Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology（麻省理工学院卡弗里天体物理与空间研究研究所）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；Williams College（威廉姆斯学院）；Adler Planetarium（阿德勒天文馆）；NSF-Simons AI Institute for the Sky (SkAI)（NSF-Simons 天空人工智能研究所）
We investigate secular evolution in hierarchical quadruple systems as a formation channel of mass-gap black holes (with masses of about $3-5$ $M_{\odot}$) in systems that will eventually lead to binary black hole mergers detectable by ground-based gravitational wave detectors (LIGO/Virgo). We show that in a 3+1 hierarchical system, two episodes of induced mergers would first cause two neutron stars to merge and form a mass-gap black hole, which will subsequently merge with another (more massive) black hole through a second induced merger. We demonstrate that such systems are stable to flybys, …
The merging black-hole (BH) binaries GW190412, GW190814 and GW190521 from the third LIGO/VIRGO observing run exhibit some extraordinary properties, including highly asymmetric masses, significant spin, and component mass in the "mass gap". These features can be explained if one or both components of the binary are the remnants of previous mergers. In this paper, we explore hierarchical mergers in multiple stellar systems, taking into account the natal kick and mass loss due to the supernova explosion (SN) on each component, as well as the merger kick received by the merger remnant. The binarie…
School of Physics and Astronomy, Monash University（莫纳什大学物理与天文学院）；OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery（OzGrav：ARC引力波发现卓越中心）；Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut（马克斯·普朗克引力物理学研究所，阿尔伯特·爱因斯坦研究所）；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；David A. Dunlap Department of Astronomy and Astrophysics, University of Toronto（多伦多大学大卫·A·邓肯天文学与天体物理系）；Department of Physics, University of Toronto（多伦多大学物理系）
Neutron star (NS) mergers provide us with information rich in physics using multi-messenger astrophysical observations. One of the probable remnants of such a merger is a differentially rotating hot hypermassive neutron star. The stability of the merger remnant depends crucially on the underlying Equation of State (EoS) and thus provides a method to probe the nature of dense matter in NSs. In this work, we search for possible signatures of strangeness containing matter in the NS interior on the secular stability of the merger remnant. We also use recently proposed methods to make a rough estim…
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 ($χ_\mathrm{eff}$), the precession spin parameter ($χ_\mathrm{p}$), and the chirp mass ($m_\mathrm{chirp}$) expected in hierarchical mergers. Under a wide range of assumptions, hierarchical mergers produce (i) a monotonic increase of the average of the typi…
The mergers of binaries containing neutron stars and stellar-mass black holes are the most promising sources for direct detection in gravitational waves by the interferometers Advanced LIGO and Virgo over the next few years. The concurrent detection of electromagnetic emission from these events would greatly enhance the scientific return of these discoveries. Here we review the state of the art in modeling the electromagnetic signal of neutron star binary mergers across different phases of the merger and multiple wavelengths. We focus on those observables which provide the most sensitive diagn…
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, $\sim50-120~M_\odot$. 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 merg…
One of the proposed channels of binary black hole mergers involves dynamical interactions of three black holes. In such scenarios, it is possible that all three black holes merge in a so-called hierarchical merger chain, where two of the black holes merge first and then their remnant subsequently merges with the remaining single black hole. Depending on the dynamical environment, it is possible that both mergers will appear within the observable time window. Here we perform a search for such merger pairs in the public available LIGO and Virgo data from the O1/O2 runs. Using a frequentist p-val…
The catalog of gravitational-wave events is growing, and so are our hopes of constraining the underlying astrophysics of stellar-mass black-hole mergers by inferring the distributions of, e.g., masses and spins. While conventional analyses parametrize this population with simple phenomenological models, we propose an emulation-based approach that can compare astrophysical simulations against gravitational-wave data. We combine state-of-the-art deep-learning techniques with hierarchical Bayesian inference and exploit our approach to constrain the properties of repeated black-hole mergers from t…
Mass-Ratio Reversal as an Alternative to Hierarchical Mergers for GW241011
Nevada Center for Astrophysics, University of Nevada, Las Vegas（内华达大学拉斯维加斯分校天体物理中心）；Department of Physics and Astronomy, University of Nevada, Las Vegas（内华达大学拉斯维加斯分校物理与天文系）；Department of Physics, Anhui Normal University（安徽师范大学物理系）；The Hong Kong Institute for Astronomy and Astrophysics, The University of Hong Kong（香港大学香港天文及天体物理研究所）；Department of Physics, The University of Hong Kong（香港大学物理系）
A massive millisecond magnetar may survive a merger of a neutron star (NS) binary, which would continuously power the merger ejecta. We develop a generic dynamic model for the merger ejecta with energy injection from the central magnetar. The ejecta emission (the "merger-nova") powered by the magnetar peaks in the UV band and the peak of lightcurve progressively shifts to an earlier epoch with increasing frequency. A magnetar-powered mergernova could have an optical peak brightness comparable to a supernova, which is a few tens or hundreds times brighter than the radioactive-powered merger-nov…
Neutron star mergers have been proposed as the main source of heavy $r$-process nucleosynthesis in the Universe. However, the mergers' significant expected delay after binary formation is in tension with observed very early $r$-process enrichment, e.g., in the dwarf galaxy Reticulum II. The LIGO and Virgo gravitational-wave observatories discovered two binary mergers with lighter companion masses ($\sim 2.6$ M$_\odot$) similar to the total mass of many binary neutron star systems in the Galaxy. The progenitor of such mergers could be a neutron star binary orbiting a black hole. Here we show th…
Aligned Hierarchical Black Hole Mergers in Active-Galactic-Nuclei Disks Revealed by GWTC-4
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台暗物质与空间天文重点实验室）；Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江理工大学理论与宇宙物理研究所）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）
We analyze the distinguishability of populations of coalescing binary neutron stars, neutron-star black-hole binaries, and binary black holes, whose gravitational-wave signatures are expected to be observed by the advanced network of ground-based interferometers LIGO and Virgo. We consider population-synthesis predictions for plausible merging binary distributions in mass space, along with measurement accuracy estimates from the main gravitational-wave parameter-estimation pipeline. We find that for our model compact-object binary mass distribution, we can always distinguish binary neutron sta…
We explore hierarchical black hole (BH) mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs), accounting for both original and dynamically assembled binary BHs (BBHs). We find that the median mass of both first- and nth-generation dynamical mergers is larger in GCs and YSCs with respect to NSCs, because the lighter BHs are ejected by supernova kicks from the lower-mass clusters. Also, first- and nth-generation BH masses are strongly affected by the metallicity of the progenitor stars: the median mass of the primary BH of a nth-generation merger is $\s…
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…
