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Register a new userSignatures of Hierarchical Mergers in Black Hole Spin and Mass distribution
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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 ($chi_mathrm{eff}$), the precession spin parameter ($chi_mathrm{p}$), 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 typical total spin for merging binaries, which we characterize with ${bar chi}_mathrm{typ}equiv overline{(chi_mathrm{eff}^2+chi_mathrm{p}^2)^{1/2}}$, up to roughly the maximum $m_mathrm{chirp}$ among first-generation (1g) BHs, and (ii) a plateau at ${bar chi}_mathrm{typ}sim 0.6$ at higher $m_mathrm{chirp}$. 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 $m_mathrm{chirp}$. The GW data observed in LIGO/Virgo O1--O3a prefers an increase in ${bar chi}_mathrm{typ}$ at low $m_mathrm{chirp}$, which is consistent with the growth of the BH spin magnitude by hierarchical mergers, at $sim 2 sigma$ confidence. A Bayesian analysis suggests that 1g BHs have the maximum mass of $sim 15$--$30,M_odot$ if the majority of mergers are of high-generation BHs (not among 1g-1g BHs), which is consistent with mergers in active galactic nucleus disks and/or nuclear star clusters, while if mergers mainly originate from globular clusters, 1g BHs are favored to have non-zero spin magnitudes of $sim 0.3$. 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 $gtrsim O(100)$.
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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.
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 progenitors metallicity. In our fiducial model, we form black holes (BHs) with masses up to $sim{}10^3$ M$_odot$ in NSCs and up to $sim{}10^2$ M$_odot$ in both GCs and YSCs. When escape velocities in excess of 100 km~s$^{-1}$ are considered, BHs with mass $>10^3$ M$_odot$ 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 $sim{}10$ to $sim{} 60$ Gpc$^{-3}$ yr$^{-1}$; hierarchical BBHs in NSCs account for $sim{}10^{-2}- 0.2$ Gpc$^{-3}$ yr$^{-1}$, with a strong upper limit of $sim{}10$ 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.
Many proposed scenarios for black hole (BH) mergers involve a tertiary companion that induces von Zeipel-Lidov-Kozai (ZLK) eccentricity cycles in the inner binary. An attractive feature of such mechanisms is the enhanced merger probability when the octupole-order effects, also known as the eccentric Kozai mechanism, are important. This can be the case when the tertiary is of comparable mass to the binary components. Since the octupole strength [$propto (1-q)/(1+q)$] increases with decreasing binary mass ratio $q$, such ZLK-induced mergers favor binaries with smaller mass ratios. We use a combination of numerical and analytical approaches to fully characterize the octupole-enhanced binary BH mergers and provide analytical criteria for efficiently calculating the strength of this enhancement. We show that for hierarchical triples with semi-major axis ratio $a/a_{rm out}gtrsim 0.01$-$0.02$, the binary merger fraction can increase by a large factor (up to $sim 20$) as $q$ decreases from unity to $0.2$. The resulting mass ratio distribution for merging binary BHs produced in this scenario is in tension with the observed distribution obtained by the LIGO/VIRGO collaboration, although significant uncertainties remain about the initial distribution of binary BH masses and mass ratios.
We simulate the star cluster, made of stars in the main sequence and different black hole (BH) remnants, around SgrA* at the center of the Milky Way galaxy. Tracking stellar evolution, we find the BH remnant masses and construct the BH mass function. We sample 4 BH species and consider the impact of the mass-function in the dynamical evolution of system. Starting from an initial 6 dimensional family of parameters and using an MCMC approach, we find the best fits to various parameters of model by directly comparing the results of the simulations after $t = 10.5$ Gyrs with current observations of the stellar surface density, stellar mass profile and the mass of SgrA*. Using these parameters, we study the dynamical evolution of system in detail. We also explore the mass-growth of SgrA* due to tidally disrupted stars and swallowed BHs. We show that the consumed mass is dominated for the BH component with larger initial normalization as given by the BH mass-function. Assuming that about 10% of the tidally disrupted stars contribute in the growth of SgrA* mass, stars make up the second dominant effect in enhancing the mass of SgrA*. We consider the detectability of the GW signal from inspiralling stellar mass BHs around SgrA* with LISA. Computing the fraction of the lifetime of every BH species in the LISA band, with signal to noise ratio $gtrsim 8$, to their entire lifetime, and rescaling this number with the total number of BHs in the system, we find that the total expected rate of inspirals per Milky-Way sized galaxy per year is $10^{-5}$. Quite interestingly, the rate is dominated for the BH component with larger initial normalization as dictated by the BH mass-function. We interpret it as the second signature of the BH mass-function.
The gravitational wave event GW190521 involves the merger of two black holes of $sim 85text{M}_odot$ and $sim 66text{M}_odot$ forming an intermediate-mass black hole (IMBH) of mass $sim 142text{M}_odot$. Both progenitors are challenging to explain within standard stellar evolution as they belong to the upper black-hole mass gap. We propose a dynamical formation pathway for this IMBH based on multiple hierarchical mergers of progenitors in the core of a dense star cluster. We identified such scenarios from analysis of a set of 58 direct N-body simulations using NBODY6-gpu. In one of our canonical runs aimed at describing the evolution of a star cluster with $N=10^5$ stars and typical globular cluster properties, we observe a stellar black hole undergoing a chain of seven binary mergers in 6 Gyr, attaining a final mass of $97.8text{M}_odot$. We discuss the dynamical interactions that lead to the final IMBH product, as well as the evolution of the black hole population in that simulation. From the analysis of all simulations in our dataset we observe additional smaller chains, tentatively inferring that an IMBH formation through chain mergers is expected in the lifetime of a typical (i.e. median mass) globular cluster with probability $0.01 lesssim p lesssim 0.1$. Using this order-of-magnitude estimate and comoving star formation rates we show our results are broadly consistent with the mean rate implied by GW190521, and we discuss implications for future gravitational wave detections of IMBHs.
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