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The spin of intermediate-mass black holes (IMBHs) growing through repeated black hole mergers in stellar clusters statistically asymptotes to zero. Putative observations of IMBHs with dimensionless spin parameter $\chi\gtrsim 0.6$ would require a phase of coherent gas accretion to spin up the black hole. We estimate the amount of gas necessary to produce a given IMBH spin. If the observed IMBH mass and spin are $M\gtrsim 1000~M_\odot$ and $\chi\gtrsim 0.6$, respectively, the IMBH must have coherently accreted at least $\sim 100~M_\odot$ of gas. In this scenario, as long as the spin is not maximal, the IMBH can only accrete at most half of its mass. Our estimates can constrain the relative contribution of accretion and mergers to the growth of IMBHs in dense stellar environments., Comment: 10 pages, 7 figures

Astrophysical scenarios for the formation and evolution of intermediate-mass black holes (IMBHs) in the mass range $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$ remain uncertain, but future ground-based gravitational-wave (GW) interferometers will probe the lower end of the IMBH mass range. We study the detectability of IMBH binary mergers and the measurability of their parameters with next-generation ground-based detector networks consisting of various combinations of Cosmic Explorer (CE) and Einstein Telescope (ET) interferometers. We find that, for binaries with component masses $m_{1,2}\sim 1000\,M_\odot$, an optimal 3-detector network can constrain the masses with errors $\lesssim 0.1\%$ ($\lesssim 1\%$) at $z=0.5$ ($z=2$), and the source redshift can be measured with percent-level accuracy or better at $z\lesssim 2$. The redshift of lighter binaries ($m_{1,2}\lesssim 300\,M_\odot$) can still be measured with $O(10)\%$ accuracy even at $z=10$. Binaries with $z\lesssim 0.5$ can be localized within $1\,\rm{deg}^2$ for $m_{1,2}\lesssim 1000\,M_\odot$, and within $0.1\,\rm{deg}^2$ for comparable mass systems. The sky localization is good enough that it may be possible to cross-correlate GW searches with galaxy catalogs and to search for electromagnetic counterparts to IMBH mergers. We also point out that the low-frequency sensitivity of the detectors is crucial for IMBH detection and parameter estimation. It will be interesting to use our results in conjunction with population synthesis codes to constrain astrophysical IMBH formation models., Comment: 18 pages, 11 figures. All data is available at https://zenodo.org/records/13829385

Resolving the formation channel(s) of merging binary black holes is a key goal in gravitational-wave astronomy. The orbital eccentricity is believed to be a precious tracer of the underlying formation pathway, but is largely dissipated during the usually long inspiral between black hole formation and merger. Most gravitational-wave sources are thus expected to enter the sensitivity windows of current detectors on configurations that are compatible with quasi-circular orbits. In this paper, we investigate the impact of "negligible" residual eccentricity -- lower than currently detectable by LIGO/Virgo -- on our ability to infer the formation history of binary black holes, focusing in particular on their spin orientations. We trace the evolution of both observed and synthetic gravitational-wave events backward in time, while resampling their residual eccentricities to values that are below the detectability threshold. Eccentricities in-band as low as $\sim 10^{-4}$ can lead to significant biases when reconstructing the spin directions, especially in the case of loud, highly precessing systems. Residual eccentricity thus act like a systematic uncertainty for our astrophysical inference. As a mitigation strategy, one can marginalize the posterior distribution over the residual eccentricity using astrophysical predictions., Comment: 10 pages, 4 figures, 2 tables

Rapid formation of supermassive black holes occurs in dense nuclear star clusters that are initially gas-dominated. Stellar-mass black hole remnants of the most massive cluster sink into the core, where a massive runaway black hole forms as a consequence of combined effects of repeated mergers and Eddington-limited gas accretion. The associated gravitational wave signals of high-redshift extreme mass-ratio inspirals are a unique signature of the nuclear star cluster scenario., Comment: 4 pages, 3 figures

In the aftermath of a binary black hole merger event, the gravitational wave signal emitted by the remnant black hole is modeled as a superposition of damped sinusoids known as quasinormal modes. While the dominant quasinormal modes originating from linear black hole perturbation theory have been studied extensively in this post-merger "ringdown" phase, more accurate models of ringdown radiation include the nonlinear modes arising from higher-order perturbations of the remnant black hole spacetime. We explore the detectability of quadratic quasinormal modes with both ground- and space-based next-generation detectors. We quantify how predictions of the quadratic mode detectability depend on the quasinormal mode starting times. We then calculate the signal-to-noise ratio of quadratic modes for several detectors and binary black hole populations, focusing on the ($220\times220$) mode - i.e., on the quadratic term sourced by the square of the linear $(220)$ mode. For the events with the loudest quadratic mode signal-to-noise ratios, we additionally compute statistical errors on the mode parameters in order to further ascertain the distinguishability of the quadratic mode from the linear quasinormal modes. The astrophysical models used in this paper suggest that while the quadratic mode may be detectable in at most a few events with ground-based detectors, the prospects for detection with the Laser Interferometer Space Antenna (LISA) are more optimistic., Comment: 21 pages, 16 figures, 2 tables; revised to match published version; new plots in App. D

The ground-based gravitational wave (GW) detectors LIGO and Virgo have enabled the birth of multi-messenger GW astronomy via the detection of GWs from merging stellar-mass black holes (BHs) and neutron stars (NSs). GW170817, the first binary NS merger detected in GWs and all bands of the electromagnetic spectrum, is an outstanding example of the impact that GW discoveries can have on multi-messenger astronomy. Yet, GW170817 is only one of the many and varied multi-messenger sources that can be unveiled using ground-based GW detectors. In this contribution, we summarize key open questions in the astrophysics of stellar-mass BHs and NSs that can be answered using current and future-generation ground-based GW detectors, and highlight the potential for new multi-messenger discoveries ahead., Comment: Review submitted to the Frontiers Research Topic "The Dynamic Universe: Realizing the Potential of Time Domain and Multimessenger Astrophysics"

Stellar evolution predicts the existence of a mass gap for black hole remnants produced by pair-instability supernova dynamics, whose lower and upper edges are very uncertain. We study the possibility of constraining the location of the upper end of the pair-instability mass gap, which is believed to appear around ${m_\text{min}} \sim130M_\odot$, using gravitational wave observations of compact binary mergers with next-generation ground-based detectors. While high metallicity may not allow for the formation of first-generation black holes on the "far side" beyond the gap, metal-poor environments containing Population III stars could lead to such heavy black hole mergers. We show that, even in the presence of contamination from other merger channels, next-generation detectors will measure the location of the upper end of the mass gap with a relative precision close to $\Delta {m_\text{min}}/{m_\text{min}} \simeq 4\% (N_\text{det}/100 )^{-1/2}$ at 90% C.L., where $N_\text{det} $ is the number of detected mergers with both members beyond the gap. These future observations could reduce current uncertainties in nuclear and astrophysical processes controlling the location of the gap., Comment: 12 pages, 6 figures

The population of binary black hole mergers observed in gravitational waves, together with astrophysical simulations, can help us to understand the properties of the progenitors and the binary formation mechanisms in different astrophysical scenarios. Here we focus on dynamical formation in star clusters. We use the third gravitational-wave transient catalog (GWTC-3) and Rapster, a rapid code to simulate cluster dynamics, to show that it is possible to construct the single-event likelihood of star cluster properties from individual observations. We find that the measured primary mass in a binary black hole merger correlates with the measured star cluster mass, because the mass spectrum of the primary component increases with the mass of the cluster. This trend may be caused by two physical mechanisms: (i) the more efficient production of hierarchical mergers with primary mass above $\sim 40~M_{\odot}$ for cluster masses of $\gtrsim 10^6~M_{\odot}$, and (ii) the suppression of more massive first-generation binaries, which happens because ejected binaries do not merge within the lookback time for cluster masses of $\lesssim 10^5~M_{\odot}$. The formalism presented here can be generalized to infer the population properties of binary progenitors in more realistic scenarios involving multiple formation channels., Comment: 5 pages, 3 figures. Calculations are shown in the python notebooks: https://gitlab.com/ken_ng/single-cluster-inference

We address two important questions in gravitational-wave astronomy. What is the astrophysical formation scenario leading to black-hole binary mergers? Did some of the merging black holes form hierarchically through previous generations of mergers? Leveraging fast-to-generate astrophysical simulations from the rapster code and a random forest algorithm, we develop a pipeline to accurately classify the most likely generation and formation scenario of dynamically formed BHs on an event-by-event basis. We test our framework on four merger events with features suggesting a dynamical origin: the large total mass event GW190521, GW190412 (with large mass asymmetry), and two events with effective spins antialigned with the orbital angular momentum (GW191109 and GW200225). Within the models we consider, and assuming these events to be formed dynamically, we find that one of the component black holes in GW190521 formed from a previous merger with high probability ($\gtrsim 85\%$). GW190521, GW191109 and GW200225 are compatible with formation through three-body interactions, while the most likely formation channel for GW190412 are two-body captures. We also rule out that GW191109 contains only first-generation black holes with a probability of 97$\%$. Our pipeline could be useful to identify the evolutionary path of individual GW observations once it is trained on more comprehensive sets of binary formation simulations., Comment: 9 pages, 2 figures. Public code at: https://github.com/aantonelli94/TheBHClassifier

Nuclear star clusters, which fragment into metal-poor stars in situ at the centers of protogalaxies, provide ideal environments for the formation of intermediate-mass black holes with masses $10^3-10^6M_\odot$. We utilize the semianalytic model implemented in Rapster, a public rapid cluster evolution code. We implement simple recipes for stellar collisions and gas accretion/expulsion into the code and identify the regimes where each channel contributes to the dynamical formation of intermediate-mass black holes via repeated mergers of stellar black hole seeds. We find that intermediate-mass black hole formation in gas-rich environments is almost inevitable if the initial mean density of the nuclear cluster is $>10^8M_\odot\,{\rm pc}^{-3}$. A million solar mass black hole can form within 100~Myr in the heaviest ($>10^7M_\odot$) and most compact ($<0.5~{\rm pc}$) nuclear clusters. We demonstrate that by today these resemble the observed range of nuclear clusters in dwarf galaxies and that there are potential gravitational-wave signatures of the massive black hole formation process., Comment: 13 pages, 7 figures, matches published version

Gravitational-wave observations have just started probing the properties of black hole binary merger populations. The observation of binaries with very massive black holes and significantly asymmetric masses motivates the study of dense star clusters as astrophysical environments which can produce such events dynamically. In this paper we present Rapster (for "Rapid cluster evolution"), a new code designed to rapidly model binary black hole population synthesis and the evolution of massive star clusters based on simple, yet realistic prescriptions. We also perform a thorough comparison with the Cluster Monte Carlo code and find generally good agreement. The code can be used to generate large populations of dynamically formed binary black holes., Comment: 34 pages, 10 figures, 1 table. Manuscript and code were significantly revised in response to the referees' comments. Matches the published version. The Rapster code and data are publicly available at https://github.com/Kkritos/Rapster and https://zenodo.org/records/10626210

Current gravitational-wave observations set the most stringent bounds on the abundance of primordial black holes (PBHs) in the solar mass range. This constraint, however, inherently relies on the merger rate predicted by PBH models. Previous analyses have focused mainly on two binary formation mechanisms: early Universe assembly out of decoupling from the Hubble expansion and dynamical capture in present-day dark matter structures. Using reaction rates of three-body processes studied in the astrophysical context, we show that, under conservative assumptions, three-body interactions in PBH halos efficiently produce binaries. Those binaries form at high redshift in Poisson-induced PBH small-scale structures and a fraction is predicted to coalesce and merge within the current age of the Universe, at odds with the dynamical capture scenario where they merge promptly. In general, we find that this channel predicts rates comparable to the dynamical capture scenario. However, binaries formed from three-body interactions do not significantly contribute to the overall PBH merger rate unless PBHs made up a dominant fraction of the dark matter above the solar mass range, a scenario that is ruled out by current constraints. Our results support strong bounds on the PBH abundance in the stellar mass range derived from Laser Interferometer Gravitational-Wave Observatory/Virgo/KAGRA observations. Finally, we show that both dynamical channels are always subdominant compared to early Universe assembly for PBH mergers in the asteroid mass range, while we expect it to become relevant in scenarios where PBHs are initially strongly clustered., Comment: 13 pages, 3 figures

Near-extremal primordial black holes stable over cosmological timescales may constitute a significant fraction of the dark matter. Due to their charge the coalescence rate of such black holes is enhanced inside clusters and the non-extremal merger remnants are prone to Hawking evaporation. We demonstrate that if these clusters of near-extremal holes contain a sufficient number of members to survive up to low redshift, the hard photons from continued evaporation begin to dominate the high energy diffuse background. We find that the diffuse photon flux can be observed for a monochromatic mass spectrum of holes lighter than about $10^{12}\rm g$. We place upper bounds on their abundance respecting the current bounds set by gamma ray telescopes. Furthermore, the gravitational wave background induced at the epoch of primordial black hole formation may be detectable by future planned and proposed ground-based and space-borne gravitational wave observatories operating in the mHz to kHz frequency range and can be an important tool for studying light charged primordial black holes over masses in the range $\rm 10^{12}g - 10^{19}g$., Comment: 13 pages, 3 figures

The LIGO-Virgo collaboration reported in their third run the coalescence event GW190814 involving a 2.6 $M_{\odot}$ object with a 23 $M_{\odot}$ black hole. In this letter we study the conditions under which Thorne-$\dot{\textrm{Z}}$ytkow objects (T$\dot{\textrm{Z}}$Os) can be connected to that type of events. We evaluate first the rate of appearance of T$\dot{\textrm{Z}}$Os in the local Universe. Under the assumption that T$\dot{\textrm{Z}}$Os eventually become low mass gap black holes we evaluate how those black holes end up in binaries with other stellar mass black holes and compare to the reported rate for GW190814-type of events (1-23 $\textrm{Gpc}^{-3} \textrm{yr}^{-1}$). We find that T$\dot{\textrm{Z}}$Os in dense stellar clusters can not explain the LIGO-Virgo rate without a T$\dot{\textrm{Z}}$Os population in the field providing a dominant contribution. We also find that T$\dot{\textrm{Z}}$Os formed within hierarchical triple systems in the field with the third more distant star being the progenitor of a stellar mass black hole, may be able to give a rate comparable to that of GW190814-type events. In that case, future observations should discover mergers between stellar mass and low mass gap black holes, with the lower mass spanning the entire low mass gap range., Comment: 5 pages and 2 figures

Recently, the LIGO-Virgo collaborations have reported the coalescence of a binary involving a black hole and a low-mass gap object (LMGO) with mass in the range $\sim2.5-5M_\odot$. Such detections, challenge our understanding of the black hole and neutron star mass spectrum, as well as how such binaries evolve especially if isolated. In this work we study the dynamical formation of compact object pairs, via multiple binary-single exchanges that occur at the cores of globular clusters. We start with a population of binary star systems, which interact with single compact objects as first generation black holes and LMGOs. We evaluate the rate of exchange interactions leading to the formation of compact object binaries. Our calculations include all possible types of binary-single exchange interactions and also the interactions of individual stars with compact object binaries that can evolve their orbital properties, leading to their eventual merger. We perform our calculations for the full range of the observed Milky Way globular cluster environments. We find that the exchanges are efficient in forming hard compact object binaries at the cores of dense astrophysical stellar environments. Furthermore, if the population size of the LMGOs is related to that of neutron stars, the inferred merger rate density of black hole-LMGO binaries inside globular clusters in the local Universe is estimated to be about $0.1 \, \text{Gpc}^{-3}\text{yr}^{-1}$., Comment: 18 pages, 10 figures and 3 appendices

The $N$-body problem is of historical significance because it was the first implementation of the Newtonian dynamical laws for the description of our Solar System. Motivated by this, the project's goal is to revisit this problem for small $N$ and find a solution for the trajectories of specific two-body and three-body configurations as well as the planetary orbits of our Solar System using a fourth order Runge-Kutta explicit iterative method. We find an adequate agreement in our results with planetary trajectories found online., Comment: 15 pages, 7 figures

There is a growing expectation that the gravitational wave detectors will start probing the stochastic gravitational wave backgrounds in the following years. We explore the spectral shapes of gravitational waves induced to second order by scalar perturbations and presumably have been produced in the early universe. We calculate the gravitational wave spectra generated during radiation and kination eras together with the associated primordial black hole counterpart. We employ power spectra for the primordial curvature perturbation generated by $\alpha$-attractors and nonminimal derivative coupling inflation models as well as Gaussian and delta-type shapes. We demonstrate the ability of the tensor modes to constrain the spectrum of the primordial curvature perturbations and discriminate among inflationary models. Gravitational wave production during kination and radiation era can also be distinguished by their spectral shapes and amplitudes., Comment: 18 pages, 8 figures, 2 appendices. Journal Version

The multitude of binary black hole coalescence detections in gravitational waves has renewed our interest on environments that can be the cradle of these mergers. In this work we study merger rates of binary black holes in globular clusters that are among the most dense stellar environments and a natural place for the creation of black hole binaries. To model these systems with all their variations we rely on the observational properties of the known Milky Way globular clusters. We consider direct capture events between black holes, as well as soft interactions of black hole binaries with stars as third bodies that accelerate the evolution of these binaries. We find that binary black holes from direct captures merge at an averaged rate of $0.3-5 \times 10^{-11}$ yr$^{-1}$ per cluster. Third body soft interactions are a much more prominent channel giving an averaged rate of $2-4 \times 10^{-10}$ yr$^{-1}$ per cluster. Those rates in globular clusters can lead to a cumulative merger rate of about 100 mergers per year up to redshift of 1, i.e. a significant fraction of the detectable in the near future binary black hole coalescence events. Further observations of cluster properties both in terms of their masses, profile properties, velocity dispersion of stars and their cosmological distribution, will allow us to better constrain the contribution of these environments to the detectable coalescence events rate., Comment: 16 pages, 6 figures and 2 appendices