Massive Black Hole Binaries Research Articles

Populating the Upper Black Hole Mass Gap through Stellar Collisions in Young Star Clusters

Abstract Theoretical modeling of massive stars predicts a gap in the black hole (BH) mass function above ∼40–50 M ⊙ for BHs formed through single star evolution, arising from (pulsational) pair-instability supernovae (PISNe). However, in dense star clusters, dynamical channels may exist that allow construction of BHs with masses in excess of those allowed from single star evolution. The detection of BHs in this so-called “upper-mass gap” would provide strong evidence for the dynamical processing of BHs prior to their eventual merger. Here, we explore in detail the formation of BHs with masses within or above the pair-instability gap through collisions of young massive stars in dense star clusters. We run a suite of 68 independent cluster simulations, exploring a variety of physical assumptions pertaining to growth through stellar collisions, including primordial cluster mass segregation and the efficiency of envelope stripping during collisions. We find that as many as ∼20% of all BH progenitors undergo one or more collisions prior to stellar collapse and up to ∼1% of all BHs reside within or above the pair-instability gap through the effects of these collisions. We show that these BHs readily go on to merge with other BHs in the cluster, creating a population of massive BH mergers at a rate that may compete with the “multiple-generation” merger channel described in other analyses. This has clear relevance for the formation of very massive BH binaries as recently detected by the Laser Interferometer Gravitational-Wave Observatory/Virgo in GW190521. Finally, we describe how stellar collisions in clusters may provide a unique pathway to PISNe and briefly discuss the expected rate of these events and other electromagnetic transients.

Observing the inspiral of coalescing massive black hole binaries with LISA in the era of multimessenger astrophysics

Massive black hole binaries (MBHBs) of $10^5 \, \rm M_\odot - 3 \times 10^7 \, \rm M_\odot $ merging in low redshift galaxies ($z\le4$) are sufficiently loud to be detected weeks before coalescence with the Laser Interferometer Space Antenna (LISA). This allows us to perform the parameter estimation $on$ $the$ $fly$, i.e. as a function of the time to coalescence during the inspiral phase, relevant for early warning of the planned LISA protected periods and for searches of electromagnetic signals. In this work, we study the evolution of the sky position, luminosity distance, chirp mass and mass ratio uncertainties as function of time left before merger. Overall, light systems with total intrinsic mass $\rm M_{\rm tot} = 3 \times 10^5 \, \rm M_\odot$ are characterized by smaller uncertainties than heavy ones ($\rm M_{\rm tot} = 10^7 \, \rm M_\odot$) during the inspiral. Luminosity distance, chirp mass and mass ratio are well constrained at the end of the inspiral. Concerning sky position, at $z=1$, MBHBs with $\rm M_{\rm tot} = 3 \times 10^5 \, \rm M_\odot$ can be localized with a median precision of $\simeq 10^2 \, \rm deg^2 (\simeq 1 \, \rm deg^2)$ at 1 month (1 hour) from merger, while the sky position of heavy MBHBs can be determined to $10 \, \rm deg^2$ only 1 hour before merger. However the uncertainty around the median values broadens with time, ranging in between 0.04 -- 20 $\rm deg^2$ (0.3 -- 3 $\times 10^3 \, \rm deg^2$) for light (heavy) systems at 1 hour before merger. At merger the sky localization improves down to $\simeq 10^{-1} \, \rm deg^2$ for all masses. For the benefit of the observer community, we provide the full set of data from our simulations and simple and ready-to-use analytical fits to describe the time evolution of uncertainties in the aforementioned parameters, valid for systems with total mass between $10^5$--$10^7 \, \rm M_\odot$ and redshift $0.3$--$3$.

Basic considerations for the observability of kinematically offset binary AGN

ABSTRACT The gravitational waves from massive black hole (MBH) binaries are expected to be detected by pulsar timing arrays in the next few years. While they are a promising source for multimessenger observations as binary active galactic nuclei (AGNs), few convincing candidates have been identified in electromagnetic surveys. One approach to identifying candidates has been through spectroscopic surveys searching for offsets or time-dependent offsets of broad emission lines (BLs), which may be characteristic of Doppler shifts from binary orbital motion. In this study, we predict the parameter space of MBH binaries that should be kinematically detectable. There is a delicate trade-off between requiring binary separations to be large enough for BL regions to remain attached to one of the AGNs, but also small enough such that their orbital velocity is detectable. We find that kinematic signatures are only observable for the lower mass secondary AGN, for binaries with total masses above about $10^8 \, \textrm {M}_{\odot }$, and separations between 0.1 and 1 pc. We motivate our usage of a kinematic offset sensitivity of 103 km s−1, and a sensitivity to changing offsets of 102 km s−1. With these parameters, and an Eddington ratio of 0.1, we find that $0.5{{\ \rm per\ cent}}$ of binaries have detectable offsets, and only $0.03{{\ \rm per\ cent}}$ have detectable velocity changes. Overall, kinematic binary signatures should be expected in fewer than one in 104 AGNs. Better characterizing the intrinsic variability of BLs is crucial to understanding and vetting MBH binary candidates. This requires multi-epoch spectroscopy of large populations of AGNs over a variety of time-scales.

On the Origin of GW190521-like Events from Repeated Black Hole Mergers in Star Clusters

Abstract LIGO and Virgo have reported the detection of GW190521, from the merger of a binary black hole (BBH) with a total mass around 150 M ⊙. While current stellar models limit the mass of any black hole (BH) remnant to about 40–50 M ⊙, more massive BHs can be produced dynamically through repeated mergers in the core of a dense star cluster. The process is limited by the recoil kick (due to anisotropic emission of gravitational radiation) imparted to merger remnants, which can escape the parent cluster, thereby terminating growth. We study the role of the host cluster metallicity and escape speed in the buildup of massive BHs through repeated mergers. Almost independent of host metallicity, we find that a BBH of about 150 M ⊙ could be formed dynamically in any star cluster with escape speed ≳200 km s−1, as found in galactic nuclear star clusters as well as the most massive globular clusters and super star clusters. Using an inspiral-only waveform, we compute the detection probability for different primary masses (≥60 M ⊙) as a function of secondary mass and find that the detection probability increases with secondary mass and decreases for larger primary mass and redshift. Future additional detections of massive BBH mergers will be of fundamental importance for understanding the growth of massive BHs through dynamics and the formation of intermediate-mass BHs.

Black Hole Genealogy: Identifying Hierarchical Mergers with Gravitational Waves

Abstract In dense stellar environments, the merger products of binary black hole mergers may undergo additional mergers. These hierarchical mergers are naturally expected 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, imprinted by the orbital angular momentum of the previous mergers. 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 spin spectrum of a population including the possibility of hierarchical mergers. We employ a phenomenological model that captures the properties of merging binary black holes from simulations of globular clusters. Inspired by recent work on the formation of low-spin black holes, we include a zero-spin subpopulation. We analyze binary black holes from LIGO and Virgo’s first two observing runs, and find that this catalog is consistent with having no hierarchical mergers. We find that the most massive system in this catalog, GW170729, is mostly likely a first-generation merger, having a 4% probability of being a hierarchical merger assuming a 5 × 105 M ⊙ globular cluster mass. Using our model, we find that 99% of first-generation black holes in coalescing binaries have masses below M ⊙, and the fraction of binaries with near-zero component spins is less than (90% probability). Upcoming observations will determine if hierarchical mergers are a common source of gravitational waves.

Global torques and stochasticity as the drivers of massive black hole pairing in the young Universe

ABSTRACT The forthcoming Laser Interferometer Space Antenna (LISA) will probe the population of coalescing massive black hole (MBH) binaries up to the onset of structure formation. Here, we simulate the galactic-scale pairing of ∼106 M⊙ MBHs in a typical, non-clumpy main-sequence galaxy embedded in a cosmological environment at z = 7–6. In order to increase our statistical sample, we adopt a strategy that allows us to follow the evolution of six secondary MBHs concomitantly. We find that the magnitude of the dynamical-friction-induced torques is significantly smaller than that of the large-scale, stochastic gravitational torques arising from the perturbed and morphologically evolving galactic disc, suggesting that the standard dynamical friction treatment is inadequate for realistic galaxies at high redshift. The dynamical evolution of MBHs is very stochastic, and a variation in the initial orbital phase can lead to a drastically different time-scale for the inspiral. Most remarkably, the development of a galactic bar in the host system either significantly accelerates the inspiral by dragging a secondary MBH into the centre, or ultimately hinders the orbital decay by scattering the MBH in the galaxy outskirts. The latter occurs more rarely, suggesting that galactic bars overall promote MBH inspiral and binary coalescence. The orbital decay time can be an order of magnitude shorter than what would be predicted relying on dynamical friction alone. The stochasticity and the important role of global torques have crucial implications for the rates of MBH coalescences in the early Universe: both have to be accounted for when making predictions for the upcoming LISA observatory.

Binary black holes in young star clusters: the impact of metallicity

ABSTRACT Young star clusters are the most common birthplace of massive stars and are dynamically active environments. Here, we study the formation of black holes (BHs) and binary black holes (BBHs) in young star clusters, by means of 6000 N-body simulations coupled with binary population synthesis. We probe three different stellar metallicities (Z = 0.02, 0.002, and 0.0002) and two initial-density regimes (density at the half-mass radius ρh ≥ 3.4 × 104 and ≥1.5 × 102 M⊙ pc−3 in dense and loose star clusters, respectively). Metal-poor clusters tend to form more massive BHs than metal-rich ones. We find ∼6, ∼2, and <1 per cent of BHs with mass mBH > 60 M⊙ at Z = 0.0002, 0.002, and 0.02, respectively. In metal-poor clusters, we form intermediate-mass BHs with mass up to ∼320 M⊙. BBH mergers born via dynamical exchanges (exchanged BBHs) can be more massive than BBH mergers formed from binary evolution: the former (latter) reach total mass up to ∼140 M⊙ (∼80 M⊙). The most massive BBH merger in our simulations has primary mass ∼88 M⊙, inside the pair-instability mass gap, and a mass ratio of ∼0.5. Only BBHs born in young star clusters from metal-poor progenitors can match the masses of GW 170729, the most massive event in first and second observing run (O1 and O2), and those of GW 190412, the first unequal-mass merger. We estimate a local BBH merger rate density ∼110 and ∼55 Gpc−3 yr−1, if we assume that all stars form in loose and dense star clusters, respectively.

The TianQin project: Current progress on science and technology

Abstract TianQin is a planned space-based gravitational wave (GW) observatory consisting of three Earth-orbiting satellites with an orbital radius of about $10^5 \, {\rm km}$. The satellites will form an equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4} \, {\rm Hz}$ and $1 \, {\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe and exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new-generation $17 \, {\rm cm}$ single-body hollow corner-cube retro-reflector which was launched with the QueQiao satellite on 21 May 2018; a new laser-ranging station equipped with a $1.2 \, {\rm m}$ telescope has been constructed and the station has successfully ranged to all five retro-reflectors on the Moon; and the TianQin-1 experimental satellite was launched on 20 December 2019—the first-round result shows that the satellite has exceeded all of its mission requirements.

The Erratic Path to Coalescence of LISA Massive Black Hole Binaries in Subparsec-resolution Simulations of Smooth Circumnuclear Gas Disks

Abstract We perform high-resolution simulations to follow the orbital decay of 5 × 105 and 107 M ⊙ massive black hole (MBH) pairs embedded in a circumnuclear gas disk (CND), from the CND scale (100 pc) down to 0.1–0.01 pc, the scale at which a circumbinary disk (CBD) could form. The MBHs’ erratic orbital evolution is characterized by three stages: (i) a slow initial decay that leads to some circularization; (ii) a fast-migration phase, analogous to type III migration for massive planets in protoplanetary disks, in which angular momentum is efficiently drained by disk-driven torques arising from the co-orbital region of the secondary MBH, at a distance of 1–3 Hill radii; and (iii) a very slow decay phase, in which orbital angular momentum can even increase. In this last stage, a CBD forms when the parsec-scale decay rate becomes small enough to allow sufficient time for a cavity to be carved. When this happens, the MBH separation nearly stalls in our higher-resolution run. We suggest an empirically modified gap-opening criterion that takes into account such timescale effects, as well as other deviations from standard assumptions. Interestingly, a CBD does not form in the lower-resolution runs, resulting in a faster subparsec decay. Our findings show that the subparsec MBH pairing in gaseous disks is a stochastic and fragile process. Additional mechanisms, such as the stellar-driven hardening, may be necessary to guarantee that the gravitational wave emission phase is entered and the MBHs become accessible to future detectors such as the Laser Interferometer Space Antenna.

Does Matter Matter? Using the Mass Distribution to Distinguish Neutron Stars and Black Holes

Abstract Gravitational-wave detectors have opened a new window through which we can observe black holes (BHs) and neutron stars (NSs). Analyzing the 11 detections from LIGO/Virgo’s first gravitational-wave catalog, GWTC-1, we investigate whether the power-law fit to the BH mass spectrum can also accommodate the binary neutron star (BNS) event GW170817, or whether we require an additional feature, such as a mass gap in between the NS and BH populations. We find that with respect to the power-law fit to binary black hole (BBH) masses, GW170817 is an outlier at the 0.13% level, suggesting a distinction between NS and BH masses. A single power-law fit across the entire mass range is in mild tension with (a) the detection of one source in the BNS mass range (∼1–2.5 M ⊙), (b) the absence of detections in the “mass-gap” range (∼2.5–5 M ⊙), and (c) the detection of 10 sources in the BBH mass range (≳5 M ⊙). Instead, the data favor models with a feature between NS and BH masses, including a mass gap (Bayes factor of 4.6) and a break in the power law, with a steeper slope at NS masses compared to BH masses (91% credibility). We estimate the merger rates of compact binaries based on our fit to the global mass distribution, finding and . We conclude that, even in the absence of any prior knowledge of the difference between NSs and BHs, the gravitational-wave data alone already suggest two distinct populations of compact objects.

GPU-accelerated massive black hole binary parameter estimation with LISA

The Laser Interferometer Space Antenna (LISA) is slated for launch in the early 2030s. A main target of the mission is massive black hole binaries that have an expected detection rate of $\sim20$ yr$^{-1}$. We present a parameter estimation analysis for a variety of massive black hole binaries. This analysis is performed with a graphics processing unit (GPU) implementation comprising the phenomhm waveform with higher-order harmonic modes and aligned spins; a fast frequency-domain LISA detector response function; and a GPU-native likelihood computation. The computational performance achieved with the GPU is shown to be 500 times greater than with a similar CPU implementation, which allows us to analyze full noise-infused injections at a realistic Fourier bin width for the LISA mission in a tractable and efficient amount of time. With these fast likelihood computations, we study the effect of adding aligned spins to an analysis with higher-order modes by testing different configurations of spins in the injection, as well as the effect of varied and fixed spins during sampling. Within these tests, we examine three different binaries with varying mass ratios, redshifts, sky locations, and detector-frame total masses ranging over three orders of magnitude. We discuss varied correlations between the total masses and mass ratios; unique spin posteriors for the larger mass binaries; and the constraints on parameters when fixing spins during sampling, allowing us to compare to previous analyses that did not include aligned spins.

Defeating stochasticity: coalescence time-scales of massive black holes in galaxy mergers

ABSTRACT The coalescence of massive black hole binaries (BHBs) in galactic mergers is the primary source of gravitational waves (GWs) at low frequencies. Current estimates of GW detection rates for the Laser Interferometer Space Antenna and the Pulsar Timing Array vary by three orders of magnitude. To understand this variation, we simulate the merger of equal-mass, eccentric, galaxy pairs with central massive black holes and shallow inner density cusps. We model the formation and hardening of a central BHB using the fast multiple method as a force solver, which features a O(N) scaling with the number N of particles and obtains results equivalent to direct-summation simulations. At N ∼ 5 × 105, typical for contemporary studies, the eccentricity of the BHBs can vary significantly for different random realizations of the same initial condition, resulting in a substantial variation of the merger time-scale. This scatter owes to the stochasticity of stellar encounters with the BHB and decreases with increasing N. We estimate that N ∼ 107 within the stellar half-light radius suffices to reduce the scatter in the merger time-scale to ∼10 per cent. Our results suggest that at least some of the uncertainty in low-frequency GW rates owes to insufficient numerical resolution.

Impact of subdominant modes on the interpretation of gravitational-wave signals from heavy binary black hole systems

Over the past year, a handful of new gravitational wave models have been developed to include multiple harmonic modes thereby enabling for the first time fully Bayesian inference studies including higher modes to be performed. Using one recently-developed numerical relativity surrogate model, NRHybSur3dq8, we investigate the importance of higher modes on parameter inference of coalescing massive binary black holes. We focus on examples relevant to the current three-detector network of observatories, with a detector-frame mass set to $120 M_\odot$ and with signal amplitude values that are consistent with plausible candidates for the next few observing runs. We show that for such systems the higher mode content will be important for interpreting coalescing binary black holes, reducing systematic bias, and computing properties of the remnant object. Even for comparable-mass binaries and at low signal amplitude, the omission of higher modes can influence posterior probability distributions. We discuss the impact of our results on source population inference and self-consistency tests of general relativity. Our work can be used to better understand asymmetric binary black hole merger events, such as GW190412. Higher modes are critical for such systems, and their omission usually produces substantial parameter biases.

Taiji program: Gravitational-wave sources

We review potential low-frequency gravitational-wave sources, which are expected to be detected by Taiji, a Chinese space-based gravitational-wave detector, estimate the detection rates of these gravitational-wave sources and present the parameter estimation of massive black hole binaries.

Properties of OB star−black hole systems derived from detailed binary evolution models

Context. The recent gravitational wave measurements have demonstrated the existence of stellar mass black hole binaries. It is essential for our understanding of massive star evolution to identify the contribution of binary evolution to the formation of double black holes. Aims. A promising way to progress is investigating the progenitors of double black hole systems and comparing predictions with local massive star samples, such as the population in 30 Doradus in the Large Magellanic Cloud (LMC). Methods. With this purpose in mind, we analysed a large grid of detailed binary evolution models at LMC metallicity with initial primary masses between 10 and 40 M⊙, and identified the model systems that potentially evolve into a binary consisting of a black hole and a massive main-sequence star. We then derived the observable properties of such systems, as well as peculiarities of the OB star component. Results. We find that ∼3% of the LMC late-O and early-B stars in binaries are expected to possess a black hole companion when stars with a final helium core mass above 6.6 M⊙ are assumed to form black holes. While the vast majority of them may be X-ray quiet, our models suggest that these black holes may be identified in spectroscopic binaries, either by large amplitude radial velocity variations (≳50 km s−1) and simultaneous nitrogen surface enrichment, or through a moderate radial velocity (≳10 km s−1) and simultaneous rapid rotation of the OB star. The predicted mass ratios are such that main-sequence companions can be excluded in most cases. A comparison to the observed OB+WR binaries in the LMC, Be and X-ray binaries, and known massive black hole binaries supports our conclusion. Conclusions. We expect spectroscopic observations to be able to test key assumptions in our models, with important implications for massive star evolution in general and for the formation of double black hole mergers in particular.

Fake Massive Black Holes in the Milli-Hertz Gravitational-wave Band

Abstract In gravitational-wave (GW) astronomy accurate measurement of the source parameters, such as mass, relies on accurate waveform templates. Currently, templates are developed assuming that a source, such as a stellar-mass binary black hole (BBH), is residing in a vacuum. However, astrophysical models predict that BBHs could form in gaseous environments, such as common envelopes, stellar cores, and accretion disks of active galactic nuclei. Here we revisit the impact of gas on the GW waveforms of BBHs with a focus on the early inspiral phase when the GW frequency is around milli-Hertz. We show that for these BBHs, gas friction could dominate the dynamical evolution and hence duplicate chirp signals. The relevant hydrodynamical timescale, τ gas, could be much shorter than the GW radiation timescale, τ gw, in the above astrophysical scenarios. As a result, the observed chirp mass is higher than the real one by a factor of if the gas effect is ignored in the data analysis. This kind of error also results in an overestimation of the source distance by a factor of . By performing matched-filtering analysis in the milli-Hertz band, we prove that the gas-dominated signals are practically indistinguishable from the chirp signals of those more massive BBHs residing in a vacuum environment. Such fake massive objects in the milli-Hertz band, if not appropriately accounted for in the future, may alter our understanding of the formation, evolution, and detection of BBHs.

Search for nonlinear memory from subsolar mass compact binary mergers

We present the first results of the search for nonlinear memory from subsolar mass binary black hole (BBH) mergers during the second observing run (O2) of the LIGO and Virgo detectors. The oscillatory chirp signal from the inspiral and merger of low mass BBHs ($M_\mathrm{Tot} \leq 0.4 M_\odot$) are at very high frequencies and fall outside the sensitivity band of the current ground-based detectors. However, the non-oscillatory memory signal during the merger saturates towards the lower frequencies and can be detected for those proposed BBHs. We show in this work that the morphology of the memory signal depends minimally upon the source parameters of the binary, thus only the overall amplitude of the signal changes and hence the result can be interpolated for extremely low mass BBH mergers. We did not find any signal which can be interpreted as a memory signal and we place upper limits on the rate of BBH mergers with $M_\mathrm{Tot} \leq 0.4 M_\odot$ for the first time.

Dark-energy instabilities induced by gravitational waves

We point out that dark-energy perturbations may become unstable in the presence of a gravitational wave of sufficiently large amplitude. We study this effect for the cubic Horndeski operator (braiding), proportional to αB. The scalar that describes dark-energy fluctuations features ghost and/or gradient instabilities for gravitational-wave amplitudes that are produced by typical binary systems. Taking into account the populations of binary systems, we conclude that the instability is triggered in the whole Universe for |αB |≳ 10−2, i.e. when the modification of gravity is sizeable. The instability is triggered by massive black-hole binaries down to frequencies corresponding to 1010 km: the instability is thus robust, unless new physics enters on even longer wavelengths. The fate of the instability and the subsequent time-evolution of the system depend on the UV completion, so that the theory may end up in a state very different from the original one. The same kind of instability is present in beyond-Horndeski theories for |αH| ≳ 10−20. In conclusion, the only dark-energy theories with sizeable cosmological effects that avoid these problems are k-essence models, with a possible conformal coupling with matter.

Prospects for improving cosmological parameter estimation with gravitational-wave standard sirens from Taiji

Taiji, a space-based gravitational-wave observatory, consists of three satellites forming an equilateral triangle with arm length of 3×106 km, orbiting around the Sun. Taiji is able to observe the gravitational-wave standard siren events of massive black hole binary (MBHB) merger, which is helpful in probing the expansion of the universe. In this paper, we preliminarily forecast the capability of Taiji for improving cosmological parameter estimation with the gravitational-wave standard siren data. We simulate five-year standard siren data based on three fiducial cosmological models and three models of MBHB's formation and growth. It is found that the standard siren data from Taiji can effectively break the cosmological parameter degeneracies generated by the cosmic microwave background (CMB) anisotropies data, especially for dynamical dark energy models. The constraints on cosmological parameters are significantly improved by the data combination CMB + Taiji, compared to the CMB data alone. Compared to the current optical cosmological observations, Taiji can still provide help in improving the cosmological parameter estimation to some extent. In addition, we consider an ideal scenario to investigate the potential of Taiji on constraining cosmological parameters. We conclude that the standard sirens of MBHB from Taiji will become a powerful cosmological probe in the future.

Cosmic archaeology with massive stellar black hole binaries

ABSTRACT The existence of massive stellar black hole binaries (MBHBs), with primary black hole masses $\ge 31 \, \mathrm{ M}_\odot$, was proven by the detection of the gravitational wave (GW) event GW150914 during the first LIGO/Virgo observing run (O1), and successively confirmed by seven additional GW signals discovered in the O1 and O2 data. By adopting the galaxy formation model gamesh coupled with binary population synthesis (BPS) calculations, here we investigate the origin of these MBHBs by selecting simulated binaries compatible in mass and coalescence redshifts. We find that their cosmic birth rates peak in the redshift range 6.5 ≤ z ≤ 10, regardless of the adopted BPS. These MBHBs are then old systems forming in low-metallicity ($Z \sim [0.01\!-\!0.1] \, Z_{\odot }$), low-stellar-mass galaxies, before the end of cosmic reionization, i.e. significantly beyond the peak of cosmic star formation. GW signals generated by coalescing MBHBs open up new possibilities to probe the nature of stellar populations in remote galaxies, at present too faint to be detected by available electromagnetic facilities.