Massive Black Hole Binaries Research Articles

Premerger localization of intermediate mass binary black holes with LISA and prospects of joint observations with Athena and LSST

The planned Laser Interferometric Space Antenna (LISA) will be able to detect gravitational waves (GWs) from intermediate mass binary black holes (IMBBHs) in the mass range $\sim 10^{2} \mbox{-} 10^{4}\,M_{\odot}$ up to a redshift $z\sim20$. Modulation effects due to orbital motion of LISA around the Sun facilitate precise premerger localization of the sources, which in turn would help in electromagnetic (EM) followups. In this work, we calculate the uncertainties in sky position, luminosity distance, and time of coalescence as a function of time to coalescence. For representative masses of the IMBBHs, we synthesize a population of binaries uniformly located and oriented on a sphere of radius 3 Gpc and compute the projected parameter measurement uncertainties using the Fisher information matrix. We find that for systems with a total mass of $10^3\,M_{\odot}$, the errors in the sky position and luminosity distance are $\sim 0.4\,\text{deg}^2$ and $\sim 6\%$, respectively, one day prior to coalescence. The coalescence time can be predicted with an uncertainty $\lesssim 10$ sec, one day before coalescence. We also find that for $10^3\,M_{\odot}$, around $40\%$ ($100\%$) of the population has a source localization that is smaller than the field of view of Athena (LSST) one day before the merger. These extremely precise measurements can be used to alert ground-based GW detectors and EM telescopes about the time and location of these mergers. We also discuss mechanisms that may produce EM emission from IMBBH mergers and study its detectability using the planned Legacy Survey of Space and Time (LSST) in the optical and Athena in the x-ray bands. Detection of an EM transient may provide us vital clues about the environments where these mergers occur and the distance estimation can pave the way for cosmography.

On Detecting Nearby Nanohertz Gravitational Wave Sources via Pulsar Timing Arrays

Massive binary black holes (MBBHs) in nearby galactic centers, if any, may be nanohertz gravitational wave (GW) sources for pulsar timing arrays (PTAs) to detect. Normally the objective GWs for PTA experiments are approximated as plane waves because their sources are presumably located far away. For nearby GW sources, however, this approximation may be inaccurate due to the curved GW wave front and the GW strength changes along the paths of PTA pulsar pulses. In this paper, we analyze the near-field effect in the PTA detection of nearby sources and find it is important if the source distance is less than a few tens of megaparsecs, and ignoring this effect may lead to a significant signal-to-noise underestimation especially when the source distance is comparable to the pulsar distances. As examples, we assume a nanohertz MBBH source located at either the Galactic Center (GC) or the Large Magellanic Cloud (LMC) according to the observational constraints/hints on the MBBH parameter space, and estimate its detectability by current/future PTAs. We find that the GC MBBH may be detectable by the Square Kilometer Array PTA. Detecting the LMC MBBH is challenging; however, if a number (N ≳ 10) of stable millisecond pulsars can be found in the LMC center, the MBBH may be detectable via a PTA formed by these pulsars. We further illustrate the near-field effects on the PTA detection of an isotropic GW background contributed mainly by nearby GW sources, and the resulting angular correlation is similar to the Hellings–Downs curve.

Do unequal-mass binary black hole systems have larger χeff? Probing correlations with copulas in gravitational-wave astronomy

ABSTRACT The formation history of binary black hole systems is imprinted on the distribution of their masses, spins, and eccentricity. While much has been learned studying these parameters in turn, recent studies have explored the joint distribution of binary black hole parameters in two or more dimensions. Most notably, it has recently been argued that binary black hole mass ratio and effective inspiral spin χeff are anticorrelated. We point out a previously overlooked subtlety in such 2D population studies: in order to conduct a controlled test for correlation, one ought to fix the two marginal distributions – lest the purported correlation be driven by improved fit in just one dimension. We address this subtlety using a tool from applied statistics: the copula density function. We use the previous work correlating mass ratio and χeff as a case study to demonstrate the power of copulas in gravitational-wave astronomy while scrutinizing their astrophysical inferences. Our findings, however, affirm their conclusions that binary black holes with unequal component masses exhibit larger χeff (98.7 per cent credibility). We conclude by discussing potential astrophysical implications of these findings as well as prospects for future studies using copulas.

Cost minimization in acquisition for gravitational wave surrogate modeling

Gravitational wave science is dependent upon expensive numerical simulations, which provide the foundational understanding of binary merger radiation needed to interpret observations of massive binary black holes. The high cost of these simulations limits large-scale campaigns to explore the binary black hole parameter space. Surrogate models have been developed to efficiently interpolate between simulation results, but these models require a sufficiently comprehensive sample to train on. Acquisition functions can be used to identify points in the domain for simulation. We develop a new acquisition function which accounts for the cost of simulating new points. We show that when applied to a 3D domain of binary mass ratio and dimensionless nonprecessing spins, the accumulated cost of simulation is reduced by a factor of about 10.

Tests of gravitational-wave birefringence with the open gravitational-wave catalog

We report the results of testing gravitational-wave birefringence using the largest population of gravitational-wave events currently available. Gravitational-wave birefringence, which can arise from the effective field theory extension of general relativity, occurs when the parity symmetry is broken, causing the left- and right-handed polarizations to propagate following different equations of motion. We perform Bayesian inference on the 94 events reported by the 4th-Open Gravitational-wave Catalog (4-OGC) using a parity-violating waveform. We find no evidence for a violation of general relativity in the vast majority of events. However, the most massive event, GW190521, and the second most massive event, GW191109, show intriguing non-zero results for gravitational-wave birefringence. We find that the probability of association between GW190521 and the possible electromagnetic (EM) counterpart reported by Zwicky Transient Facility (ZTF) is increased when assuming birefringence. Excluding GW190521 and GW191109, the parity-violating energy scale is constrained to $M_\mathrm{PV} > 0.05$ GeV at $90\%$ credible interval, which is an improvement over previous results from twelve events by a factor of five. We discuss the implications of our results on modified gravity and possible alternative explanations such as waveform systematics. More detections of massive binary black hole mergers from the upcoming LIGO/Virgo/KAGRA run will shed light on the true origin of the apparent birefringence.

Resolving the Peak of the Black Hole Mass Spectrum

Gravitational-wave (GW) detections of binary black hole (BH) mergers have begun to sample the cosmic BH mass distribution. The evolution of single stellar cores predicts a gap in the BH mass distribution due to pair-instability supernovae (PISNe). Determining the upper and lower edges of the BH mass gap can be useful for interpreting GW detections of merging BHs. We use MESA to evolve single, nonrotating, massive helium cores with a metallicity of Z = 10−5, until they either collapse to form a BH or explode as a PISN, without leaving a compact remnant. We calculate the boundaries of the lower BH mass gap for S-factors in the range S(300 keV) = (77,203) keV b, corresponding to the ±3σ uncertainty in our high-resolution tabulated 12C(α,γ)16O reaction rate probability distribution function. We extensively test temporal and spatial resolutions for resolving the theoretical peak of the BH mass spectrum across the BH mass gap. We explore the convergence with respect to convective mixing and nuclear burning, finding that significant time resolution is needed to achieve convergence. We also test adopting a minimum diffusion coefficient to help lower-resolution models reach convergence. We establish a new lower edge of the upper mass gap as M lower ≃ M ⊙ from the ±3σ uncertainty in the 12C(α, γ)16O rate. We explore the effect of a larger 3α rate on the lower edge of the upper mass gap, finding M lower ≃ M ⊙. We compare our results with BHs reported in the Gravitational-Wave Transient Catalog.

Binary black hole mergers from young massive clusters in the pair-instability supernova mass gap

Context. The recent discovery of the binary black hole (BBH) merger event GW190521, between two black holes (BHs) of ≈100 Msamp, in addition to other massive BBH merger events involving BHs within the pair-instability supernova (PSN) mass gap have sparked widespread debate on the origin of such extreme gravitational-wave (GW) events. GW190521 simultaneously triggers two critical questions: how BHs can appear within the ‘forbidden’ PSN gap and, if they do, how they get to participate in general-relativistic (GR) mergers. Aims. In this study, I investigate whether dynamical interactions in young massive clusters (YMCs) serve as a viable scenario for assembling PSN-gap BBH mergers. Methods. To that end, I explore a grid of 40 new evolutionary models of a representative YMC of initial mass and size Mcl = 7.5 × 104 Msamp (N ≈ 1.28 × 105) and rh = 2 pc, respectively. The model grid ranges over metallicity 0.0002 ≤ Z ≤ 0.02 and comprises initial cluster configurations of King central concentration parameters W0 = 7 and 9. In each model, all BH progenitor stars are initially in primordial binaries following observationally motivated distributions. All cluster models are evolved with the direct, relativistic N-body code NBODY7, incorporating up-to-date remnant formation, BH natal spin, and GR merger recoil schemes. Results. Binary black hole mergers from these model cluster computations agree well with the masses and effective spin parameters, χeff, of the events from the latest gravitational-wave transient catalogue (GWTC). In particular, GW190521-like, that is to say ≈200 Msamp, low χeff events are produced via a dynamical merger among BHs derived from star-star merger products. GW190403_051519-like, that is PSN-gap, highly asymmetric, high χeff events result from mergers involving BHs that are spun up via matter accretion or a binary interaction. The resulting present-day, differential intrinsic merger rate density, within the PSN gap, accommodates that from GWTC well. Conclusions. This study demonstrates that, subject to model uncertainties, the tandem of massive binary evolution and dynamical interactions in ≲100 Myr-old, low metallicity YMCs in the Universe can plausibly produce GR mergers involving PSN-gap BHs and in rates consistent with that from up-to-date GW observations. Such clusters can produce extreme events similar to GW190521 and GW190403_051519. The upper limit of the models’ GW190521-type event rate is within the corresponding LIGO-Virgo-KAGRA (LVK)-estimated rate limits, although the typical model rate lies below LVK’s lower limit. The present YMC models yield a merger rate density of 0−3.8 × 10−2 yr−1 Gpc−3 for GW190521-type events. They produce GW190403_051519-like events at a rate within 0−1.6 × 10−1 yr−1 Gpc−3 and their total BBH-merger yield within the PSN gap is 0−8.4 × 10−1 yr−1 Gpc−3.

Merging of unequal mass binary black holes in non-axisymmetric galactic nuclei

In this work, we study the stellar-dynamical hardening of unequal mass supermassive black hole (SMBH) binaries in the central regions of merging galactic nuclei. We present a comprehensive set of direct N-body simulations of the problem, varying both the total mass and the mass ratio of the SMBH binary (SMBHB). Simulations were carried out with the φ-GPU N-body code, which enabled us to fully exploit supercomputers equipped with graphic processing units (GPUs). As a model for the galactic nuclei, we adopted initial axisymmetric, rotating models, aimed at reproducing the properties of a galactic nucleus emerging from a galaxy merger event, containing two SMBHs which were unbound initially. We found no ‘final-parsec problem’, as our SMBHs tend to pair and shrink without showing significant signs of stalling. This confirms earlier results and extends them to large particle numbers and rotating systems. We find that the SMBHB hardening depends on the binary-reduced mass ratio via a single parameter function. Our results suggest that, at a fixed value for the SMBHB primary mass, the merger time of highly asymmetric binaries is up to four order of magnitudes smaller than the equal-mass binaries. This can significantly affect the population of SMBHs potentially detectable as gravitational wave sources.

Extreme mass ratio inspirals triggered by massive black hole binaries: from relativistic dynamics to cosmological rates

ABSTRACT Extreme mass ratio inspirals (EMRIs) are compact binary systems characterized by a mass ratio q = m/M in the range 10−9–10−4 and represent primary gravitational wave (GW) sources for the forthcoming Laser Interferometer Space Antenna (LISA). While their standard formation channel involves relaxation processes deflecting compact objects on very low angular momentum orbits around the central massive black hole, a number of alternative formation channels has been proposed, including binary tidal break-up, migration in accretion discs and secular and chaotic dynamics around a massive black hole binary (MBHB). In this work, we take an extensive closer look at this latter scenario, investigating how EMRIs can be triggered by MBHBs, formed in the aftermath of galaxy mergers. By employing a suite of relativistic three-body simulations, we evaluate the efficiency of EMRI formation for different parameters of the MBHB, assessing the importance of both secular and chaotic dynamics. By modelling the distribution of compact objects in galaxy nuclei, we estimate the resulting EMRI formation rate, finding that EMRI are produced in a sharp burst, with peak rates that are 10–100 times higher than the standard two-body relaxation channel, lasting for 106–108 yr. By coupling our results with an estimate of the cosmic MBHB merger rate, we finally forecast that LISA could observe ${\cal O}(10)$ EMRIs per year formed by this channel.

Redshift factor and the small mass-ratio limit in binary black hole simulations

We present a calculation of the Detweiler redshift factor in binary black hole simulations based on its relation to the surface gravity. The redshift factor has far-reaching applications in analytic approximations, gravitational self-force calculations, and conservative two-body dynamics. By specializing to nonspinning, quasicircular binaries with mass ratios ranging from ${m}_{A}/{m}_{B}=1$ to ${m}_{A}/{m}_{B}=9.5$ we are able to recover the leading small-mass-ratio (SMR) prediction with relative differences of order ${10}^{\ensuremath{-}5}$ from simulations alone. The next-to-leading order term that we extract agrees with the SMR prediction arising from self-force calculations, with differences of a few percent. These deviations from the first-order conservative prediction are consistent with nonadiabatic effects that can be accommodated in an SMR expansion. This fact is also supported by a comparison to the conservative post-Newtonian prediction of the redshifts. For the individual redshifts, a reexpansion in terms of the symmetric mass ratio $\ensuremath{\nu}$ does not improve the convergence of the series. However we find that when looking at the sum of the redshift factors of both back holes, ${z}_{A}+{z}_{B}$, which is symmetric under the exchange of the masses, a reexpansion in $\ensuremath{\nu}$ accelerates its convergence. Our work provides further evidence of the surprising effectiveness of SMR approximations in modeling even comparable mass binary black holes.

Data Release for "Avoiding a Cluster Catastrophe: Retention Efficiency and the Binary Black Hole Mass Spectrum"

Data Release for "Avoiding a Cluster Catastrophe: Retention Efficiency and the Binary Black Hole Mass Spectrum"

Data Release for "Avoiding a Cluster Catastrophe: Retention Efficiency and the Binary Black Hole Mass Spectrum"

Data Release for "Avoiding a Cluster Catastrophe: Retention Efficiency and the Binary Black Hole Mass Spectrum"

Massive Black Hole Binaries from the TNG50-3 Simulation. I. Coalescence and LISA Detection Rates

We evaluate the cosmological coalescence and detection rates for massive black hole (MBH) binaries targeted by the gravitational wave observatory Laser Interferometer Space Antenna (LISA). Our calculation starts with a population of gravitationally unbound MBH pairs, drawn from the TNG50-3 cosmological simulation, and follows their orbital evolution from kiloparsec scales all the way to coalescence using a semi-analytic model developed in our previous work. We find that for the majority of MBH pairs that coalesce within a Hubble time dynamical friction is the most important mechanism that determines their coalescence rate. Our model predicts an MBH coalescence rate ≲0.45 yr−1 and a LISA detection rate ≲0.34 yr−1. Most LISA detections should originate from 106 to 106.8 M ⊙ MBHs in gas-rich galaxies at redshifts 1.6 ≤ z ≤ 2.4 and have a characteristic signal-to-noise ratio S/N ∼100. We however find a dramatic reduction in the coalescence and detection rates, as well as the average S/N, if the effects of radiative feedback from accreting MBHs are taken into account. In this case, the MBH coalescence rate is reduced by 78% (to ≲0.1 yr−1), and the LISA detection rate is reduced by 94% (to 0.02 yr−1), whereas the average S/N is ∼10. We emphasize that our model provides a conservative estimate of the LISA detection rates, due to the limited MBH mass range in TNG50-3, consistent with other works in the literature that draw their MBH pairs from cosmological simulations.

Landscape of massive black-hole spectroscopy with LISA and the Einstein Telescope

Measuring the quasi-normal mode~(QNM) spectrum emitted by a perturbed black-hole~(BH) --~also known as BH spectroscopy~-- provides an excellent opportunity to test the predictions of general relativity in the strong-gravity regime. We investigate the prospects and precision of BH spectroscopy in massive binary black hole ringdowns, one of the primary science objectives of the future Laser Interferometric Space Antenna~(LISA) mission. We simulate various massive binary BH population models, featuring competing prescriptions for the Delays between galaxy and BH mergers, for the impact of supernova feedback on massive BH growth, and for the initial population of high redshift BH seeds (light versus heavy seeds). For each of these scenarios, we compute the average number of expected events for precision BH spectroscopy using a Fisher-matrix analysis. We find that, for any heavy seed scenario, LISA will measure the dominant mode frequency within ${\cal O}(0.1) \%$ relative uncertainty and will estimate at least 3 independent QNM parameters within $1 \%$ error. The most optimistic heavy seed scenarios produce $\mathcal{O}(100)$ events with $1 \%$ measurability for 3 or more QNM quantities during LISA's operational time. On the other hand, light seed scenarios produce lighter merger remnants, which ring at frequencies higher than LISA's sensitivity. Interestingly, the light seed models give rise to a fraction of mergers in the band of Einstein Telescope, allowing for the measurement of 3 QNM parameters with $\sim 10 \%$ relative errors in approximately a few to ten events/yr. More precise BH spectroscopy in the light seed scenarios would require instruments operating in the deciHertz band.

How many extragalactic stellar mass binary black holes will be detected by space gravitational-wave interferometers?

ABSTRACT On the basis of GWTC-3, we discuss the detection prospect of extragalactic binary black holes (BBHs) by space gravitational-wave interferometers, mainly targeting BBHs in the range of chirp masses with abundant detections. In particular, we directly incorporate the chirp mass distribution of the 62 BBHs detected so far at high significance. We find that, due to the reduction of both the comoving merger rate and a weighted average of chirp masses, the expected detection numbers are generally much smaller than the results obtained by the same authors immediately after the report of GW150914. For LISA, the total BBH detections in the chirp mass range are estimated to be Ntot ∼ 2(T/4yr)3/2(ρthr/10)−3, dominated by nearly monochromatic BBHs (ρthr: the detection threshold, T: the observational period). TianQin will have a total detection number Ntot similar to LISA. Meanwhile, TianQin has potential to find Nmer ∼ 0.6(T/4yr)7/4(ρthr/10)−3 BBHs that merge in the observational period. This number for merging BBHs is 4–5 times larger than that of LISA because of the difference of the optimal bands. We also investigate prospects for joint operations of multiple detectors, finding that concurrent observations will be more advantageous than sequential ones.

No slip gravity in light of LISA standard sirens

ABSTRACT Standard sirens (SS) are the gravitational wave analogue of the astronomical standard candles, and can provide powerful information about the dynamics of the Universe up to very high z values. In this work, we generate three mock SS catalogues based on the merger of massive black hole binaries which are expected to be observed in the LISA operating frequency band. Then, we perform an analysis to test modifications of general relativity (GR) inspired by the no slip gravity framework. We find that in the best scenarios, we can constrain the free parameters which quantify deviations from GR to 21 per cent accuracy, while the Hubble parameter can be simultaneously fit to 6 per cent accuracy. In combination with CMB information, we find a 15 per cent accuracy on the modified gravity free parameters and 0.7 per cent accuracy on the Hubble parameter. The SS events at very large cosmological distances to be observed in LISA band will provide a unique way to test nature of gravity, but in the context of the analysis performed here, it will not be possible to distinguish the no slip gravity from GR.

Stable Mass Transfer Can Explain Massive Binary Black Hole Mergers with a High-spin Component

Recent gravitational-wave observations showed that binary black hole (BBH) mergers with massive components are more likely to have high effective spins. In the model of isolated binary evolution, BH spins mainly originate from the angular momenta of the collapsing cores before BH formation. Both observations and theories indicate that BHs tend to possess relatively low spins; the origin of fast-spinning BHs remains a puzzle. We investigate an alternative process that stable Case A mass transfer may significantly increase BH spins during the evolution of massive BH binaries. We present detailed binary evolution calculations and find that this process can explain the observed high spins of some massive BBH mergers under the assumption of mildly super-Eddington accretion.

The Redshift Evolution of the Binary Black Hole Merger Rate: A Weighty Matter

Gravitational-wave detectors are starting to reveal the redshift evolution of the binary black hole (BBH) merger rate, R BBH(z). We make predictions for R BBH(z) as a function of black hole mass for systems originating from isolated binaries. To this end, we investigate correlations between the delay time and black hole mass by means of the suite of binary population synthesis simulations, COMPAS. We distinguish two channels: the common envelope (CE), and the stable Roche-lobe overflow (RLOF) channel, characterized by whether the system has experienced a common envelope or not. We find that the CE channel preferentially produces BHs with masses below about 30 M ⊙ and short delay times (t delay ≲ 1 Gyr), while the stable RLOF channel primarily forms systems with BH masses above 30 M ⊙ and long delay times (t delay ≳ 1 Gyr). We provide a new fit for the metallicity-dependent specific star formation rate density based on the Illustris TNG simulations, and use this to convert the delay time distributions into a prediction of R BBH(z). This leads to a distinct redshift evolution of R BBH(z) for high and low primary BH masses. We furthermore find that, at high redshift, R BBH(z) is dominated by the CE channel, while at low redshift, it contains a large contribution (∼40%) from the stable RLOF channel. Our results predict that, for increasing redshifts, BBHs with component masses above 30 M ⊙ will become increasingly scarce relative to less massive BBH systems. Evidence of this distinct evolution of R BBH(z) for different BH masses can be tested with future detectors.

Milli-Hertz Gravitational-wave Background Produced by Quasiperiodic Eruptions

Extreme-mass-ratio inspirals (EMRIs) are important targets for future space-borne gravitational-wave (GW) detectors, such as the Laser Interferometer Space Antenna (LISA). Recent works suggest that EMRIs may reside in a population of newly discovered X-ray transients called “quasiperiodic eruptions” (QPEs). Here, we follow this scenario and investigate whether LISA could in the future detect the QPEs. We consider two specific models, in which the QPEs are made of either stellar-mass objects moving on circular orbits around massive black holes (MBHs) or white dwarfs (WDs) on eccentric orbits around MBHs. We find that in either case the five QPEs detected so far are too weak to be resolvable by LISA. However, if QPEs are made of eccentric WD–MBH binaries, they radiate GWs over a wide range of frequencies. The broad spectra overlap to form a background that peaks in the milli-Hertz band and has a signal-to-noise ratio of 9–17 even in the most pessimistic scenario. The presence of this GW background in the LISA band could impact future searches for seed black holes at high redshift as well as stellar-mass binary black holes in the local universe.

On the detectability of massive black hole merger events by Laser Interferometry Space Antenna

ABSTRACTThe launch of space-based gravitational-wave (GW) detectors (e.g. Laser Interferometry Space Antenna; LISA) and current and upcoming Pulsar Timing Arrays will extend the GW window to low frequencies, opening new investigations into dynamical processes involving massive black hole binaries (MBHBs) and their mergers across cosmic time. MBHBs are expected to be among the primary sources for the upcoming low-frequency (10−4–10−1 Hz) window probed by LISA. It is important to investigate the expected supermassive BH merger rates and associated signals, to determine how potential LISA events are affected by physics included in current models. To study this, we post-process the large population of MBHBs in the Illustris simulation to account for dynamical friction time delays associated with BH infall/inspiral. We show that merger delays associated with binary evolution have the potential to decrease the expected merger rates, with $M_{\rm {BH}}\ \gt\ 10^6\ \mathrm{M}_\odot$ MBHBs (the lowest mass in Illustris) decreasing from ∼3 to ∼0.1 yr−1, and shifting the merger peak from z ∼2 to ∼1.25. During this time, we estimate that accretion grows the total merging mass by as much as 7x the original mass. Importantly, however, dynamical friction-associated delays (which shift the mergers toward lower redshift and higher masses) lead to a stronger signal/strain for the emitted GWs in the LISA band, increasing mean frequency from 10−3.1 to 10−3.4–10−4.0 Hz, and mean strain from 10−17.2 to 10−16.3–10−15.3. Finally, we show that after including a merger delay and associated MBH growth, mergers still tend to lie on the typical MBH–M* relation, but with an increased likelihood of an undermassive BH.