Massive Black Hole Binaries Research Articles

Gravitational self-lensing in populations of massive black hole binaries

ABSTRACT The community may be on the verge of detecting low-frequency gravitational waves from massive black hole binaries (MBHBs), but no examples of binary active galactic nuclei (AGN) have been confirmed. Because MBHBs are intrinsically rare, the most promising detection methods utilize photometric data from all-sky surveys. Gravitational self-lensing has recently been proposed as a method of detecting AGN in close separation binaries. In this study, we calculate the detectability of lensing signatures in realistic populations of simulated MBHBs. Within our model assumptions, we find that VRO’s LSST should be able to detect tens to hundreds of self-lensing binaries, with the rate uncertainty depending primarily on the orientation of AGN discs relative to their binary orbits. Roughly a quarter of lensing detectable systems should also show detectable Doppler boosting signatures. If AGN discs tend to be aligned with the orbit, lensing signatures are very nearly achromatic, while in misaligned configurations, the bluer optical bands are lensed more than redder ones. Whether substantial obscuring material (e.g. a dusty torus) will be present in close binaries remains uncertain, but our estimates suggest that a substantial fraction of systems would still be observable in this case.

GW190521 formation via three-body encounters in young massive star clusters

ABSTRACT GW190521 is the most massive binary black hole (BBH) merger observed to date, and its primary component lies in the pair-instability (PI) mass gap. Here, we investigate the formation of GW190521-like systems via three-body encounters in young massive star clusters. We performed 2 × 105 simulations of binary-single interactions between a BBH and a massive $\ge {60}\,$M⊙ black hole (BH), including post-Newtonian terms up to the 2.5 order and a prescription for relativistic kicks. In our initial conditions, we take into account the possibility of forming BHs in the PI mass gap via stellar collisions. If we assume that first-generation BHs have low spins, $\sim {0.17}{{\ \rm per\ cent}}$ of all the simulated BBH mergers have component masses, effective and precessing spin, and remnant mass and spin inside the $90{{\ \rm per\ cent}}$ credible intervals of GW190521. Seven of these systems are first-generation exchanged binaries, while five are second-generation BBHs. We estimate a merger rate density $\mathcal {R}_{\rm GW190521}\sim {0.03}\,$Gpc$^{-3}\,$yr−1 for GW190521-like binaries formed via binary-single interactions in young star clusters. This rate is extremely sensitive to the spin distribution of first-generation BBHs. Stellar collisions, second-generation mergers and dynamical exchanges are the key ingredients to produce GW190521-like systems in young star clusters.

Universal features of gravitational waves emitted by superkick binary black hole systems

We use numerical relativity to study the merger and ringdown stages of ``superkick'' binary black hole systems (those with equal mass and antiparallel spins). We find a universal way to describe the mass and current quadrupole gravitational waves emitted by these systems during the merger and ringdown stage: (i) The time evolutions of these waves are insensitive to the progenitor's parameters (spins) after being normalized by their own peak values. (ii) The peak values, which encode all the spin information of the progenitor, can be consistently fitted to formulas inspired by post-Newtonian theory. We find that the universal evolution of the mass quadrupole wave can be accurately modeled by the so-called Backwards One-Body (BOB) model. However, the BOB model, in its present form, leads to a lower waveform match and a significant parameter-estimation bias for the current quadrupole wave. We also decompose the ringdown signal into seven overtones, and study the dependence of mode amplitudes on the progenitor's parameters. Such dependence is found to be insensitive to the overtone index (up to a scaling factor). Finally, we use the Fisher matrix technique to investigate how the ringdown waveform can be at least as important for parameter estimation as the inspiral stage. Assuming the Cosmic Explorer, we find the contribution of ringdown portion dominates as the total mass exceeds $\ensuremath{\sim}250\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. For massive binary black hole (BBH) systems, the accuracy of parameter measurement is improved by incorporating the information of ringdown---the ringdown sector gives rise to a different parameter correlation from inspiral stage; hence, the overall parameter correlation is reduced in full signal.

Stellar hardening of massive black hole binaries: the impact of the host rotation

ABSTRACT Massive black hole binaries (MBHBs) with masses of ∼104 to $\sim 10^{10} \, \mathrm{M}_{\odot {}}$ are one of the main targets for currently operating and forthcoming space-borne gravitational wave observatories. In this paper, we explore the effect of the stellar host rotation on the bound binary hardening efficiency, driven by three-body stellar interactions. As seen in previous studies, we find that the centre of mass (CoM) of a prograde MBHB embedded in a rotating environment starts moving on a nearly circular orbit about the centre of the system shortly after the MBHB binding. In our runs, the oscillation radius is ≈ 0.25 (≈ 0.1) times the binary influence radius for equal mass MBHBs (MBHBs with mass ratio 1:4). Conversely, retrograde binaries remain anchored about the centre of the host. The binary shrinking rate is twice as fast when the binary CoM exhibits a net orbital motion, owing to a more efficient loss cone repopulation even in our spherical stellar systems. We develop a model that captures the CoM oscillations of prograde binaries; we argue that the CoM angular momentum gain per time unit scales with the internal binary angular momentum, so that most of the displacement is induced by stellar interactions occurring around the time of MBHB binding, while the subsequent angular momentum enhancement gets eventually quashed by the effect of dynamical friction. The effect of the background rotation on the MBHB evolution may be relevant for LISA sources, that are expected to form in significantly rotating stellar systems.

First-order velocity memory effect from compact binary coalescing sources

It has long been known that gravitational waves from compact binary coalescing sources are responsible for a first-order displacement memory effect experienced by a pair of freely falling test masses. This constant displacement is sourced from the non-vanishing final gravitational-wave strain present in the wave's after-zone, often referred to as the non-linear memory effect, and is of the same order of magnitude as the strain from the outgoing quadrupole radiation. Hence, this prediction of general relativity is verifiable experimentally by measurement of the final relative separation between test masses that comprise gravitational-wave detectors. In a separate context, independent calculations have demonstrated that exact, sandwich, plane wave spacetimes exhibit a velocity memory effect: a non-zero relative velocity, gained by a pair of test masses in free fall, after the passage of a gravitational wave. In this paper, we find that in addition to the known constant displacement memory effect test masses experience, a velocity memory effect at leading order arises due to the non-linear nature of gravitational waves from compact binary sources. We discuss the magnitude of the first-order velocity memory effect in the context of observing gravitational-wave radiation from super massive binary black hole mergers in LISA.

The Competing Effect of Gas and Stars in the Evolution of Massive Black Hole Binaries

Abstract Massive black hole binaries are predicted to form during the hierarchical assembly of cosmic structures and will represent the loudest sources of low-frequency gravitational waves (GWs) detectable by present and forthcoming GW experiments. Before entering the GW-driven regime, their evolution is driven by the interaction with the surrounding stars and gas. While stellar interactions are found to always shrink the binary, recent studies predict the possibility of binary outspiral mediated by the presence of a gaseous disk, which could endlessly delay the coalescence and impact the merger rates of massive binaries. Here we implement a semianalytical treatment that follows the binary evolution under the combined effect of stars and gas. We find that binaries may outspiral only if they accrete near or above their Eddington limit and only until their separation reaches the gaseous disk self-gravitating radius. Even in case of an outspiral, the binary eventually reaches a large enough mass for GW to take over and drive it to coalescence. The combined action of stellar hardening, mass growth, and GW-driven inspiral brings binaries to coalescence in a few hundreds of megayears at most, implying that gas-driven expansion will not severely affect the detection prospects of upcoming GW facilities.

Effect of data gaps on the detectability and parameter estimation of massive black hole binaries with LISA

Massive black hole binaries are expected to provide the strongest gravitational wave signals for the Laser Interferometer Space Antenna (LISA), a space mission targeting $\ensuremath{\sim}\mathrm{mHz}$ frequencies. As a result of the technological challenges inherent in the mission's design, implementation, and long duration (4 yr nominal), the LISA data stream is expected to be affected by relatively long gaps where no data is collected (either because of hardware failures, or because of scheduled maintenance operations, such as repointing of the antennas toward the Earth). Depending on their mass, massive black hole binary signals may range from quasitransient to very long lived, and it is unclear how data gaps will impact detection and parameter estimation of these sources. Here, we will explore this question by using state-of-the-art astrophysical models for the population of massive black hole binaries. We will investigate the potential detectability of massive black hole binary signals by observing the effect of gaps on their signal-to-noise ratios. We will also assess the effect of the gaps on parameter estimation for these sources, using the Fisher information matrix formalism as well as full Bayesian analyses. Overall, we find that the effect of data gaps due to regular maintenance of the spacecraft is negligible, except for systems that coalesce within such a gap. The effect of unscheduled gaps, however, will probably be more significant than that of scheduled ones.

Circumbinary disc self-gravity governing supermassive black hole binary mergers

Abstract Understanding the interaction of massive black hole binaries with their gaseous environment is crucial since at sub-parsec scales the binary is too wide for gravitational wave emission to take over and to drive the two black holes to merge. We here investigate the interaction between a massive black hole binary and a self-gravitating circumbinary disc using 3D smoothed particle hydrodynamics simulations. We find that, when the disc self-gravity regulates the angular momentum transport, the binary semi-major axis decreases regardless the choice of disc masses and temperatures, within the range we explored. In particular, we find that the disc initial temperature (hence the disc aspect ratio) has little effect on the evolution of the binary since discs with the same mass self-regulate towards the same temperature. Initially warmer discs cause the binary to shrink on a slightly shorter timescale until the disc has reached the self-regulated equilibrium temperature. More massive discs drive the binary semi-major axis to decrease at a faster pace compared to less massive discs and result in faster binary eccentricity growth even after the initial-condition-dependent transient evolution. Finally we investigate the effect that the initial cavity size has on the binary-disc interaction and we find that, in the self-gravitating regime, an initially smaller cavity leads to a much faster binary shrinking, as expected. Our results are especially important for very massive black hole binaries such as those in the PTA band, for which gas self gravity cannot be neglected.

The Detectability of Kiloparsec-scale Dual Active Galactic Nuclei: The Impact of Galactic Structure and Black Hole Orbital Properties

Abstract Observational searches for dual active galactic nuclei (dAGNs) at kiloparsec separations are crucial for understanding the role of galaxy mergers in the evolution of galaxies. In addition, kiloparsec-scale dAGNs may serve as the parent population of merging massive black hole (MBH) binaries, an important source of gravitational waves. We use a semi-analytical model to describe the orbital evolution of unequal mass MBH pairs under the influence of stellar and gaseous dynamical friction in post-merger galaxies. We quantify how the detectability of approximately 40,000 kpc-scale dAGNs depends on the structure of their host galaxies and the orbital properties of the MBH pair. Our models indicate that kiloparsec-scale dAGNs are most likely to be detected in gas-rich post-merger galaxies with smaller stellar bulges and relatively massive, rapidly rotating gas disks. The detectability is also increased in systems with MBHs of comparable masses following low eccentricity prograde orbits. In contrast, dAGNs with retrograde, low eccentricity orbits are some of the least detectable systems among our models. The dAGNs in models in which the accreting MBHs are allowed to exhibit radiative feedback are characterized by a significantly lower overall detectability. The suppression in detectability is most pronounced in gas-rich merger remnant galaxies, where radiation feedback is more likely to arise. If so, then large, relatively gas-poor galaxies may be the best candidates for detecting dAGNs.

Estimate of the gravitational-wave background from the observed cosmological distribution of quasars

We study the gravitational-wave background from the observed cosmological quasar distribution. Using the DR9Q quasar catalogue from the ninth data release of the Sloan Digital Sky Survey (SDSS), we create a complete, statistically consistent sample of quasars from $z=0.3$ to $5.4$. Employing the spectroscopic information from the catalogue we estimate the masses of the supermassive black holes hosted by the quasars in the sample, resulting in a log-normal distribution of mean $10^{8.32\pm0.33}M_{\odot}$. The computation of the individual gravitational-wave strains relies on specific functional forms derived from simulations of gravitational collapse and mergers of massive black hole binaries. The background gravitational-wave emission is assembled by adding up the individual signals from each quasar modelled as plane waves whose interference can be constructive or destructive depending on the quasar evolutionary state. Our results indicate that the estimated gravitational-wave background discussed in this work could only be marginally detectable by LISA. This conclusion might change if more complete quasar catalogs than that provided by the SDSS were available.

Ultra-short-period massive black hole binary candidates in LSST as LISA ‘verification binaries’

ABSTRACT The Legacy Survey of Space and Time (LSST) by the Vera C. Rubin Observatory is expected to discover tens of millions of quasars. A significant fraction of these could be powered by coalescing massive black hole (MBH) binaries, since many quasars are believed to be triggered by mergers. We show that under plausible assumptions about the luminosity functions, lifetimes, and binary fractions of quasars, we expect the full LSST quasar catalogue to contain between 20 and 100 million compact MBH binaries with masses M = 105–9M⊙, redshifts z = 0–6, and orbital periods P = 1–70 d. Their light-curves are expected to be distinctly periodic, which can be confidently distinguished from stochastic red-noise variability, because LSST will cover dozens, or even hundreds of cycles. A very small subset of 10–150 ultracompact (P ≲ 1 d) binary quasars among these will, over ∼5–15 yr, evolve into the mHz gravitational-wave frequency band and can be detected by LISA. They can therefore be regarded as ‘LISA verification binaries’, analogous to short-period Galactic compact-object binaries. The practical question is how to find these handful of ‘needles in the haystack’ among the large number of quasars: this will likely require a tailored co-adding analysis optimized for this purpose.

GW190521 formation scenarios via relativistic accretion

The recent gravitational wave transient GW190521 has been interpreted by the LIGO-Virgo collaboration (LVC) as sourced by a binary black hole (BH) merger. According to the LVC parameter estimation, at least one of these progenitors falls into the so-called pair-instability supernova mass gap. This raises the important question of how and when these progenitors formed.In this paper we use an accretion model with super-Eddington mass accretion rate obtained from General Relativity hydrodynamics simulations to analyse the scenario wherein the GW190521 original progenitors (OPs) formed at lower masses (and spins) and grew to their estimated LVC parameters by relativistic accretion. We consider that the environment wherein the binary is immersed has density gradients as well as a dependence on the Mach number of the gas. Taking the LVC parameter estimation at z = 0.82 as the endpoint of the accretion evolution, we estimate the initial masses and spins of the OPs at three different red-shifts z = 100, 50, and 20. We found three distinct possible types of OPs: (i) 10-4 M ☉ - 3 M ☉ almost non-rotating (with Kerr spin parameter a ☆ < 10-2) primordial BHs; (ii) 3M ☉ - 40M ☉ slowly rotating (10-2 < a ☆ < 0.5) stellar mass BHs; (iii) 40M ☉ - 70M ☉ BHs with a moderate spin parameter a ☆ ∼ 0.5, which could originate from the collapse of high mass Pop III stars. The mass spread is due to varying the density gradient and the relativistic Mach number of the cosmic plasma; the variation of the masses due to the origin at different red-shifts, on the other hand, is negligible, ∼ 2%.For high Mach number scenarios, the BHs have low mass and spin accretion rates, leading to OPs with masses and spins close to the GW190521 LVC estimated values.We have also compared our results with previous studies where the Newtonian accretion model was used, finding relativistic corrections of ∼ 13% for the OPs masses. In particular, the relativistic model leads to smaller initial masses.

The Time Delay Distribution and Formation Metallicity of LIGO-Virgo’s Binary Black Holes

Abstract We derive the first constraints on the time delay distribution of binary black hole (BBH) mergers using the LIGO-Virgo Gravitational-Wave Transient Catalog. Assuming that the progenitor formation rate follows the star formation rate (SFR), the data favor that 43%–100% of mergers have delay times &lt;4.5 Gyr (90% credibility). Adopting a model for the metallicity evolution, we derive joint constraints for the metallicity-dependence of the BBH formation efficiency and the distribution of time delays between formation and merger. Short time delays are favored regardless of the assumed metallicity dependence, although the preference for short delays weakens as we consider stricter low-metallicity thresholds for BBH formation. For a p(τ) ∝ τ −1 time delay distribution and a progenitor formation rate that follows the SFR without metallicity dependence, we find that τ min &lt; 2.2 Gyr, whereas considering only the low-metallicity Z &lt; 0.3 Z ⊙ SFR, τ min &lt; 3.0 Gyr (90% credibility). Alternatively, if we assume long time delays, the progenitor formation rate must peak at higher redshifts than the SFR. For example, for a p(τ) ∝ τ −1 time delay distribution with τ min = 4 Gyr, the inferred progenitor rate peaks at z &gt; 3.9 (90% credibility). Finally, we explore whether the inferred formation rate and time delay distribution vary with BBH mass.

Unveiling the gravitational universe at \u03bc-Hz frequencies

We propose a space-based interferometer surveying the gravitational wave (GW) sky in the milli-Hz to μ-Hz frequency range. By the 2040s, the μ-Hz frequency band, bracketed in between the Laser Interferometer Space Antenna (LISA) and pulsar timing arrays, will constitute the largest gap in the coverage of the astrophysically relevant GW spectrum. Yet many outstanding questions related to astrophysics and cosmology are best answered by GW observations in this band. We show that a μ-Hz GW detector will be a truly overarching observatory for the scientific community at large, greatly extending the potential of LISA. Conceived to detect massive black hole binaries from their early inspiral with high signal-to-noise ratio, and low-frequency stellar binaries in the Galaxy, this instrument will be a cornerstone for multimessenger astronomy from the solar neighbourhood to the high-redshift Universe.

The Emergence of Structure in the Binary Black Hole Mass Distribution

Abstract We use the gravitational wave signals from binary black hole merger events observed by LIGO and Virgo to reconstruct the underlying mass and spin distributions of the population of merging black holes. We reconstruct the population using the mixture model framework VAMANA using observations in GWTC-2 occurring during the first two observing runs and the first half of the third run (O1, O2, and O3a). Our analysis identifies a structure in the chirp mass distribution of the observed population. Specifically, we identify peaks in the chirp mass distribution at 8, 14, 26, and 45 M ⊙ and a complementary structure in the component mass distribution with an excess of black holes at masses of 9, 16, 45, and 57 M ⊙. Intriguingly, for both the distributions, the location of subsequent peaks are separated by a factor of around two and there is a lack of mergers with chirp masses of 10–12 M ⊙. The appearance of multiple peaks is a feature of a hierarchical merger scenario when, due to a gap in the black hole mass spectrum, a pile-up occurs at the first peak followed by mergers of lower mass black holes to hierarchically produce higher mass black holes. However, cross-generation merger peaks and observations with high spins are also predicted to occur in such a scenario that we are not currently observing. The results presented are limited in measurement accuracy due to small numbers of observations but if corroborated by future gravitational wave observations these features have far-reaching implications.

Chemically homogeneous evolution: a rapid population synthesis approach

ABSTRACT We explore chemically homogeneous evolution (CHE) as a formation channel for massive merging binary black holes (BBHs). We develop methods to include CHE in a rapid binary population synthesis code, Compact Object Mergers: Population Astrophysics and Statistics (compas), which combines realistic models of binary evolution with cosmological models of the star formation history of the Universe. For the first time, we simultaneously explore conventional isolated binary star evolution under the same set of assumptions. This approach allows us to constrain population properties and make simultaneous predictions about the gravitational-wave detection rates of BBH mergers for the CHE and conventional formation channels. The overall mass distribution of detectable BBHs is consistent with existing gravitational-wave observations. We find that the CHE channel may yield up to ${\sim} 70{{\ \rm per\ cent}}$ of all gravitational-wave detections of BBH mergers coming from isolated binary evolution.

The missing link in gravitational-wave astronomy

Since 2015 the gravitational-wave observations of LIGO and Virgo have transformed our understanding of compact-object binaries. In the years to come, ground-based gravitational-wave observatories such as LIGO, Virgo, and their successors will increase in sensitivity, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will provide gravitational-wave observations of massive black holes binaries. Between the sim 10–103 Hz band of ground-based observatories and the sim 10^{-4}–10− 1 Hz band of LISA lies the uncharted decihertz gravitational-wave band. We propose a Decihertz Observatory to study this frequency range, and to complement observations made by other detectors. Decihertz observatories are well suited to observation of intermediate-mass (sim 10^{2}–104M⊙) black holes; they will be able to detect stellar-mass binaries days to years before they merge, providing early warning of nearby binary neutron star mergers and measurements of the eccentricity of binary black holes, and they will enable new tests of general relativity and the Standard Model of particle physics. Here we summarise how a Decihertz Observatory could provide unique insights into how black holes form and evolve across cosmic time, improve prospects for both multimessenger astronomy and multiband gravitational-wave astronomy, and enable new probes of gravity, particle physics and cosmology.

Testing the quasar Hubble diagram with LISA standard sirens

Quasars have recently been used as an absolute distance indicator, extending the Hubble diagram to high redshift to reveal a deviation from the expansion history predicted for the standard, $\Lambda$CDM cosmology. Here we show that the Laser Interferometer Space Antenna (LISA) will efficiently test this claim with standard sirens at high redshift, defined by the coincident gravitational wave (GW) and electromagnetic (EM) observations of the merger of massive black hole binaries (MBHBs). Assuming a fiducial $\Lambda$CDM cosmology for generating mock standard siren datasets, the evidence for the $\Lambda$CDM model with respect to an alternative model inferred from quasar data is investigated. By simulating many realizations of possible future LISA observations, we find that for $50\%$ of these realizations (median result) 4 MBHB standard siren measurements will suffice to strongly differentiate between the two models, while 14 standard sirens will yield a similar result in $95\%$ of the realizations. In addition, we investigate the measurement precision of cosmological parameters as a function of the number of observed LISA MBHB standard sirens, finding that 15 events will on average achieve a relative precision of 5\% for $H_0$, reducing to 3\% and 2\% with 25 and 40 events, respectively. Our investigation clearly highlights the potential of LISA as a cosmological probe able to accurately map the expansion of the universe at $z\gtrsim 2$, and as a tool to cross-check and cross-validate cosmological EM measurements with complementary GW observations.

Evidence for different gravitational-wave sources in the NANOGrav dataset

The NANOGrav Collaboration recently reported a strong evidence for a stochastic common-spectrum process in the pulsar-timing data. We evaluate the evidence of interpreting this process as mergers of super massive black hole binaries and/or various stochastic gravitational wave background sources in the early Universe, including first-order phase transitions, cosmic strings, domain walls, and large amplitude curvature perturbations. We discuss the implications of the constraints on these possible sources. It is found that the cosmic string is the most favored source against other gravitational wave sources based on the Bayes factor analysis.

Applying clock comparison methods to pulsar timing observations

ABSTRACT Frequency metrology outperforms any other branch of metrology in accuracy (parts in 10−16) and small fluctuations (&amp;lt;10−17). In turn, among celestial bodies, the rotation speed of millisecond pulsars is by far the most stable (&amp;lt;10−18). Therefore, the precise measurement of the time of arrival (TOA) of pulsar signals is expected to disclose information about cosmological phenomena, and to enlarge our astrophysical knowledge. Related to this topic, Pulsar Timing Array projects have been developed and operated for the last decades. The TOAs from a pulsar can be affected by local emission and environmental effects, in the direction of the propagation through the interstellar medium or universally by gravitational waves from super massive black hole binaries. These effects (signals) can manifest as a low-frequency fluctuation over time, phenomenologically similar to a red noise, while the remaining pulsar intrinsic and instrumental background (noise) are white. This article focuses on the frequency metrology of pulsars. From our standpoint, the pulsar is an accurate clock, to be measured simultaneously with several telescopes in order to reject the uncorrelated white noise. We apply the modern statistical methods of time-and-frequency metrology to simulated pulsar data, and we show the detection limit of the correlated red noise signal between telescopes.