Massive Black Hole Binaries Research Articles

The minimum measurable eccentricity from gravitational waves of LISA massive black hole binaries

ABSTRACT We explore the eccentricity measurement threshold of Laser Interferometer Space Antenna (LISA) for gravitational waves radiated by massive black hole binaries (MBHBs) with redshifted BH masses Mz in the range 104.5–107.5 M⊙ at redshift z = 1. The eccentricity can be an important tracer of the environment where MBHBs evolve to reach the merger phase. To consider LISA’s motion and apply the time delay interferometry, we employ the lisabeta software and produce year-long eccentric waveforms using the inspiral-only post-Newtonian model taylorf2ecc. We study the minimum measurable eccentricity (emin, defined one year before the merger) analytically by computing matches and Fisher matrices, and numerically via Bayesian inference by varying both intrinsic and extrinsic parameters. We find that emin strongly depends on Mz and weakly on mass ratio and extrinsic parameters. Match-based signal-to-noise ratio criterion suggest that LISA will be able to detect emin ∼ 10−2.5 for lighter systems (Mz ≲ 105.5 M⊙) and ∼10−1.5 for heavier MBHBs with a 90 per cent confidence. Bayesian inference with Fisher initialization and a zero noise realization pushes this limit to emin ∼ 10−2.75 for lower-mass binaries, assuming a <50 per cent relative error. Bayesian inference can recover injected eccentricities of 0.1 and 10−2.75 for a 105 M⊙ system with an ∼10−2 per cent and an ∼10 per cent relative errors, respectively. Stringent Bayesian odds criterion ($\ln {\mathcal {B}}\gt 8$) provides nearly the same inference. Both analytical and numerical methodologies provide almost consistent results for our systems of interest. LISA will launch in a decade, making this study valuable and timely for unlocking the mysteries of the MBHB evolution.

Evidence for a Correlation between Binary Black Hole Mass Ratio and Black Hole Spins

The astrophysical origins of the binary black hole systems seen with gravitational waves are still not well understood. However, features in the distribution of black hole masses, spins, redshifts, and eccentricities provide clues into how these systems form. Much has been learned by investigating these distributions one parameter at a time. However, we can extract additional information by studying the covariance between pairs of parameters. Previous work has shown preliminary support for an anticorrelation between mass ratio q ≡ m 2/m 1 and effective inspiral spin χ eff in the binary black hole population. In this study, we test for the existence of this anticorrelation using updated data from the third gravitational-wave transient catalog and improve our copula-based framework to employ a more robust model for black hole spins. We find evidence for an anticorrelation in (q, χ eff) with 99.7% credibility. This may imply high common-envelope efficiencies, stages of super-Eddington accretion, or a tendency for binary black hole systems to undergo mass-ratio reversal during isolated evolution. Covariance in (q, χ eff) may also be used to investigate the physics of tidal spinup as well as the properties of binary black hole–forming active galactic nuclei.

Supernova calibration by gravitational waves

Hubble tension is one of the most important problems in cosmology. Although the local measurements on the Hubble constant with Type Ia supernovae (SNe Ia) are independent of cosmological models, they suffer the problem of zero-point calibration of the luminosity distance. The observations of gravitational waves (GWs) with space-based GW detectors can measure the luminosity distance of the GW source with high precision. By assuming that massive binary black hole mergers and SNe Ia occur in the same host galaxy, we study the possibility of re-calibrating the luminosity distances of SNe Ia by GWs. Then we use low-redshift re-calibrated SNe Ia to determine the local Hubble constant. We find that we need at least 7 SNe Ia with their luminosity distances re-calibrated by GWs to reach a 2% precision of the local Hubble constant. The value of the local Hubble constant is free from the problems of zero-point calibration and model dependence, so the result can shed light on the Hubble tension.

Parameter estimation of stellar mass binary black holes in the network of TianQin and LISA

Parameter estimation of stellar mass binary black holes in the network of TianQin and LISA

Disappearing thermal X-ray emission as a tell-tale signature of merging massive black hole binaries

ABSTRACT The upcoming Laser Interferometer Space Antenna (LISA) is expected to detect gravitational waves (GWs) from massive black hole binaries (MBHB). Finding the electromagnetic (EM) counterparts for these GW events will be crucial for understanding how and where MBHBs merge, measuring their redshifts, constraining the Hubble constant and the graviton mass, and for other novel science applications. However, due to poor GW sky localization, multiwavelength, time-dependent EM models are needed to identify the right host galaxy. We studied merging MBHBs embedded in a circumbinary disc (CBD) using high-resolution two-dimensional simulations, with a Γ-law equation of state, incorporating viscous heating, shock heating, and radiative cooling. We simulate the binary from large separation until after merger, allowing us to model the decoupling of the binary from the CBD. We compute the EM signatures and identify distinct features before, during, and after the merger. Our main result is a multiband EM signature: we find that the MBHB produces strong thermal X-ray emission until 1–2 d prior to the merger. However, as the binary decouples from the CBD, the X-ray-bright minidiscs rapidly shrink in size, become disrupted, and the accretion rate drops precipitously. As a result, the thermal X-ray luminosity drops by orders of magnitude, and the source remains X-ray dark for several days, regardless of any post-merger effects such as GW recoil or mass-loss. Looking for the abrupt spectral change where the thermal X-ray disappears is a tell-tale EM signature of LISA mergers that does not require extensive pre-merger monitoring.

Things That Might Go Bump in the Night: Assessing Structure in the Binary Black Hole Mass Spectrum

Several features in the mass spectrum of merging binary black holes (BBHs) have been identified using data from the Third Gravitational Wave Transient Catalog (GWTC-3). These features are of particular interest as they may encode the uncertain mechanism of BBH formation. We assess if the features are statistically significant or the result of Poisson noise due to the finite number of observed events. We simulate catalogs of BBHs whose underlying distribution does not have the features of interest, apply the analysis previously performed on GWTC-3, and determine how often such features are spuriously found. We find that one of the features found in GWTC-3, the peak at ∼35 M ☉, cannot be explained by Poisson noise alone: peaks as significant occur in 1.7% of catalogs generated from a featureless population. This peak is therefore likely to be of astrophysical origin. The data is suggestive of an additional significant peak at ∼10 M ☉, though the exact location of this feature is not resolvable with current observations. Additional structure beyond a power law, such as the purported dip at ∼14 M ☉, can be explained by Poisson noise. We also provide a publicly available package, GWMockCat, that creates simulated catalogs of BBH events with correlated measurement uncertainty and selection effects according to user-specified underlying distributions and detector sensitivities.

GRMHD study of accreting massive black hole binaries in astrophysical environment: A review

We present an overview of recent numerical advances in the theoretical characterization of massive binary black hole (MBBH) mergers in astrophysical environments. These systems are among the loudest sources of gravitational waves (GWs) in the universe and particularly promising candidates for multimessenger astronomy. Coincident detection of GWs and electromagnetic (EM) signals from merging MBBHs is at the frontier of contemporary astrophysics. One major challenge in observational efforts searching for these systems is the scarcity of strong predictions for EM signals arising before, during, and after merger. Therefore, a great effort in theoretical work to-date has been to characterize EM counterparts emerging from MBBHs concurrently to the GW signal, aiming to determine distinctive observational features that will guide and assist EM observations. To produce sharp EM predictions of MBBH mergers it is key to model the binary inspiral down to coalescence in a full general relativistic fashion by solving Einstein’s field equations coupled with the magnetohydrodynamics equations that govern the evolution of the accreting plasma in strong-gravity. We review the general relativistic numerical investigations that have explored the astrophysical manifestations of MBBH mergers in different environments and focused on predicting potentially observable smoking-gun EM signatures that accompany the gravitational signal.

Properties and merger signatures of galaxies hosting LISA coalescing massive black hole binaries

The gravitational wave (GW) antenna LISA will detect the signal from coalescing massive black hole binaries (MBHBs) of 104 − 107 M⊙, providing clues as to their formation and growth throughout cosmic history. Some of these events will be localised with a precision of several to less than a deg2, enabling the possible identification of their host galaxy. This work explores the properties of the host galaxies of LISA MBHBs below z ≲ 3. We generate a simulated lightcone using the semi-analytical model L-Galaxies applied to the merger trees of the high-resolution N-body cosmological simulation Millennium-II. The model shows that LISA MBHBs are expected to be found in optically dim (r > 20), star-forming (sSFR > 10−10 yr−1), gas-rich (fgas > 0.6), and disc-dominated (B/T < 0.7) low-mass galaxies of stellar masses 108 − 109 M⊙. However, these properties are indistinguishable from those of galaxies harbouring single massive black holes of comparable mass, making it difficult to select LISA hosts among the whole population of low-mass galaxies. Motivated by this, we explore the possibility of using merger signatures to select LISA hosts. We find that 40%−80% of the galaxies housing LISA MBHBs display merger features related to the interaction that brought the secondary MBH to the galaxy. Despite this, around 60% of dwarf galaxies placed in the surroundings of the LISA hosts will show these kinds of features as well, challenging the unequivocal detection of LISA hosts through the search for merger signatures. Consequently, the detection of an electromagnetic transient associated with the MBHB merger will be vital in order to pinpoint the star-forming dwarf galaxy where these binary systems evolve and coalesce.

Implications of pulsar timing array observations for LISA detections of massive black hole binaries

ABSTRACT Pulsar timing arrays (PTAs) and the Laser Interferometer Space Antenna (LISA) will open complementary observational windows on massive black hole binaries (MBHBs), i.e. with masses in the range ${\sim} 10^6\!-\!10^{10}\, \rm M_{\odot }$. While PTAs may detect a stochastic gravitational wave background from a population of MBHBs, during operation LISA will detect individual merging MBHBs. To demonstrate the profound interplay between LISA and PTAs, we estimate the number of MBHB mergers that one can expect to observe with LISA by extrapolating direct observational constraints on the MBHB merger rate inferred from PTA data. For this, we postulate that the common signal observed by PTAs (and consistent with the increased evidence recently reported) is an astrophysical background sourced by a single MBHB population. We then constrain the LISA detection rate, $\mathcal {R}$, in the mass–redshift space by combining our Bayesian-inferred merger rate with LISA’s sensitivity to spin-aligned, inspiral–merger–ringdown waveforms. Using an astrophysically informed formation model, we predict a $95{{\, \rm per\, cent}}$ upper limit on the detection rate of $\mathcal {R} \lt 134\, {\rm yr}^{-1}$ for binaries with total masses in the range $10^7\!-\!10^8\, \rm M_{\odot }$. For higher masses, i.e. ${\gt} 10^8\, \rm M_{\odot }$, we find $\mathcal {R} \lt 2\, (1)\, \mathrm{yr}^{-1}$ using an astrophysically informed (agnostic) formation model, rising to $11 \, (6)\, \mathrm{yr}^{-1}$ if the LISA sensitivity bandwidth extends down to 10−5 Hz. Forecasts of LISA science potential with PTA background measurements should improve as PTAs continue their search.

Massive binary black holes from Population II and III stars

ABSTRACT Population III stars, born from the primordial gas in the Universe, lose a negligible fraction of their mass via stellar winds and possibly follow a top-heavy mass function. Hence, they have often been regarded as the ideal progenitors of massive black holes (BHs), even above the pair instability mass gap. Here, we evolve a large set of Population III binary stars (metallicity Z = 10−11) with our population-synthesis code sevn, and compare them with Population II binary stars (Z = 10−4). In our models, the lower edge of the pair-instability mass gap corresponds to a BH mass of ≈86 (≈91) M⊙ for single Population III (II) stars. Overall, we find only mild differences between the properties of binary BHs (BBHs) born from Population III and II stars, especially if we adopt the same initial mass function and initial orbital properties. Most BBH mergers born from Population III and II stars have primary BH mass below the pair-instability gap, and the maximum secondary BH mass is <50 M⊙. Only up to ≈3.3 per cent (≈0.09 per cent) BBH mergers from Population III (II) progenitors have primary mass above the gap. Unlike metal-rich binary stars, the main formation channel of BBH mergers from Population III and II stars involves only stable mass transfer episodes in our fiducial model.

The role of stellar expansion on the formation of gravitational wave sources

ABSTRACT Massive stars are the progenitors of black holes and neutron stars, the mergers of which can be detected with gravitational waves (GW). The expansion of massive stars is one of the key factors affecting their evolution in close binary systems, but it remains subject to large uncertainties in stellar astrophysics. For population studies and predictions of GW sources, the stellar expansion is often simulated with the analytic formulae from Hurley et al. (2000). These formulae need to be extrapolated and are often considered outdated. In this work, we present five different prescriptions developed from 1D stellar models to constrain the maximum expansion of massive stars. We adopt these prescriptions to investigate how stellar expansion affects mass transfer interactions and in turn the formation of GW sources. We show that limiting radial expansion with updated 1D stellar models, when compared to the use of Hurley et al. (2000) radial expansion formulae, does not significantly affect GW source properties (rates and masses). This is because most mass transfer events leading to GW sources are initialized in our models before the donor star reaches its maximum expansion. The only significant difference was found for the mass distribution of massive binary black hole mergers (Mtot > 50 M⊙) formed from stars that may evolve beyond the Humphreys–Davidson limit, whose radial expansion is the most uncertain. We conclude that understanding the expansion of massive stars and the origin of the Humphrey–Davidson limit is a key factor for the study of GW sources.

Failed supernovae as a natural explanation for the binary black hole mass distribution

Context. As the number of detected gravitational wave sources increases, the better we can understand the mass distribution of binary black holes (BBHs). This “stellar graveyard” shows several features, including an apparent mass gap that makes the distribution bimodal. In turn, the observed chirp mass distribution appears to be trimodal. Aims. We aim to investigate the extent to which we can explain the observed mass distribution based on stellar evolution, specifically with the hypothesis that the mass gap is caused by the difference between successful and failed supernovae (SNe). Methods. We posed a hypothetical remnant function, based on the literature of stellar evolution simulations, which relates initial mass to remnant mass, while including a “black hole island” and producing a bimodal remnant distribution. Moreover, we looked at observed type II SN rates in an attempt to detect the effect of failed SNe. Finally, using a simplified estimation of binary evolution, we determined the remnant distribution resulting from our remnant function and compared it with observations. Results. We find that failed SNe lower type II SN rates by approximately 25%, but the inferred rate from SN surveys is not accurate enough to confirm this. Furthermore, our estimation based on the remnant function produces a mass distribution that matches the general shape of the observed distributions of individual as well as chirp masses. Conclusions. Based on our research, we conclude that the failed SN mechanism and the presence of the black hole island are a natural hypothesis for explaining the individual BBH mass distribution and chirp mass distribution. However, to obtain a firmer conclusion, more detailed simulations are needed.

Constraints on the Galactic centre environment from Gaia hypervelocity stars III: insights on a possible companion to Sgr A*

ABSTRACT We consider a scenario in which Sgr A* is in a massive black hole binary (MBHB) with an as-of-yet undetected supermassive or intermediate-mass black hole companion. Dynamical encounters between this MBHB and single stars in its immediate vicinity would eject hypervelocity stars (HVSs) with velocities beyond the Galactic escape velocity of the Galaxy. In this work, we use existing HVS observations to constrain for the first time the existence of a companion to Sgr A*. We simulate the ejection of HVSs via the ‘MBHB slingshot’ scenario and show that the population of HVSs detectable today depends strongly on the companion mass and the separation of the MBHB. We demonstrate that the lack of uncontroversial HVS candidates in Gaia Data Release 3 places a firm upper limit on the mass of a possible Sgr A* companion. Within one milliparsec of Sgr A*, our results exclude a companion more massive than $2000 \, \mathrm{M_\odot }$. If Sgr A* recently merged with a companion black hole, our findings indicate that unless this companion was less massive than $500 \, \mathrm{M_\odot }$, this merger must have occurred at least 10 Myr ago. These results complement and improve upon existing independent constraints on a companion to Sgr A* and show that large regions of its parameter space can now be ruled out.

LitePIG: a lite parameter inference system for the gravitational wave in the millihertz band

We present a Python based parameter inference system for the gravitational wave (GW) measured in the millihertz band. This system includes the following features: the GW waveform originated from the massive black hole binaries (MBHB), the stationary instrumental Gaussian noise, the higher-order harmonic modes, the full response function from the time delay interferometry and the Gaussian likelihood function with the dynamic nested parameter sampler. In particular, we highlight the role of higher-order modes. By including these modes, the luminosity distance estimation precision can be improved roughly by a factor of 50, compared with the case with only the leading order (ℓ = 2, ∣m∣ = 2) mode. This is due to the response functions of different harmonic modes on the inclination angle are different. Hence, it can help to break the distance-inclination degeneracy. Furthermore, we show the robustness of testing general relativity (GR) by using higher-order harmonics. Our results show that the GW from MBHB can simultaneously constrain four of the higher harmonic amplitudes (deviation from GR) with 95% confidence level of , , and , respectively.

Binary black hole mergers from population III stars: uncertainties from star formation and binary star properties

ABSTRACT Population III (Pop. III) binary stars likely produced the first stellar-born binary black hole (BBH) mergers in the Universe. Here, we quantify the main sources of uncertainty for the merger rate density evolution and mass spectrum of Pop. III BBHs by considering four different formation histories and 11 models of the initial orbital properties of Pop. III binary stars. The uncertainty on the orbital properties affects the BBH merger rate density by up to two orders of magnitude, models with shorter orbital periods leading to higher BBH merger rates. The uncertainty on the star formation history has a substantial impact on both the shape and the normalization of the BBH merger rate density: the peak of the merger rate density shifts from z ∼ 8 up to z ∼ 16 depending on the assumed star formation rate, while the maximum BBH merger rate density for our fiducial binary population model spans from ∼2 to ∼30 Gpc−3 yr−1. The typical BBH masses are not affected by the star formation rate model and only mildly influenced by the binary population parameters. The primary black holes born from Pop. III stars tend to be rather massive (30–40 M⊙) with respect to those born from metal-rich stars (8–10 M⊙). We estimate that the Einstein Telescope will detect 10–104 Pop. III BBH mergers per year, depending on the star formation history and binary star properties.

Circumbinary Accretion: From Binary Stars to Massive Binary Black Holes

We review recent works on the dynamics of circumbinary accretion, including time variability, angular momentum transfer between the disk and the binary, and the secular evolution of accreting binaries. These dynamics impact stellar binary formation/evolution, circumbinary planet formation/migration, and the evolution of (super)massive black hole binaries. We discuss the dynamics and evolution of inclined/warped circumbinary disks and connect with observations of protoplanetary disks. A special kind of circumbinary accretion involves binaries embedded in big disks, which may contribute to the mergers of stellar-mass black holes in AGN disks. Highlights include the following: ▪Circumbinary accretion is highly variable, being modulated at P b (the binary period) or ∼5P b, depending on the binary eccentricity e b and mass ratio q b.▪The inner region of the circumbinary disk can develop coherent eccentric structure, which may modulate the accretion and affect the physical processes (e.g., planet migration) taking place in the disk.▪Over long timescales, circumbinary accretion steers binaries toward equal masses, and it does not always lead to binary orbital decay. The secular orbital evolution depends on the binary parameters (e b and q b) and on the thermodynamic properties of the accreting gas.▪A misaligned disk around a low-eccentricity binary tends to evolve toward coplanarity due to viscous dissipation. But when e b is significant, the disk can evolve toward “polar alignment,” with the disk plane perpendicular to the binary plane.

On the formation of GW190521-like binary black hole merger systems

ABSTRACT GW190521 is the most massive merging binary black hole (BBH) system detected so far. At least one of the component BHs was measured to lie within the pair-instability supernova (PISN) mass gap (∼50–135 M⊙), making its formation a mystery. However, the transient observed signal allows alternative posterior distributions. There was suggestion that GW190521 could be an intermediate-mass ratio inspiral, with the component masses m1 ∼ 170 M⊙ and m2 ∼ 16 M⊙, happening to straddle the PISN mass gap. Under this framework, we perform binary population synthesis to explore the formation of GW190521-like systems via isolated binary evolution. We numerically calculate the binding energy parameter for massive stars at different metallicities, and employ them in our calculation for common envelope evolution. Our results prefer that the progenitor binaries formed in metal-poor environment with $\rm Z\le 0.0016$. The predicted merger rate density within redshift z = 1.1 is ${\sim} 4\times 10^{-5}{\text {--}}5\times 10^{-2} \, \rm Gpc^{-3}yr^{-1}$. We expect that such events are potentially observable by upcoming both space and ground-based gravitational wave detectors.

Can gravitational-wave memory help constrain binary black-hole parameters? A LISA case study

Besides the transient effect, the passage of a gravitational wave also causes a persistent displacement in the relative position of an interferometer's test masses through the nonlinear memory effect. This effect is generated by the gravitational backreaction of the waves themselves, and encodes additional information about the source. In this work, we explore the implications of using this information for the parameter estimation of massive binary black holes with LISA. Based on a Fisher analysis for nonprecessing black hole binaries, our results show that the memory can help to reduce the degeneracy between the luminosity distance and the inclination for binaries observed only for a short time ($\ensuremath{\sim}\mathrm{few}\text{ }\mathrm{hours}$) before merger. To assess how many such short signals will be detected, we utilized state-of-the-art predictions for the population of massive black hole binaries and models for the gaps expected in the LISA data. We forecast from tens to few hundreds of binaries with observable memory, but only $\ensuremath{\sim}\mathcal{O}(0.1)$ events in 4 years for which the memory helps to reduce the degeneracy between distance and inclination. Based on this, we conclude that the new information from the nonlinear memory, while promising for testing general relativity in the strong field regime, has probably a limited impact on further constraining the uncertainty on massive black hole binary parameters with LISA.

Post-Keplerian waveform model for binary compact object as sources of space-based gravitational wave detector and its implications

Binary compact objects will be among the important sources for the future space-based gravitational wave detectors. Such binary compact objects include stellar massive binary black hole, binary neutron star, binary white dwarf and mixture of these compact objects. Regarding to the relatively low frequency, the gravitational interaction between the two objects of the binary is weak. Post-Newtonian approximation of general relativity is valid. Previous works about the waveform model for such binaries in the literature consider the dynamics for specific situations which involve detailed complicated matter dynamics between the two objects. We here take a different idea. We adopt the trick used in pulsar timing detection. For any gravity theories and any detailed complicated matter dynamics, the motion of the binary can always be described as a post-Keplerian expansion. And a post-Keplerian gravitational waveform model will be reduced. Instead of object masses, spins, matter’s equation of state parameters and dynamical parameters beyond general relativity, the involved parameters in our post-Keplerian waveform model are the Keplerian orbit elements and their adiabatic variations. Respect to current planning space-based gravitational wave detectors including LISA, Taiji and Tianqin, we find that the involved waveform model parameters can be well determined. And consequently the detail matter dynamics of the binary can be studied then. For binary with purely gravitational interactions, gravity theory can be constrained well.

Probing z ≳ six massive black holes with gravitational waves

ABSTRACT We investigate the coalescence of massive black hole ($M_{\rm BH}\gtrsim 10^{6}~\rm {\rm M}_{\odot }$) binaries (MBHBs) at 6 < z < 10 by adopting a suite of cosmological hydrodynamical simulations of galaxy formation, zoomed-in on biased (>3σ) overdense regions (Mh ∼ 1012 M⊙ dark matter haloes at z = 6) of the Universe. We first analyse the impact of different resolutions and AGN feedback prescriptions on the merger rate, assuming instantaneous mergers. Then, we compute the halo bias correction factor due to the overdense simulated region. Our simulations predict merger rates that range between 3 and 15 $\rm yr^{-1}$ at z ∼6, depending on the run considered, and after correcting for a bias factor of ∼20−30. For our fiducial model, we further consider the effect of delay in the MBHB coalescence due to dynamical friction. We find that 83 per cent of MBHBs will merge within the Hubble time, and 21 per cent within 1 Gyr, namely the age of the Universe at z > 6. We finally compute the expected properties of the gravitational wave (GW) signals and find the fraction of LISA detectable events with high signal-to-noise ratio (SNR > 5) to range between 66 per cent and 69 per cent. However, identifying the electro-magnetic counterpart of these events remains challenging due to the poor LISA sky localization that, for the loudest signals ($\mathcal {M}_c\sim 10^6~{{\rm M}_{\odot }}$ at z = 6), is around 10 $\rm deg^2$.