Supermassive Black Hole Binary Mergers Research Articles

Mass-redshift dependency of supermassive black hole binaries for the gravitational wave background

ABSTRACT Studying how the black hole (BH)–(galaxy) bulge mass relation evolves with redshift provides valuable insights into the co-evolution of supermassive black holes and their host galaxies. However, obtaining accurate measurement of BH masses is challenging due to the bias towards the most massive and luminous galaxies. Instead, we focus on the BH and bulge masses as they vary with redshift using the EAGLE, Illustris, TNG100, TNG300, Horizon-AGN, and SIMBA large-scale cosmological simulations. We use an analytical astrophysical model with galaxy stellar mass function, pair fraction, merger time-scale and BH–bulge mass relation extended to include redshift evolution. The model can predict the intensity of the gravitational wave background (GWB) produced by a population of supermassive black hole binary (SMBHB) as a function of the frequency. This allows us to compare the predictions of this model with the constraints of pulsar timing array observations. Here, we employ Bayesian analysis for the parameter inference. We find that all six simulations are consistent $\le 3.5\sigma$ with a range of simulated GWB spectra. By fixing the BH–bulge mass parameters to the simulations we analyse the changes in the constraints on the other astrophysical parameters. Furthermore, we also examine the variation in SMBHB merger rate with mass and redshift between these large-scale simulations.

Probing the delay time of supermassive black hole binary mergers with gravitational waves

ABSTRACT Merging supermassive black hole binaries are expected as a consequence of galaxy mergers, yet the detailed evolution path and underlying merging mechanisms of these binaries are still subject to large theoretical uncertainties. In this work, we propose to combine the (future) gravitational wave measurements of supermassive black hole binary merger events with the galaxy merger rate distributions from galaxy surveys/cosmological simulations, to infer the delay time of binary mergers, as a function of binary mass. The delay time encodes key information about binary evolution, which can be used to test the predictions of various evolution models. With a Mock data set of supermassive black hole binary merger events, we discuss how to infer the distribution of delay time with hierarchical Bayesian inference and test evolution models with the Bayesian model selection method. The astrophysical model uncertainties are also considered in the hierarchical Bayesian inference and Bayesian model selection.

X-ray view of a merging supermassive black hole binary candidate SDSS J1430+2303: Results from the first ∼200 days of observations

Context. Recently we discovered an unprecedented supermassive black hole binary (SMBHB) candidate in the nearby Seyfert galaxy SDSS J1430+2303, which is predicted to merge within three years. X-ray spectroscopy may bring unique kinematic evidence for the last inspiraling stage, when the binary is too close to allow each of them to hold an individual broad line region. Aims. We try to confirm the unique SMBHB merger event and understand the associated high-energy processes from a comprehensive X-ray view. Methods. We observed SDSS J1430+2303 with XMM-Newton, NuSTAR, Chandra, and Swift spanning the first ∼200 days since its discovery. Results. X-ray variability, up to a factor of 7, has been detected on a timescale of a few days. The broadband spectrum from 0.2–70 keV can be well fitted with a model consisting of a power law and a relativistic reflection covered by a warm absorber. The properties of the warm absorber changed dramatically, for example, with a decrease in the line-of-sight velocity from ∼0.2c to ∼0.02c, between the two XMM-Newton observations separated by only 19 days, which can be naturally understood in the context of the SMBHB; although, the clumpy wind scenario cannot be completely excluded. Broad Fe Kα emission has been robustly detected, though its velocity shift or profile change is not yet measurable. Further longer X-ray observations are highly encouraged to detect the expected orbital motion of the binary.

The Gravitational Wave Universe Toolbox

Context.As the importance of gravitational wave (GW) astrophysics increases rapidly, astronomers interested in GWs who are not experts in this field sometimes need to get a quick idea of what GW sources can be detected by certain detectors, and the accuracy of the measured parameters.Aims.The GW-Toolbox is a set of easy-to-use, flexible tools to simulate observations of the GW universe with different detectors, including ground-based interferometers (advanced LIGO, advanced VIRGO, KAGRA, Einstein Telescope, Cosmic Explorer, and also customised interferometers), space-borne interferometers (LISA and a customised design), and pulsar timing arrays mimicking the current working arrays (EPTA, PPTA, NANOGrav, IPTA) and future ones. We include a broad range of sources, such as mergers of stellar-mass compact objects, namely black holes, neutron stars, and black hole–neutron star binaries, supermassive black hole binary mergers and inspirals, Galactic double white dwarfs in ultra-compact orbit, extreme-mass-ratio inspirals, and stochastic GW backgrounds.Methods.We collected methods to simulate source populations and determine their detectability with various detectors. Our aim is to provide a comprehensive description of the methodology and functionality of the GW-Toolbox.Results.The GW-Toolbox produces results that are consistent with previous findings in the literature, and the tools can be accessed via a website interface or as a Python package. In the future, this package will be upgraded with more functions.

An estimate of the stochastic gravitational wave background from the MassiveBlackII simulation

ABSTRACT A population of supermassive black hole (SMBH) binaries is expected to generate a stochastic gravitational wave background (SGWB) in the pulsar timing array (PTA) frequency range of 10−9 to $10^{-7}\, {\rm Hz}$. Detection of this signal is a current observational goal and so predictions of its characteristics are of significant interest. In this work, we use SMBH binary mergers from the MassiveBlackII simulation to estimate the characteristic strain of the stochastic background. We examine both a gravitational wave (GW) driven model of binary evolution and a model which also includes the effects of stellar scattering and a circumbinary gas disc. Results are consistent with PTA upper limits and similar to estimates in the literature. The characteristic strain at a reference frequency of $1\, {\rm yr}^{-1}$ is found to be $A_{\rm {yr}^{-1}}= 6.9 \times 10^{-16}$ and $A_{\rm {yr}^{-1}}= 6.4 \times 10^{-16}$ in the GW-driven and stellar scattering/gas disc cases, respectively. Using the latter approach, our models show that the SGWB is mildly suppressed compared to the purely GW-driven model as frequency decreases inside the PTA frequency band.

Discovering new forces with gravitational waves from supermassive black holes

Supermassive black hole binary mergers generate a stochastic gravitational wave background detectable by pulsar timing arrays. While the amplitude of this background is subject to significant uncertainties, the frequency dependence is a robust prediction of general relativity. We show that the effects of new forces beyond the Standard Model can modify this prediction and introduce unique features into the spectral shape. In particular, we consider the possibility that black holes in binaries are charged under a new long-range force, and we find that pulsar timing arrays are capable of robustly detecting such forces. Supermassive black holes and their environments can acquire charge due to high-energy particle production or dark sector interactions, making the measurement of the spectral shape a powerful test of fundamental physics.

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.

Prospects of probing dark energy with eLISA: Standard versus null diagnostics

ABSTRACT Gravitational waves from supermassive black hole binary mergers along with an electromagnetic counterpart have the potential to shed ‘light’ on the nature of dark energy in the intermediate redshift regime. Accurate measurement of dark energy parameters at intermediate redshift is extremely essential to improve our understanding of dark energy, and to possibly resolve a couple of tensions involving cosmological parameters. We present a Fisher matrix forecast analysis in the context of eLISA to predict the errors for three different cases: the non-interacting dark energy with constant and evolving equation of state (EoS), and the interacting dark sectors with a generalized parametrization. In all three cases, we perform the analysis for two separate formalisms, namely, the standard EoS formalism and the Om parametrization which is a model-independent null diagnostic for a wide range of fiducial values in both phantom and non-phantom regions, to make a comparative analysis between the prospects of these two diagnostics in eLISA. Our analysis reveals that it is wiser and more effective to probe the null diagnostic instead of the standard EoS parameters for any possible signature of dark energy at intermediate redshift measurements like eLISA.

Constraining astrophysical observables of galaxy and supermassive black hole binary mergers using pulsar timing arrays

ABSTRACT We present an analytic model to describe the supermassive black hole binary (SMBHB) merger rate in the Universe with astrophysical observables: galaxy stellar mass function, pair fraction, merger time-scale, and black hole–host galaxy relations. We construct observational priors and compute the allowed range of the characteristic spectrum hc of the gravitational wave background (GWB) to be 10−16 < hc < 10−15 at a frequency of f = 1 yr−1. We exploit our parametrization to tackle the problem of astrophysical inference from pulsar timing array (PTA) observations. We simulate a series of upper limits and detections and use a nested sampling algorithm to explore the parameter space. Corroborating previous results, we find that the current PTA non-detection does not place significant constraints on any observables; however, either future upper limits or detections will significantly enhance our knowledge of the SMBHB population. If a GWB is not detected at a level of hc(f = 1 yr−1) = 10−17, our current understanding of galaxy and SMBHB mergers is disfavoured at a 5σ level, indicating a combination of severe binary stalling, overestimating of the SMBH–host galaxy relations, and extreme dynamical properties of merging SMBHBs. Conversely, future detections of a Square Kilometre Array (SKA)-type instrument will allow to constrain the normalization of the SMBHB merger rate in the Universe, the time between galaxy pairing and SMBHB merging, the normalization of the SMBH–host galaxy relations and the dynamical binary properties, including their eccentricity and density of stellar environment.

Testing the Binary Hypothesis: Pulsar Timing Constraints on Supermassive Black Hole Binary Candidates

Abstract The advent of time domain astronomy is revolutionizing our understanding of the universe. Programs such as the Catalina Real-time Transient Survey (CRTS) or the Palomar Transient Factory (PTF) surveyed millions of objects for several years, allowing variability studies on large statistical samples. The inspection of ≈250 k quasars in CRTS resulted in a catalog of 111 potentially periodic sources, put forward as supermassive black hole binary (SMBHB) candidates. A similar investigation on PTF data yielded 33 candidates from a sample of ≈35 k quasars. Working under the SMBHB hypothesis, we compute the implied SMBHB merger rate and we use it to construct the expected gravitational wave background (GWB) at nano-Hz frequencies, probed by pulsar timing arrays (PTAs). After correcting for incompleteness and assuming virial mass estimates, we find that the GWB implied by the CRTS sample exceeds the current most stringent PTA upper limits by almost an order of magnitude. After further correcting for the implicit bias in virial mass measurements, the implied GWB drops significantly but is still in tension with the most stringent PTA upper limits. Similar results hold for the PTF sample. Bayesian model selection shows that the null hypothesis (whereby the candidates are false positives) is preferred over the binary hypothesis at about 2.3σ and 3.6σ for the CRTS and PTF samples respectively. Although not decisive, our analysis highlights the potential of PTAs as astrophysical probes of individual SMBHB candidates and indicates that the CRTS and PTF samples are likely contaminated by several false positives.

ARE WE THERE YET? TIME TO DETECTION OF NANOHERTZ GRAVITATIONAL WAVES BASED ON PULSAR-TIMING ARRAY LIMITS

ABSTRACT Decade-long timing observations of arrays of millisecond pulsars have placed highly constraining upper limits on the amplitude of the nanohertz gravitational-wave stochastic signal from the mergers of supermassive black hole binaries (∼10−15 strain at f = 1 yr−1). These limits suggest that binary merger rates have been overestimated, or that environmental influences from nuclear gas or stars accelerate orbital decay, reducing the gravitational-wave signal at the lowest, most sensitive frequencies. This prompts the question whether nanohertz gravitational waves (GWs) are likely to be detected in the near future. In this Letter, we answer this question quantitatively using simple statistical estimates, deriving the range of true signal amplitudes that are compatible with current upper limits, and computing expected detection probabilities as a function of observation time. We conclude that small arrays consisting of the pulsars with the least timing noise, which yield the tightest upper limits, have discouraging prospects of making a detection in the next two decades. By contrast, we find large arrays are crucial to detection because the quadrupolar spatial correlations induced by GWs can be well sampled by many pulsar pairs. Indeed, timing programs that monitor a large and expanding set of pulsars have an ∼80% probability of detecting GWs within the next 10 years, under assumptions on merger rates and environmental influences ranging from optimistic to conservative. Even in the extreme case where 90% of binaries stall before merger and environmental coupling effects diminish low-frequency gravitational-wave power, detection is delayed by at most a few years.

ASSESSING PULSAR TIMING ARRAY SENSITIVITY TO GRAVITATIONAL WAVE BURSTS WITH MEMORY

Highly energetic astrophysical phenomena like supermassive black hole binary (SMBHB) mergers are predicted to emit prodigious amounts of gravitational waves (GWs). An anticipated component of the gravitational waveform known as "memory" is permanent and non-oscillatory. For SMBHB mergers, the memory is created primarily during the most violent moments of the inspiral immediately preceding the final plunge and ring-down when the strongest gravitational fields are at work and the non-linearities of general relativity are most pronounced. The essentially time-domain nature of memory makes it forbiddingly difficult to detect with ground based GW detectors, leaving pulsar timing array (PTA) experiments as the most promising means by which it may be detected and studied. In this paper, we discuss how GW bursts with memory (BWMs) influence pulsar timing experiments and develop methods to assess how sensitive modern timing efforts are to such GW events. We discuss how PTA searches for BWMs can be used to constrain the rate of BWMs and how these constraints relate to information regarding the population of SMBHBs.

WITNESSING THE BIRTH OF A QUASAR

The coalescence of a supermassive black hole binary (SMBHB) is thought to be accompanied by an electromagnetic (EM) afterglow, produced by the viscous infall of the surrounding circumbinary gas disk after the merger. It has been proposed that once the merger has been detected in gravitational waves (GWs) by LISA, follow-up EM searches for this afterglow can help identify the EM counterpart of the LISA source. Here we study whether the afterglows may be sufficiently bright and numerous to be detectable in EM surveys alone. The viscous afterglow, which lasts for years to decades for SMBHBs in LISA's sensitivity window, is characterized by rapid increases in both the bolometric luminosity and in the spectral hardness of the source. If quasar activity is triggered by the same major galaxy mergers that produce SMBHBs, then the afterglow could be interpreted as a signature of the birth of a quasar. Using an idealized model for the post-merger viscous spreading of the circumbinary disk and the resulting light curve, and using the observed luminosity function of quasars as a proxy for the SMBHB merger rate, we delineate the survey requirements for identifying such birthing quasars. If circumbinary disks have a high disk surface density and viscosity, an all-sky soft X-ray survey with a sensitivity of ~<3x10^-14 erg s^-1 cm^-2 and a time resolution of ~months could identify dozens of birthing quasars with sustained brightening rates of >10%/yr. If >1% of the X-ray emission is reprocessed into optical frequencies, birthing quasars could also be identified in optical transient surveys such as the LSST. Distinguishing a birthing quasar from other variable sources may be facilitated by the monotonic hardening of its spectrum, but will likely remain challenging. This reinforces the notion that joint EM-plus-GW observations offer the best prospects for identifying the EM signatures of SMBHB mergers.

Massive black hole binary mergers within subparsec scale gas discs

We study the efficiency and dynamics of supermassive black hole binary mergers driven by angular momentum loss to small-scale gas discs. Such binaries form after major galaxy mergers, but their fate is unclear since hardening through stellar scattering becomes very inefficient at sub-parsec distances. Gas discs may dominate binary dynamics on these scales, and promote mergers. Using numerical simulations, we investigate the evolution of the semi-major axis and eccentricity of binaries embedded within geometrically thin gas discs. Our simulations directly resolve angular momentum transport within the disc, which at the radii of interest is likely dominated by disc self-gravity. We show that the binary decays at a rate which is in good agreement with analytical estimates, while the eccentricity grows. Saturation of eccentricity growth is not observed up to values e > � 0.35. Accretion onto the black holes is variable, and is roughly modulated by the binary orbital frequency. Scaling our results, we analytically estimate the maximum rate of binary decay that is possible without fragmentation occuring within the surrounding gas disc, and compare that rate to an estimate of the stellar dynamical hardening rate. For binary masses in the range 10 5 M⊙ < � M < � 10 8 M⊙ we find that decay due to gas discs may dominate for separations below a � 10 −2 pc 0.1 pc, in the regime where the disc is optically thick. The minimum merger time scale is shorter than the Hubble time for M < � 10 7 M⊙. This implies that gas discs could commonly attend relatively low mass black hole mergers, and that a significant population of binaries might exist at separations of a few hundredths of a pc, where the combined decay rate is slowest. For more massive binaries, where this mechanism fails to act quickly enough, we suggest that scattering of stars formed within a fragmenting gas disc could act as a significant additional sink of binary angular momentum.

A hierarchical search for gravitational waves from supermassive black hole binary mergers

We present a method to search for gravitational waves from coalescing supermassive binary black holes in LISA data. The search utilizes the -statistic to maximize over, and determine the values of, the extrinsic parameters of the binary system. The intrinsic parameters are searched over hierarchically using stochastically generated multi-dimensional template banks to recover the masses, sky location and coalescence time of the binary. We present the results of this method applied to the Mock LISA Data Challenge 1B data set.

Premerger localization of gravitational-wave standard sirens with LISA: Harmonic mode decomposition

The continuous improvement in localization errors (sky position and distance) in real time as LISA observes the gradual inspiral of a supermassive black hole binary can be of great help in identifying any prompt electromagnetic counterpart associated with the merger. We develop a new method, based on a Fourier decomposition of the time-dependent, LISA-modulated gravitational-wave signal, to study this intricate problem. The method is faster than standard Monte Carlo simulations by orders of magnitude. By surveying the parameter space of potential LISA sources, we find that counterparts to supermassive black hole binary mergers with total mass $M\ensuremath{\sim}{10}^{5}--{10}^{7}{\mathrm{M}}_{\ensuremath{\bigodot}}$ and redshifts $z\ensuremath{\lesssim}3$ can be localized to within the field of view of astronomical instruments ($\ensuremath{\sim}{\mathrm{deg}}^{2}$) typically hours to weeks prior to coalescence. This will allow a triggered search for variable electromagnetic counterparts as the merger proceeds, as well as monitoring of the most energetic coalescence phase. A rich set of astrophysical and cosmological applications would emerge from the identification of electromagnetic counterparts to these gravitational-wave standard sirens.