Search

X-ray quasi-periodic eruptions (QPEs) are intense soft X-ray bursts from the nuclei of nearby low-mass galaxies typically lasting about one hour and repeating every few. Their physical origin remains debated, although so-called impacts models in which a secondary orbiting body pierces through the accretion disc around the primary supermassive black hole (SMBH) in an extreme mass-ratio inspiral (EMRI) system are considered promising. In this work, we study the QPE timing properties of GSN 069, the first galactic nucleus in which QPEs were identified, primarily focusing on Observed minus Calculated (O-C) diagrams. The O-C data in GSN 069 are consistent with a super-orbital modulation on tens of days whose properties do not comply with the impacts model. We suggest that rigid precession of a misaligned accretion disc or, alternatively, the presence of a second SMBH forming a sub-milliparsec binary with the inner EMRI is needed to reconcile the model with the data. In both cases, the quiescent accretion disc emission should also be modulated on similar timescales. Current X-ray monitoring indicates that this might be the case, although a longer baseline of higher-cadence observations is needed to confirm the tentative X-ray flux periodicity on firm statistical grounds. Future dedicated monitoring campaigns will be crucial to test the overall impacts plus modulation model in GSN 069, and to distinguish between the two proposed modulating scenarios. If our interpretation is correct, QPEs in GSN 069 represent the first electromagnetic detection of a short-period EMRI system in an external galaxy, opening the way to future multi-messenger astronomical observations. [abridged], Comment: Accepted for publication in A&A

Pulsar Timing Array (PTA) collaborations gather high-precision timing measurements of pulsars with the aim of detecting gravitational wave (GW) signals. A major challenge lies in the identification and characterization of the different sources of noise that may hamper their sensitivity to GWs. The presence of time-correlated noise that resembles the target signal might give rise to degeneracies that can directly impact the detection statistics. In this work, we focus on the covariance that exists between a "chromatic" dispersion measure (DM) noise and an "achromatic" stochastic gravitational wave background (GWB). "Chromatic" associated to the DM noise means that its amplitude depends on the frequency of the incoming pulsar photons measured by the radio-telescope. Several frequency channels are then required to accurately characterise its chromatic features and when the coverage of incoming frequency is poor, it becomes impossible to disentangle chromatic and achromatic noise contributions. In this paper, we explore this situation by injecting realistic GWB into 100 realizations of two mock versions of the second data release (DR2) of the European PTA (EPTA), characterized by different frequency coverage. The first dataset is a faithful copy of DR2, in which the first half of the data is dominated by only one frequency channel of observation; the second one is identical except for a more homogeneous frequency coverage across the full dataset. We show that for 91% of the injections, a better frequency coverage leads to an improved statistical significance (~1.3dex higher log Bayes factor on average) of the GWB and a better characterization of its properties. We propose a metric to quantify the degeneracy between DM and GWB parameters and show that it is correlated with a loss of significance for the recovered GWB and an increase in the GWB bias towards a higher and flatter spectral shape.

Extreme Mass Ratio Inspirals (EMRIs) are key observational targets for the Laser Interferometer Space Antenna (LISA) mission. Unresolvable EMRI signals contribute to forming a gravitational wave background (GWB). Characterizing the statistical features of the GWB from EMRIs is of great importance, as EMRIs will ubiquitously affect large segments of the inference scheme. In this work, we apply a frequentist test for GWB Gaussianity and stationarity, exploring three astrophysically-motivated EMRI populations. We construct the resulting signal by combining state-of-the-art EMRI waveforms and a detailed description of the LISA response with time-delay interferometric variables. Depending on the brightness of the GWB, our analysis demonstrates that the resultant EMRI foregrounds show varying degrees of departure from the usual statistical assumptions that the GWBs are both Gaussian and Stationary. If the GWB is non-stationary with non-Gaussian features, this will challenge the robustness of Gaussian-likelihood model, when applied to global inference results, e.g. foreground estimation, background detection, and individual-source parameters reconstruction., Comment: 12 pages, 5 figures, 3 tables

One of the primary sources of gravitational waves (GWs) anticipated to be detected by the Laser Interferometer Space Antenna (LISA) are Galactic double white dwarf binaries (DWDs). However, most of these binaries will be unresolved, and their GWs will overlap incoherently, creating a stochastic noise known as the Galactic foreground. Similarly, the population of unresolved systems in the Milky Way's (MW) satellites is expected to contribute to a stochastic gravitational wave background (SGWB). Due to their anisotropy and the annual motion of the LISA constellation, both the Galactic foreground and the satellite SGWB fall into the category of cyclostationary processes. Leveraging this property, we develop a purely frequency-based method to study LISA's capability to detect the MW foreground and SGWBs from the most promising MW satellites. We analyze both mock data generated by an astrophysically motivated SGWB spectrum, and realistic ones from a DWD population generated via binary population synthesis. We are able to recover or put constrains on the candidate foregrounds, reconstructing -- in the presence of noise uncertainties -- their sky distribution and spectrum. Our findings highlight the significance of the interplay between the astrophysical spectrum and LISA's sensitivity to detect the satellites' SGWB. Considering an astrophysically motivated prior on the satellite positions improves their detectability, which becomes otherwise challenging in the presence of the Galactic foreground. Furthermore, we explore the potential to observe a hypothetical satellite located behind the Galactic disk. Our results suggest that a Large Magellanic Cloud-like satellite could indeed be observable by LISA., Comment: 19 pages, 13 figures, 2 tables

Extreme mass ratio inspirals (EMRIs) are anticipated to be primary gravitational wave sources for LISA (Laser Interferometer Space Antenna). They form in dense nuclear clusters when a compact object (CO) is captured by the central massive black holes (MBHs) due to frequent two-body interactions among orbiting objects. We present a novel Monte Carlo approach to evolve the post-Newtonian (PN) equations of motion of a CO orbiting an MBH accounting for two-body relaxation locally on the fly, without the assumption of orbit-averaging. We estimate the fraction $S(a_0)$ of EMRIs to total captures (including direct plunges, DPs) as a function of the initial semi-major axis $a_0$ for COs around MBHs of $M_\bullet\in[10^4\,{\rm M}_\odot,4\times10^6\,{\rm M}_\odot]$. Previous results indicate $S(a_0)\rightarrow 0$ at large $a_0$, with a sharp transition from EMRIs to DPs around a critical scale $a_{\rm c}$. This notion has been recently challenged for low-mass MBHs, with EMRIs forming at $a\gg a_{\rm c}$, the so-called "cliffhangers''. Our simulations confirm their existence, at larger numbers than previously expected. Cliffhangers start to appear for $M_\bullet\lesssim3\times 10^5\,{\rm M}_\odot$ and can account for up to 55% of the overall EMRIs formed. We find $S(a_0)\gg 0$ for $a\gg a_{\rm c}$, reaching values as high as 0.6 for $M_\bullet=10^4\,{\rm M}_\odot$, much larger than previously found. We find that the PN description of the system greatly enhances the number of EMRIs by shifting $a_{\rm c}$ to larger values at all MBH masses, and that the local treatment of relaxation significantly boosts the number of cliffhangers for small MBHs. Our work shows the limitations of standard assumptions for estimating EMRI formation rates, most importantly their dynamical models. Future estimates of rates and properties of EMRIs detectable by LISA should account for these improvements., Comment: 22 pages, 15 figures, 1 table. To be submitted to A&A

Recent observations by pulsar timing arrays indicate the presence of gravitational wave signals, likely from supermassive black hole binaries. These binaries can produce two types of signals: a stochastic gravitational wave background (GWB) or deterministic continuous gravitational waves (CGW). Correctly separating these signals is essential for accurate signal recovery and interpretation. This paper investigates the interaction between GWB and CGW signals within current analysis pipelines, focusing on misinterpretations and biases in parameter estimation when these signals are analyzed separately or together. We conducted several simulations based on the European PTA 24.8-year dataset. First, we injected either a GWB or a CGW. We compared parameter estimation using different search models, including Earth term only, combined Earth and pulsar term CGW templates, and correlated (HD) or uncorrelated (CURN) power law GWB templates. Our findings show that, when searched independently, the GWB and CGW signals can be misinterpreted as each other, and only a combined search can recover the true signal present. For datasets containing both a GWB and a CGW, failure to account for the CGW biases the recovery of the GWB. However, a combined search allows for the recovery of both GWB and CGW parameters without significant bias. Care must be taken with the method used to perform combined searches on these multi-component datasets, as the CGW pulsar term can be misinterpreted as a CURN. This can be avoided by direct searches for an HD correlated GWB plus a CGW. Our study underscores the importance of combined searches to ensure unbiased recovery of GWB parameters in the presence of strong CGWs, which is crucial for interpreting signals recently found in PTA data and represents a step toward a robust framework for disentangling stochastic and deterministic GW signals in future, more sensitive datasets.

Pulsar Timing Array (PTA) collaborations reported evidence of a nano-Hz stochastic gravitational wave background (sGWB) compatible with an adiabatically inspiraling population of massive black hole binaries (MBHBs). Despite the large uncertainties, the relatively flat spectral slope of the recovered signal suggests a possible prominent role of MBHB dynamical coupling with the environment or/and the presence of an eccentric MBHB population. This work aims at studying the capabilities of future PTA experiments to detect single MBHBs under the realistic assumption that the sGWB is originated from an eccentric binary population coupled with its environment. To this end, we generalize the standard signal-to-noise ratio (SNR) and Fisher Information Matrix calculations used in PTA for circular MBHBs to the case of eccentric systems. We consider an ideal 10-year MeerKAT and 30-year SKA PTAs and apply our method over a wide number of simulated eccentric MBHB populations. We find that the number of resolvable MBHBs for the SKA (MeerKAT) PTA is ${\sim}\,30$ ($4$) at $\rm SNR\,{>}\,5$ (${>}\,3$), featuring an increasing trend for larger eccentricity values of the MBHB population. This is the result of eccentric MBHBs at ${\lesssim}\,10^{-9}\, \rm Hz$ emitting part of their power at high harmonics, thus reaching the PTA sensitivity band. Our results also indicate that resolved MBHBs do not follow the eccentricity distribution of the underlying MBHB population, but prefer low eccentricity values (${<}\,0.6$). Finally, the recovery of binary intrinsic properties and sky-localization do not depend on the system eccentricity, while orbital parameters such as eccentricity and initial orbital phase show clear trends. Although simplified, our results show that SKA will enable the detection of tens of MBHBs, projecting us into the era of precision gravitational wave astronomy at nano-Hz frequencies., Comment: 17 pages, 11 figures, submitted to A&A

Recent results from pulsar timing arrays (PTAs) show evidence for a gravitational wave background (GWB) consistent with a population of unresolved supermassive black hole (SMBH) binaries (BHBs). While the data do not yet constrain the slope of the spectrum, this appears to flatten at the lowest frequencies, deviating from the power-law shape expected for circular binaries evolving solely due to gravitational wave (GW) emission. Interestingly, such flattening can be explained with a population of eccentric rather than circular binaries. The eccentricity of BHBs is notoriously difficult to predict based simply on the parameters of the host galaxies and the initial galactic orbit, as it is subject to stochastic effects. We study the evolution of the eccentricity of BHBs formed in galactic mergers with cosmological initial conditions from pairing to coalescence, with a focus on potential PTA sources. We select galactic mergers from the IllustrisTNG100-1 simulation and re-simulate them at high resolution with the N-body code Griffin down to binary separations of the order of a parsec. We then estimate coalescence timescales with a semi-analytical model of the evolution under the effects of GW emission and stellar hardening. We find that most mergers in IllustrisTNG100-1 occur on highly eccentric orbits, and that the eccentricity of BHBs at binary formation correlates with the initial eccentricity of the merger, if this is no larger than approximately 0.9. For extremely eccentric mergers, the binaries tend to form with modest eccentricities. We discuss the implications of these results on the interpretation of the observed GWB., Comment: 10 pages, 11 figures, Accepted for publication in MNRAS

The Lunar Gravitational-wave Antenna (LGWA) is a proposed array of next-generation inertial sensors to monitor the response of the Moon to gravitational waves (GWs). Given the size of the Moon and the expected noise produced by the lunar seismic background, the LGWA would be able to observe GWs from about 1 mHz to 1 Hz. This would make the LGWA the missing link between space-borne detectors like LISA with peak sensitivities around a few millihertz and proposed future terrestrial detectors like Einstein Telescope or Cosmic Explorer. In this article, we provide a first comprehensive analysis of the LGWA science case including its multi-messenger aspects and lunar science with LGWA data. We also describe the scientific analyses of the Moon required to plan the LGWA mission.

Two-body relaxation may drive stars onto near-radial orbits around a massive black hole, resulting in a tidal disruption event (TDE). In some circumstances, stars are unlikely to undergo a single terminal disruption, but rather to have a sequence of many grazing encounters with the black hole. It has long been unclear what is the physical outcome of this sequence: each of these encounters can only liberate a small amount of stellar mass, but may significantly alter the orbit of the star. We study the phenomenon of repeating partial tidal disruptions (pTDEs) by building a semi-analytical model that accounts for mass loss and tidal excitation. In the empty loss cone regime, where two-body relaxation is weak, we estimate the number of consecutive partial disruptions that a star can undergo, on average, before being significantly affected by two-body encounters. We find that in this empty loss cone regime, a star will be destroyed in a sequence of weak pTDEs, possibly explaining the tension between the low observed TDE rate and its higher theoretical estimates., Comment: Open Journal of Astrophysics, accepted for publication

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase., Comment: 155 pages, with executive summary and table of contents

We study spectral and time variability of accreting massive black hole binaries (MBHBs) at milli-pc separations surrounded by a geometrically thin circumbinary disc. We present the first computed spectral energy distribution (SED) and light curves (LCs) from 3D hyper-Lagrangian resolution hydrodynamic simulations of these systems. We model binaries with mass of $10^6$ M$_\odot$, eccentricities e=0, 0.9 and mass ratio q=0.1,1. The circumbinary disc has initial aspect ratio of 0.1, features an adiabatic equation of state, and evolves under the effect of viscous heating, black body cooling and self gravity. To compute the SED, we consider black body emission from each disc element and we add an X-ray corona with luminosity proportional to that of the mini-discs around each black hole. We find significant variability of the SED, especially at high energies, which translates into LCs displaying modulations of a factor of ~ 2 in optical and of ~ 10 in UV and X-rays. We focus on flux variability in the optical band which will be probed by the Vera Rubin Observatory (VRO). Modulations on the orbital period and half of the orbital period are evident in all systems. In equal mass binaries, we find another longer timescale modulation, linked to an over-density forming at the inner edge of the disc. Considering the VRO properties, we find that equal mass, circular binaries are unlikely to be identified, due to the lack of prominent peaks in their Fourier spectra. Conversely, unequal mass and/or eccentric binaries can be singled out up to z ~ 0.5 (for systems with $L_{\rm bol}\approx10^{42}$ erg s$^{-1}$) and z ~ 2 (for systems with $L_{\rm bol}\approx10^{44}$ erg s$^{-1}$). Identifying electromagnetic signatures of MBHBs at separations $\sim 10^{-4}-10^{-2}$ pc is crucial for understanding the physics of the future Laser Interferometer Space Antenna sources and the origin of the GW background., Comment: 14 pages, 11 figures, A&A submitted

Using the 3D smoothed particle hydrodynamics code PHANTOM, we investigate the evolution of the orbital properties of massive black hole binaries embedded in massive discs where gravitational instabilities (GIs) triggered by the disc self-gravity are the only source of angular momentum transport. In particular, we investigate the evolution of binaries with different initial eccentricities $e_0=0.05,\,0.5,\,0.8$ and mass ratios $q=0.1,\,0.3,\,0.9$. Our simulations suggest that there might not be a unique value of critical eccentricity. We find initially more eccentric binaries to tend to higher asymptotic eccentricity values than more circular ones. This implies that there is a range of critical eccentricity values, that depends on the initial condition of the system. In particular, we find the width of this range to be narrower for more unequal binaries. We furthermore measure preferential accretion onto our binaries, finding more accretion onto the primary only for mass ratio $q=0.3$ and eccentricity $e=0.8$. We discuss how this might have implications for the amplitude of the gravitational wave background detected by Pulsar Timing Arrays (PTA) experiments. We finally measure the corresponding value of the viscosity parameter $\alpha$ in our simulations and discuss how this depends on the binary properties., Comment: 7 pages, A&A submitted

Pulsar Timing Array (PTA) experiments worldwide recently reported evidence of a nHz stochastic gravitational wave background (sGWB) compatible with the existence of slowly inspiralling massive black hole (MBH) binaries (MBHBs). The shape of the signal contains valuable information about the evolution of $z<1$ MBHs above $\rm 10^8 M_{\odot}$, suggesting a faster dynamical evolution of MBHBs towards the gravitational-wave-driven inspiral or a larger MBH growth than usually assumed. In this work, we investigate if the nHz sGWB could also provide constraints on the population of merging lower-mass MBHBs ($\rm {<} 10^7 \, M_{\odot}$) detectable by LISA. To this end, we use the $\texttt{L-Galaxies}$ semi-analytical model applied to the $\texttt{Millennium}$ suite of simulations. We generate a population of MBHs compatible simultaneously with current electromagnetic and nHz sGWB constraints by including the possibility that, in favourable environments, MBHs can accrete gas beyond the Eddington limit. The predictions of the model show that the global (integrated up to high-$z$) LISA detection rate is {\it not} significantly affected when compared to a fiducial model whose nHz sGWB signal is ${\sim}\,2$ times smaller. In both cases, the global rate yields ${\sim}\,12 \rm yr^{-1}$ and is dominated by systems of $\rm 10^{5-6} M_{\odot}$. The main differences are limited to low-$z$ ($z<3$), high-mass (${>}\rm 10^6\, M_{\odot}$) LISA MBHBs. The model compatible with the latest PTA results predicts up to ${\sim}\,1.6$ times more detections, with a rate of ${\sim}1\rm yr^{-1}$. We find that these LISA MBHB systems have 50\% probability of shining with bolometric luminosities $>10^{43}\rm erg/s$. Hence, in case PTA results are confirmed and given the current MBH modelling, our findings suggest there will be higher chances to perform multimessenger studies with LISA MBHB than previously expected., Comment: 16 pages; Submitted to A&A

We study the dynamical evolution of quasi-circular equal mass massive black hole binaries embedded in circumbinary discs from separations of $\sim 100R_{\rm g}$ down to the merger, following the post merger evolution. The binary orbit evolves owing to the presence of the gaseous disc and the addition of Post-Newtonian (PN) corrections up to the 2.5 PN order, therefore including the dissipative gravitational wave back-reaction. We investigate two cases of a relatively cold and warm circumbinary discs, with aspect ratios $H/R=0.03,\,0.1$ respectively, employing 3D hyper-Lagrangian resolution simulations with the {\sc gizmo}-MFM code. We extract spectral energy distributions and light curves in different frequency bands (i.e. X-ray, optical and UV) from the simulations. We find a clear two orders of magnitude drop in the X-ray flux right before merger if the disc is warm while we identify a significant increase in the UV flux regardless of the disc temperature. The optical flux shows clear distinctive modulations on the binary orbital period and on the cavity edge period, regardless of the disc temperature. We find that the presence of a cold disc can accelerate the coalescence of the binary by up to 130 seconds over the last five days of inspiral, implying a phase shift accumulation of about $\pi\,$radians compared to the binary evolution in vacuum. These differences are triggered by the presence of the gaseous disc and might have implications on the waveforms that can be in principle detected. We discuss the implications that these distinctive signatures might have for existing and upcoming time domain surveys and for multimessenger astronomy., Comment: 10 pages, A&A submitted

Detecting stochastic gravitational wave backgrounds (SGWBs) with The Laser Interferometer Space Antenna (LISA) is among the mission science objectives. Disentangling SGWBs of astrophysical and cosmological origin is a challenging task, further complicated by the noise level uncertainties. In this study, we introduce a Bayesian methodology to infer upon SGWBs, taking inspiration from Gaussian stochastic processes. We investigate the suitability of the approach for signal of unknown spectral shape. We do by discretely exploring the model hyperparameters, a first step towards a more efficient transdimensional exploration. We apply the proposed method to a representative astrophysical scenario: the inference on the astrophysical foreground of Extreme Mass Ratio Inspirals, recently estimated in~\cite{Pozzoli2023}. We find the algorithm to be capable of recovering the injected signal even with large priors, while simultaneously providing estimate of the noise level., Comment: 16 pages, 10 figures, 0 tables

Massive black hole binaries (MBHBs) are binary systems formed by black holes with mass exceeding millions of solar masses, expected to form and evolve in the nuclei of galaxies. The extreme compact nature of such objects determines a loud and efficient emission of Gravitational Waves (GWs), which can be detected by the Pulsar Timing Array (PTA) experiment in the form of a Gravitational Wave Background (GWB), i.e. a superposition of GW signals coming from different sources. The modelling of the GWB requires some assumptions on the binary population and the exploration of the whole involved parameter space is prohibitive as it is computationally expensive. We here train a Neural Network (NN) model on a semi-analytical modelling of the GWB generated by an eccentric population of MBHBs that interact with the stellar environment. We then use the NN to predict the characteristics of the GW signal in regions of the parameter space that we did not sample analytically. The developed framework allows us to quickly predict the level, shape and variance of the GWB signals produced in different universe realisations., Comment: 8 pages, submitted to A&A

The detection of gravitational waves with Pulsar Timing Arrays (PTAs) requires precise measurement of the difference between the pulsars' timing models and their observed pulses, as well as dealing with numerous and sometimes hard to diagnose sources of noise. Outliers may have an impact on this already difficult procedure, especially if the methods used are not robust to such anomalous observations. Until now, no complete and practical quantification of their effects on PTA data has been provided. With this work, we aim to fill this gap. We corrupt simulated datasets featuring an increasing degree of complexity with varying percentages of uniformly distributed outliers and investigate the impact of the latter on the recovery of the injected gravitational wave signals and pulsar noise terms. We found that the gravitational waves signal, due to its expected correlation, is more robust against these anomalous observations when compared to the other injected processes. This result is especially relevant in the context of the emerging statistical evidence for the gravitational wave background in PTA datasets, further strengthening those claims., Comment: 14 pages, 15 figures

We investigate the detectability of single-event coalescing black hole binaries with total mass of $100-600 M_{\odot}$ at cosmological distances ($5 \lesssim z \lesssim 20$) with the next generation of terrestrial gravitational wave observatories, specifically Einstein Telescope and Cosmic Explorer. Our ability to observe these binaries is limited by the low-frequency performance of the detectors. Higher-order Multipoles of the gravitational wave signal are observable in these systems, and detection of such multipoles serves to both b the mass range over which black hole binaries are observable and improve the recovery of their individual masses and redshift. For high redshift systems of $\sim 200 M_{\odot}$ we will be able to confidently infer that the redshift is at least $z=12$, and for systems of $\sim 400 M_{\odot}$ we can infer a minimum redshift of at least $z=8$. We discuss the impact that these observations will have in narrowing uncertainties on the existence of the pair-instability mass-gap, and their implications on the formation of the first stellar black holes that could be seeds for the growth of supermassive black holes powering high-$z$ quasars., Comment: 19 pages, 16 figures

State-of-the-art searches for gravitational waves (GWs) in pulsar timing array (PTA) datasets model the signal as an isotropic, Gaussian and stationary process described by a power-law. In practice, none of these properties are expected to hold for an incoherent superposition of GWs generated by a cosmic ensemble of supermassive black hole binaries (SMBHBs), which is expected to be the primary signal in the PTA band. We perform a systematic investigation of the performance of current search algorithms, using a simple power law model to characterize GW signals in realistic datasets. We use, as the baseline dataset, synthetic realisations of timing residuals mimicking the European PTA (EPTA) second data release (DR2). Thus, we include in the dataset uneven time stamps, achromatic and chromatic red noise and multi-frequency observations. We then inject timing residuals from an ideal isotropic, Gaussian, single power-law stochastic process and from a realistic population of SMBHBs, performing a methodical investigation of the recovered signal. We find that current search models are efficient at recovering the GW signal, but several biases can be identified due to the signal-template mismatch, which we identify via probability-probability (P-P) plots and quantify using Kolmogorov-Smirnov (KS) statistics. We discuss our findings in light of the signal observed in the EPTA DR2 and corroborate its consistency with an SMBHB origin., Comment: 15 pages, 12 figures, 4 Tables. Published version

With its capacity to observe $\sim 10^{5-6}$ faint active galactic nuclei (AGN) out to redshift $z\approx 6$, Roman is poised to reveal a population of $10^{4-6}\, {\rm M_\odot}$ black holes during an epoch of vigorous galaxy assembly. By measuring the light curves of a subset of these AGN and looking for periodicity, Roman can identify several hundred massive black hole binaries (MBHBs) with 5-12 day orbital periods, which emit copious gravitational radiation and will inevitably merge on timescales of $10^{3-5}$ years. During the last few months of their merger, such binaries are observable with the Laser Interferometer Space Antenna (LISA), a joint ESA/NASA gravitational wave mission set to launch in the mid-2030s. Roman can thus find LISA precursors, provide uniquely robust constraints on the LISA source population, help identify the host galaxies of LISA mergers, and unlock the potential of multi-messenger astrophysics with massive black hole binaries., Comment: White Paper for the Nancy Grace Roman Space Telescope's Core Community Surveys (https://roman.gsfc.nasa.gov/science/ccs_white_papers.html)

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 timescale 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 $\leq 3.5\sigma$ with a range of simulated GWB spectra. By fixing the BH-bulge mass parameters to the simulations we analyze 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., Comment: 20 pages, 16 figures, 3 tables, 1 appendix figure and 1 appendix table

The gravitational wave (GW) antenna LISA will detect the signal from coalescing massive black hole binaries (MBHBs) of $\rm 10^4\,{-}\,10^7\, M_{\odot}$, providing clues on their formation and growth along cosmic history. Some of these events will be localized with a precision of several to less than a deg$^2$, enabling the possible identification of their host galaxy. This work explores the properties of the host galaxies of LISA MBHBs below $z\,{\lesssim}\,3$. We generate a simulated lightcone by using the semi-analytical model $\mathrm{\texttt{L-Galaxies}}$ applied on the merger trees of the high-resolution N-body cosmological simulation $\mathrm{\texttt{Millennium-II}}$. The model shows that LISA MBHBs are expected to be found in optically dim ($r\,{>}\,20$), star-forming ($\rm sSFR\,{>}\,10^{-10}\, \rm yr^{-1}$), gas-rich ($f_{\rm gas}\,{>}\,0.6$) and disc-dominated ($\rm B/T\,{<}\,0.7$) \textit{low-mass galaxies} of stellar masses $10^8\,{-}\,10^9 M_{\odot}$. However, these properties are indistinguishable from those of galaxies harboring single massive black holes with comparable mass, making difficult the selection of 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 which brought the secondary MBH to the galaxy. Despite this, around 60% of dwarf galaxies placed in the surroundings of the LISA hosts will show such kind of features as well, challenging the unequivocal detection of LISA hosts through the search of merger signatures. Consequently, the detection of an electromagnetic transient associated with the MBHB merger will be vital to pinpoint the star-forming dwarf galaxy where these binary systems evolve and coalesce., Comment: 17 pages, 14 figures, Submitted to A&A

We investigate the coalescence of massive black hole ($M_{\rm BH}\gtrsim 10^{6}~\rm M_{\odot}$) binaries (MBHBs) at $63 \sigma$) overdense regions ($M_h\sim 10^{12}~\rm M_{\odot}$ dark matter halos 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 - 15 $\rm yr^{-1}$ at $z\sim 6$, depending on the run considered, and after correcting for a bias factor of $\sim 20-30$. 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 66-69 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 $\rm deg^2$., Comment: 17 pages, 11 figures, 3 tables. Accepted for publication in MNRAS

We use the latest constraints on the population of stellar origin binary black holes (SOBBH) from LIGO/Virgo/KAGRA (LVK) observations, to estimate the stochastic gravitational wave background (SGWB) they generate in the frequency band of LISA. We account for the faint and distant binaries, which contribute the most to the SGWB, by extending the merger rate at high redshift assuming it tracks the star formation rate. We adopt different methods to compute the SGWB signal: an analytical evaluation, Monte Carlo sums over SOBBH population realisations, and a method that accounts for the role of the detector by simulating LISA data and iteratively removing resolvable signals until only the confusion noise is left, allowing for the extraction of both the expected SGWB and the number of resolvable SOBBHs. Since the latter are few for SNR thresholds larger than five, we confirm that the spectral shape of the SGWB in the LISA band follows the analytical prediction of a power law. We infer the probability distribution of the SGWB amplitude from the LVK GWTC-3 posterior of the binary population model; its interquartile range of $h^2\Omega_\mathrm{GW}(f=3\times10^{-3}\,\mathrm{Hz}) \in [5.65,\,11.5]\times10^{-13}$ is in agreement with most previous estimates. We perform a MC analysis to assess LISA's capability to detect and characterise this signal. Accounting for both the instrumental noise and the galactic binaries foreground, with four years of data, LISA will be able to detect the SOBBH SGWB with percent accuracy, narrowing down the uncertainty on the amplitude by one order of magnitude with respect to the range of possible amplitudes inferred from the population model. A measurement of this signal by LISA will help to break the degeneracy among some of the population parameters, and provide interesting constraints, in particular on the redshift evolution of the SOBBH merger rate., Comment: 39 pages, 15 figures. Prepared for submission to JCAP

The shrinking of a binary orbit driven by the interaction with a gaseous circumbinary disc, initially advocated as a potential way to catalyze the binary merger, has been recently debated in the case of geometrically thick (i.e. with $H/R\gtrsim 0.1$) discs. However, a clear consensus is still missing mainly owing to numerical limitations, such as fixed orbit binaries or lack of resolution inside the cavity carved by the binary in its circumbinary disc. In this work, we asses the importance of evolving the binary orbit by means of hydrodynamic simulations performed with the code {\sc gizmo} in meshless-finite-mass mode. In order to model the interaction between equal mass circular binaries and their locally isothermal circumbinary discs, we enforce hyper-Lagrangian resolution inside the cavity. We find that fixing the binary orbit ultimately leads to an overestimate of the gravitational torque that the gas exerts on the binary, and in an underestimate of the torque due to the accretion of material onto the binary components. Furthermore, we find that the modulation of the accretion rate on the binary orbital period is strongly suppressed in the fixed orbit simulation, while it is clearly present in the live binary simulations. This has potential implications for the prediction of the observable periodicities in massive black hole binary candidates., Comment: 7 pages, 8 figures, accepted for publication in MNRAS

X-ray quasi-periodic eruptions (QPEs) represent a recently discovered example of extreme X-ray variability associated with supermassive black holes. These are high-amplitude bursts recurring every few hours that are detected in the soft X-ray band from the nuclei of nearby galaxies whose optical spectra lack the broad emission lines typically observed in unobscured active galaxies. The physical origin of this new X-ray variability phenomenon is still unknown and several theoretical models have been presented. However, no attempt has been made so far to account for the varying QPE recurrence time and luminosity in individual sources, nor for the diversity of the QPE phenomenology in the different known erupters. We present a semi-analytical model based on an extreme mass-ratio inspiral (EMRI) system where the secondary intersects, along its orbit, a rigidly precessing accretion disc surrounding the primary. We assume that QPEs result from emission from an adiabatically expanding, initially optically thick gas cloud expelled from the disc plane at each impact. We produced synthetic X-ray light curves, which we then compared with X-ray data from four QPE sources: GSN 069, eRO-QPE1, eRO-QPE2, and RX J1301.9+2747. Our model aptly reproduces the diversity of QPE properties between the considered objects and it is also able to naturally account for the varying QPE amplitudes and recurrence times in individual sources. Future implementations will enable us to refine the match with the data and to estimate the system parameters precisely, making additional use of multi-epoch QPE data. We briefly discuss the nature of the secondary object, as well as the possible implications of our findings for the EMRI population at large., Comment: 11 pages, 7 figures, accepted for publication in A&A

Primordial black holes (PBH), supposedly formed in the very early Universe, have been proposed as a possible viable dark matter candidate. In this work we characterize the expected gravitational wave (GW) losses from a population of PBHs orbiting Sgr A$^{\star}$, the super-massive black hole at the Galactic center (GC), and assess the signal detectability by the planned space-borne interferometer LISA and by the proposed next generation space-borne interferometer $\mu$Ares. Assuming that PBHs indeed form the entire diffuse mass allowed to reside within the orbit of the S2 star, we compute an upper limit to the expected GW signal both from resolved and non-resolved sources, under the further assumptions of monochromatic mass function and thermally distributed eccentricities. By comparing with our previous work where PBHs on circular orbits were assumed, we show for 1 M$_{\odot}$ PBHs how the GW signal from high harmonics over a 10 year data stream increases by a factor of six the chances of LISA detectability, from the $\approx 10\%$ of the circular case, to $\approx 60\%$, whereas multiple sources can be identified in $20\%$ of our mock populations. The background signal, made by summing up all non resolved sources, should be certainly detectable thanks to the PBHs with higher eccentricity evolving under two body relaxation. In the case of $\mu$Ares, because of its improved sensitivity in the $\mu$Hz band, one third of the entire population of PBHs orbiting Sgr A$^{\star}$ would be resolved. The background noise from the remaining non resolved sources should be detectable as well. Finally we present the results for different PBH masses., Comment: 11 pages, 9 figures

Tidal disruption events (TDEs) of stars operated by massive black holes (MBHs) will be detected in thousands by upcoming facilities such as the Vera Rubin Observatory. In this work, we assess the rates of standard total TDEs, destroying the entire star, and partial TDEs, in which a stellar remnant survives the interaction, by solving 1-D Fokker-Planck equations. Our rate estimates are based on a novel definition of the loss cone whose size is commensurate to the largest radius at which partial disruptions can occur, as motivated by relativistic hydrodynamical simulations. Our novel approach unveils two important results. First, partial TDEs can be more abundant than total disruptions by a factor of a few to a few tens. Second, the rates of complete stellar disruptions can be overestimated by a factor of a few to a few tens if one neglects partial TDEs, as we find that many of the events classified at total disruptions in the standard framework are in fact partial TDEs. Accounting for partial TDEs is particularly relevant for galaxies harbouring a nuclear stellar cluster featuring many events coming from the empty loss cone. Based on these findings, we stress that partial disruptions should be considered when constraining the luminosity function of TDE flares; accounting for this may reconcile the theoretically estimated TDE rates with the observed ones., Comment: 12 pages + Appendix, MNRAS, accepted

Extreme mass ratio inspirals (EMRIs) are among the primary targets for the Laser Interferometer Space Antenna (LISA). The extreme mass ratios of these systems result in relatively weak GW signals, that can be individually resolved only for cosmologically nearby sources (up to $z\approx2$). The incoherent piling up of the signal emitted by unresolved EMRIs generate a confusion noise, that can be formally treated as a stochastic GW background (GWB). In this paper, we estimate the level of this background considering a collection of astrophysically motivated EMRI models, spanning the range of uncertainties affecting EMRI formation. To this end, we employed the innovative Augmented Analytic Kludge waveforms and used the full LISA response function. For each model, we compute the GWB SNR and the number of resolvable sources. Compared to simplified computations of the EMRI signals from the literature, we find that for a given model the GWB SNR is lower by a factor of $\approx 2$ whereas the number of resolvable sources drops by a factor 3-to-5. Nonetheless, the vast majority of the models result in potentially detectable GWB which can also significantly contribute to the overall LISA noise budget in the 1-10 mHz frequency range.

The search for gravitational waves using Pulsar Timing Arrays (PTAs) is a computationally expensive complex analysis that involves source-specific noise studies. As more pulsars are added to the arrays, this stage of PTA analysis will become increasingly challenging. Therefore, optimizing the number of included pulsars is crucial to reduce the computational burden of data analysis. Here, we present a suite of methods to rank pulsars for use within the scope of PTA analysis. First, we use the maximization of the signal-to-noise ratio as a proxy to select pulsars. With this method, we target the detection of stochastic and continuous gravitational wave signals. Next, we present a ranking that minimizes the coupling between spatial correlation signatures, namely monopolar, dipolar, and Hellings & Downs correlations. Finally, we also explore how to combine these two methods. We test these approaches against mock data using frequentist and Bayesian hypothesis testing. For equal-noise pulsars, we find that an optimal selection leads to an increase in the log-Bayes factor two times steeper than a random selection for the hypothesis test of a gravitational wave background versus a common uncorrelated red noise process. For the same test but for a realistic EPTA dataset, a subset of 25 pulsars selected out of 40 can provide a log-likelihood ratio that is $89\%$ of the total, implying that an optimally selected subset of pulsars can yield results comparable to those obtained from the whole array. We expect these selection methods to play a crucial role in future PTA data combinations.

LISA will extend the search for gravitational waves (GWs) at $0.1\,{-}\,100$ mHz where loud signals from coalescing binary black holes of $ 10^4 \,{-}\,10^7\,\rm M_{\odot}$ are expected. Depending on their mass and luminosity distance, the uncertainty in the LISA sky-localization decreases from hundreds of deg$^2$ during the inspiral phase to fractions of a deg$^2$ after the merger. By using the semi-analytical model L-Galaxies applied to the Millennium-I merger trees, we generate a simulated Universe to identify the hosts of $z\,{\leq}\,3$ coalescing binaries with total mass of $3\,{\times}\,10^{5}$, $3\,{\times}\,10^6$ and $3\,{\times}\,10^7\rm M_{\odot}$, and varying mass ratio. We find that, even at the time of merger, the number of galaxies around the LISA sources is too large (${\gtrsim}\,10^2$) to allow direct host identification. However, if an X-ray counterpart is associated to the GW sources at $z\,{<}\,1$, all LISA fields at merger are populated by ${\lesssim}\,10$ AGNs emitting above ${\sim}\, 10^{-17} \, \rm erg\,cm^{-2}\,s^{-1}$. For sources at higher redshifts, the poorer sky-localization causes this number to increase up to ${\sim}\, 10^3$. Archival data from eRosita will allow discarding ${\sim}\, 10\%$ of these AGNs, being too shallow to detect the dim X-ray luminosity of the GW sources. Inspiralling binaries in an active phase with masses ${\lesssim}\,10^6\rm M_{\odot}$ at $z\,{\leq}\,0.3$ can be detected, as early as $10$ hours before the merger, by future X-ray observatories in less than a few minutes. For these systems, ${\lesssim}\,10$ AGNs are within the LISA sky-localization area. Finally, the LISA-Taiji network would guarantee the identification of an X-ray counterpart $10$ hours before merger for all binaries at $z\,{\lesssim}\,1$., Comment: 25 pages, 14 Figures, To be submitted to MNRAS

Parsec-scale massive black hole binaries (MBHBs) are expected to form in hierarchical models of structure formation. Even though different observational strategies have been designed to detect these systems, a theoretical study is a further guide for their search and identification. In this work, we investigate the hosts properties and the electromagnetic signatures of massive black holes gravitationally bound on parsec-scales with primary mass $\rm {>}\,10^7\,M_{\odot}$. For that, we construct a full-sky lightcone by the use of the semi-analytical model L-Galaxies in which physically motivated prescriptions for the formation and evolution of MBHBs have been included. Our predictions show that the large majority of the MBHBs are placed either in spiral galaxies with a classical bulge structure or in elliptical galaxies. Besides, the scaling relations followed by MBHBs are indistinguishable from the ones of single massive black holes. We find that the occupation fraction of parsec-scale MBHBs reaches up to ${\sim}\,50\%$ in galaxies with $\rm M_{stellar}\,{>}\,10^{11}\, M_{\odot}$ and drops below 10\% for $\rm M_{stellar}\,{<}\,10^{11}\, M_{\odot}$. Our model anticipates that the majority of parsec-scale MBHBs are unequal mass systems and lie at $z\,{\sim}\,0.5$, with ${\sim}\,20$ objects per $\rm deg^2$ in the sky. However, most of these systems are inactive, and only $1\,{-}\,0.1$ objects per $\rm deg^2$ have an electromagnetic counterpart with a bolometric luminosity in excess of $10^{43}$ erg/s. Very luminous phases of parsec-scale MBHBs are more common at $z\,{>}\,1$ but the number of binaries per $\rm deg^2$ is ${\lesssim}\,0.01$ at $\rm L_{\rm bol}\,{>}\,10^{45} \rm erg/s$., Comment: 19 pages, 16 Figures, Accepted by MNRAS

Binaries of relatively massive black holes like GW190521 have been proposed to form in dense gas environments, such as the disks of Active Galactic Nuclei (AGNs), and they might be associated with transient electromagnetic counterparts. The interactions of this putative environment with the binary could leave a significant imprint at the low gravitational wave frequencies observable with the Laser Interferometer Space Antenna (LISA). We show that LISA will be able to detect up to ten GW190521-like black hole binaries, with sky position errors $\lesssim1$ deg$^2$. Moreover, it will measure directly various effects due to the orbital motion around the supermassive black hole at the center of the AGN, especially the Doppler modulation and the Shapiro time delay. Thanks to a careful treatment of their frequency domain signal, we were able to perform the full parameter estimation of Doppler and Shapiro-modulated binaries as seen by LISA. We find that the Doppler and Shapiro effects will allow for measuring the AGN parameters (radius and inclination of the orbit around the AGN, central black hole mass) with up to percent-level precision. Properly modeling these low-frequency environmental effects is crucial to determine the binary formation history, as well as to avoid biases in the reconstruction of the source parameters and in tests of general relativity with gravitational waves., Comment: 13+4 pages, 7+1 figures v3: corrected typo in Fig 5

In this paper we develop a computationally efficient, two-population, time-dependent Fokker-Plank approach in the two dimensions of energy and angular momentum to study the rates of tidal disruption events (TDEs), extreme mass ratio inspirals (EMRIs) and direct plunges occurring around massive black holes (MBHs) in galactic nuclei. We test our code by exploring a wide range of the astrophysically relevant parameter space, including MBH masses, galaxy central densities and inner density slopes. We find that mass segregation and, more in general, the time dependency of the distribution function regulate the event rate: TDEs always decline with time, whereas EMRIs and plunges reach a maximum and undergo a subsequent nearly exponential decay. Once suitably normalized, the rates associated to different choices of MBH mass and galaxy density overlap nearly perfectly. Based on this, we provide a simple scaling that allows to reproduce the time-dependent event rates for any MBH mass and underlying galactic nucleus. Although our peak rates are in general agreement with the literature relying on the steady-state (non-time dependent) assumption, those can be sustained on a timescale that strongly depends on the properties of the system. In particular this can be much shorter than a Gyr for relatively light MBHs residing in dense systems. This warns against using steady state models to compute global TDE, EMRI and plunge rates and calls for a more sophisticated, time dependent treatment of the problem., Comment: 14 pages, 10 figures, submitted to MNRAS

The observation of a population of massive black hole binaries (MBHBs) is key for our complete understanding of galaxy mergers and for the characterization of the expected gravitational waves (GWs) signal. However, MBHBs still remain elusive with only a few candidates proposed to date. Among these, SDSSJ143016.05+230344.4 ('tick-tock' hereafter) is the only candidate with a remarkably well sampled light curve showing a clear reduction of the modulation period and amplitude over three years of observations. This particular feature has been recently claimed to be the signature of a MBHB that is about to merge. In this paper, we provide an optical follow-up of the tick-tock source using the Rapid Eye Mount (REM) telescope. The decreasing luminosity observed in our follow up is hardly explained within the binary scenario. We speculate about an alternative scenario that might explain the observed light curve through relativistic Lense-Thirring precession of an accretion disc around a single massive black hole., Comment: 9 pages, 2 figure, accepted for publication in MNRAS

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 disks 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 a 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 10$^6$--10$^8$ years. 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., Comment: 18 pages, 15 figures, accepted for publication in MNRAS

The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA's first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultracompact stellar-mass binaries, massive black hole binaries, and extreme or intermediate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.

In this work we characterize the expected gravitational wave signal detectable by the planned space-borne interferometer LISA and the proposed next generation space-borne interferometer $\mu$Ares arising from a population of primordial black holes orbiting Sgr A*, the super-massive black hole at the Galactic center. Assuming that such objects indeed form the entire diffuse mass allowed by the observed orbit of S2 in the Galactic center, under the simplified assumption of circular orbits and monochromatic mass function, we assess the expected signal in gravitational waves, either from resolved and non-resolved sources. We estimate a small but non negligible chance of $\simeq$ 10% of detecting one single 1 M$_{\odot}$ primordial black hole with LISA in a 10-year-long data stream, while the background signal due to unresolved sources would essentially elude any reasonable chance of detection. On the contrary, $\mu$Ares, with a $\simeq$ 3 orders-of-magnitude better sensitivity at $\simeq$ 10$^{-5}$ Hz, would be able to resolve $\simeq$ 140 solar mass primordial black holes in the same amount of time, while the unresolved background should be observable with an integrated signal-to-noise ratio $\gtrsim$ 100. Allowing the typical PBH mass to be in the range 0.01-10 M$_{\odot}$ would increase LISA chance of detection to $\simeq$ 40% towards the lower limit of the mass spectrum. In the case of $\mu$Ares, instead, we find a "sweet spot" just about 1 M$_{\odot}$, a mass for which the number of resolvable events is indeed maximized., Comment: 10 pages, 11 figures; Referee reviewed

Coalescing supermassive black hole binaries (BHBs) are expected to be the loudest sources of gravitational waves (GWs) in the Universe. Detection rates for ground or space-based detectors based on cosmological simulations and semi-analytic models are highly uncertain. A major difficulty stems from the necessity to model the BHB from the scale of the merger to that of inspiral. Of particular relevance to the GW merger timescale is the binary eccentricity. Here we present a self-consistent numerical study of the eccentricity of BHBs formed in massive gas-free mergers from the early stages of the merger to the hardening phase, followed by a semi-analytical model down to coalescence. We find that the early eccentricity of the unbound black hole pair is largely determined by the initial orbit. It systematically decreases during the dynamical friction phase. The eccentricity at binary formation is affected by stochasticity and noise owing to encounters with stars, but preserves a strong correlation with the initial orbital eccentricity. Binding of the black holes is a phase characterised by strong perturbations, and we present a quantitative definition of the time of binary formation. During hardening the eccentricity increases in minor mergers, unless the binary is approximately circular, but remains largely unchanged in major mergers, in agreement with predictions from semi-analytical models based on isotropic scattering experiments. Coalescence times due to hardening and GW emission in gas-poor non-rotating ellipticals are <~0.5 Gyr for the large initial eccentricities (0.5 < e < 0.9) typical of galaxy mergers in cosmological simulations., Comment: 15 pages, 13 figures, accepted for publication in MNRAS

The study of the interaction of a massive black hole binary with its gaseous environment is crucial in order to be able to predict merger rates and possible electromagnetic counterparts of gravitational wave signals. The evolution of the binary semi-major axis resulting from this interaction has been recently debated, and a clear consensus is still missing, also because of several numerical limitations, i.e. fixed orbit binaries or lack of resolution inside the cavity carved by the binary in its circumbinary disc. Using on-the-fly particle-splitting in the 3D meshless code gizmo, we achieve hyper-Lagrangian resolution, which allows us to properly resolve the dynamics inside the cavity, and in particular for the first time the discs that form around the two components of a live binary surrounded by a locally isothermal gaseous circumbinary disc. We show that the binary orbit decays with time for very cold and very warm discs and that the result of the interaction in the intermediate regime is strongly in uenced by the disc viscosity as this essentially regulates the fraction of mass contained in the discs around the binary components as well as the fraction that is accreted by the binary. We find the balance between these two quantities to determine whether the binary semi-major axis decreases with time., Comment: 8 pages, published in ApJL

The next generation of ground-based gravitational-wave detectors will observe coalescences of black holes and neutron stars throughout the cosmos, thousands of them with exceptional fidelity. The Science Book is the result of a 3-year effort to study the science capabilities of networks of next generation detectors. Such networks would make it possible to address unsolved problems in numerous areas of physics and astronomy, from Cosmology to Beyond the Standard Model of particle physics, and how they could provide insights into workings of strongly gravitating systems, astrophysics of compact objects and the nature of dense matter. It is inevitable that observatories of such depth and finesse will make new discoveries inaccessible to other windows of observation. In addition to laying out the rich science potential of the next generation of detectors, this report provides specific science targets in five different areas in physics and astronomy and the sensitivity requirements to accomplish those science goals. This report is the second in a six part series of reports by the GWIC 3G Subcommittee: i) Expanding the Reach of Gravitational Wave Observatories to the Edge of the Universe, ii) The Next Generation Global Gravitational Wave Observatory: The Science Book (this report), iii) 3G R&D: R&D for the Next Generation of Ground-based Gravitational Wave Detectors, iv) Gravitational Wave Data Analysis: Computing Challenges in the 3G Era, v) Future Ground-based Gravitational-wave Observatories: Synergies with Other Scientific Communities, and vi) An Exploration of Possible Governance Models for the Future Global Gravitational-Wave Observatory Network., Comment: 69 pages, 18 figures

Massive stellar origin black hole binaries (SBHBs), originating from stars above the pair-instability mass gap, are primary candidates for multiband gravitational wave (GW) observations. Here we study the possibility to use them as effective dark standard sirens to constrain cosmological parameters. The long lasting inspiral signal emitted by these systems is accessible by the future $Laser \; Interferometer \; Space \; Antenna$ (LISA), while the late inspiral and merger are eventually detected by third generation ground-based telescopes such as the $Einstein \; Telescope$ (ET). The direct measurement of the luminosity distance and the sky position to the source, together with the inhomogeneous redshift distribution of possible host galaxies, allow us to infer cosmological parameters by probabilistic means. The efficiency of this statistical method relies in high parameter estimation performances. We show that this multiband approach allows a precise determination of the Hubble constant H$_0$ with just ${\cal O}(10)$ detected sources. For selected SBHB population models, assuming $4$ ($10$) years of LISA observations, we find that H$_0$ is typically determined at $\sim 2\%$ ($\sim 1.5\%$), whereas $\Omega_m$ is only mildly constrained with a typical precision of $30\%$ ($20\%$). We discuss the origin of some outliers in our final estimates and we comment on ways to reduce their presence., Comment: Updated results. 18 pages, 9 figures. Accepted for publication in PRD

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 semi-analytical 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 few hundreds Myr at most, implying that gas-driven expansion will not severely affect the detection prospects of upcoming GW facilities., Comment: 11 pages, 6 figures, Published in ApJ Letters

We estimate the amplitude of the nano-Hz stochastic gravitational wave background (GWB) resulting from an unresolved population of inspiralling massive black hole binaries (MBHBs). To this aim, we use the L-Galaxies semi-analytical model applied on top of the Millennium merger trees. The dynamical evolution of MBHBs includes dynamical friction, stellar and gas binary hardening, and gravitational wave feedback. At the frequencies proved by the \textit{Pulsar Timing Array} experiments, our model predicts an amplitude of ${\sim}1.2\,{\times}\,10^{-15}$ at ${\sim}\,3\,{\times}\,10^{-8}\, \rm Hz$ in agreement with current estimations. The contribution to the background comes primarily from equal mass binaries with chirp masses above $\rm 10^{8}\, M_{\odot}$. We then consider the recently detected common red noise in NANOGrav, PPTA, and EPTA data, working under the hypothesis that it is indeed a stochastic GWB coming from MBHBs. By boosting the massive black hole growth via gas accretion, we show that our model can produce a signal with an amplitude $A\approx 2-3 {\times}\,10^{-15}$. There are, however, difficulties in predicting this background level without mismatching key observational constraints such as the quasar bolometric luminosity functions or the local black hole mass function. This highlights how current and forthcoming gravitational wave observations can, for the first time, confront galaxy and black hole evolution models., Comment: 17 pages, 11 Figures, Accepted by MNRAS

The science objectives of the LISA mission have been defined under the implicit assumption of a 4 yr continuous data stream. Based on the performance of LISA Pathfinder, it is now expected that LISA will have a duty cycle of $\approx 0.75$, which would reduce the effective span of usable data to 3 yr. This paper reports the results of a study by the LISA Science Group, which was charged with assessing the additional science return of increasing the mission lifetime. We explore various observational scenarios to assess the impact of mission duration on the main science objectives of the mission. We find that the science investigations most affected by mission duration concern the search for seed black holes at cosmic dawn, as well as the study of stellar-origin black holes and of their formation channels via multi-band and multi-messenger observations. We conclude that an extension to 6 yr of mission operations is recommended., Comment: 50 pages, 19 figures, 5 tables. Matches version published in GERG

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., Comment: 9 pages, submitted to MNRAS on June 1st 2021

I review the scientific potential of the Laser Interferometer Space Antenna (LISA), a space-borne gravitational wave (GW) observatory to be launched in the early 30s'. Thanks to its sensitivity in the milli-Hz frequency range, LISA will reveal a variety of GW sources across the Universe, from our Solar neighbourhood potentially all the way back to the Big Bang, promising to be a game changer in our understanding of astrophysics, cosmology and fundamental physics. This review dives in the LISA Universe, with a specific focus on black hole science, including the formation and evolution of massive black holes in galaxy centres, the dynamics of dense nuclei and formation of extreme mass ratio inspirals, and the astrophysics of stellar-origin black hole binaries., Comment: Mini review. Contribution to the volume "Gravitational Waves: A New Window to the Universe", Published in Frontiers in Astronomy and Space Science. Guest Editors Rosalba Perna and Bruno Giacomazzo