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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

We investigate the effect of dynamically coupling gas torques with gravitational wave (GW) emission during the orbital evolution of an equal-mass massive black hole binary (MBHB). We perform hydrodynamical simulations of eccentric MBHBs with total mass $M=10^6~{\rm M}_\odot$ embedded in a prograde locally isothermal circumbinary disk (CBD). We evolve the binary from $53$ to $30$ Schwarzschild radii separations using up to 2.5 post-Newtonian (PN) corrections to the binary dynamics, which allow us to follow the GW-driven in-spiral. For the first time, we report the measurement of gas torques onto a live binary a few years before the merger, with and without concurrent GW radiation. We also identify and measure a novel GW-gas coupling term in the in-spiral rate that makes gas effects an order of magnitude stronger than the gas-only contribution. We show that the evolution rate ($\dot a$) of the MBHB can be neatly expressed as the sum of the GW rate ($\dot a_{\rm GW}$), the pure gas-driven rate ($\dot a_{\rm gas}$), and their cross-term $\propto\dot a_{\rm GW}\dot a_{\rm gas}$. The source-frame gas-induced dephasing in the GW waveform is equivalent to losing $\sim0.5$ GW cycles over the expected $\sim1700$ cycles in a vacuum, which LISA should detect at redshift $z=1$. We also propose a phenomenological model that captures the essence of simulations and can be used to perform Bayesian inference. Our results show how GWs alone can be used to probe the astrophysical properties of CBDs and have important implications on multi-messenger strategies aimed at studying the environments of MBHBs., Comment: 8 pages, 4 figures. To be submitted to ApJ Letters

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

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

Quasi-periodic eruptions (QPEs) are an extreme X-ray variability phenomenon associated with low-mass supermassive black holes. First discovered in the nucleus of the galaxy GSN 069, they have been so far securely detected in five other galaxies, including RX J1301.9+2747. When detected, the out-of-QPE emission (quiescence) is consistent with the high-energy tail of thermal emission from an accretion disk. We present the X-ray and radio properties of RX J1301.9+2747, both in quiescence and during QPEs. We analyse X-ray data taken during five XMM-Newton observations between 2000 and 2022. The last three observations were taken in coordination with radio observations with the Karl G. Jansky Very Large Array. We also make use of EXOSAT, ROSAT, and Chandra archival observations taken between 1983 and 2009. XMM-Newton detected 34 QPEs of which 8 have significantly lower amplitudes than the others. No correlated radio/X-ray variability was observed during QPEs. In terms of timing properties, the QPEs in RX J1301.9+2747 do not exhibit the striking regularity observed in the discovery source GSN 069. In fact there is no clear repetition pattern between QPEs: the average time separation between their peaks is about four hours, but it can be as short as one, and as long as six hours. The QPE spectral properties of RX J1301.9+2747 as a function of energy are however very similar to those of GSN 069 and of other QPE sources. The quiescent emission of RX J1301.9+2747 is more complex than that of GSN 069, as it requires a soft X-ray excess-like component in addition to the thermal emission from the accretion disk. Its long-term X-ray quiescent flux variations are of low-amplitude and not strictly monotonic, with a general decay over $\sim 22$ years. We discuss our observational results in terms of some of the ideas and models that have been proposed so far for the physical origin of QPEs., Comment: Accepted for publication in Astronomy & Astrophysics. 22 pages and 17 figures in the main text; 11 pages, 5 tables, and 4 figures in the Appendix. Abstract shortened to comply with arXiv requirements

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

According to the hierarchical formation paradigm, galaxies form through mergers of smaller entities and massive black holes (MBHs), if lurking at their centers, migrate to the nucleus of the newly formed galaxy, where they form binary systems. The formation and evolution of MBH binaries, and in particular their coalescence timescale, is very relevant for current and future facilities aimed at detecting the gravitational-wave signal produced by the MBH close to coalescence. While most of the studies targeting this process are based on hydrodynamic simulations, the high computational cost makes a complete parameter space exploration prohibitive. Semi-analytic approaches represent a valid alternative, but they require ad-hoc prescriptions for the mass loss of the merging galaxies in minor mergers due to tidal stripping, which is not commonly considered or at most modelled assuming very idealised geometries. In this work, we propose a novel, effective model for the tidal stripping in axisymmetric potentials, to be implemented in semi-analytic models. We validate our semi-analytic approach against N-body simulations considering different galaxy sizes, inclinations, and eccentricities, finding only a moderate dependence on the orbit eccentricity. In particular, we find that, for almost circular orbits, our model mildly overestimates the mass loss, and this is due to the adjustment of the stellar distribution after the mass is removed. Nonetheless, the model exhibits a very good agreement with simulations in all the considered conditions, and thus represents an extremely powerful addition to semi-analytic calculations., Comment: 15 pages, 8 figures, 2 tables. Accepted for publication on A&A

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

Quasi-Periodic Eruptions (QPEs) are luminous X-ray outbursts recurring on hour timescales, observed from the nuclei of a growing handful of nearby low-mass galaxies. Their physical origin is still debated, and usually modeled as (a) accretion disk instabilities or (b) interaction of a supermassive black hole (SMBH) with a lower mass companion in an extreme mass-ratio inspiral (EMRI). EMRI models can be tested with several predictions related to the short- and long-term behavior of QPEs. In this study, we report on the ongoing 3.5-year NICER and XMM-Newton monitoring campaign of eRO-QPE1, which is known to exhibit erratic QPEs that have been challenging for the simplest EMRI models to explain. We report 1) complex, non-monotonic evolution in the long-term trends of QPE energy output and inferred emitting area; 2) the disappearance of the QPEs (within NICER detectability) in October 2023, then reappearance by January 2024 at a luminosity $\sim$100x fainter (and temperature $\sim$3x cooler) than initial discovery; 3) radio non-detections with MeerKAT and VLA observations partly contemporaneous with our NICER campaign (though not during outbursts); and 4) the presence of a possible $\sim$6-day modulation of the QPE timing residuals, which aligns with the expected nodal precession timescale of the underlying accretion disk. Our results tentatively support EMRI-disk collision models powering the QPEs, and we demonstrate that the timing modulation of QPEs may be used to jointly constrain the SMBH spin and disk density profile., Comment: Accepted for publication in ApJ

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

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

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

Massive black holes are key inhabitants of the nuclei of galaxies. Moreover, their astrophysical relevance has gained significant traction in recent years, thanks especially to the amazing results that are being (or will be) delivered by instruments such as the James Webb Space Telescope, Pulsar Timing Array projects and LISA. In this Chapter, we aim to detail a broad set of aspects related to the astrophysical nature of massive black holes embedded in galactic nuclei, with a particular focus on recent and upcoming advances in the field. In particular, we will address questions such as: What shapes the relations connecting the mass of massive black holes with the properties of their host galaxies? How do massive black holes form in the early Universe? What mechanisms keep on feeding them so that they can attain very large masses at z = 0? How do binaries composed of two massive black holes form and coalesce into a single, larger black hole? Here we present these topics from a mainly theoretical viewpoint and discuss how present and upcoming facilities may enhance our understanding of massive black holes in the near future., Comment: All authors equally contributed to the Chapter writing. To appear as Chapter 3 in the book "Black Holes in the Era of Gravitational Wave Astronomy", ed. Arca Sedda, Bortolas, Spera, pub. Elsevier

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

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)

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

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.

Dual active galaxy nuclei (dAGNs) trace the population of post-merger galaxies and are the precursors to massive black hole (MBH) mergers, an important source of gravitational waves that may be observed by LISA. In Paper I of this series, we used the population of nearly 2000 galaxy mergers predicted by the TNG50-3 simulation to seed semi-analytic models of the orbital evolution and coalescence of MBH pairs with initial separations of about 1 kpc. Here, we calculate the dAGN luminosities and separation of these pairs as they evolve in post-merger galaxies, and show how the coalescence fraction of dAGNs changes with redshift. We find that because of the several Gyr long dynamical friction timescale for orbital evolution, the fraction of dAGNs that eventually end in a MBH merger grows with redshift and does not pass 50% until a redshift of 1. However, dAGNs in galaxies with bulge masses >10^10 solar masses, or comprised of near-equal mass MBHs, evolve more quickly and have higher than average coalescence fractions. At any redshift, dAGNs observed with small separations (> 0.7 kpc) have a higher probability of merging in a Hubble time than more widely separated systems. As found in Paper I, radiation feedback effects can significantly reduce the number of MBH mergers, and this could be manifested as a larger than expected number of widely separated dAGNs. We present a method to estimate the MBH coalescence rate as well as the potential LISA detection rate given a survey of dAGNs. Comparing these rates to the eventual LISA measurements will help determine the efficiency of dynamical friction in post-merger galaxies., Comment: Submitted to ApJ, 13 pages, 8 figures

We present MORDOR (MORphological DecOmposeR, a new algorithm for structural decomposition of simulated galaxies based on stellar kinematics. The code measures the properties of up to five structural components (a thin/cold and a thick/warm disc, a classical and a secular bulge, and a spherical stellar halo), and determines the properties of a stellar bar (if present). A comparison with other algorithms presented in the literature yields overall good agreement, with MORDOR displaying a higher flexibility in correctly decomposing systems and identifying bars in crowded environments (e.g. with ongoing fly-bys, often observable in cosmological simulations). We use MORDOR to analyse galaxies in the TNG50 simulation and find the following: ($i$) the thick disc component undergoes the strongest evolution in the binding energy-circularity plane, as expected when disc galaxies decrease their turbulent-rotational support with cosmic time; ($ii$) smaller galaxies (with stellar mass, $10^{9} \lesssim M_{*} / {\rm M_{\odot}} \leq 5 \times 10^{9}$) undergo a major growth in their disc components after $z\sim 1$, whereas ($iii$) the most massive galaxies ($5 \times 10^{10} < M_{*} / {\rm M_{\odot}} \leq 5\times10^{11}$) evolve toward more spheroidal dominated objects down to $z=0$ due to frequent gravitational interactions with satellites; ($iv$) the fraction of barred galaxies grows rapidly at high redshift and stabilizes below $z\sim 2$, except for the most massive galaxies that show a decrease in the bar occupation fraction at low redshift; ($v$) galaxies with $M_{*} \sim 10^{11}~{\rm M_{\odot}}$ exhibit the highest relative occurrence of bars at $z=0$, in agreement with observational studies. We publicly release MORDOR and the morphological catalogue of TNG50 galaxies., Comment: 20 pages, 20 figures. Submitted to MNRAS. MORDOR is available at https://github.com/thanatom/mordor. The catalogue is available at www.tng-project.org/zana22

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

We make use of z = 0 samples of strongly barred and unbarred disc galaxies from the TNG100 and TNG50 cosmological hydrodynamical simulations to assess the performance of the simple disc instability criterion proposed by Efstathiou, Lake & Negroponte (1982) (ELN-criterion). We find that strongly barred galaxies generally assemble earlier, are more star-dominated in their central regions, and have more massive and more compact discs than unbarred galaxies. The ELN-criterion successfully identifies ~75% and ~80% of the strongly barred and the unbarred galaxies, respectively. Strongly barred galaxies that the criterion fails to identify tend to have more extended discs, higher spin values and bars that assembled later than is typical for the bulk of the barred population. The bars in many of these cases appear to be produced by an interaction with a close neighbour (i.e. to be externally triggered) rather than to result from secular growth in the disc. On the other hand, we find that unbarred galaxies misclassified as barred by the ELN-criterion typically have stellar discs similar to those of barred galaxies, although more extended in the vertical direction and less star-dominated in their central regions, possibly reflecting later formation times. In addition, the bulge component of these galaxies is significantly more prominent at early times than in the strongly barred sample. Thus, the ELN-criterion robustly identifies secular bar instabilities in most simulated disc galaxies, but additional environmental criteria are needed to account for interaction-induced bar formation., Comment: 15 pages, 12 Figures, Accepted by 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.

We evaluate the cosmological coalescence and detection rates for massive black hole (MBH) binaries targeted by the gravitational wave observatory Laser Interferometer Space Antenna (LISA). Our calculation starts with a population of gravitationally unbound MBH pairs, drawn from the TNG50-3 cosmological simulation, and follows their orbital evolution from kpc scales all the way to coalescence using a semi-analytic model developed in our previous work. We find that for a majority of MBH pairs that coalesce within a Hubble time dynamical friction is the most important mechanism that determines their coalescence rate. Our model predicts a MBH coalescence rate < 0.45/ yr and a LISA detection rate < 0.34/ yr. Most LISA detections should originate from 10^6 - 10^6.8 solar masses MBHs in gas-rich galaxies at redshifts 1.6 < z < 2.4, and have a characteristic signal to noise ratio SNR ~ 100. We however find a dramatic reduction in the coalescence and detection rates, as well as the average SNR, if the effects of radiative feedback from accreting MBHs are taken into account. In this case, the MBH coalescence rate is reduced by 78% (to < 0.1/ yr), and the LISA detection rate is reduced by 94% (to 0.02/ yr), whereas the average SNR is ~ 10. We emphasize that our model provides a lower limit on the LISA detection rate, consistent with other works in the literature that draw their MBH pairs from cosmological simulations., Comment: Accepted to ApJ, 20 pages, 10 figures

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

We use the magnetic-hydrodynamical simulation TNG50 to study the evolution of barred massive disc galaxies. Massive spiral galaxies are already present as early as $z=4$, and bar formation takes place already at those early times. The bars grow longer and stronger as the host galaxies evolve, with the bar sizes increasing at a pace similar to that of the disc scale lengths. The bar fraction mildly evolves with redshift for galaxies with $M_{*}\geq10^{10}M\odot$, being greater than $\sim40\%$ at $0.5

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

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

Variable active galactic nuclei showing periodic light curves have been proposed as massive black hole binary (MBHB) candidates. In such scenarios the periodicity can be due to relativistic Doppler-boosting of the emitted light. This hypothesis can be tested through the timing of scattered polarized light. Following the results of polarization studies in type I nuclei and of dynamical studies of MBHBs with circumbinary discs, we assume a coplanar equatorial scattering ring, whose elements contribute differently to the total polarized flux, due to different scattering angles, levels of Doppler boost, and line-of-sight time delays. We find that in the presence of a MBHB, both the degree of polarization and the polarization angle have periodic modulations. The minimum of the polarization degree approximately coincides with the peak of the light curve, regardless of the scattering ring size. The polarization angle oscillates around the semi-minor axis of the projected MBHB orbital ellipse, with a frequency equal either to the binary's orbital frequency (for large scattering screen radii), or twice this value (for smaller scattering structures). These distinctive features can be used to probe the nature of periodic MBHB candidates and to compile catalogs of the most promising sub-pc MBHBs. The identification of such polarization features in gravitational-wave detected MBHBs would enormously increase the amount of physical information about the sources, allowing the measurement of the individual masses of the binary components, and the orientation of the line of nodes on the sky, even for monochromatic gravitational wave signals., Comment: 11 pages, 6 figures, submitted to MNRAS

In this paper, we systematically explore the impact of a galactic bar on the inspiral time-scale of a massive object (MO) within a Milky Way-like galaxy. We integrate the orbit of MOs in a multi-component galaxy model via a semi-analytical approach that accounts for dynamical friction generalized to rotationally supported backgrounds. We compare the MO evolution in a galaxy featuring a Milky Way-like rotating bar to the evolution within an analogous axisymmetric galaxy without the bar. In agreement with previous studies, we find that the bar presence may significantly affect the inspiral, sometimes making it shorter by a factor of a few, sometimes hindering it for a Hubble time. The erratic behaviour is mainly impacted by the relative phase at which the MO encounters the stronger bar-induced resonances. In particular, the effect of the bar is more prominent for initially in-plane, prograde MOs, especially those crossing the bar co-rotation radius or outer Lindblad resonance. In the barred galaxy, we find the sinking of the most massive MOs (>~10^7.5 Msun) approaching the galaxy from large separations (>~8 kpc) to be most efficiently hampered. Neglecting the effect of global torques associated with the non-symmetric mass distribution is thus not advisable even within an idealized, smooth galaxy model; we further note that spiral patterns are unlikely to affect the inspiral due to their transient and fluctuating nature. We speculate that the sinking efficiency of massive black holes involved in minor galaxy mergers may be hampered in barred galaxies, making them less likely to host a gravitational wave signal accessible to low-frequency detectors., Comment: 19 pages, 12 figures, 2 tables. MNRAS, accepted

Third Generation ground based Gravitational Wave Interferometers, like the Einstein Telescope (ET), Cosmic Explorer (CE), and the Laser Interferometer Space Antenna (LISA) will detectcoalescing binary black holes over a wide mass spectrum and across all cosmic epochs. We track the cosmological growth of the earliest light and heavy seeds that swiftly transit into the supermassive domain using a semi analytical model for the formation of quasars at $z=6.4$, 2 and $0.2$, in which we follow black hole coalescences driven by triple interactions. We find that light seed binaries of several $10^2$ M$_\odot$ are accessible to ET with a signal-to-noise ratio ($S/N$) of $10-20$ at $620$). Mergers involving heavy seeds ($\sim 10^5 M_\odot - 10^6 M_\odot$) would be within reach up to $z=20$ in the LISA frequency domain. The lower-z model predicts $11.25(18.7)$ ET(LISA) events per year, overall., Comment: 16 pages, 8 figures accepted for publication in MNRAS

Galaxies are self-gravitating structures composed by several components encompassing spherical, axial and triaxial symmetry. Although real systems feature heterogeneous components whose properties are intimately connected, semi-analytical approaches often exploit the linearity of the Poisson's equation to represent the potential and mass distribution of a multi-component galaxy as the sum of the individual components. In this work, we expand the semi-analytical framework developed in Bonetti et al. (2020) by including both a detailed implementation of the gravitational potential of exponential disc (modelled with a ${\rm sech}^2$ and an exponential vertical profile) and an accurate prescription for the dynamical friction experienced by massive perturbers in composite galaxy models featuring rotating disc structures. Such improvements allow us to evolve arbitrary orbits either within or outside the galactic disc plane. We validate the results obtained by our numerical model against public semi-analytical codes as well as full N-body simulations, finding that our model is in excellent agreement to the codes it is compared with. The ability to reproduce the relevant physical processes responsible for the evolution of massive perturber orbits and its computational efficiency make our framework perfectly suited for large parameter-space exploration studies., Comment: 17 pages, 9 figures; accepted for publication in MNRAS

Extreme mass ratio inspirals (EMRIs), i.e. binary systems comprised by a compact stellar-mass object orbiting a massive black hole, are expected to be among the primary gravitational wave (GW) sources for the forthcoming LISA mission. The astrophysical processes leading to the formation of such systems still remain poorly understood, resulting into large uncertainties in the predicted cosmic rate of these sources, spanning at least three orders of magnitude. As LISA can individually resolve mostly EMRIs up to $z\gtrsim1$, the ensemble of signals below its detection threshold will add up incoherently forming an unresolved confusion noise, which can be formally described as a stochastic background. We perform an extensive study of this background by considering a collection of astrophysically motivated EMRI formation scenarios, spanning current uncertainties. We find that, for most astrophysical models, this signal is easily detectable by LISA, with signal to noise ratios of several hundreds. In fiducial EMRI models -- predicting hundreds of EMRI detections during mission operations -- the background level is comparable to the LISA noise, affecting the performance of the instrument around 3 mHz. In extreme cases, this background can even "erase" the whole LISA sensitivity bucket in the 2-10 mHz frequency range. This points to the need of a better understanding of EMRIs' astrophysics for a full assessment of the LISA mission potential., Comment: 19 pages, 12 figures, accepted for publication in PRD

Massive black hole binaries (MBHBs) of $10^5 \, \rm M_\odot - 3 \times 10^7 \, \rm M_\odot $ merging in low redshift galaxies ($z\le4$) are sufficiently loud to be detected weeks before coalescence with the Laser Interferometer Space Antenna (LISA). This allows us to perform the parameter estimation $on$ $the$ $fly$, i.e. as a function of the time to coalescence during the inspiral phase, relevant for early warning of the planned LISA protected periods and for searches of electromagnetic signals. In this work, we study the evolution of the sky position, luminosity distance, chirp mass and mass ratio uncertainties as function of time left before merger. Overall, light systems with total intrinsic mass $\rm M_{\rm tot} = 3 \times 10^5 \, \rm M_\odot$ are characterized by smaller uncertainties than heavy ones ($\rm M_{\rm tot} = 10^7 \, \rm M_\odot$) during the inspiral. Luminosity distance, chirp mass and mass ratio are well constrained at the end of the inspiral. Concerning sky position, at $z=1$, MBHBs with $\rm M_{\rm tot} = 3 \times 10^5 \, \rm M_\odot$ can be localized with a median precision of $\simeq 10^2 \, \rm deg^2 (\simeq 1 \, \rm deg^2)$ at 1 month (1 hour) from merger, while the sky position of heavy MBHBs can be determined to $10 \, \rm deg^2$ only 1 hour before merger. However the uncertainty around the median values broadens with time, ranging in between 0.04 -- 20 $\rm deg^2$ (0.3 -- 3 $\times 10^3 \, \rm deg^2$) for light (heavy) systems at 1 hour before merger. At merger the sky localization improves down to $\simeq 10^{-1} \, \rm deg^2$ for all masses. For the benefit of the observer community, we provide the full set of data from our simulations and simple and ready-to-use analytical fits to describe the time evolution of uncertainties in the aforementioned parameters, valid for systems with total mass between $10^5$--$10^7 \, \rm M_\odot$ and redshift $0.3$--$3$., Comment: 31 pages, 24 figures and 6 tables. Accepted for publication in Physical Review D

We revisit the predictions for the merger rate of massive black hole binaries detectable by the Laser Interferometer Space Antenna (LISA) and their background signal for pulsar-timing arrays. We focus on the effect of the delays between the merger of galaxies and the final coalescence of black hole binaries, and on supernova feedback on the black hole growth. By utilizing a semi-analytic galaxy formation model, not only do we account for the driving the evolution of binaries at separations $\lesssim 1$ pc (gas-driven migration, stellar hardening and triple/quadruple massive black hole systems), but we also improve on previous studies by accounting for the time spent by black hole pairs from kpc down to pc separation. We also include the effect of supernova feedback, which may eject gas from the nuclear region of low-mass galaxies, thus hampering the growth of black holes via accretion and suppressing their orbital migration in circumbinary disks. Despite including these novel physical effects, we predict that the LISA detection rate should still be $\gtrsim 2 \mbox{yr}^{-1}$, irrespective of the model for the black hole seeds at high redshifts. Scenarios where black holes form from $\sim100 M_\odot$ seeds are more significantly impacted by supernova feedback. We also find that for detectable events, the merging black holes typically have mass ratios between $\sim 0.1$ and $1$. Predictions for the stochastic background in the band of pulsar-timing array experiments are instead rather robust, and show only a mild dependence on the model., Comment: 17 pages, 10 figures and 2 tables. Matches version published in ApJ

The forthcoming Laser Interferometer Space Antenna (LISA) will probe the population of coalescing massive black hole (MBH) binaries up to the onset of structure formation. Here we simulate the galactic-scale pairing of $\sim10^6 M_\odot$ MBHs in a typical, non-clumpy main-sequence galaxy embedded in a cosmological environment at $z = 7-6$. In order to increase our statistical sample, we adopt a strategy that allows us to follow the evolution of six secondary MBHs concomitantly. We find that the magnitude of the dynamical-friction induced torques is significantly smaller than that of the large-scale, stochastic gravitational torques arising from the perturbed and morphologically evolving galactic disc, suggesting that the standard dynamical friction treatment is inadequate for realistic galaxies at high redshift. The dynamical evolution of MBHs is very stochastic, and a variation in the initial orbital phase can lead to a drastically different time-scale for the inspiral. Most remarkably, the development of a galactic bar in the host system either significantly accelerates the inspiral by dragging a secondary MBH into the centre, or ultimately hinders the orbital decay by scattering the MBH in the galaxy outskirts. The latter occurs more rarely, suggesting that galactic bars overall promote MBH inspiral and binary coalescence. The orbital decay time can be an order of magnitude shorter than what would be predicted relying on dynamical friction alone. The stochasticity, and the important role of global torques, have crucial implications for the rates of MBH coalescences in the early Universe: both have to be accounted for when making predictions for the upcoming LISA observatory., Comment: Accepted for publication in MNRAS; 15 pages, 10 Figures, 2 Tables

We present and validate a novel semi-analytical approach to study the effect of dynamical friction on the orbits of massive perturbers in rotating stellar discs. We find that dynamical friction efficiently circularises the orbit of co-rotating perturbers, while it constantly increases the eccentricity of counter-rotating ones until their angular momenta reverse, then once again promoting circularisation. Such "drag toward circular corotation" could shape the distribution of orientations of kinematically decoupled cores in disc galaxies, naturally leading to the observed larger fraction of co-rotating cores., Comment: 7 pages, 3 figures, accepted for publication in MNRAS

We study the dynamical evolution of eccentric massive black hole binaries (MBHBs) interacting with unbound stars by means of an extensive set of three body scattering experiments. Compared to previous studies, we extend the investigation down to a MBHB mass ratio of $q=m_2/m_1=10^{-4}$, where $m_1$ and $m_2$ are the masses of the primary and secondary hole respectively. Contrary to a simple extrapolation from higher mass ratios, we find that for $q\lesssim 10^{-3}$ the eccentricity growth rate becomes negative, i.e., the binary {\it circularises} as it shrinks. This behaviour is due to the subset of interacting stars captured in metastable counter-rotating orbits; those stars tend to extract angular momentum from the binary, promoting eccentricity growth for $q>10^{-3}$, but tend to inject angular momentum into the binary driving it towards circularisation for $q<10^{-3}$. The physical origin of this behaviour requires a detailed study of the orbits of this subset of stars and is currently under investigation. Our findings might have important consequences for intermediate MBHs (IMBHs) inspiralling onto MBHs (e.g. a putative $10^3\rm M_{\odot}$ black hole inspiralling onto SgrA$^*$)., Comment: 6 pages, 5 figures; accepted for publication in MNRAS

We propose a space-based interferometer surveying the gravitational wave (GW) sky in the milli-Hz to $\mu$-Hz frequency range. By the 2040s', the $\mu$-Hz frequency band, bracketed in between the Laser Interferometer Space Antenna (LISA) and pulsar timing arrays, will constitute the largest gap in the coverage of the astrophysically relevant GW spectrum. Yet many outstanding questions related to astrophysics and cosmology are best answered by GW observations in this band. We show that a $\mu$-Hz GW detector will be a truly overarching observatory for the scientific community at large, greatly extending the potential of LISA. Conceived to detect massive black hole binaries from their early inspiral with high signal-to-noise ratio, and low-frequency stellar binaries in the Galaxy, this instrument will be a cornerstone for multimessenger astronomy from the solar neighbourhood to the high-redshift Universe., Comment: 28 pages, 8 figures; White Paper submitted to ESA's Voyage 2050 call for papers on behalf of the LISA Consortium 2050 Task Force

In current stellar evolutionary models, the occurrence of pair instability supernovae implies the lack of stellar black holes (BHs) with masses between about $[60, \, 120] \, \rm{M}_\odot$, resulting in the presence of an upper mass gap in the BH mass distribution. In this Letter, we develop a fiducial model describing BHs beyond the pair instability gap, by convolving the initial mass function and star formation rate with the metallicity evolution across cosmic time. Under the ansatz that the underlying physics of binary formation does not change beyond the gap, we then construct the cosmic population of merging BH binaries. The detection rate of BH binaries with both mass components above the gap, is found to range between $\simeq [0.4,\,7] \, \rm{yr}^{-1}$ for LIGO/Virgo at design sensitivity and $[10, \, 460] \, \rm{yr}^{-1}$ for third-generation ground based detectors, considering the most pessimistic and optimistic scenarios. LISA can detect individually these binaries up to thousands of years from coalescence. The number of events merging in less than four years, which enable multi-band observation in sequence, is expected in the range $[1, \, 20]$. While ET will detect all these events, LIGO/Virgo is expected to detect $\lesssim 50\%$ of them. Finally, we estimate that the gravitational-wave background from unresolved sources in the LISA band may be in principle detected with a signal-to-noise ratio between $ \simeq 2.5$ and $\simeq 80$., Comment: 7 pages, 4 figures. Accepted to ApJL

Coalescing neutron star binary (NSB) systems are primary candidates for $r$-process enrichment of galaxies. The recent detection of $r$-process elements in ultra-faint dwarf (UFD) galaxies and the abundances measured in classical dwarfs challenges the NSB merger scenario both in terms of coalescence time scales and merger locations. In this paper, we focus on the dynamics of NSBs in the gravitational potentials of different types of host galaxies and on its impact on the subsequent galactic enrichment. We find that, for a $\sim t^{-1}$ delay time distribution, even when receiving a low kick ($\sim 10~{\rm km~s^{-1}}$) from the second supernova explosion, in shallow dwarf galaxy potentials NSBs tend to merge with a large off-set from the host galaxy. This results in a significant geometrical dilution of the amount of produced $r-$process elements that fall back and pollute the host galaxy gas reservoir. The combination of dilution and small number statistics produces a large scatter in the expected $r$-process enrichment within a single UFD or classical dwarf galaxy. Comparison between our results and observed europium abundances reveals a tension that even a systematic choice of optimistic parameters in our models cannot release. Such a discrepancy could point to the need of additional $r$-process production sites that suffer less severe dilution or to a population of extremely fast merging binaries., Comment: 18 pages, 11 figures, MNRAS accepted

In the local universe, black holes of $10^{5-6}$ M$_{\odot}$ are hosted in galaxies displaying a variety of stellar profiles and morphologies. These black holes are the anticipated targets of LISA, the Laser Interferometer Space Antenna that will detect the low-frequency gravitational-wave signal emitted by binary black holes in this mass interval. In this paper, we infer upper limits on the lifetime of binary black holes of $10^{5-6}$ M$_{\odot}$ and up to $10^8$ M$_{\odot}$, forming in galaxy mergers, exploring two underlying stellar density profiles, by Dehnen and by Prugniel & Simien, and by exploiting local scaling relations between the mass of the black holes and several quantities of their hosts. We focus on the phase of the dynamical evolution when the binary is transitioning from the hardening phase ruled by the interaction with single stars to the phase driven by the emission of gravitational waves. We find that different stellar profiles predict very distinct trends with binary mass, with lifetimes ranging between fractions of a Gyr to more than 10 Gyr, and with a spread of about one order of magnitude, given by the uncertainties in the observed correlations, which are larger in the low-mass tail of the observed black hole population., Comment: 11 pages, 6 figures; published on MNRAS

Coalescing massive black hole binaries (MBHBs) of $10^{4-7} \rm M_{\odot}$, forming in the aftermath of galaxy mergers, are primary targets of the space mission LISA, the {\it Laser Interferometer Space Antenna}. An assessment of LISA detection prospects requires an estimate of the abundance and properties of MBHBs that form and evolve during the assembly of cosmic structures. To this aim, we employ a semi-analytic model to follow the co-evolution of MBHBs within their host galaxies. We identify three major evolutionary channels driving the binaries to coalescence: two standard paths along which the binary evolution is driven by interactions with the stellar and/or gaseous environment, and a novel channel where MBHB coalescence occurs during the interaction with a third black hole. For each channel, we follow the orbital evolution of MBHBs with physically motivated models that include a self-consistent treatment of the orbital eccentricity. We find that LISA will detect between $\approx 25$ and $\approx 75$ events per year depending on the seed model. We show that triple-induced coalescences can range from a few detected events up to $\sim 30\%$ of the total detected mergers. Moreover, even if the standard gas/stars-driven evolutionary channels should fail and MBHBs were to stall, triple interactions would still occur as a result of the hierarchical nature of galaxy formation, resulting in about $\approx 10$ to $\approx 20$ LISA detections per year. Remarkably, triple interactions among the black holes can produce coalescing binaries with large eccentricities ($\gtrsim 0.9$) upon entrance into the LISA band. This eccentricity will remain significant ($\sim 0.1$) also at merger, requiring suitable templates for parameter estimation., Comment: 17 pages, 10 figures, Accepted MNRAS