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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; ultra-compact stellar-mass binaries, massive black hole binaries, and extreme or interme-diate 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.

A tidal disruption event (TDE) occurs when a star is destroyed by the strong tidal shear of a massive black hole (MBH). The accumulation of TDE observations over the last years has revealed that post-starburst galaxies are significantly overrepresented in the sample of TDE hosts. Here we address the post-starburst preference by investigating the decline of TDE rates in a Milky-Way like nuclear stellar cluster featuring either a monochromatic (1 M\\(\\odot\\)) or a complete, evolved stellar mass function. In the former case, the decline of TDE rates with time is very mild, and generally up to a factor of a few in 10 Gyr. Conversely, if a complete mass function is considered, a strong TDE burst over the first 0.1-1 Gyr is followed by a considerable rate drop, by at least an order of magnitude over 10 Gyr. The decline starts after a mass segregation time-scale, and it is more pronounced assuming a more top-heavy initial mass function and/or an initially denser nucleus. Our results thus suggest that the post-starburst preference can be accounted for in realistic systems featuring a complete stellar mass function, even in moderately dense galactic nuclei. Overall, our findings support the idea that starbursting galactic nuclei are characterized by a top-heavy initial mass function; we speculate that accounting for this can reconcile the discrepancy between observed and theoretically predicted TDE rates even in quiescent galaxies.

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.

One of the most promising gravitational wave (GW) sources detectable by the forthcoming LISA observatory are the so-called extreme-mass ratio inspirals (EMRIs), i.e. GW-driven inspirals of stellar-mass compact objects onto supermassive black holes (SMBHs). In this paper, we suggest that supernova (SN) kicks may trigger EMRIs in galactic nuclei by scattering newborn stellar black holes and neutron stars on extremely eccentric orbits; as a consequence, the time-scale over which these compact objects are expected to inspiral onto the central SMBH via GW emission may become shorter than the time-scale for other orbital perturbations to occur. By applying this argument to the Galactic Centre, we show that the S-cluster and the clockwise disc are optimal regions for the generation of such events: one SN out of about 10 000 (100 000) occurring in the S-cluster (clockwise disc) is expected to induce an EMRI. If we assume that the natal kicks affecting stellar black holes are significantly slower than those experienced by neutron stars, we find that most SN-driven EMRIs involve neutron stars. We further estimate the time spanning from the SN to the final plunge onto the SMBH to be of the order of few Myr. Finally, we extrapolate the rate of SN-driven EMRIs per Milky Way to be up to 10^-8/yr, thus we expect that LISA will detect up to a few tens of SN-driven EMRIs every year.

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.

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.

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.

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

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.

Massive black hole binary (MBHB) mergers will be detectable in large numbers by the Lisa Interferometer Space Antenna (LISA), which will thus provide new insights on how they form via repeated dark matter (DM) halo and galaxy mergers. Here we present a simple analytical model to generate a population of MBHB mergers based on a theoretical prescription that connects them to DM halo mergers. The high flexibility of our approach allows us to explore the broad and uncertain range of MBH seeding and growth mechanisms, as well as the different effects behind the interplay between MBH and galactic astrophysics. Such a flexibility is fundamental for the successful implementation and optimisation of the hierarchical Bayesian parameter estimation approach that here we apply to the MBHB population of LISA for the first time. Our inferred population hyper-parameters are chosen as proxies to characterise the MBH--DM halo mass scaling relation, the occupation fraction of MBHs in DM halos and the delay between halo and MBHB mergers. We find that LISA will provide tight constraints at the lower-end of the MBH-halo scaling relation, well complementing EM observations which are biased towards large masses. Furthermore, our results suggest that LISA will constrain some features of the MBH occupation fraction at high redshift, as well as merger time delays of the order of a few hundreds of Myr, opening the possibility to constrain dynamical evolution time scales such as the dynamical friction. The analysis presented here constitutes a first attempt at developing a hierarchical Bayesian inference approach to the LISA MBHB population, opening the way for several further improvements and investigations.