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The scenario of feedback-free starbursts (FFB), which predicts excessively bright galaxies at cosmic dawn as observed using JWST, may provide a natural setting for black hole (BH) growth. This involves the formation of intermediate-mass seed BHs and their runaway mergers into super-massive BHs with high BH-to-stellar mass ratios and low AGN luminosities. We present a scenario of merger-driven BH growth in FFB galaxies and study its feasibility. BH seeds form within the building blocks of the FFB galaxies, namely, thousands of compact star clusters, each starbursting in a free-fall time of a few Myr before the onset of stellar and supernova feedback. The BH seeds form by rapid core collapse in the FFB clusters, in a few free-fall times, sped up by the migration of massive stars due to the young, broad stellar mass function and stimulated by a `gravo-gyro' instability due to internal cluster rotation and flattening. BHs of $10^4 M_\odot$ are expected in $10^6 M_\odot$ FFB clusters within sub-kpc galactic disks at $z \sim 10$. The BHs then migrate to the galaxy center by dynamical friction, hastened by the compact FFB stellar galactic disk configuration. Efficient mergers of the BH seeds will produce $10^{6-8} M_\odot$ BHs with a BH-to-stellar mass ratio $\sim 0.01$ by $z \sim 4-7$, as observed. The growth of the central BH by mergers can overcome the bottleneck introduced by gravitational wave recoils if the BHs inspiral within a relatively cold disk or if the escape velocity from the galaxy is boosted by a wet compaction event. Such events, common in massive galaxies at high redshifts, can also help by speeding up the inward BH migration and by providing central gas to assist with the final parsec problem. The cold disk version of the FFB scenario provides a feasible route for the formation of supermassive BHs., Comment: 24 pages, 14 figures

Ultralight scalars emerge naturally in several motivated particle physics scenarios and are viable candidates for dark matter. While laboratory detection of such bosons is challenging, their existence in nature can be imprinted on measurable properties of astrophysical black holes (BHs). The phenomenon of superradiance can convert the BH spin kinetic energy into a bound cloud of scalars. In this letter, we propose a new technique for directly measuring the mass of a dark cloud around a spinning BH. We compare the measurement of the BH spin obtained with two independent electromagnetic techniques: continuum fitting and iron K$\alpha$ spectroscopy. Since the former technique depends on a dynamical observation of the BH mass while the latter does not, a mismatch between the two measurements can be used to infer the presence of additional extended mass around the BH. We find that a precision of $\sim 1\%$ on the two spin measurements is required to exclude the null hypothesis of no dark mass around the BH at a 2$\sigma$ confidence level for dark masses about a few percent of the BH mass, as motivated in some superradiance scenarios., Comment: 12 pages, 3 figures, 1 table. Main text 5 pages, 2 figures, 1 table

The volumetric rate of tidal disruption events (TDEs) encodes information on the still-unknown demographics of central massive black holes (MBHs) in low-mass galaxies ($\lesssim 10^9$~M$_\odot$). Theoretical TDE rates from model galaxy samples can extract this information, but this requires accurately defining the nuclear stellar density structures. This region is typically dominated by nuclear star clusters (NSCs), which have been shown to increase TDE rates by orders of magnitude. Thus, we assemble the largest available sample of pc-scale 3-D density profiles that include NSC components. We deproject the PSF-deconvolved surface brightness profiles of 91 nearby galaxies of varying morphology and combine these with nuclear mass-to-light ratios estimated from measured colors or spectral synthesis to create 3-D mass density profiles. We fit the inner 3-D density profile to find the best-fit power-law density profile in each galaxy. We compile this information as a function of galaxy stellar mass to fit new empirical density scaling relations. These fits reveal positive correlations between galaxy stellar mass and central stellar density in both early- and late-type galaxies. We find that early-type galaxies have somewhat higher densities and shallower profiles relative to late-type galaxies at the same mass. We also use the density profiles to estimate the influence radius of each galaxy's MBH and find that the sphere of influence was likely resolved in most cases. These new relations will be used in future works to build mock galaxy samples for dynamical TDE rate calculations, with the aim of constraining MBH demographics in low-mass galaxies., Comment: 18 pages, 6 figures, 1 table. Accepted by AAS Journals

Advances in time domain astronomy have produced a growing population of flares from galactic nuclei, including both tidal disruption events (TDEs) and flares in active galactic nuclei (AGN). Because TDEs are uncommon and AGN variability is abundant, large-amplitude AGN flares are usually not categorized as TDEs. While TDEs are normally channelled by the collisional process of two-body scatterings over relaxation timescale, the quadrupole moment of a gas disk alters the stellar orbits, allowing them to collisionlessly approach the central massive black hole (MBH). This leads to an effectively enlarged loss cone, the \emph{loss wedge}. Earlier studies found a moderate enhancement, up to a factor $\sim 2-3$, of TDE rates $\dot{N}_{\rm 2b} $ for a static axisymmetric perturbation. Here we study the loss wedge problem for an evolving AGN disk, which can capture large number of stars into the growing loss wedge over much shorter times. The rates $\dot{N}_{\rm cl}$ of collisionless TDEs produced by these time-evolving disks are much higher than the collisional rates $\dot{N}_{\rm 2b}$ in a static loss wedge. We calculate the response of a stellar population to the axisymmetric potential of an adiabatically growing AGN disk and find that the highest rates of collisionless TDEs are achieved for the largest (i) MBH masses $M_{\bullet}$ and (ii) disk masses $M_{\rm d}$. For $M_{\bullet}\sim 10^7 M_\odot$ and $M_{\rm d} \sim 0.1 M_{\bullet}$, the rate enhancement can be up to a factor $\dot{N}_{\rm cl}/\dot{N}_{\rm 2b} \sim 10$. The orbits of collisionless TDEs sometimes have a preferred orientation in apses, carrying implications for observational signatures of resulting flares., Comment: Submitted to ApJ; 24 pages, 8 figures; comments are welcome

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

In this paper, we continue our analysis of the chaotic four-body problem by presenting a general ansatz-based analytic treatment using statistical mechanics, where each outcome of the four-body problem is regarded as some variation of the three-body problem (e.g., when two single stars are produced, called the 2+1+1 outcome, each ejection event is modeled as its own three-body interaction by assuming that the ejections are well separated in time). This is a generalization of the statistical mechanics treatment of the three-body problem based on the density-of-states formalism. In our case, we focus on the interaction of two binary systems, after which we divide our results into three possible outcome scenarios (2+2, 2+1+1, and 3+1). For each outcome, we apply an ansatz-based approach to deriving analytic distribution functions that describe the properties of the products of chaotic four-body interactions involving point particles. To test our theoretical distributions, we perform a set of scattering simulations in the equal-mass point particle limit using FEWBODY. We compare our final theoretical distributions to the simulations for each particular scenario, finding consistently good agreement between the two. The highlights of our results include that binary-binary scatterings act to systematically destroy binaries producing instead a single binary and two ejected stars or a stable triple, the 2+2 outcome produces the widest binaries and the 2+1+1 outcome produces the most compact binaries., Comment: 10 pages, 8 figures. Comments are welcome

Accretion discs in active galactic nuclei (AGN) foster black hole (BH) formation, growth, and mergers. Stellar mass BHs migrate inwards under the influence of hydrodynamical torques unless they encounter a region where the torque flips sign. At these migration traps, BHs accumulate and merge via dynamical or gas-assisted interactions, producing high-frequency LIGO/Virgo/KAGRA (LVK) gravitational wave (GW) sources and potentially cutting off the supply of extreme mass ratio inspirals that would otherwise make low-frequency, {\it LISA}-band GWs. In this paper, we study the interplay between different types of migration torques, focusing especially on the ``thermal torques'' generated by the thermal response of the AGN to embedded stellar-mass BHs that accrete through their own mini-discs.In contrast to previous work, we find that Type I torques cannot produce migration traps on their own, but thermal torques often do, particularly in low-mass AGN. The migration traps produced by thermal torques exist at much larger radii ($\sim 10^{3-5}$ gravitational radii) than do previously identified Type I traps, carrying implications for GW populations at multiple frequencies. Finally, we identify a bifurcation of AGN discs into two regimes: migration traps exist below a critical AGN luminosity, and do not at higher luminosities. This critical luminosity is fit as $\log_{10} L_{\rm AGN}^c = 45 - 0.32 \log_{10}{(\alpha/0.01)}$ where $\alpha$ is the AGN alpha viscosity parameter, a range compatible with recent claims that LVK GWs are not preferentially associated with high-luminosity AGN., Comment: Accepted to MNRAS

The overcooling of cool core clusters is a persistent puzzle in the astrophysics of galaxy clusters. We propose that it may naturally be resolved via interactions between the baryons of the intracluster medium (ICM) and its dark matter (DM). DM-baryon interactions can inject heat into the ICM to offset bremmstrahlung cooling, but these interactions are also strongly constrained by existing experiments and astrophysical observations. We survey existing constraints and combine these with the energetic needs of an observed sample of cool core clusters. We find that a robust parameter space exists for baryon-DM scattering solutions to the cooling flow problem, provided that only a sub-component of DM interacts strongly with the baryons. Interestingly, baryon-DM scattering is a thermally stable heating source so long as the baryon temperature is greater than $1/3-1/2$ the DM temperature, a condition that seems to be satisfied observationally., Comment: 11 pages, 2 figures; corrected figure 1

Extreme mass ratio inspirals (EMRIs) occur when stellar-mass compact objects begin a gravitational wave (GW) driven inspiral into massive black holes. EMRI waveforms can precisely map the surrounding spacetime, making them a key target for future space-based GW interferometers such as {\it LISA}, but their event rates and parameters are massively uncertain. One of the largest uncertainties is the ratio of true EMRIs (which spend at least thousands of orbits in the {\it LISA} band) and direct plunges, which are in-band for at most a handful of orbits and are not detectable in practice. In this paper, we show that the traditional dichotomy between EMRIs and plunges -- EMRIs originate from small semimajor axes, plunges from large -- does not hold for intermediate-mass black holes with masses $M_\bullet \lesssim 10^5 M_\odot$. In this low-mass regime, a plunge always has an $\mathcal{O}(1)$ probability of failing and transitioning into a novel ``cliffhanger'' EMRI. Cliffhanger EMRIs are more easily produced for larger stellar-mass compact objects, and are less likely for smaller ones. This new EMRI production channel can dominate volumetric EMRI rates $\dot{n}_{\rm EMRI}$ if intermediate-mass black holes are common in dwarf galactic nuclei, potentially increasing $\dot{n}_{\rm EMRI}$ by an order of magnitude., Comment: 8 pages, 6 figures, comments welcome

We predict late-time optical/UV emission from tidal disruption events (TDEs) from our slim accretion disc model \citep{Wen20} and explore the impact of the black hole mass $M_\bullet$, black hole spin $a_\bullet$, and accretion disc size. We use these synthetic spectra to successfully fit the multi-band \emph{Swift} observations of ASASSN-14li at >350 days, setting only the host galaxy extinction and outer disc radius as free parameters and employing the $M_\bullet$, $a_\bullet$, disc inclination, and disc accretion rates derived from fitting 10 epochs of ASASSN-14li's X-ray spectra with the slim disc. To address the nature of the \emph{early}-time optical/UV emission, we consider two models: shock dissipation and reprocessing. We find that (1) the predicted late-time optical/UV colour (e.g., $u-w2$) is insensitive to black hole and disc parameters unless the disc spreads quickly; (2) a starburst galaxy extinction model is required to fit the data, consistent with ASASSN-14li's post-starburst host; (3) surprisingly, the outer disc radius is $\approx$2$\times$ the tidal radius and $\sim$constant at late times, showing that viscous spreading is slow or non-existent; (4) the shock model can be self-consistent if $M_\bullet \lesssim 10^{6.75}$M$_\odot$, i.e., on the low end of ASASSN-14li's $M_\bullet$ range ($10^{6.5-7.1}$M$_\odot$; 1$\sigma$ CL); larger black hole masses require disruption of an unrealistically massive progenitor star; (5) the gas mass needed for reprocessing, whether by a quasi-static or an outflowing layer, can be $<0.5$M$_\odot$, consistent with a (plausible) disruption of a solar-mass star., Comment: 15 pages, 10 figures. Accepted for publication in MNRAS

We present $N\mathrm{-body} $ simulations, including post-Newtonian dynamics, of dense clusters of low-mass stars harbouring central black holes (BHs) with initial masses of 50, 300, and 2000 $\mathrm{M_{\odot}}$. The models are evolved with the $N\mathrm{-body} $ code \textsc{bifrost} to investigate the possible formation and growth of massive BHs by the tidal capture of stars and tidal disruption events (TDEs). We model star-BH tidal interactions using a velocity-dependent drag force, which causes orbital energy and angular momentum loss near the BH. About $\sim 20-30$ per cent of the stars within the spheres of influence of the black holes form Bahcall-Wolf cusps and prevent the systems from core collapse. Within the first 40 Myr of evolution, the systems experience 500 up to 1300 TDEs, depending on the initial cluster structure. Most ($> 95$ per cent) of the TDEs originate from stars in the Bahcall-Wolf cusp. We derive an analytical formula for the TDE rate as a function of the central BH mass, density and velocity dispersion of the clusters ($\dot{N}_{\mathrm{TDE}} \propto M\mathrm{_{BH}} \rho \sigma^{-3}$). We find that TDEs can lead a 300 $\mathrm{M_{\odot}}$ BH to reach $\sim 7000 \mathrm{M_{\odot}}$ within a Gyr. This indicates that TDEs can drive the formation and growth of massive BHs in sufficiently dense environments, which might be present in the central regions of nuclear star clusters., Comment: 17 pages, 18 figures

A star wandering close enough to a massive black hole (MBH) can be ripped apart by the tidal forces of the black hole. The advent of wide-field surveys at many wavelengths has quickly increased the number of tidal disruption events (TDEs) observed, and has revealed that i) observed TDE rates are lower than theoretical predictions and ii) E+A galaxies are significantly overrepresented. This overrepresentation further worsens the tension between observed and theoretically predicted TDEs for non-E+A galaxies. Classical loss cone theory focuses on the cumulative effect of many weak scatterings. However, a strong scattering can remove a star from the distribution before it can get tidally disrupted. Most stars undergoing TDEs come from within the radius of influence, the densest environments of the universe. In such environments, close encounters rare elsewhere become non-negligible. We revise the standard loss cone theory to take into account classical two-body interactions as well as strong scattering, collisions, tidal captures, and study under which conditions close encounters can shield the loss cone. We i) analytically derive the impact of strong scattering and other close encounters, ii) compute time-dependent loss cone dynamics including both weak and strong encounters, and iii) derive analytical solutions to the Fokker-Planck equation with strong scattering. We find that i) TDE rates can be reduced to up to an order of magnitude and ii) strong shielding preferentially reduces deeply plunging stars. We also show that stellar overdensities, one possible explanation for the E+A preference, can fail to increase TDE rates when taking into account strong scattering., Comment: 14 pages, 10 figures, Accepted for publication MNRAS

The classical radiation pressure instability has been a persistent theoretical feature of thin, radiatively efficient accretion disks with accretion rates 1 to 100 per cent of the Eddington rate. But there is only limited evidence of its occurrence in nature: rapid heartbeat oscillations of a few X-ray binaries and now, perhaps, the new class of hourly X-ray transients called quasi-periodic eruptions (QPEs). The accretion disks formed in tidal disruption events (TDEs) have been observed to peacefully trespass through the range of unstable accretion rates without exhibiting any clear sign of the instability. We try to explain the occurrence or otherwise of this instability in these systems, by constructing steady state 1D models of thin magnetic accretion disks. The local magnetic pressure in the disk is assumed to be dominated by toroidal fields arising from a dynamo sourced by magneto-rotational instability (MRI). We choose a physically motivated criterion of MRI saturation, validated by recent magnetohydrodynamic simulations, to determine the strength of magnetic pressure in the disk. The resulting magnetic pressure support efficiently shrinks: (1) the parameter space of unstable mass accretion rates, explaining the absence of instability in systems such as TDEs and (2) the range of unstable radii in the inner accretion disk, which can shorten the quasi-periods of instability limit-cycles by more than three orders of magnitude, explaining the observed periods ( a few hrs) of QPEs. In addition to examining stability properties of strongly magnetized disks, we predict other observational signatures such as spectral hardening factors and jet luminosities to test the compatibility of our disk models with observations of apparently stable TDE disks., Comment: Submitted to MNRAS

Information about the structure and composition of biopsy specimens can assist in disease monitoring and diagnosis. In principle, this can be acquired from Raman and infrared (IR) hyperspectral images (HSIs) that encode information about how a sample's constituent molecules are arranged in space. Each tissue section/component is defined by a unique combination of spatial and spectral features, but given the high dimensionality of HSI datasets, extracting and utilising them to segment images is non-trivial. Here, we show how networks based on deep convolutional autoencoders (CAEs) can perform this task in an end-to-end fashion by first detecting and compressing relevant features from patches of the HSI into low-dimensional latent vectors, and then performing a clustering step that groups patches containing similar spatio-spectral features together. We showcase the advantages of using this end-to-end spatio-spectral segmentation approach compared to i) the same spatio-spectral technique not trained in an end-to-end manner, and ii) a method that only utilises spectral features (spectral k-means) using simulated HSIs of porcine tissue as test examples. Secondly, we describe the potential advantages/limitations of using three different CAE architectures: a generic 2D CAE, a generic 3D CAE, and a 2D CNN architecture inspired by the recently proposed UwU-net that is specialised for extracting features from HSI data. We assess their performance on IR HSIs of real colon samples. We find that all architectures are capable of producing segmentations that show good correspondence with HE stained adjacent tissue slices used as approximate ground truths, indicating the robustness of the CAE-driven approach for segmenting biomedical HSI data. Additionally, we stress the need for more accurate ground truth information to rigorously compare the advantages offered by each architecture.

The Ultraviolet Transient Astronomy Satellite (ULTRASAT) is a space-borne near UV telescope with an unprecedented large field of view (200 sq. deg.). The mission, led by the Weizmann Institute of Science and the Israel Space Agency in collaboration with DESY (Helmholtz association, Germany) and NASA (USA), is fully funded and expected to be launched to a geostationary transfer orbit in Q2/3 of 2025. With a grasp 300 times larger than GALEX, the most sensitive UV satellite to date, ULTRASAT will revolutionize our understanding of the hot transient universe, as well as of flaring galactic sources. We describe the mission payload, the optical design and the choice of materials allowing us to achieve a point spread function of ~10arcsec across the FoV, and the detector assembly. We detail the mitigation techniques implemented to suppress out-of-band flux and reduce stray light, detector properties including measured quantum efficiency of scout (prototype) detectors, and expected performance (limiting magnitude) for various objects., Comment: Presented in the SPIE Astronomical Telescopes + Instrumentation 2022

The "no-hair" theorem can, in principle, be tested at the center of the Milky Way by measuring the spin and the quadrupole moment of Sgr A$^*$ with the orbital precession of S-stars, measured over their full periods. Contrary to the original method, we show why it is possible to test the no-hair theorem using observations from only a single star, by measuring precession angles over a half-orbit. There are observational and theoretical reasons to expect S-stars to spin rapidly, and we have quantified the effect of stellar spin, via spin-curvature coupling (the leading-order manifestation of the Mathisson-Papapetrou-Dixon equations), on future quadrupole measurements. We find that they will typically suffer from errors of order a few percentage points, but for some orbital parameters, the error can be much higher. We re-examine the more general problem of astrophysical noise sources that may impede future quadrupole measurements, and find that a judicious choice of measurable precession angles can often eliminate individual noise sources. We have derived optimal combinations of observables to eliminate the large noise source of mass precession, the novel noise of spin-curvature coupling due to stellar spin, and the more complicated noise source arising from transient quadrupole moments in the stellar potential., Comment: Minor changes made for consistency with PRD version

Tidal disruption events occur when stars are ripped apart by massive black holes, and result in highly luminous, multi-wavelength flares. Optical/UV observations of tidal disruption events (TDEs) contradict simple models of TDE emission, but the debate between alternative models (e.g. shock power or reprocessed accretion power remains unsettled, as the dynamic range of the problem has so far prevented ab initio hydrodynamical simulations. Consequently, past simulations have resorted to unrealistic parameter choices, artificial mass injection schemes or very short run-times. Here we present a 3D radiation-hydrodynamic simulation of a TDE flare from disruption to peak emission, with typical astrophysical parameters. At early times, shocks near pericenter power the light curve and a novel source of X-ray emission, but circularization and outflows are inefficient. Near peak light, stream-disk shocks efficiently circularize returning debris, power stronger outflows, and reproduce observed peak optical/UV luminosities. Peak emission in this simulation is shock-powered, but upper limits on accretion power become competitive near peak light as circularization runs away. This simulation shows how deterministic predictions of TDE light curves and spectra can be calculated using moving-mesh hydrodynamics algorithms., Comment: Updated to match final version accepted for publication. Movies at https://www.youtube.com/watch?v=O3IWCPO_Thk https://www.youtube.com/watch?v=_kpBQjwf3Z4

We apply the theory of nonlinear resonance capture to the problem of a black hole binary (BHB) orbiting a supermassive black hole (SMBH) while embedded in the accretion disk of an active galactic nucleus (AGN). If successful, resonance capture can trigger dramatic growth in the BHB eccentricity, with important consequences for the BHB merger timescale, as well as for the gravitational wave (GW) signature of such an eccentric merger. This resonance capture may occur when the orbital period around the SMBH (the "outer binary") and the apsidal precession of the BHB (the "inner binary") are in a 1:1 commensurability. This effect is analogous to the phenomenon of lunar evection resonance in the early Sun-Earth-Moon system, with the distinction that in the present case, the BHB apsidal precession is due to general relativity, rather than rotationally-induced distortion. In contrast to the case of lunar evection, however, the inner binary undergoes orbital decay driven by GW emission, rather than orbital expansion driven by tidal dissipation. This distinction fundamentally alters the three-body dynamics, forbidding resonance capture, and limiting eccentricity growth. However, if the BHB migrates through of a gaseous AGN disk, the change in the outer binary can counterbalance the suppressing effect of BHB decay, permitting evection resonance capture and the production of eccentric BHB mergers. We compute the likelihood of resonance capture assuming an agnostic distribution of parameters for the three bodies involved and for the properties of the AGN disk. We find that intermediate-mass ratio BHBs (involving an intermediate-mass black hole and a stellar-mass black hole) are the most likely to be captured into evection resonance and thus undergo an eccentric merger. We also compute the GW signature of these mergers, showing that they can enter the LISA band while eccentric., Comment: 15 pages (before references and appendices), 11 figures, comments welcome

We present a tabulated version of our slim disk model for fitting tidal disruption events (TDEs). We create a synthetic X-ray spectral library by ray-tracing stationary general relativistic slim disks and including gravitational redshift, Doppler, and lensing effects self-consistently. We introduce the library to reduce computational expense and increase access for fitting future events. Fitting requires interpolation between the library spectra; the interpolation error in the synthetic flux is generally $<10\%$ (it can rise to $40\%$ when the disk is nearly edge-on). We fit the X-ray spectra of the TDEs ASASSN-14li and ASASSN-15oi, successfully reproducing our earlier constraints on black hole mass $M_\bullet$ and spin $a_\bullet$ from full on-the-fly ray-tracing. We use the library to fit mock observational data to explore the degeneracies among parameters, finding that 1) hotter thermal disk and edge-on inclination angle spectra offer tighter constraints on $M_\bullet$ and $a_\bullet$; 2) the constraining power of spectra on $M_\bullet$ and $a_\bullet$ increases as a power-law with the number of X-ray counts, and the index of the power law is higher for hotter thermal disk spectra; 3) multi-epoch X-ray spectra partially break the degeneracy between $M_\bullet$ and $a_\bullet$; 4) the time-dependent level of X-ray absorption can be constrained from spectral fitting. The tabulated model and slim disk model are {\href{https://doi.org/10.25739/hfhz-xn60}{here.}, Comment: Accepted for Publication in ApJ

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 analyze Chandra X-ray Observatory imaging of 108 galaxies hosting nuclear star clusters (NSCs) to search for signatures of massive black holes (BHs). NSCs are extremely dense stellar environments with conditions that can theoretically facilitate massive BH formation. Recent work by Stone et al. (2017) finds that sufficiently dense NSCs should be unstable to the runaway growth of a stellar mass BH into a massive BH via tidal captures. Furthermore, there is a velocity dispersion threshold ($40\;\rm{km\;s^{-1}}$) above which NSCs should inevitably form a massive BH. To provide an observational test of these theories, we measure X-ray emission from NSCs and compare to the measured velocity dispersion and tidal capture runaway timescale. We find that NSCs above the $40\;\rm{km\;s^{-1}}$ threshold are X-ray detected at roughly twice the rate of those below (after accounting for contamination from X-ray binaries). These results are consistent with a scenario in which dense, high-velocity NSCs can form massive BHs, providing a formation pathway that does not rely on conditions found only at high redshift., Comment: Resubmitted to AAS Journals on March 1, 2022

Dynamical friction is often modeled with reasonable accuracy by the widely used Chandrasekhar formula. However, in some circumstances, Chandrasekhar's local and uniform approximations can break down severely. An astrophysically important example is the "core stalling" phenomenon seen in N-body simulations of massive perturber inspiralling into the near-harmonic potential of a stellar system's constant-density core (and possibly also in direct observations of dwarf galaxies with globular clusters). In this paper we use the linearized collisionless Boltzmann equation to calculate the global response of a cored galaxy to the presence of a massive perturber. We evaluate the density deformation, or wake, due to the perturber and study its geometrical structure to better understand the phenomenon of core stalling. We also evaluate the dynamical friction torque acting on perturber from the Lynden-Bell--Kalnajs (LBK) formula. In agreement with past work, we find that the dynamical friction force arising from corotating resonances is greatly weakened, relative to the Chandrasekhar formula, inside a constant density core. In contrast to past work, however, we find that a population of previously neglected high-order and non-corotating resonances sustain a minimum level of frictional torque at ~10 % of the torque from Chandrasekhar formula. This suggests that complete core stalling likely requires phenomena beyond the LBK approach; we discuss several possible explanations. Additionally, to study core stalling for multiple perturbers, we investigate approximate secular dynamical interactions (akin to Lidov-Kozai dynamics) between two perturbers orbiting a cored stellar system and derive a criterion for instability arising due to their close encounters., Comment: Submitted for publication to MNRAS; comments are welcome

A star that approaches a supermassive black hole (SMBH) on a circular extreme mass ratio inspiral (EMRI) can undergo Roche lobe overflow (RLOF), resulting in a phase of long-lived mass-transfer onto the SMBH. If the interval separating consecutive EMRIs is less than the mass-transfer timescale driven by gravitational wave emission (typically ~1-10 Myr), the semi-major axes of the two stars will approach each another on scales of <~ hundreds to thousands of gravitational radii. Close flybys tidally strip gas from one or both RLOFing stars, briefly enhancing the mass-transfer rate onto the SMBH and giving rise to a flare of transient X-ray emission. If both stars reside in an common orbital plane, these close interactions will repeat on a timescale as short as hours, generating a periodic series of flares with properties (amplitudes, timescales, sources lifetimes) remarkably similar to the "quasi-periodic eruptions" (QPEs) recently observed from galactic nuclei hosting low-mass SMBHs. A cessation of QPE activity is predicted on a timescale of months to years, due to nodal precession of the EMRI orbits out of alignment by the SMBH spin. Channels for generating the requisite coplanar EMRIs include the tidal separation of binaries (Hills mechanism) or Type I inwards migration through a gaseous AGN disk. Alternative scenarios for QPEs, that invoke single stellar EMRIs on an eccentric orbit undergoing a runaway sequence of RLOF events, are strongly disfavored by formation rate constraints., Comment: 13 pages, 4 figures, submitted to ApJ

We present new two-fluid models of accretion disks in active galactic nuclei (AGNs) that aim to address the long-standing problem of Toomre instability in AGN outskirts. In the spirit of earlier works by Sirko & Goodman and others, we argue that Toomre instability is eventually self-regulated via feedback produced by fragmentation and its aftermath. Unlike past semianalytic models, which (i) adopt local prescriptions to connect star formation rates to heat feedback, and (ii) assume that AGN disks self-regulate to a star-forming steady state (with Toomre parameter Q=1), we find that feedback processes are both temporally and spatially nonlocal. The accumulation of many stellar-mass black holes (BHs) embedded in AGN gas eventually displaces radiation, winds and supernovae from massive stars as the dominant feedback source. The nonlocality of feedback heating, in combination with the need for heat to efficiently mix throughout the gas, gives rise to steady-state AGN solutions that can have Q>>1 and no ongoing star formation. We find self-consistent steady-state solutions in much of the parameter space of AGN mass and accretion rate. These solutions harbor large populations of embedded compact objects that may grow in mass by factors of a few over the AGN lifetime, including into the lower and upper mass gaps. These feedback-dominated AGN disks differ significantly in structure from commonly used 1D disk models, which has broad implications for gravitational-wave-source formation inside AGNs., Comment: 26 pages, 18 figures, 4 appendices. Comments are welcome

The discovery of gravitational wave radiation from merging black holes (BHs) also uncovered BHs with masses in the range of ~20-160 Msun. In contrast, the most massive Galactic stellar-mass BH currently known has a mass ~21 Msun. While low-mass X-ray binaries (LMXBs) will never independently evolve into a binary BH system, and binary evolution effects can play an important role explaining the different BH masses found through studies of X-ray binaries and gravitational wave events, (electromagnetic) selection effects may also play a role in this discrepancy. Assuming BH LMXBs originate in the Galactic Plane, we show that the spatial distribution of the current sample of confirmed and candidate BH LMXBs are both biased to sources that lie at a large distance from the Plane. Specifically, most of the confirmed and candidate BH LMXBs are found at a Galactic height larger than 3 times the scale height for massive star formation. In addition, the confirmed BH LMXBs are found at larger distances to the Galactic Center than the candidate BH LMXBs. Interstellar absorption makes candidate BH LMXBs in the Plane and those in the Bulge too faint for a dynamical mass measurement using current instrumentation. Given the observed and theoretical evidence for BH natal and/or Blaauw kicks, their relation with BH mass and binary orbital period, and the relation between outburst recurrence time and BH mass, the observational selection effects imply that the current sample of confirmed BH LMXBs is biased against the most massive BHs., Comment: 17 pages, 3 figures, 2 tables, accepted for publication in ApJ

We simultaneously and successfully fit the multi-epoch X-ray spectra of the tidal disruption event (TDE) 3XMM J215022.4-055108 using a modified version of our relativistic slim disk model that now accounts for angular momentum losses from radiation. We explore the effects of different disk properties and of uncertainties in the spectral hardening factor fc and redshift z on the estimation of the black hole mass M and spin a. Across all choices of theoretical priors, we constrain M to less than 2.2e4 Ms at 1 sigma confidence. Assuming that the TDE host is a star cluster associated with the adjacent, brighter, barred lenticular galaxy at z=0.055, we constrain M and a to be (1.75+0.45-0.05)e4 Ms and 0.8+0.12-0.02, respectively, at 1 sigma confidence. The high, but sub-extremal, spin suggests that, if this intermediate mass black hole (IMBH) has grown significantly since formation, it has acquired its last e-fold in mass in a way incompatible with both the standard and chaotic limits of gas accretion. Ours is the first clear IMBH with a spin measurement. As such, this object represents a novel laboratory for astro-particle physics; its M and a place tight limits on the existence of ultralight bosons, ruling out those with masses 1.0e-15 to 1.0e-16 eV., Comment: 19 pages, 10 figure and 5 tables. Accepted for publication in Apj

After a star has been tidally disrupted by a black hole, the debris forms an elongated stream. We start by studying the evolution of this gas before its bound part returns to the original stellar pericenter. While the axial motion is entirely ballistic, the transverse directions of the stream are usually thinner due to the confining effects of self-gravity. This basic picture may also be influenced by additional physical effects such as clump formation, hydrogen recombination, magnetic fields and the interaction with the ambient medium. We then examine the fate of this stream when it comes back to the vicinity of the black hole to form an accretion flow. Despite recent progress, the hydrodynamics of this phase remains uncertain due to computational limitations that have so far prevented us from performing a fully self-consistent simulation. Most of the initial energy dissipation appears to be provided by a self-crossing shock that results from an intersection of the stream with itself. The debris evolution during this collision depends on relativistic apsidal precession, expansion of the stream from pericenter, and nodal precession induced by the black hole spin. Although the combined influence of these effects is not fully understood, current works suggest that this interaction is typically too weak to significantly circularize the trajectories, with its main consequence being an expansion of the shocked gas. Global simulations of disc formation using simplified initial conditions find that the debris experiences additional collisions that cause its orbits to become more circular until eventually settling into a thick structure. These works suggest that this process completes faster for more relativistic encounters due to stronger shocks. However, important aspects still remain to be understood at the time of writing, due to numerical challenges and the complexity of this process., Comment: Accepted by Space Science Reviews, Springer. Chapter in ISSI review book: "The Tidal Disruption of Stars by Massive Black Holes"

When a star passes close to a supermassive black hole (BH), the BH's tidal forces rip it apart into a thin stream, leading to a tidal disruption event (TDE). In this work, we study the post-disruption phase of TDEs in general relativistic hydrodynamics (GRHD) using our GPU-accelerated code H-AMR. We carry out the first grid-based simulation of a deep-penetration TDE ($\beta$=7) with realistic system parameters: a black-hole-to-star mass ratio of $10^6$, a parabolic stellar trajectory, and a nonzero BH spin. We also carry out a simulation of a tilted TDE whose stellar orbit is inclined relative to the BH midplane. We show that for our aligned TDE, an accretion disk forms due to the dissipation of orbital energy with $\sim$20 percent of the infalling material reaching the BH. The dissipation is initially dominated by violent self-intersections and later by stream-disk interactions near the pericenter. The self-intersections completely disrupt the incoming stream, resulting in five distinct self-intersection events separated by approximately 12 hours and a flaring in the accretion rate. We also find that the disk is eccentric with mean eccentricity e$\approx$0.88. For our tilted TDE, we find only partial self-intersections due to nodal precession near pericenter. Although these partial intersections eject gas out of the orbital plane, an accretion disk still forms with a similar accreted fraction of the material to the aligned case. These results have important implications for disk formation in realistic tidal disruptions. For instance, the periodicity in accretion rate induced by the complete stream disruption may explain the flaring events from Swift J1644+57., Comment: Accepted to MNRAS on November 23rd, 2021, 23 pages, 25 figures, uses mnras.cls. Comments welcome. Movies available at https://www.youtube.com/playlist?list=PL7YbfRC6zxzAqIPXWbJgXpr4Wq_nwHiDu

Tidal disruption events (TDEs) are among the brightest transients in the optical, ultraviolet, and X-ray sky. These flares are set into motion when a star is torn apart by the tidal field of a massive black hole, triggering a chain of events which is -- so far -- incompletely understood. However, the disruption process has been studied extensively for almost half a century, and unlike the later stages of a TDE, our understanding of the disruption itself is reasonably well converged. In this Chapter, we review both analytical and numerical models for stellar tidal disruption. Starting with relatively simple, order-of-magnitude physics, we review models of increasing sophistication, the semi-analytic ``affine formalism,'' hydrodynamic simulations of the disruption of polytropic stars, and the most recent hydrodynamic results concerning the disruption of realistic stellar models. Our review surveys the immediate aftermath of disruption in both typical and more unusual TDEs, exploring how the fate of the tidal debris changes if one considers non-main sequence stars, deeply penetrating tidal encounters, binary star systems, and sub-parabolic orbits. The stellar tidal disruption process provides the initial conditions needed to model the formation of accretion flows around quiescent massive black holes, and in some cases may also lead to directly observable emission, for example via shock breakout, gravitational waves or runaway nuclear fusion in deeply plunging TDEs., Comment: Review chapter in book: 'The Tidal Disruption of Stars by Massive Black Holes', Space Science Reviews, Springer. Comments welcome

We develop a new model for X-ray emission from tidal disruption events (TDEs), applying stationary general relativistic ``slim disk'' accretion solutions to supermassive black holes (SMBHs) and then ray-tracing the photon trajectories from the image plane to the disk surface, including gravitational redshift, Doppler, and lensing effects self-consistently. We simultaneously and successfully fit the multi-epoch XMM-Newton X-ray spectra for two TDEs: ASASSN-14li and ASASSN-15oi. We test explanations for the observed, unexpectedly slow X-ray brightening of ASASSN-15oi, including delayed disk formation and variable obscuration by a reprocessing layer. We propose a new mechanism that better fits the data: a ``Slimming Disk'' scenario in which accretion onto an edge-on disk slows, reducing the disk height and exposing more X-rays from the inner disk to the sightline over time.For ASASSN-15oi, we constrain the SMBH mass to $4.0^{+2.5}_{-3.1} \times 10^6M_\odot$. For ASASSN-14li, the SMBH mass is $10^{+1}_{-7}\times 10^6M_\odot$ and the spin is $>0.3$. For both TDEs, our fitted masses are consistent with independent estimates; for ASASSN-14li, application of the external mass constraint narrows our spin constraint to $>0.85$. The mass accretion rate of ASASSN-14li decays slowly, as $\propto t^{-1.1}$, perhaps due to inefficient debris circularization. Over $\approx$1100 days, its SMBH has accreted $\Delta M \approx 0.17 M_\odot$, implying a progenitor star mass of $> 0.34 M_\odot$, i.e., no ``missing energy problem.'' For both TDEs, the hydrogen column density declines to the host galaxy plus Milky Way value after a few hundred days, suggesting a characteristic timescale for the depletion or removal of obscuring gas., Comment: Accepted for publication in ApJ

Tidal disruption events occur rarely in any individual galaxy. Over the last decade, however, time-domain surveys have begun to accumulate statistical samples of these flares. What dynamical processes are responsible for feeding stars to supermassive black holes? At what rate are stars tidally disrupted in realistic galactic nuclei? What may we learn about supermassive black holes and broader astrophysical questions by estimating tidal disruption event rates from observational samples of flares? These are the questions we aim to address in this Chapter, which summarizes current theoretical knowledge about rates of stellar tidal disruption, and compares theoretical predictions to the current state of observations., Comment: Accepted for publication in Springer Space Science Reviews. Chapter in ISSI review, "The Tidal Disruption of Stars by Massive Black Holes," vol. 79

We explore the galaxy structure of four tidal disruption event (TDE) host galaxies on 30 pc to kpc scales using HST WFC3 multi-band imaging. The star formation histories of these hosts are diverse, including one post-starburst galaxy (ASASSN-14li), two hosts with recent weak starbursts (ASASSN-14ae and iPTF15af), and one early type (PTF09ge). Compared to early type galaxies of similar stellar masses, the TDE hosts have higher central surface brightnesses and stellar mass surface densities on 30-100 pc scales. The TDE hosts do not show the large, kpc-scale tidal disruptions seen in some post-starburst galaxies; the hosts have low morphological asymmetries similar to those of early type galaxies. The lack of strong asymmetries are inconsistent with a recent major (~1:1 mass) merger, although minor ($\lesssim$1:3) mergers are possible. Given the time elapsed since the end of the starbursts in the three post-burst TDE hosts and the constraints on the merger mass ratios, it is unlikely that a bound supermassive black hole binary (SMBHB) has had time to coalesce. The TDE hosts have low central (<140 pc) ellipticities compared to early type galaxies. The low central ellipticities disfavor a strong radial anisotropy as the cause for the enhanced TDE rate, although we cannot rule out eccentric disks at the scale of the black hole gravitational radius of influence (~1 pc). These observations suggest that the high central stellar densities are a more important driver than SMBHBs or radial anisotropies in increasing the TDE rate in galaxies with recent starbursts., Comment: Accepted for publication in ApJ. 22 pages, 12 figures

The three-body problem is arguably the oldest open question in astrophysics, and has resisted a general analytic solution for centuries. Various implementations of perturbation theory provide solutions in portions of parameter space, but only where hierarchies of masses or separations exist. Numerical integrations show that bound, non-hierarchical triples of Newtonian point particles will almost always disintegrate into a single escaping star and a stable, bound binary, but the chaotic nature of the three-body problem prevents the derivation of tractable analytic formulae deterministically mapping initial conditions to final outcomes. However, chaos also motivates the assumption of ergodicity, suggesting that the distribution of outcomes is uniform across the accessible phase volume. Here, we use the ergodic hypothesis to derive a complete statistical solution to the non-hierarchical three-body problem, one which provides closed-form distributions of outcomes (e.g. binary orbital elements) given the conserved integrals of motion. We compare our outcome distributions to large ensembles of numerical three-body integrations, and find good agreement, so long as we restrict ourselves to "resonant" encounters (the ~50% of scatterings that undergo chaotic evolution). In analyzing our scattering experiments, we identify "scrambles" (periods in time where no pairwise binaries exist) as the key dynamical state that ergodicizes a non-hierarchical triple. The generally super-thermal distributions of survivor binary eccentricity that we predict have notable applications to many astrophysical scenarios. For example, non-hierarchical triples produced dynamically in globular clusters are a primary formation channel for black hole mergers, but the rates and properties of the resulting gravitational waves depend on the distribution of post-disintegration eccentricities., Comment: 54 pages, 8 figures

Gravitational perturbations on an exoplanet from a massive outer body, such as the Kozai-Lidov mechanism, can pump the exoplanet's eccentricity up to values that will destroy it via a collision or strong interaction with its parent star. During the final stages of this process, any exomoons orbiting the exoplanet will be detached by the star's tidal force and placed into orbit around the star. Using ensembles of three and four-body simulations, we demonstrate that while most of these detached bodies either collide with their star or are ejected from the system, a substantial fraction, ~10%, of such "orphaned" exomoons (with initial properties similar to those of the Galilean satellites in our own solar system) will outlive their parent exoplanet. The detached exomoons generally orbit inside the ice line, so that strong radiative heating will evaporate any volatile-rich layers, producing a strong outgassing of gas and dust, analogous to a comet's perihelion passage. Small dust grains ejected from the exomoon may help generate an opaque cloud surrounding the orbiting body but are quickly removed by radiation blow-out. By contrast, larger solid particles inherit the orbital properties of the parent exomoon, feeding an eccentric disk of solids that drains more gradually onto the star via Poynting-Robertson drag, and which could result in longer-timescale dimming of the star. For characteristic exomoon evaporation times of ~ 1e5-1e6 yr, attenuation of the stellar light arising from one or more out-gassing exomoons provides a promising explanation for both the dipping and secular dimming behavior observed from KIC 8462852 (Boyajian's Star)., Comment: 16 pages, 7 figures, submitted to MNRAS

LISA will open the mHz band of gravitational waves (GWs) to the astronomy community. The strong gravity which powers the variety of GW sources in this band is also crucial in a number of important astrophysical processes at the current frontiers of astronomy. These range from the beginning of structure formation in the early universe, through the origin and cosmic evolution of massive black holes in concert with their galactic environments, to the evolution of stellar remnant binaries in the Milky Way and in nearby galaxies. These processes and their associated populations also drive current and future observations across the electromagnetic (EM) spectrum. We review opportunities for science breakthroughs, involving either direct coincident EM+GW observations, or indirect multimessenger studies. We argue that for the US community to fully capitalize on the opportunities from the LISA mission, the US efforts should be accompanied by a coordinated and sustained program of multi-disciplinary science investment, following the GW data through to its impact on broad areas of astrophysics. Support for LISA-related multimessenger observers and theorists should be sized appropriately for a flagship observatory and may be coordinated through a dedicated mHz GW research center., Comment: Submitted to the Astro2020 Decadal Survey call for science white papers

The tidal destruction of a star by a massive black hole, known as a tidal disruption event (TDE), is commonly modeled using the "frozen-in" approximation. Under this approximation, the star maintains exact hydrostatic balance prior to entering the tidal sphere (radius $r_{\rm t}$), after which point its internal pressure and self-gravity become instantaneously negligible and the debris undergoes ballistic free fall. We present a suite of hydrodynamical simulations of TDEs with high penetration factors $\beta \equiv r_{\rm t}/r_{\rm p} = 5-7$, where $r_{\rm p}$ is the pericenter of the stellar center of mass, calculated using a Voronoi-based moving-mesh technique. We show that basic assumptions of the frozen-in model, such as the neglect of self-gravity inside $r_{\rm t}$, are violated. Indeed, roughly equal fractions of the final energy spread accumulate exiting and entering the tidal sphere, though the frozen-in prediction is correct at the order-of-magnitude level. We also show that an $\mathcal{O}(1)$ fraction of the debris mass remains transversely confined by self-gravity even for large $\beta$ which has implications for the radio emission from the unbound debris and, potentially, for the circularization efficiency of the bound streams., Comment: comments welcome

The question of how supermassive black holes (SMBHs) grow over cosmic time is a major puzzle in high-energy astrophysics. One promising approach to this problem is via the study of tidal disruption flares (TDFs). These are transient events resulting from the disruption of stars by quiescent supermassive black holes at centers of galaxies. A meter-class X-ray observatory with a time resolution $\sim$ a millisecond and a spectral resolution of a few eV at KeV energies would be revolutionary as it will facilitate high signal to noise spectral-timing studies of several cosmological TDFs. It would open a new era of astrophysics where SMBHs in TDFs at cosmic distances can be studied in similar detail as current studies of much nearer, stellar-mass black hole binaries. Using Athena X-ray observatory as an example, we highlight two specific aspects of spectral-timing analysis of TDFs. (1) Detection of X-ray quasi-periodic oscillations (QPOs) over a redshift range and using these signal frequencies to constrain the spin evolution of SMBHs, and (2) Time-resolved spectroscopy of outflows/winds to probe super-Eddington accretion. SMBH spin distributions at various redshifts will directly allow us to constrain their primary mode of growth as higher spins are predicted due to spin-up for prolonged accretion-mode growth, while lower spins are expected for growth via mergers due to angular momentum being deposited from random directions. A meter-class X-ray telescope will also be able to characterize relativistic TDFs, viz., SwJ1644+57-like events, out to a redshift greater than 8, i.e., it would facilitate detailed spectral-timing studies of TDFs by the youngest SMBHs in the Universe., Comment: Submitted to Astro2020 (Astronomy and Astrophysics Decadal Survey)

We present new medium resolution, optical long-slit spectra of a sample of 6 UV/optical and 15 X-ray selected tidal disruption event candidate host galaxies. We measure emission line ratios from the optical spectra, finding that the large majority of hosts are quiescent galaxies, while those displaying emission lines are generally consistent with star-formation dominated environments; only 3 sources show clear evidence of nuclear activity. We measure bulge velocity dispersions using absorption lines and infer host black hole (BH) masses using the M-$\sigma$ relation. While the optical and X-ray host BH masses are statistically consistent with coming from the same parent distribution, the optical host distribution has a visible peak near $M_{\rm BH} \sim 10^6 M_\odot$, whereas the X-ray host distribution appears flat in $M_{\rm BH}$. We find a subset of X-ray selected candidates that are hosted in galaxies significantly less luminous (M$_{\rm g}$$\sim$-16) and less massive (stellar mass$\sim$10$^{8.5-9}$M$_{\odot}$) than those of optical events. Using statistical tests we find suggestive evidence that, in terms of black hole mass, stellar mass and absolute magnitude, the hard X-ray hosts differ from the UV/optical and soft X-ray samples. Similar to individual studies, we find that the emission region size for the X-ray sample is much smaller than the optical emission region, consistent with a compact accretion disk. We find a typical Eddington ratio of the X-ray emission is $\sim$0.01, as opposed to the optical events which have L$_{\rm BB}$$\sim$L$_{\rm Edd}$., Comment: Version accepted for publication

The immense tidal forces of massive black holes can rip apart stars that come too close to them. As the resulting stellar debris spirals inwards, it heats up and emits x-rays when near the black hole. Here, we report the discovery of an exceptionally stable 131-second x-ray quasi-periodicity from a black hole after it disrupted a star. Using a black hole mass indicated from host galaxy scaling relations implies that, (1) this periodicity originates from very close to the black hole's event horizon, and (2) the black hole is rapidly spinning. Our findings suggest that other disruption events with similar highly sensitive observations likely also exhibit quasi-periodicities that encode information about the fundamental properties of their black holes., Comment: Re-submitted after minor comments from referees