A tidal disruption event (TDE) occurs when a star plunges through a supermassive black hole's tidal radius, at which point the star's self-gravity is overwhelmed by the tidal gravity of the black hole. In a partial TDE, where the star does not reach the full disruption radius, only a fraction of the star's mass is tidally stripped while the rest remains intact in the form of a surviving core. Analytical arguments have recently suggested that the temporal scaling of the fallback rate of debris to the black hole asymptotes to $t^{-9/4}$ for partial disruptions, effectively independently of the mass of the intact core. We present hydrodynamical simulations that verify the existence of this predicted, $t^{-9/4}$ scaling. We also define a break timescale -- the time at which the fallback rate transitions from a $t^{-5/3}$ scaling to the characteristic $t^{-9/4}$ scaling -- and measure this break timescale as a function of the impact parameter and the surviving core mass. These results deepen our understanding of the properties and breadth of possible fallback curves expected from TDEs and will therefore facilitate more accurate interpretation of data from wide-field surveys.
After the tidal disruption of a star by a massive black hole, disrupted stellar debris can fall back to the hole at a rate significantly exceeding its Eddington limit. To understand how black hole mass affects the duration of super-Eddington accretion in tidal disruption events, we first run a suite of simulations of the disruption of a Solar-like star by a supermassive black hole of varying mass to directly measure the fallback rate onto the hole, and we compare these fallback rates to the analytic predictions of the "frozen-in" model. Then, adopting a Zero-Bernoulli Accretion flow as an anal…
The disruption of a star by a supermassive black hole generates a sudden bright flare. Previous studies have focused on the disruption by single black holes, for which the fallback rate decays as~$\propto t^{-5/3}$. In this paper, we generalise the study to the case of a supermassive black hole binary (SMBHB), using both analytical estimates and hydrodynamical simulations, looking for specific observable signatures. The range of binary separation for which it is possible to distinguish between the disruption created by a single or a binary black hole concerns typically separations of order a f…
Mergers are fundamental to the standard paradigm of galaxy evolution, and provide a natural formation mechanism for supermassive black hole binaries. The formation process of such a binary can have a direct impact on the rate at which stars are tidally disrupted by one or the other black hole, and the luminous signature of the tidal disruption itself can have distinct imprints of a binary companion. In this chapter we review our current understanding of the influence of black hole binarity on the properties of tidal disruption events. We discuss the rates of tidal disruption by supermassive bl…
We use a simple framework to calculate the time evolution of the composition of the fallback material onto a supermassive black hole arising from the tidal disruption of main sequence stars. We study stars with masses between 0.8 and 3.0 $M_\odot$, at evolutionary stages from zero-age main sequence to terminal-age main sequence, built using the Modules for Experiments in Stellar Astrophysics code. We show that most stars develop enhancements in nitrogen ($^{14}$N) and depletions in carbon ($^{12}$C) and oxygen ($^{16}$O) over their lifetimes, and that these features are more pronounced for hig…
The tidal disruption of stars by supermassive black holes (SMBHs) can be used to probe the SMBH mass function, the properties of individual stars, and stellar dynamics in galactic nuclei. Upcoming missions will detect thousands of TDEs, and accurate theoretical modeling is required to interpret the data with precision. Here we analyze the influence of more realistic stellar structure on the outcome of TDEs; in particular, we compare the fallback rates -- being the rate at which tidally-disrupted debris returns to the black hole -- from progenitors generated with the stellar evolution code {\sc…
We investigate the merger of a neutron star (of compaction ratio $0.1$) in orbit about a spinning black hole in full general relativity with a mass ratio of $5:1$, allowing for the star to have an initial magnetization of $10^{12} {\rm Gauss}$. We present the resulting gravitational waveform and analyze the fallback accretion as the star is disrupted. The evolutions suggest no significant effects from the initial magnetization. We find that only a negligible amount of matter becomes unbound; $99%$ of the neutron star material has a fallback time of 10 seconds or shorter to reach the region of …
Tidal disruption events, which occur when a star is shredded by the tidal field of a supermassive black hole, provide a means of fueling black hole accretion. Here we show, using a combination of three body orbit integrations and hydrodynamic simulations, that these events are also capable of generating circumbinary rings of gas around tight supermassive black hole binaries with small mass ratios. Depending on the thermodynamics, these rings can either fragment into clumps that orbit the binary, or evolve into a gaseous circumbinary disc. We argue that tidal disruptions provide a direct means …
In dense star clusters, such as globular and open clusters, dynamical interactions between stars and black holes (BHs) can be extremely frequent, leading to various astrophysical transients. Close encounters between a star and a stellar mass BH make it possible for the star to be tidally disrupted by the BH. Due to the relative low mass of the BH and the small cross section of the tidal disruption event (TDE) for cases with high penetration, disruptions caused by close encounters are usually partial disruptions. The existence of the remnant stellar core and its non-negligible mass compared to …
A tidal disruption event (TDE) occurs when a supermassive black hole disrupts a nearby passing star by tidal forces. The subsequent fallback accretion of the stellar debris results in a luminous transient outburst. Modeling the light curve of such an event may reveal important information, for example the mass of the central black hole. This paper presents the TiDE software based on semi-analytic modeling of TDEs. This object-oriented code contains different models for the accretion rate and the fallback timescale $t_{\rm min}$. We compare the resulting accretion rates to each other and with h…
Eccentric nuclear disks (ENDs) are a type of star cluster in which the stars lie on eccentric, apsidally-aligned orbits in a disk around a central supermassive black hole (SMBH). These disks can produce a high rate of tidal disruption events (TDEs) via secular gravitational torques. Previous studies of ENDs have included stars with only one mass. Here, we present the first study of an eccentric nuclear disk with two stellar species. We show that ENDs show radial mass segregation consistent with previous results from other cluster types. Additionally, ENDs show vertical mass segregation by whic…
Tidal disruption by massive black holes is a phenomenon, during which a large part of gravitational energy can be released on a very short time-scale. The time-scales and energies involved during X-ray and IR flares observed in Galactic centre suggest that they may be related to tidal disruption events. Furthermore, aftermath of a tidal disruption of a star by super-massive black hole has been observed in some galaxies, e.g. RX J1242.6-1119A. All these discoveries increased the demand for tools for tidal disruption study in curved space-time. Here we summarise our study of general relativistic…
We analyze the outcome of the interaction between a stellar binary and a supermassive black hole binary (SMBHB) by performing a large number of gravitational scattering experiments. Most of the encounters result in either the ejection of an intact binary or the ejection of two individual stars following the tidal breakup of the binary. However, tidal disruption events (TDEs) and mergers constitute a few percent of the outcomes, and double, temporally distinct TDEs (i.e., separated by at least one orbit of the supermassive black hole binary) occur at the percent level. We also demonstrate that …
We compute the rates of capture of stars by supermassive black holes, using time-dependent Fokker--Planck equation with initial conditions that have a deficit of stars on low-angular-momentum orbits. One class of initial conditions has a gap in phase space created by a binary black hole, and the other has a globally tangentially-anisotropic velocity distribution. We find that for galactic nuclei that are younger than ~0.1 relaxation times, the flux of stars into the black hole is suppressed with respect to the steady-state value. This effect may substantially reduce the number of observable ti…
This article provides a summary of XMM-Newton highlights on stellar tidal disruption events. First found with ROSAT, ongoing and upcoming sky surveys will detect these events in the 1000s. In X- rays, tidal disruption events (TDEs) provide us with powerful new probes of accretion physics under extreme conditions and on short timescales and of relativistic effects near the SMBH, of the formation and evolution of disk winds near or above the Eddington limit, and of the processes of high-energy emission from newly launched radio jets. TDEs serve as signposts of the presence of dormant, single bla…
The tidal disruption of a star by a massive black hole is expected to yield a luminous flare of thermal emission. About two dozen of these stellar tidal disruption flares (TDFs) may have been detected in optical transient surveys. However, explaining the observed properties of these events within the tidal disruption paradigm is not yet possible. This theoretical ambiguity has led some authors to suggest that optical TDFs are due to a different process, such as a nuclear supernova or accretion disk instabilities. Here we present a test of a fundamental prediction of the tidal disruption event …
The destruction of a star by the tides of a supermassive black hole (SMBH) powers a bright accretion flare, and the theoretical modeling of such tidal disruption events (TDEs) can provide a direct means of inferring SMBH properties from observations. Previously it has been shown that TDEs with $β= r_{\rm t}/r_{\rm p} = 1$, where $r_{\rm t}$ is the tidal disruption radius and $r_{\rm p}$ is the pericenter distance of the star, form an in-plane caustic, or ``pancake,'' where the tidally disrupted debris is compressed into a one-dimensional line within the orbital plane of the star. Here we show …
Tidal disruption events (TDEs) observed in massive galaxies with inferred central black hole masses $M_h > 10^8 \ M_\odot$ are presumptive candidates for TDEs by lower mass secondaries in binary systems. We use hydrodynamic simulations to quantify the characteristics of such TDEs, focusing on extreme mass ratio binaries and mpc separations where the debris stream samples the binary potential. The simulations are initialised with disruption trajectories from 3-body integrations of stars with parabolic orbits with respect to the binary center of mass. The most common outcome is found to be the f…
The tidal disruption of a star by a supermassive black hole leads to a short-lived thermal flare. Despite extensive searches, radio follow-up observations of known thermal stellar tidal disruption flares (TDFs) have not yet produced a conclusive detection. We present a detection of variable radio emission from a thermal TDF, which we interpret as originating from a newly-launched jet. The multi-wavelength properties of the source present a natural analogy with accretion state changes of stellar mass black holes, suggesting all TDFs could be accompanied by a jet. In the rest frame of the TDF, o…
Supermassive Binary Black Holes (SMBBHs) with sub-pc separations form in the course of galaxy mergers, if both galaxies harbour massive black holes. Clear observational evidence for them however still eludes us. We propose a novel method of identifying these systems by means of reverberation mapping their circumbinary disk after a tidal disruption event has ionized it. The tidal disruption of a star at the secondary leads to strong asymmetries in the disk response. We model the shape of the velocity--delay maps for various toy disk models and more realistic gas distributions obtained by SPH si…
We propose a semi-analytical model for the self-intersection of the fallback stream in tidal disruption events (TDEs). When the initial periapsis is less than about 15 gravitational radii, a large fraction of the shocked gas is unbound in the form of a collision-induced outflow (CIO). This is because large apsidal precession causes the stream to self-intersect near the local escape speed at radius much below the apocenter. The rest of the fallback gas is left in more tightly bound orbits and quickly joins the accretion flow. We propose that the CIO is responsible for reprocessing the hard emis…
The Galactic Center has been under intense scrutiny in the recent years thanks to the unprecedented missions aiming at measuring the gas and star dynamics near the supermassive black hole (SMBH) and at finding gravitational wave (GW) signatures of inspiralling stellar black holes. In the crowded environment of galactic nuclei, the two-body interactions alter the distribution of stars on long timescales, making them drift in energy and angular momentum. We present a simplified analytical treatment of the scattering processes in galactic stellar nuclei, assuming all stars have the same mass. We …
We describe a model of tidal disruption events (TDEs) with input physical parameters that include the black hole (BH) mass $M_{\bullet}$, the specific orbital energy $E$, the angular momentum $J$, the star mass $M_{\star}$ and radius $R_{\star}$. We calculate the rise time of the TDEs, the peak bolometric luminosity in terms of these physical parameters and a typical light curve of TDEs for various All Sky Survey (ASS) and Deep Sky Survey (DSS) missions. We then derive the expected detection rates and discuss the follow up of TDEs through observations in various spectral bands from X-rays to r…
We construct a time-dependent relativistic accretion model for tidal disruption events (TDEs) with an $α-$viscosity and the pressure dominated by gas pressure. We also include the mass fallback rate $\dot{M}_f$ for both full and partial disruption TDEs, and assume that the infalling debris forms a seed disc in time $t_c$, which evolves due to the mass addition from the infalling debris and the mass loss via accretion onto the black hole. Besides, we derive an explicit form for the disc height that depends on the angular momentum parameter in the disc. We show that the surface density of the di…
The tidal force from a supermassive black hole can rip apart a star that passes close enough in what is known as a Tidal Disruption Event. Typically half of the destroyed star remains bound to the black hole and falls back on highly eccentric orbits, forming an accretion flow which powers a luminous flare. In this paper we use analytical and numerical calculations to explore the effect of stellar rotation on the fallback rate of material. We find that slowly spinning stars ($Ω_* \lesssim 0.01 Ω_{\rm{breakup}}$) provide only a small perturbation to fallback rates found in the non-spinning case.…
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 kno…
General relativistic hydrodynamics of stellar tidal disruptions in Kerr spacetime: methods, validation, and first applications
Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Hamburger Sternwarte, Universität Hamburg（汉堡天文台，汉堡大学）；The Oskar Klein Centre, Department of Astronomy, AlbaNova, Stockholm University（奥斯卡·克莱因中心，阿尔巴诺瓦，斯德哥尔摩大学天文学系）
Time domain optical surveys have discovered roughly a dozen candidate stellar tidal disruption flares in the last five years, and future surveys like the {\it Large Synoptic Survey Telescope} will likely find hundreds to thousands more. These tidal disruption events (TDEs) present an interesting puzzle: a majority of the current TDE sample is hosted by rare post-starburst galaxies, and tens of percent are hosted in even rarer E+A galaxies, which make up $\sim 0.1\%$ of all galaxies in the local universe. E+As are therefore overrepresented among TDE hosts by 1-2 orders of magnitude, a discrepan…
Highly energetic stellar tidal disruption events (TDEs) provide a way to study black hole characteristics and their environment. We simulate TDEs with the PHANTOM code in a general relativistic and Newtonian description of a supermassive black hole's gravity. Stars, which are placed on parabolic orbits with different parameters $β$, are constructed with the stellar evolution code MESA and therefore have realistic stellar density profiles. We study the mass fallback rate of the debris $\dot{M}$ and its dependence on the $β$, stellar mass and age as well as the black hole's spin and the choice o…
We investigate interactions of stellar binaries in galactic nuclear clusters with a massive black hole (MBH). We consider binaries on highly eccentric orbits around the MBH that change due to random gravitational interactions with other stars in the nuclear stellar cluster. The pericenters of the orbits perform a random walk, and we consider cases where this random walk slowly brings the binary to the Hills tidal separation radius (the so-called empty loss-cone regime). However, we find that in a majority of cases the expected separation does not occur and instead the members of the binary mer…
We present unpublished data from a tidal disruption candidate in NGC 3599 which show that the galaxy was already X-ray bright 18 months before the measurement which led to its classification. This removes the possibility that the flare was caused by a classical, fast-rising, short-peaked, tidal disruption event. Recent relativistic simulations indicate that the majority of disruptions will actually take months or years to rise to a peak, which will then be maintained for longer than previously thought. NGC 3599 could be one of the first identified examples of such an event. The optical spectra…
A likely tidal disruption of a star by the intermediate-mass black hole (IMBH) of a dwarf galaxy was recently identified in association with Abell 1795. Without deep spectroscopy for this very faint object, however, the possibility of a more massive background galaxy or even a disk-instability flare from a weak AGN could not be dismissed. We have now obtained 8 hours of Gemini spectroscopy which unambiguously demonstrate that the host galaxy is indeed an extremely low-mass $(M_\ast\sim 3\times 10^8\; {\rm M}_{\odot})$ galaxy in Abell 1795, comparable to the least-massive galaxies determined to…
While once rare, observations of stars being tidally disrupted by supermassive black holes are quickly becoming commonplace. To continue to learn from these events it is necessary to robustly and systematically compare our growing number of observations with theory. We present a tidal disruption module for the Modular Open Source Fitter for Transients (MOSFiT) and the results from fitting 14 tidal disruption events (TDEs). Our model uses FLASH simulations of TDEs to generate bolometric luminosities and passes these luminosities through viscosity and reprocessing transformation functions to cre…
Upon entering the tidal sphere of a supermassive black hole, a star is ripped apart by tides and transformed into a stream of debris. The ultimate fate of that debris, and the properties of the bright flare that is produced and observed, depends on a number of parameters, including the energy of the center of mass of the original star. Here we present the results of a set of smoothed particle hydrodynamics simulations in which a $1~M_\odot $, $γ= 5/3$ polytrope is disrupted by a $10^6 ~M_\odot$ supermassive black hole. Each simulation has a pericenter distance of $r_{\rm p} = r_{\rm t}$ (i.e.,…
We present the results of relativistic smoothed particle hydrodynamics simulations of tidal disruptions of stars by rotating supermassive black holes, for a wide range of impact parameters and black hole spins. For deep encounters, we find that: relativistic precession creates debris geometries impossible to obtain with the Newtonian equations; part of the fluid can be launched on plunging orbits, reducing the fallback rate and the mass of the resulting accretion disc; multiple squeezings and bounces at periapsis may generate distinctive X-ray signatures resulting from the associated shock bre…
We present late-time observations of the tidal disruption event candidate PS1-10jh. UV and optical imaging with HST/WFC3 localize the transient to be coincident with the host galaxy nucleus to an accuracy of 0.023 arcsec, corresponding to 66 pc. The UV flux in the F225W filter, measured 3.35 rest-frame years after the peak of the nuclear flare, is consistent with a decline that continues to follow a $t^{-5/3}$ power-law with no spectral evolution. Late epochs of optical spectroscopy obtained with MMT ~ 2 and 4 years after the peak, enable a clean subtraction of the host galaxy from the early s…
We present the STARS library, a grid of tidal disruption event (TDE) simulations interpolated to provide the mass fallback rate ($dM/dt$) to the black hole for a main-sequence star of any stellar mass, stellar age, and impact parameter. We use a one-dimensional stellar evolution code to construct stars with accurate stellar structures and chemical abundances, then perform tidal disruption simulations in a three-dimensional adaptive-mesh hydrodynamics code with a Helmholtz equation of state, in unprecedented resolution: from 131 to 524 cells across the diameter of the star. The interpolated lib…
We study tidal disruption and subsequent mass fallback for stars approaching supermassive black holes on bound orbits, by performing three dimensional Smoothed Particle Hydrodynamics simulations with a pseudo-Newtonian potential. We find that the mass fallback rate decays with the expected -5/3 power of time for parabolic orbits, albeit with a slight deviation due to the self-gravity of the stellar debris. For eccentric orbits, however, there is a critical value of the orbital eccentricity, significantly below which all of the stellar debris is bound to the supermassive black hole. All the mas…
A star on a nearly radial trajectory approaching a massive black hole (MBH) gets tidally disrupted if it comes sufficiently close to the MBH. Here we explore what happens to binary stars whose centers of mass approach the MBH on nearly radial orbits. The interaction with the MBH often leads to both stars being disrupted in sequence. We argue that such events could produce light curves that are substantially different from those of the single disruptions, with possible features such as two local maxima. Tidal forces from the MBH can also lead the binary components to collide; these merger produ…
Accretion onto black holes is an efficient mechanism in converting the gas mass-energy into energetic outputs as radiation, wind and jet. Tidal disruption events, in which stars are tidally torn apart and then accreted onto supermassive black holes, offer unique opportunities of studying the accretion physics as well as the wind and jet launching physics across different accretion regimes. In this review, we systematically describe and discuss the models that have been developed to study the accretion flows and jets in tidal disruption events. A good knowledge of these physics is not only need…
A star destroyed by a supermassive black hole (SMBH) in a tidal disruption event (TDE) enables the study of SMBHs. We propose that the distance within which a star is completely destroyed by a SMBH, defined $r_{\rm t, c}$, is accurately estimated by equating the SMBH tidal field (including numerical factors) to the maximum gravitational field in the star. We demonstrate that this definition accurately reproduces the critical $β_{\rm c} = r_{\rm t}/r_{\rm t, c}$, where $r_{\rm t} = R_{\star}\left(M_{\bullet}/M_{\star}\right)^{1/3}$ is the standard tidal radius with $R_{\star}$ and $M_{\star}$ t…
Tidal disruption events are an excellent probe for supermassive black holes in distant inactive galaxies because they show bright multi-wavelength flares lasting several months to years. AT2019dsg presents the first potential association with neutrino emission from such an explosive event.
We study the rates of tidal disruption of stars by intermediate-mass to supermassive black holes on bound to unbound orbits by using high-accuracy direct N-body experiments. The approaching stars from the star cluster to the black hole can take three types of orbit: eccentric, parabolic, and hyperbolic orbits. Since the mass fallback rate shows a different variability depending on these orbital types, we can classify tidal disruption events (TDEs) into three main categories: eccentric, parabolic, and hyperbolic TDEs. Respective TDEs are characterized by two critical values of the orbital eccen…
Tidal disruption events (TDEs) show a correlation between the UV to X-ray spectral index and the Eddington ratio, with non-thermal X-ray emission at the low Eddington ratio. We consider the corona surrounding the accretion disc as a non-thermal X-ray source. We construct a time-dependent and non-relativistic advective accretion disc-corona model for TDEs. The infalling debris is assumed to form a seed disc in time $t_c$, that evolves due to the mass gain from the infalling debris at the constant outer radius with a mass fallback rate $\dot{M}_{\rm fb}$ and the mass loss through accretion onto …
Close encounters between stellar-mass black holes (BHs) and stars occur frequently in dense star clusters and in the disks of active galactic nuclei (AGNs). Recent studies have shown that in highly eccentric close encounters, the star can be tidally disrupted by the BH (micro-tidal disruption event, or micro-TDE), resulting in rapid mass accretion and possibly bright electromagnetic signatures. Here we consider a scenario in which the star might approach the stellar-mass BH in a gradual, nearly circular inspiral, under the influence of dynamical friction on a circum-binary gas disk or three-bo…
This is the second in a series of papers presenting the results of fully general relativistic simulations of stellar tidal disruptions in which the stars' initial states are realistic main-sequence models. In the first paper (Paper I), we gave an overview of this program and discussed the principal observational implications of our work. Here we describe our calculational method and provide details about the outcomes of full disruptions, focusing on the stellar mass dependence of the outcomes for a black hole of mass $10^{6}\rm{M}_{\odot}$. We consider eight different stellar masses, from $0.1…
Galaxy mergers produce supermassive black hole binaries, which emit gravitational waves prior to their coalescence. We perform three-dimensional hydrodynamic simulations to study the tidal disruption of stars by such a binary in the final centuries of its life. We find that the gas stream of the stellar debris moves chaotically in the binary potential and forms accretion disks around both black holes. The accretion light curve is modulated over the binary orbital period owing to relativistic beaming. This periodic signal allows to detect the decay of the binary orbit due to gravitational wave …
We study the mass fallback rate of tidally disrupted stars on marginally bound and unbound orbits around a supermassive black hole (SMBH) by performing three-dimensional smoothed particle hydrodynamic (SPH) simulations with three key parameters: the star is modeled by a polytrope with two different indexes ($n=1.5$ and $3$). The stellar orbital properties are characterized by five orbital eccentricities ranging from $e=0.98$ to $1.02$ and five different penetration factors ranging from $β=1$ to $3$, where $β$ represents the ratio of the tidal disruption to pericenter distance radii. We derive …
