We consider misaligned accretion discs formed after tidal disruption events occurring when a star encounters a supermassive rotating black hole. We use the linear theory of warped accretion discs to find the disc shape when the stream produced by the disrupted star provides a source of mass and angular momentum that is misaligned with the black hole. The evolution of the surface density and aspect ratio is found from a one dimensional vertically averaged model.
We extend previous work which assumed a quasi-stationary disc to allow unrestricted dynamical propagation of disc tilt and twist through time dependent backgrounds. We consider a smaller value of the viscosity parameter, $α=0.01,$ finding the dynamics varies significantly.
At early times the disc inclination is found to be nearly uniform at small radii where the aspect ratio is large. However, since torques arise from the Lense-Thirring effect and the stream there is non uniform precession. We propose a simple model for this requiring only the background surface density and aspect ratio.
At these times the $α\sim 0.01$ disc exhibits a new feature. An inclined hot inner region joins an outer low inclination cool region via a thin transition front propagating outwards with a speed exceeding that of bending waves in the cool region. These waves accumulate where the propagation speeds match producing an inclination spike separating inner and outer discs. At late times a sequence of quasi-stationary configurations approximates disc shapes at small radii. We discuss observational implications of our results.
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…
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…
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 …
A bright flare from a galactic nucleus followed at late times by a $t^{-5/3}$ decay in luminosity is often considered the signature of the complete tidal disruption of a star by a massive black hole. The flare and power-law decay are produced when the stream of bound debris returns to the black hole, self-intersects, and eventually forms an accretion disk or torus. In the canonical scenario of a solar-type star disrupted by a $10^{6}\; M_\odot$ black hole, the time between the disruption of the star and the formation of the accretion torus could be years. We present fully general relativistic …
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…
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 …
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.
Black holes and wormholes are solutions of Einstein's field equations, both of which, from afar, look like a central mass. We show here that although at large distances both behave like Newtonian objects, close to the event horizon or to the throat, black holes and wormholes have different tidal effects on stars, due to their respective geometries. We quantify this difference by a numerical procedure in the Schwarzschild black hole and the exponential wormhole backgrounds, and compare the peak fallback rates of tidal debris in these geometries. The tidal disruption rates in these backgrounds a…
We discuss the gravitational wave emission and the orbital evolution of a hierarchical triple system composed of an inner binary black hole (BBH) and an outer tertiary. Depending on the kick velocity at the merger, the merged BBH could tidally disrupt the tertiary. Even though the fraction of BBH mergers accompanied by such disruptions is expected to be much smaller than unity, the existence of a tertiary and its basic parameters (e.g. semimajor axis, projected mass) can be examined for more than 1000 BBHs with the space GW detector LISA and its follow-on missions. This allows us to efficientl…
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…
We propose an approximate approach for studying the relativistic regime of stellar tidal disruptions by rotating massive black holes. It combines an exact relativistic description of the hydrodynamical evolution of a test fluid in a fixed curved spacetime with a Newtonian treatment of the fluid's self-gravity. Explicit expressions for the equations of motion are derived for Kerr spacetime using two different coordinate systems. We implement the new methodology within an existing Newtonian Smoothed Particle Hydrodynamics code and show that including the additional physics involves very little e…
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…
Tidal disruption of a neutron star near naked singularity
Charotar University of Science and Technology（查科塔尔科学与技术大学）；Ahmedabad University（艾哈迈达巴德大学）；Tata Institute of Fundamental Research（塔塔基础研究所）；Massachusetts Institute of Technology（麻省理工学院）
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…
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 m…
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…
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…
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…
Stars on orbits with pericenters sufficiently close to the supermassive black hole at the center of their host galaxy can be ripped apart by tidal stresses. Some of the resulting stellar debris becomes more tightly bound to the hole and can potentially produce an observable flare called a tidal-disruption event (TDE). We provide a self-consistent, unified treatment of TDEs by non-spinning (Schwarzschild) black holes, investigating several effects of general relativity including changes to the boundary in phase space that defines the loss-cone orbits on which stars are tidally disrupted or capt…
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 …
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…
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 …
The tidal disruption of a star by a supermassive black hole (SMBH) is a highly energetic event with consequences dependent on the degree to which the star plunges inside the SMBH's tidal sphere. We introduce a new analytic model for tidal disruption events (TDEs) to analyze the dependence of these events on beta, the ratio of the tidal radius to the orbital pericenter. We find, contrary to most previous work, that the spread in debris energy for a TDE is largely constant for all beta. This result has important consequences for optical transient searches targeting TDEs, which we discuss. We qua…
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…
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…
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 rela…
Numerical simulations have historically played a major role in understanding the hydrodynamics of the tidal disruption process. Given the complexity of the geometry of the system, the challenges posed by the problem have indeed stimulated much work on the numerical side. Smoothed Particles Hydrodynamics methods, for example, have seen their very first applications in the context of tidal disruption and still play a major role to this day. Likewise, initial attempts at simulating the evolution of the disrupted star with the so-called affine method have been historically very useful. In this Cha…
We present an online, open and comprehensive template library of gravitational waveforms produced during the tidal disruptions of stars by massive black holes, spanning a broad space of parameters. We build this library thanks to a new feature that we implement in the general relativistic version of PHANTOM, a smoothed particle hydrodynamics code for three dimensional simulations in general relativity. We first perform a series of numerical tests to show that the gravitational wave (GW) signal obtained is in excellent agreement with the one expected from theory. This benchmark is done for well…
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…
A white dwarf (WD) captured into a high-eccentricity orbit around a massive black hole (MBH) may undergo many pericenter passages before tidal disruption. During these passages, the tidal potential of the MBH excites internal oscillations or waves in the WD, and the dissipation of these oscillations can significantly influence the physical properties of the WD prior to its disruption. We calculate the amplitude of the tidally excited gravity (buoyancy) waves in the WD as a function of the pericenter distance and eccentricity for realistic WD models, under the assumption that these outgoing gra…
The tidal disruption of a star by a supermassive black hole provides us with a rare glimpse of these otherwise dormant beasts. It has long been predicted that the disruption will be accompanied by a thermal `flare', powered by the accretion of bound stellar debris. Several candidate disruptions have been discovered in this manner at optical, UV and X-ray wavelengths. Here we explore the observational consequences if a modest fraction of the accretion power is channeled into an ultra-relativistic outflow. We show that a relativistic jet decelerates due to its interaction with the interstellar m…
An ELT system with its large aperture and sensitive optical and near infrared imager spectrographs will make major contributions to the study of stars ripped apart by supermassive black holes.
This is a White Paper in support of the mission concept of the Large Observatory for X-ray Timing (LOFT), proposed as a medium-sized ESA mission. We discuss the potential of LOFT for the study of jetted tidal disruption events. For a summary, we refer to the paper.
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…
We present numerical relativity results of tidal disruptions of white dwarfs from ultra-close encounters with a spinning, intermediate mass black hole. These encounters require a full general relativistic treatment of gravity. We show that the disruption process and prompt accretion of the debris strongly depend on the magnitude and orientation of the black hole spin. However, the late-time accretion onto the black hole follows the same decay, $\dot{M}$ ~ t^{-5/3}, estimated from Newtonian gravity disruption studies. We compute the spectrum of the disk formed from the fallback material using a…
Off-center stellar tidal disruption flares have been suggested to be a powerful probe of recoiling supermassive black holes (SMBHs) out of galactic centers due to anisotropic gravitational wave radiations. However, off-center tidal flares can also be produced by SMBHs in merging galaxies. In this paper, we computed the tidal flare rates by dual SMBHs in two merging galaxies before the SMBHs become self-gravitationally bounded. We employ an analytical model to calculate the tidal loss-cone feeding rates for both SMBHs, taking into account two-body relaxation of stars, tidal perturbations by the…
Our current understanding of the curved space-time around supermassive black holes is based on actively accreting black holes, which make up only ten per cent or less of the overall population. X-ray observations of that small fraction reveal strong gravitational redshifts that indicate that many of these black holes are rapidly rotating; however, selection biases suggest that these results are not necessarily reflective of the majority of black holes in the Universe. Tidal disruption events, where a star orbiting an otherwise dormant black hole gets tidally shredded and accreted onto the blac…
We investigate the pre-disruption gravitational dynamics and post-disruption hydrodynamics of the tidal disruption of stars by supermassive black hole (SMBH) binaries. We focus on binaries with relatively low mass primaries ($10^6M_{\odot}$), moderate mass ratios, and separations with reasonably long gravitational wave inspiral times (tens of Myr). First, we generate a large ensemble (between 1 and 10 million) of restricted three-body integrations to quantify the statistical properties of tidal disruptions by circular SMBH binaries of initially-unbound stars. Compared to the reference case of …
Among the many intriguing aspects of optically discovered tidal disruption events (TDEs) is that their temperatures are lower than expected and that the temperature does not evolve as rapidly with decreasing fallback rate as would be expected in standard disk theory. We show that this can be explained qualitatively using an idea proposed by Laor & Davis in the context of normal active galactic nuclei: that larger accretion rates imply stronger winds and thus that the accretion rate through the inner disk only depends weakly on the inflow rate at the outer edge of the disk. We also show that re…
