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 higher mass stars. We find that, in an accretion-powered tidal disruption flare, these features become prominent only after the time of peak of the fallback rate and appear at earlier times for stars of increasing mass. We postulate that no severe compositional changes resulting from the fallback material should be expected near peak for a wide range of stellar masses and, as such, are unable to explain the extreme helium-to-hydrogen line ratios observed in some TDEs. On the other hand, the resulting compositional changes could help explain the presence of nitrogen-rich features, which are currently only detected after peak. When combined with the shape of the light curve, the time evolution of the composition of the fallback material provides a clear method to help constrain the nature of the disrupted star. This will enable a better characterization of the event by helping break the degeneracy between the mass of the star and the mass of the black hole when fitting tidal disruption light curves.
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…
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…
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…
We construct a menu of objects that can give rise to bright flares when disrupted by massive black holes (BHs), ranging from planets to evolved stars. Through their tidal disruption, main sequence and evolved stars can effectively probe the existence of otherwise quiescent supermassive BHs and white dwarfs can probe intermediate mass BHs. Many low-mass white dwarfs possess extended hydrogen envelopes, which allow for the production of prompt flares in disruptive encounters with moderately massive BHs of $10^5$ to $10^7~M_\odot$--masses that may constitute the majority of massive BHs by number.…
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 …
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 …
White dwarf stars that enter the tidal radius of black holes with masses $\lesssim$ $10^5$ M$_{\odot}$ are doomed to be ripped apart by tidal forces. Black holes in this mass range between stellar black holes and supermassive black holes have not been conclusively identified so the detection of a tidal disruption of a white dwarf would provide clear evidence for the existence of intermediate-mass black holes. In this review, we present a theoretical and observational overview of the transient events that result from the tidal disruptions of white dwarfs by intermediate-mass black holes. This i…
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…
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 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.…
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）
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 present the first simulations of the tidal disruption of stars with realistic structures and compositions by massive black holes (BHs). We build stars in the stellar evolution code MESA and simulate their disruption in the 3D adaptive-mesh hydrodynamics code FLASH, using an extended Helmholtz equation of state and tracking 49 elements. We study the disruption of a 1$M_\odot$ star and 3$M_\odot$ star at zero-age main sequence (ZAMS), middle-age, and terminal-age main sequence (TAMS). The maximum BH mass for tidal disruption increases by a factor of $\sim$2 from stellar radius changes due to …
Whether tidal disruption events (TDEs) circularise or accrete directly as a highly eccentric disc is the subject of current research and appears to depend sensitively on the disc thermodynamics. In a previous paper we applied the theory of eccentric discs to TDE discs using an $α-$prescription for the disc stress, which leads to solutions that exhibit extreme, potentially unphysical, behaviour. In this paper we further explore the dynamical vertical structure of highly eccentric discs using alternative stress models that are better motivated by the behaviour of magnetic fields in eccentric dis…
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 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…
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 (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 …
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 $0.1…
We study the mass fallback rate of tidally disrupted stars on marginally bound and unbound orbits around a supermassive black hole (SMBH) by performing three-dimensional smoothed particle hydrodynamic (SPH) simulations with three key parameters: the star is modeled by a polytrope with two different indexes ($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 …
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…
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.
In this paper, the third in this series, we continue our study of tidal disruption events of main-sequence stars by a non-spinning $10^{6}~\rm{M}_\odot$ supermassive black hole. Here we focus on the stellar mass dependence of the outcomes of partial disruptions. As the encounter becomes weaker, the debris mass is increasingly concentrated near the outer edges of the energy distribution. As a result, the mass fallback rate can deviate substantially from a $t^{-5/3}$ power-law, becoming more like a single peak with a tail declining as $t^{-p}$ with $p\simeq2-5$. Surviving remnants are spun-up in…
We suggest "tidal double detonation": a new mechanism for a thermonuclear explosion of a white dwarf (WD) induced by a tidal disruption event (TDE). Tidal detonation is also a WD explosion induced by a TDE. In this case, helium (He) and carbon-oxygen (CO) detonation waves incinerate He~WD and CO~WD, respectively. On the other hand, for tidal double detonation, He detonation is first excited in the He shell of a CO~WD, and drives CO detonation in the CO core. We name this mechanism after the double detonation scenario in the context of type Ia supernovae. In this paper, we show tidal double det…
We present a qualitative picture of prompt emission from tidal disruptions of white dwarfs (WD) by intermediate mass black holes (IMBH). The smaller size of an IMBH compared to a supermassive black hole and a smaller tidal radius of a WD disruption lead to a very fast event with high peak luminosity. Magnetic field is generated in situ following the tidal disruption, which leads to effective accretion. Since large-scale magnetic field is also produced, geometrically thick super-Eddington inflow leads to a relativistic jet. The dense jet possesses a photosphere, which emits quasi-thermal radiat…
We demonstrate that the compact, thick disc formed in a tidal disruption event may be unstable to non-axisymmetric perturbations in the form of the Papaloizou-Pringle instability. We show this can lead to rapid redistribution of angular momentum that can be parameterised in terms of an effective Shakura-Sunyaev $α$ parameter. For remnants that have initially weak magnetic fields, this may be responsible for driving mass accretion prior to the onset of the magneto-rotational instability. For tidal disruptions around a $10^6$ M$_{\odot}$ black hole, the measured accretion rate is super-Eddington…
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…
RBS 1032 is a supersoft ($Γ\sim5$), luminous ($\sim10^{43}$ erg/s) ROSAT PSPC source which has been associated with an inactive dwarf galaxy at $z=0.026$, SDSS J114726.69+494257.8. We have analyzed an XMM-Newton observation which confirms that RBS 1032 is indeed associated with the dwarf galaxy. Moreover, RBS 1032 has undergone a factor of $\sim100-300$ decay since November 1990. This variability suggests that RBS 1032 may not be a steadily accreting intermediate-mass black hole, but rather an accretion flare from the tidal disruption of a star by the central black hole (which may or may not b…
Observations of the spectacular, blazar-like tidal disruption event (TDE) candidates Swift J1644+57 and J2058+05 show that the conditions required for accelerating protons to 10^{20} eV appear to be realized in the outer jet, and possibly in the inner jet as well. Direct and indirect estimates of the rate of jetted-TDEs, and of the energy they inject, are compatible with the observed flux of ultra-high energy cosmic rays (UHECRs) and the abundance of presently contributing sources. Thus TDE-jets can be a major source of UHECRs, even compabile with a pure proton composition.
We present simulations of the tidal disruption of a solar mass star by a $10^6M_{\odot}$ black hole. These, for the first time, cover the full time evolution of the tidal disruption event, starting well before the initial encounter and continuing until more than 90% of the bound material has returned to the vicinity of the hole. Our results are compared to the analytical prediction for the rate at which tidally-stripped gas falls back. We find that, for our chosen parameters, the overall scaling of the fallback rate, $\dot{M}_{\rm{fb}}$, closely follows the canonical $t^{-5/3}$ power-law. Howe…
This paper introduces a series of papers presenting a quantitative theory for the tidal disruption of main sequence stars by supermassive black holes. Using fully general relativistic hydrodynamics simulations and MESA-model initial conditions, we explore the pericenter-dependence of tidal disruption properties for eight stellar masses ($0.15 \leq M_*/M_\odot \leq 10$) and six black hole masses ($10^5 \leq M_{BH}/M_\odot \leq 5 \times 10^7$). We present here the results most relevant to observations. The effects of internal stellar structure and relativity decouple for both the disruption cros…
Stars approaching supermassive black holes (SMBHs) in the centers of galaxies can be torn apart by strong tidal forces. We study the physics of tidal disruption by a binary SMBH as a function of the binary mass ratio $q = M_2 / M_1$ and separation $a$, exploring a large set of points in the parameter range $q \in [0.01, 1]$ and $a/r_{t1} \in [10, 1000]$. We simulate encounters in which field stars approach the binary from the loss cone on parabolic, low angular momentum orbits. We present the rate of disruption and the orbital properties of the disrupted stars, and examine the fallback dynamic…
Tidal Disruption Events (TDEs) occur when stars pass close to supermassive black holes, and have long been predicted to emit cosmic rays and neutrinos. Recently the TDE AT2109dsg was identified in spatial and temporal coincidence with high-energy neutrino IC191001A as part of the Zwicky Transient Facility (ZTF) neutrino follow-up program, providing the first direct observational evidence supporting these objects as multi-messenger sources. In these proceedings, I will place the recent results of our ZTF neutrino follow-up program into the broader context of developments in TDE and neutrino ast…
The tidal disruption and subsequent accretion of a star by a supermassive black hole can be used as a laboratory to study the physics of relativistic jets. The ngVLA is the only planned instrument that can both discover and characterize a large number of these short-lived radio sources. In particular the high-frequency capabilities of the ngVLA enable this important leap forward. Multi-frequency radio follow-up observations (3 - 100 GHz) of tidal disruption events found in optical or X-ray surveys will provide a measurement of the jet efficiency as a function of black hole spin, thus enabling …
Active galactic nuclei (AGNs) can act as black hole assembly lines, funneling some of the stellar-mass black holes from the vicinity of the galactic center into the inner plane of the AGN disk where the black holes can merge through dynamical friction and gravitational wave emission. Here, we show that stars near the galactic center are also brought into the AGN disk, where they can be tidally disrupted by the stellar-mass black holes in the disk. Such micro-tidal disruption events (micro-TDEs) could be useful probe of stellar interaction with the AGN disk. We find that micro-TDEs in AGNs occu…
Beyond the Impulsive Approximation: The Dynamics and Radio Emission of Tidal Disruption Jets
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Department of Astronomy and Astrophysics, University of California, Santa Cruz（加州大学圣克鲁斯分校天体物理学系）
Tidal effects on clumps of material during random non-stationary accretion onto a black hole produce phenomena with distinct temporal characteristics in observed light-curves. During such non-stationary accretion events, the shape of the accreting object evolves in time, and observable quasi-periodic phenomena with variable quasi-periods are produced. A number of characteristic light-curves, obtained with numerical simulations, will be shown. Their relevance to observed phenomena will be briefly discussed.
The discovery of jets from tidal disruption events (TDEs) rejuvenated the old field of relativistic jets powered by accretion onto supermassive black holes. In this Chapter, we first review the extensive multi-wavelength observations of jetted TDEs. Then, we show that these events provide valuable information on many aspects of jet physics from a new prospective, including the on-and-off switch of jet launching, jet propagation through the ambient medium, $γ/$X-ray radiation mechanism, jet composition, and the multi-messenger picture. Finally, open questions and future prospects in this field …
