潮汐瓦解事件（TDEs）为研究中心超大质量黑洞（SMBH）及其周围吸积盘的性质，以及SMBH周围核星团中的恒星密度和速度分布提供了线索。TDE光变曲线与在抛物线遭遇SMBH时发生的标准情形的偏离，取决于恒星轨道是双曲轨道还是偏心轨道（Hayasaki et al. 2018）以及穿透因子（$β$，即潮汐瓦解半径与轨道近心点距离之比）。我们通过将直接$N$体模拟数据与解析模型进行比较，研究了被潮汐瓦解的束缚与非束缚恒星的轨道参数。从Cohn & Kulsrud（1978）的经典稳态Fokker-Planck模型出发，我们建立了一个描述这些恒星数密度分布随轨道偏心率（$e$）和$β$变化的解析模型。为此，需要对核星团的密度和速度分布以及被潮汐瓦解恒星的能量分布进行拟合，这些拟合结果从$N$体数据中获得。我们证实，在球对称核星团中，导致TDE的恒星大多数来自相空间中的完全损失锥区域，推导出偏心率-$β$空间中的解析边界，并发现这些边界得到$N$体数据的证实。由于我们的极限偏心率远小于恒星碎片完全吸积或完全逃逸的临界偏心率，我们得出结论：这些恒星仅具有非常微小的偏心率或双曲率，接近抛物线轨道。
英文摘要：
Tidal disruption events (TDEs) provide a clue to the properties of a central supermassive black hole (SMBH) and an accretion disk around it, and to the stellar density and velocity distributions in the nuclear star cluster surrounding the SMBH. Deviations of TDE light curves from the standard occurring at a parabolic encounter with the SMBH depends on whether the stellar orbit is hyperbolic or eccentric (Hayasaki et al. 2018) and the penetration factor ($β$, tidal disruption radius to orbital pericenter ratio). We study the orbital parameters of bound and unbound stars being tidally disrupted by comparison of direct $N$-body simulation data with an analytical model. Starting from the classical steady-state Fokker-Planck model of Cohn & Kulsrud (1978), we develop an analytical model of the number density distribution of those stars as a function of orbital eccentricity ($e$) and $β$. To do so fittings of the density and velocity distribution of the nuclear star cluster and of the energy distribution of tidally disrupted stars are required and obtained from $N$-body data. We confirm that most of the stars causing TDEs in a spherical nuclear star cluster originate from the full loss-cone region of phase space, derive analytical boundaries in eccentricity-$β$ space, and find them confirmed by $N$-body data. Since our limiting eccentricities are much smaller than critical eccentricities for full accretion or full escape of stellar debris, we conclude that those stars are only very marginally eccentric or hyperbolic, close to parabolic.
When a star gets too close to a supermassive black hole, it is torn apart by the tidal forces. Roughly half of the stellar mass becomes unbound and flies away at tremendous velocities - around $10^4$ km/s. In this work we explore the idea that the shock produced by the interaction of the unbound debris with the ambient medium gives rise to the synchrotron radio emission observed in several TDEs. We use a moving mesh numerical simulation to study the evolution of the unbound debris and the bow shock around it. We find that as the periapse distance of the star decreases, the outflow becomes fast…
In the tidal disruption of a star by a black hole, roughly half of the stellar mass becomes bound and falls into the black hole, while the other half is ejected at high velocity. Several previous studies have considered the emission resulting from the accretion of bound material; we consider the possibility that the unbound debris may also radiate once it has expanded and become transparent. We show that the gradual energy input from hydrogen recombination compensates for adiabatic loses over significant expansion factors. The opacity also drops dramatically with recombination, and the interna…
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 …
The kinetic energy of a star in orbit about a supermassive black hole is a significant fraction of its rest mass energy when its periapse is comparable to its tidal radius. Upon its destruction, a fraction of this energy is extracted and injected into the stellar debris, half of which becomes unbound from the black hole, with the fastest material moving at $\sim 0.03 c$. In this paper, we present a formalism for determining the fate of these unbound debris streams (UDSs) as they depart from the black hole and interact with the surrounding gas. As the density and velocity varies along the lengt…
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…
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…
ASASSN-14li is a recently-discovered tidal disruption event with an exceptionally rich data-set: spectra and lightcurves in soft X-rays, UV, optical, and radio. To understand its emission properties in all these bands, we have extended our model for post-tidal disruption accretion and photon production to estimate both soft X-ray radiation produced by the prompt accretion phase and synchrotron emission associated with the bow shock driven through an external medium by the unbound tidal debris, as well as optical and UV light. We find that fiducial values of the stellar mass ($1 M_\odot$) and b…
Stream-stream collisions play an important role for the circularization of highly eccentric streams resulting from tidal disruption events (TDEs). We perform three dimensional radiation hydrodynamic simulations to show that stream collisions can contribute significant optical and ultraviolet light to the flares produced by TDEs, and can sometimes explain the majority of the observed emission. Our simulations focus on the region near the radiation pressure dominated shock produced by a collision and track how the kinetic energy of the stream is dissipated by the associated shock. When the mass …
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 …
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.,…
A star wandering too close to a supermassive black hole (SMBH) will be tidally disrupted. Previous studies of such "tidal disruption event" (TDE) mostly focus on the stellar debris that are bound to the system, because they give rise to luminous flares. On the other hand, half of the stellar debris in principle are unbound and can stream to a great distance, but so far there is no clear evidence that this "unbound debris stream" (UDS) exists. Motivated by the fact that the circum-nuclear region around SMBHs is usually filled with dense molecular clouds (MCs), here we investigate the observatio…
We perform 3D general relativistic smoothed particle hydrodynamics (GRSPH) simulations of tidal disruption events involving 1 $M_\odot$ stars and $10^6 M_\odot$ rotating supermassive black holes. We consider stars on initially elliptical orbits both in, and inclined to, the black hole equatorial plane. We confirm that stream-stream collisions caused by relativistic apsidal precession rapidly circularise the disrupted material into a disc. For inclined trajectories we find that nodal precession induced by the black hole spin (i.e. Lense-Thirring precession) inhibits stream-stream collisions onl…
Supermassive black hole binaries (SMBHBs) are the products of frequent galaxy mergers. The coalescence of the SMBHBs is a distinct source of gravitational wave (GW) radiation. The detections of the strong GW radiation and their possible electromagnetic counterparts are essential. Numerical relativity suggests that the post-merger supermassive black hole (SMBH) gets a kick velocity up to 4000 km/s due to the anisotropic GW radiations. Here we investigate the dynamical co-evolution and interaction of the recoiling SMBHs and their galactic stellar environments with one million direct N-body simul…
Massive black hole binaries (MBHBs) are a natural byproduct of galaxy mergers. Previous studies have shown that flares from stellar tidal disruption events (TDEs) are modified by the presence of a secondary perturber, causing interruptions in the light curve. We study the dynamics of TDE debris in the presence of a milliparsec-separated MBHB by integrating ballistic particle orbits in the time-varying potential of the binary. We find that gaps in the light curve appear when material misses the accretion radius on its first return to pericentre. Subsequent recurrences can be decomposed into "co…
Odd Radio Circles or ORCs are recently discovered edge-brightened, low surface brightness circular radio sources. The progenitors and astrophysical processes responsible for their origins are presently debated. Some ORCs are host-less and some appear to be hosted in distant quiescent galaxies. Two plausible explanations consider ORCs as nearby supernova remnants with sizes a few hundred parsec in the intragroup medium of the local group of galaxies or alternatively shocked halos of a few hundred kpc extent around distant galaxies. The input shock energy required to create ORCs of a few hundred…
We study accretion processes for tidally disrupted stars approaching supermassive black holes on bound orbits, by performing three dimensional Smoothed Particle Hydrodynamics simulations with a pseudo-Newtonian potential. We find that there is a critical value of the orbital eccentricity below which all the stellar debris remains bound to the black hole. For high but sub-critical eccentricities, all the stellar mass is accreted onto the black hole in a finite time, causing a significant deviation from the canonical $t^{-5/3}$ mass fallback rate. When a star is on a moderately eccentric orbit a…
We study the stellar dynamics of the first star clusters after intermediate-mass black holes (IMBHs) are formed via runaway stellar collisions. We use the outputs of cosmological simulations of Sakurai et al. (2017) to follow the star cluster evolution in a live dark matter (DM) halo. Mass segregation within a cluster promotes massive stars to be captured by the central IMBH occasionally, causing tidal disruption events (TDEs). We find that the TDE rate scales with the IMBH mass as $\dot{N}_{\rm TDE}\sim0.3\,{\rm Myr}^{-1}(M_{\rm IMBH}/1000\,{\rm M}_{\odot})^2$. The DM component affects the st…
We have analyzed archival VLBA data for Cygnus A between 2002 and 2013, to search for radio emission from the transient discovered in 2015 by \citet{per18} approximately 0.4\arcsec~ from the nucleus of Cygnus A (Cyg A-2). \citet{per18} use VLA and VLBA archival data (between 1989 and 1997) to show that the transient rises in flux density by a factor of at least five in less than approximately 20 years. With the additional data presented here, we revise the rise time to between approximately four years and six years, based on a new detection of the source at 15.4 GHz from October 2011. Our resu…
The impact of recombination during tidal disruption events
School of Physics and Astronomy & Institute for Gravitational Wave Astronomy, University of Birmingham（伯明翰大学物理与天文学学院及引力波天文研究所）；Niels Bohr International Academy, Niels Bohr Institute（尼尔斯·玻尔国际学院，尼尔斯·玻尔研究所）
We present radio observations of the tidal disruption event candidate (TDE) XMMSL1 J0740$-$85 spanning 592 to 875 d post X-ray discovery. We detect radio emission that fades from an initial peak flux density at 1.6 GHz of $1.19\pm 0.06$ mJy to $0.65\pm 0.06$ mJy suggesting an association with the TDE. This makes XMMSL1 J0740$-$85 at $d=75$ Mpc the nearest TDE with detected radio emission to date and only the fifth TDE with radio emission overall. The observed radio luminosity rules out a powerful relativistic jet like that seen in the relativistic TDE Swift J1644+57. Instead we infer from an e…
Ultra-long gamma-ray bursts (ulGRBs) are a new population of GRBs with extreme durations of $\sim 10^{4}$ s. Leading candidates for their origin are blue supergiant collapsars, magnetars, and white dwarf tidal disruption events (WD-TDEs) caused by massive black holes (BHs). Recent observations of supernova-like (SN-like) bumps associated with ulGRBs challenged both the WD-TDE and the blue supergiant models because of the detection of SNe and the absence of hydrogen lines, respectively. We propose that WD-TDEs can accommodate the observed SN-like bumps if the fallback WD matter releases energy …
A tidal disruption event (TDE) takes place when a star passes near enough to a massive black hole to be disrupted. About half the star's matter is given elliptical trajectories with large apocenter distances, the other half is unbound. To "circularize", i.e., to form an accretion flow, the bound matter must lose a significant amount of energy, with the actual amount depending on the characteristic scale of the flow measured in units of the black hole's gravitational radius ($\sim 10^{51} (R/1000R_g)^{-1}$~erg). Recent numerical simulations \citep{Shiokawa+2015} have revealed that the circulari…
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…
Radio flares from tidal disruption events (TDEs) are generally interpreted as synchrotron emission arising from the interaction of an outflow with the surrounding circumnuclear medium (CNM). We generalize the common equipartition analysis to be applicable in cases lacking a clear spectral peak or even with just an upper limit. We show that, for detected events, there is a lower limit on the combination of the outflow's velocity $v$ and solid angle $Ω$, $\simeq vΩ^{a}$ (with $a \simeq 0.5$) that constrains the outflow's properties. Considering several possible outflow components accompanying TD…
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.…
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 $β\equiv r_{\rm t}/r_{\rm p} = 5-7$, where $r_{\rm p}$ is the pericenter of the stellar cente…
When a star comes within a critical distance to a supermassive black hole (SMBH), immense tidal forces disrupt the star, resulting in a stream of debris that falls back onto the SMBH and powers a luminous flare. In this paper, we perform hydrodynamical simulations of the disruption of a main-sequence star by a SMBH to characterize the evolution of the debris stream after a tidal disruption. We demonstrate that this debris stream is confined by self-gravity in the two directions perpendicular to the original direction of the star's travel, and as a consequence has a negligible surface area and …
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 …
Hydrodynamic Simulations of Tidal Disruption Encores
Stony Brook University（石溪大学）；University of Colorado（科罗拉多大学）；National Institute of Standards and Technology（美国国家标准与技术研究院）；The Max Planck Institute for Astrophysics（马克斯·普朗克天体物理学研究所）
A fraction of tidal disruption events (TDEs) occur in active galactic nuclei (AGNs) whose black holes possess accretion disks; these TDEs can be confused with common AGN flares. The disruption itself is unaffected by the disk, but the evolution of the bound debris stream is modified by its collision with the disk when it returns to pericenter. The outcome of the collision is largely determined by the ratio of the stream mass current to the azimuthal mass current of the disk rotating underneath the stream footprint, which in turn depends on the mass and luminosity of the AGN. To characterize TD…
Tidal capture and repeating partial tidal disruption events of giant stars
Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education（现代天文与天体物理教育部重点实验室）；School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）
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 describe how the various outcomes of stellar tidal disruption give rise to observable radiation. We separately consider the cases where gas circularizes rapidly into an accretion disc, as well as the case when shocked debris streams provide the observable emission without having fully circularized. For the rapid circularization case, we describe how outflows, absorption by reprocessing layers, and Comptonization can cause the observed radiation to depart from that of a bare disc, possibly giving rise to the observed optical/UV emission along with soft X-rays from the disc. If, instead, most…
Hydrodynamical simulation of wind production from hot accretion flows in tidal disruption events
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；Shanghai Key Lab for Astrophysics, Shanghai Normal University（上海师范大学天体物理上海市重点实验室）；Department of Physics, Chongqing University（重庆大学物理学院）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）
On the origin of anomalous dissipation in simulations of tidal disruption events
School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学院）；Department of Physics, Syracuse University（锡拉丘兹大学物理系）；Department of Astrophysical Sciences, Princeton University（普林斯顿大学天体科学系）
Close encounters between neutron stars and main-sequence stars occur in globular clusters and may lead to various outcomes. Here we study encounters resulting in tidal disruption of the star. Using $N$-body models, we predict the typical stellar masses in these disruptions and the dependence of the event rate on host cluster properties. We find that tidal disruption events occur most frequently in core-collapsed globular clusters and that roughly $25\%$ of the disrupted stars are merger products (i.e., blue straggler stars). Using hydrodynamic simulations, we model the tidal disruptions themse…
Simulations on the collision between debris stream and outer dusty torus: a possible channel for forming fast-rise and long-delayed radio outburst in tidal disruption events
We present an analytic and fully relativistic framework for studying the self-intersection of tidal disruption event (TDE) streams, restricting ourselves to the Schwarzschild spacetime. By taking advantage of the closed-form solution to the geodesic equations in the Schwarzschild metric, we calculate properties of the self-intersection without numerically evaluating the geodesic equations or making any post-Newtonian approximations. Our analytic treatment also facilitates geometric definitions of the orbital semi-major axis and eccentricity, as opposed to Newtonian formulas which lead to unphy…
We run a suite of hydrodynamics simulations of tidal disruption events (TDEs) of a white dwarf (WD) by a black hole (BH) with a wide range of WD/BH masses and orbital parameters. We implement nuclear reactions to study nucleosynthesis and its dynamical effect through release of nuclear energy. The released nuclear energy effectively increases the fraction of unbound ejecta. This effect is weaker for a heavy WD with 1.2 $\mathrm{M}_{\odot}$, because the specific orbital energy distribution of the debris is predominantly determined by the tidal force, rather than by the explosive reactions. The …
When a star comes too close to a supermassive black hole, it gets torn apart by strong tidal forces in a tidal disruption event, or TDE. Half of the elongated stream of debris comes back to the stellar pericenter where relativistic apsidal precession induces a self-crossing shock. As a result, the gas gets launched into an outflow that can experience additional interactions, leading to the formation of an accretion disc. We carry out the first radiation-hydrodynamics simulations of this process, making use of the same injection procedure to treat the self-crossing shock as in our previous adia…
We report the discovery of non-stellar hydrogen Balmer and metastable helium absorption lines accompanying a transient, high-velocity (0.05$c$) broad absorption line (BAL) system in the optical spectra of the tidal disruption event (TDE) AT2018zr ($z=0.071$). In the HST UV spectra, absorption of high- and low-ionization lines are also present at this velocity, making AT2018zr resemble a low-ionization broad absorption line (LoBAL) QSO. We conclude that these transient absorption features are more likely to arise in fast outflows produced by the TDE than absorbed by the unbound debris. In accor…
We study the emission properties of thermonuclear explosions in a helium white dwarf (WD) tidal disruption event (TDE). We consider a TDE where a 0.2 $M_{\odot}$ helium WD is disrupted by a $10^{2.5}\,M_{\odot}$ intermediate-mass black hole (IMBH). The helium WD is not only tidally disrupted but is also detonated by the tidal compression and by succeeding shocks. We focus on the emission powered by radioactive nuclei in the unbound TDE ejecta. We perform hydrodynamic simulations coupled with nuclear reactions, post-process detailed nucleosynthesis calculations, and then radiative transfer simu…
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…
We construct time-dependent one-dimensional (vertically averaged) models of accretion disks produced by the tidal disruption of a white dwarf (WD) by a binary neutron star (NS) companion. Nuclear reactions in the disk midplane burn the WD matter to increasingly heavier elements at sequentially smaller radii, releasing substantial energy which can impact the disk dynamics. A model for disk outflows is employed, by which cooling from the outflow balances other sources of heating (viscous, nuclear) in regulating the Bernoulli parameter of the midplane to a fixed value $\lesssim 0$. We perform a c…
