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Black hole - neutron star $(BH/NS)$ binaries are of interest in many ways: they are intrinsically multi-messenger systems, highly transient, radiate gravitational waves detectable by LIGO, and may produce $\gamma$-ray bursts. Although it has long been assumed that their late-stage orbital evolution is driven entirely by gravitational wave emission, we show here that in certain circumstances, mass transfer from the neutron star onto the black hole can both alter the binary's orbital evolution and significantly reduce the neutron star's mass when the fraction of its mass transferred per orbit is $\gtrsim 10^{-2}$, the neutron star's mass diminishes by order-unity, leading to mergers in which the neutron star mass is exceptionally small. The mass transfer creates a gas disk around the black hole ${\it before}$ merger that can be comparable in mass to the debris remaining after merger, i.e. $\sim 0.1 M_\odot$. These processes are most important when the initial neutron star/black hole mass ratio $q$ is in the range $\approx 0.2 - 0.8$, the orbital semimajor axis is $40 \lesssim a_0/r_g \lesssim 300 $ ($r_g \equiv GM_{\rm B}/c^2$), and the eccentricity is large, $e_0 \gtrsim 0.8$. Systems of this sort may be generated through the dynamical evolution of a triple system, as well as by other means.

Three recent global simulations of tidal disruption events (TDEs) have produced, using different numerical techniques and parameters, very similar pictures of their dynamics. In typical TDEs, after the star is disrupted by a supermassive black hole, the bound portion of the stellar debris follows highly eccentric trajectories, reaching apocenters of several thousand gravitational radii. Only a very small fraction is captured upon returning to the vicinity of the supermassive black hole. Nearly all the debris returns to the apocenter, where shocks produce a thick irregular cloud on this radial scale and power the optical/UV flare. These simulation results imply that over a few years, the thick cloud settles into an accretion flow responsible for the long term emission. Despite not being designed to match observations, the dynamical picture given by the three simulations aligns well with observations of typical events, correctly predicting the flares' total radiated energy, luminosity, temperature and emission line width. On the basis of these predictions, we provide an updated method (\sc TDEmass) to infer the stellar and black hole masses from a flare's peak luminosity and temperature. This picture also correctly predicts the luminosity observed years after the flare. In addition, we show that in a magnitude-limited survey, if the intrinsic rate of TDEs is independent of black hole mass, the detected events will preferentially have black hole masses $\sim 10^{6 \pm 0.3} M_\odot$ and stellar masses of $\sim 1-1.5 M_\odot$.

The detection of GW170817/AT2017gfo inaugurated an era of multimessenger astrophysics, in which gravitational wave and multiwavelength photon observations complement one another to provide unique insight on astrophysical systems. A broad theoretical consensus exists in which the photon phenomenology of neutron star mergers largely rests upon the evolution of the small amount of matter left on bound orbits around the black hole or massive neutron star remaining after the merger. Because this accretion disk is far from inflow equilibrium, its subsequent evolution depends very strongly on its initial state, yet very little is known about how this state is determined. Using both snapshot and tracer particle data from a numerical relativity/MHD simulation of an equal-mass neutron star merger that collapses to a black hole, we show how gravitational forces arising in a non-axisymmetric, dynamical spacetime supplement hydrodynamical effects in shaping the initial structure of the bound debris disk. The work done by hydrodynamical forces is ${\sim}10$ times greater than that due to time-dependent gravity. Although gravitational torques prior to remnant relaxation are an order of magnitude larger than hydrodynamical torques, their intrinsic sign symmetry leads to strong cancellation; as a result, hydrodynamical and gravitational torques have comparable effect. We also show that the debris disk's initial specific angular momentum distribution is sharply peaked at roughly the specific angular momentum of the merged neutron star's outer layers, a few $r_g c$, and identify the regulating mechanism.

Previously we demonstrated that the magnetorotational instability (MRI) grows vigorously in eccentric disks, much as it does in circular disks, and we investigated the nonlinear development of the eccentric MRI without vertical gravity. Here we explore how vertical gravity influences the magnetohydrodynamic (MHD) turbulence stirred by the eccentric MRI. Similar to eccentric disks without vertical gravity, the ratio of Maxwell stress to pressure, or the Shakura--Sunyaev alpha parameter, remains ~0.01, and the local sign flip in the Maxwell stress persists. Vertical gravity also introduces two new effects. Strong vertical compression near pericenter amplifies reconnection and dissipation, weakening the magnetic field. Angular momentum transport by MHD stresses broadens the mass distribution over eccentricity at much faster rates than without vertical gravity; as a result, spatial distributions of mass and eccentricity can be substantially modified in just ~5 to 10 orbits. MHD stresses in the eccentric debris of tidal disruption events may power emission $\gtrsim$1 yr after disruption.

Many studies have found that neutron star mergers leave a fraction of the stars' mass in bound orbits surrounding the resulting massive neutron star or black hole. This mass is a site of $r-$ process nucleosynthesis and can generate a wind that contributes to a kilonova. However, comparatively little is known about the dynamics determining its mass or initial structure. Here we begin to investigate these questions, starting with the origin of the disk mass. Using tracer particle as well as discretized fluid data from numerical simulations, we identify where in the neutron stars the debris came from, the paths it takes in order to escape from the neutron stars' interiors, and the times and locations at which its orbital properties diverge from those of neighboring fluid elements that end up remaining in the merged neutron star.

While supermassive binary black holes inspiral toward merger they may also experience significant accretion of matter from a surrounding disk. We study the dynamics of this system, simultaneously describing the evolving spacetime and magnetized plasma, and present the first relativistic calculation simulating two equal-mass, non-spinning black holes as they inspiral from a $20M$ ($G=c=1$) initial separation almost to merger, $\simeq 9M$ ($M$=binary mass). Our dynamical results imply important observational consequences: for instance, the accretion rate $\dot M$ onto the black holes first decreases and then reaches a plateau, dropping by only a factor of $\sim 3$ despite the rapid inspiral. An estimated bolometric light curve thus suggests some merging SMBBHs may be quite luminous past the predicted decoupling from the circumbinary disk. The minidisks through which the accretion reaches the black holes are very non-standard: Reynolds, not Maxwell, stresses dominate, and they oscillate between two states. In one part of the cycle, ``sloshing" streams transfer mass from one minidisk to the other through the L1 point at a rate $\sim 0.1\times$ the accretion rate, carrying kinetic energy at a rate that can be as large as the peak minidisk bolometric luminosity. We also discover that episodic accretion drives minidisks with time-varying tilts. The unsigned poloidal magnetic flux on the black hole event horizon is roughly constant at a dimensionless level $\phi\sim 2-3$, but doubles just before merger; if the black holes had significant spin, this flux indicates the potential for powerful jets with variability driven by binary dynamics, another prediction of potentially unique EM signatures. This simulation is the first to employ our multipatch infrastructure \pwmhd, decreasing computational expense to $\sim 3\%$ of conventional single-grid methods' cost.

Accretion of debris seems to be the natural mechanism to power the radiation emitted during a tidal disruption event (TDE), in which a supermassive black hole tears apart a star. However, this requires the prompt formation of a compact accretion disk. Here, using a fully relativistic global simulation for the long-term evolution of debris in a TDE with realistic initial conditions, we show that at most a tiny fraction of the bound mass enters such a disk on the timescale of observed flares. To "circularize" most of the bound mass entails an increase in the binding energy of that mass by a factor $\sim 30$; we find at most an order unity change. Our simulation suggests it would take a time scale comparable to a few tens of the characteristic mass fallback time to dissipate enough energy for "circularization". Instead, the bound debris forms an extended eccentric accretion flow with eccentricity $\simeq 0.4-0.5$ by $\sim 2$ fallback times. Although the energy dissipated in shocks in this large-scale flow is much smaller than the "circularization" energy, it matches the observed radiated energy very well. Nonetheless, the impact of shocks is not strong enough to unbind initially bound debris into an outflow.

Extreme tidal disruption events (eTDEs), which occur when a star passes very close to a supermassive black hole, may provide a way to observe a long-sought general relativistic effect: orbits that wind several times around a black hole and then leave. Through general relativistic hydrodynamics simulations, we show that such eTDEs are easily distinguished from most tidal disruptions, in which stars come close, but not so close, to the black hole. Following the stellar orbit, the debris in eTDEs is initially distributed in a crescent that quickly turns into tight spirals, from which some mass later falls back toward the black hole, while the remainder is ejected. Internal shocks within the infalling debris power the observed emission. The resulting light-curve rises rapidly to roughly the Eddington luminosity, maintains this level for between a few weeks and a year (depending on both the stellar mass and the black hole mass), and then drops. Most of its power is in thermal X-rays at a temperature $\sim (1-2)\times 10^{6}$ K ($\sim 100-200$ eV). The debris evolution and observational features of eTDEs are qualitatively different from ordinary TDEs, making eTDEs a new type of TDE. Although eTDEs are relatively rare for lower-mass black holes, most tidal disruptions around higher-mass black holes are extreme. Their detection offers a view of an exotic relativistic phenomenon previously inaccessible.

Quasi-Periodic Erupters (QPEs) are a remarkable class of objects exhibiting very large amplitude quasi-periodic X-ray flares. Although numerous dynamical models have been proposed to explain them, relatively little attention has been given to using the properties of their radiation to constrain their dynamics. Here we show that the observed luminosity, spectrum, repetition period, duty cycle, and fluctuations in the latter two quantities point toward a model in which: a main sequence star on a moderately eccentric orbit around a supermassive black hole periodically transfers mass to the Roche lobe of the black hole; orbital dynamics lead to mildly-relativistic shocks near the black hole; and thermal X-rays at the observed temperature are emitted by the gas as it flows away from the shock. Strong X-ray irradiation of the star by the flare itself augments the mass transfer, creates fluctuations in flare timing, and stirs turbulence in the stellar atmosphere that amplifies magnetic field to a level at which magnetic stresses can accelerate infall of the transferred mass toward the black hole.

We have added support for realistic, microphysical, finite-temperature equations of state (EOS) and neutrino physics via a leakage scheme to IllinoisGRMHD, an open-source GRMHD code for dynamical spacetimes in the Einstein Toolkit. These new features are provided by two new, NRPy+-based codes: NRPyEOS, which performs highly efficient EOS table lookups and interpolations, and NRPyLeakage, which implements a new, AMR-capable neutrino leakage scheme in the Einstein Toolkit. We have performed a series of strenuous validation tests that demonstrate the robustness of these new codes, particularly on the Cartesian AMR grids provided by Carpet. Furthermore, we show results from fully dynamical GRMHD simulations of single unmagnetized neutron stars, and magnetized binary neutron star mergers. This new version of IllinoisGRMHD, as well as NRPyEOS and NRPyLeakage, is pedagogically documented in Jupyter notebooks and fully open source. The codes will be proposed for inclusion in an upcoming version of the Einstein Toolkit.

We present multi-band ATLAS photometry for SN 2019tsf, a stripped-envelope Type Ib supernova (SESN). The SN shows a triple-peaked light curve and a late (re-)brightening, making it unique among stripped-envelope systems. The re-brightening observations represent the latest photometric measurements of a multi-peaked Type Ib SN to date. As late-time photometry and spectroscopy suggest no hydrogen, the potential circumstellar material (CSM) must be H-poor. Moreover, late (>150 days) spectra show no signs of narrow emission lines, further disfavouring CSM interaction. On the contrary, an extended CSM structure is seen through a follow-up radio campaign with Karl G. Jansky Very Large Array (VLA), indicating a source of bright optically thick radio emission at late times, which is highly unusual among H-poor SESNe. We attribute this phenomenology to an interaction of the supernova ejecta with spherically-asymmetric CSM, potentially disk-like, and we present several models that can potentially explain the origin of this rare Type Ib supernova. The warped disc model paints a novel picture, where the tertiary companion perturbs the progenitors CSM, that can explain the multi-peaked light curves of SNe, and here we apply it to SN 2019tsf. This SN 2019tsf is likely a member of a new sub-class of Type Ib SNe and among the recently discovered class of SNe that undergo mass transfer at the moment of explosion

The magnetorotational instability (MRI) has been extensively studied in circular magnetized disks, and its ability to drive accretion has been demonstrated in a multitude of scenarios. There are reasons to expect eccentric magnetized disks to also exist, but the behavior of the MRI in these disks remains largely uncharted territory. Here we present the first simulations that follow the nonlinear development of the MRI in eccentric disks. We find that the MRI in eccentric disks resembles circular disks in two ways, in the overall level of saturation and in the dependence of the detailed saturated state on magnetic topology. However, in contrast with circular disks, the Maxwell stress in eccentric disks can be negative in some disk sectors, even though the integrated stress is always positive. The angular momentum flux raises the eccentricity of the inner parts of the disk and diminishes the same of the outer parts. Because material accreting onto a black hole from an eccentric orbit possesses more energy than material tracing the innermost stable circular orbit, the radiative efficiency of eccentric disks may be significantly lower than circular disks. This may resolve the "inverse energy problem" seen in many tidal disruption events.

We perform binary neutron star (BNS) merger simulations in full dynamical general relativity with IllinoisGRMHD, on a Cartesian grid with adaptive-mesh refinement. After the remnant black hole has become nearly stationary, the evolution of the surrounding accretion disk on Cartesian grids over long timescales (1s) is suboptimal, as Cartesian coordinates over-resolve the angular coordinates at large distances, and the accreting plasma flows obliquely across coordinate lines dissipating angular momentum artificially from the disk. To address this, we present the Handoff, a set of computational tools that enables the transfer of general relativistic magnetohydrodynamic (GRMHD) and spacetime data from IllinoisGRMHD to HARM3D, a GRMHD code that specializes in modeling black hole accretion disks in static spacetimes over long timescales, making use of general coordinate systems with spherical topology. We demonstrate that the Handoff allows for a smooth and reliable transition of GRMHD fields and spacetime data, enabling us to efficiently and reliably evolve BNS dynamics well beyond merger. We also discuss future plans, which involve incorporating advanced equations of state and neutrino physics into BNS simulations using the \handoff approach.

We present fully relativistic predictions for the electromagnetic emission produced by accretion disks surrounding spinning and nonspinning supermassive binary black holes on the verge of merging. We use the code Bothros to post-process data from 3D general relativistic magnetohydrodynamic simulations via ray-tracing calculations. These simulations model the dynamics of a circumbinary disk and the mini-disks that form around two equal-mass black holes orbiting each other at an initial separation of 20 gravitational radii, and evolve the system for more than 10 orbits in the inspiral regime. We model the emission as the sum of thermal blackbody radiation emitted by an optically thick accretion disk and a power-law spectrum extending to hard X-rays emitted by a hot optically thin corona. We generate time-dependent spectra, images, and light curves at various frequencies to investigate intrinsic periodic signals in the emission, as well as the effects of the black hole spin. We find that prograde black hole spin makes mini-disks brighter since the smaller innermost stable circular orbit angular momentum demands more dissipation before matter plunges to the horizon. However, compared to mini-disks in larger separation binaries with spinning black holes, our mini-disks are less luminous: unlike those systems, their mass accretion rate is lower than in the circumbinary disk, and they radiate with lower efficiency because their inflow times are shorter. Compared to a single black hole system matched in mass and accretion rate, these binaries have spectra noticeably weaker and softer in the UV. Finally, we discuss the implications of our findings for the potential observability of these systems.

The tidal disruption event AT2019dsg was observed from radio to X-rays and was possibly accompanied by a high-energy neutrino. Previous interpretations have focused on continued injection by a central engine as the source of energy for radio emission. We show that continuous energy injection is unnecessary; the radio data can be explained by a single ejection of plasma that supplies all the energy needed. To support this assertion, we analyze the synchrotron self-absorbed spectra in terms of the equipartition model. Similar to previous analyses, we find that the energy in the radio-emitting region increases approximately $\propto t^{0.7}$ and the lengthscale of this region grows $\propto t$ at a rate $\simeq0.06c$. This event resembles the earliest stage of a supernova remnant: because the ejected mass is much greater than the shocked external mass, its velocity remains unchanged, while the energy in shocked gas grows with time. The radio-emitting material gains energy from the outflow, not continuing energy injection by the central object. Although energy injection from an accreting BH cannot be completely excluded, the energy injection rate is very different from the fallback luminosity, and maintaining constant outflow velocity requires fine-tuning demanding further physical explanation. If the neutrino association is real, the energy injection needed is much greater than for the radio emission, suggesting that the detected neutrino did not arise from the radio-emitting region.

We perform a full 3D general relativistic magnetohydrodynamical (GRMHD) simulation of an equal-mass, spinning, binary black hole approaching merger, surrounded by a circumbinary disk and with mini-disks around each black hole. For this purpose, we evolve the ideal GRMHD equations on top of an approximated spacetime for the binary that is valid in every position of space, including the black hole horizons, during the inspiral regime. We use relaxed initial data for the circumbinary disk from a previous long-term simulation, where the accretion is dominated by an $m=1$ overdensity called the lump. We compare our new spinning simulation with a previous non-spinning run, studying how spin influences the mini-disk properties. We analyze the accretion from the inner edge of the lump to the black hole, focusing on the angular momentum budget of the fluid around the mini-disks. We find that mini-disks in the spinning case have more mass over a cycle than the non-spinning case. However, in both cases, we find most of the mass received by the black holes is delivered by the direct plunging of material from the lump. We also analyze the morphology and variability of the electromagnetic fluxes and we find they share the same periodicities of the accretion rate. In the spinning case, we find that the outflows are $8$ times stronger than the non-spinning case. Our results will be useful to understand and produce realistic synthetic light curves and spectra, which can be used in future observations.

The first binary neutron star merger has already been detected in gravitational waves. The signal was accompanied by an electromagnetic counterpart including a kilonova component powered by the decay of radioactive nuclei, as well as a short $\gamma$-ray burst. In order to understand the radioactively-powered signal, it is necessary to simulate the outflows and their nucleosynthesis from the post-merger disk. Simulating the disk and predicting the composition of the outflows requires general relativistic magnetohydrodynamical (GRMHD) simulations that include a realistic, finite-temperature equation of state (EOS) and self-consistently calculating the impact of neutrinos. In this work, we detail the implementation of a finite-temperature EOS and the treatment of neutrinos in the GRMHD code HARM3D+NUC, based on HARM3D. We include formal tests of both the finite-temperature EOS and the neutrino leakage scheme. We further test the code by showing that, given conditions similar to those of published remnant disks following neutron star mergers, it reproduces both recombination of free nucleons to a neutron-rich composition and excitation of a thermal wind.

Accretion disks whose matter follows eccentric orbits can arise in multiple astrophysical situations. Unlike circular orbit disks, the vertical gravity in eccentric disks varies around the orbit. In this paper, we investigate some of the dynamical effects of this varying gravity on the vertical structure using $1D$ hydrodynamics simulations of individual gas columns assumed to be mutually non-interacting. We find that time-dependent gravitational pumping generically creates shocks near pericenter; the energy dissipated in the shocks is taken from the orbital energy. Because the kinetic energy per unit mass in vertical motion near pericenter can be large compared to the net orbital energy, the shocked gas can be heated to nearly the virial temperature, and some of it becomes unbound. These shocks affect larger fractions of the disk mass for larger eccentricity and/or disk aspect ratio. If the orbit can be maintained despite orbital energy loss, diverse initial structures evolve in only a few orbits so that they follow a limit-cycle characterized by a low-entropy midplane and a much higher entropy outer layer. In favorable cases (such as the tidal disruption of stars by supermassive black holes), these effects could be a potentially important energy dissipation and mass loss mechanism.

We present a survey of how the spectral features of black hole X-ray binary systems depend on spin, accretion rate, viewing angle, and Fe abundance when predicted on the basis of first principles physical calculations. The power law component hardens with increasing spin. The thermal component strengthens with increasing accretion rate. The Compton bump is enhanced by higher accretion rate and lower spin. The Fe K$\alpha$ equivalent width grows sub-linearly with Fe abundance. Strikingly, the K$\alpha$ profile is more sensitive to accretion rate than to spin because its radial surface brightness profile is relatively flat, and higher accretion rate extends the production region to smaller radii. The overall radiative efficiency is at least 30--100% greater than as predicted by the Novikov-Thorne model.

Accreting supermassive binary black holes (SMBBHs) are potential multi-messenger sources because they emit both gravitational wave and electromagnetic (EM) radiation. Past work has shown that their EM output may be periodically modulated by an asymmetric density distribution in the circumbinary disk, often called an "overdensity" or "lump;" this modulation could possibly be used to identify a source as a binary. We explore the sensitivity of the overdensity to SMBBH mass ratio and magnetic flux through the accretion disk. We find that the relative amplitude of the overdensity and its associated EM periodic signal both degrade with diminishing mass ratio, vanishing altogether somewhere between 1:2 and 1:5. Greater magnetization also weakens the lump and any modulation of the light output. We develop a model to describe how lump formation results from internal stress degrading faster in the lump region than it can be rejuvenated through accretion inflow, and predicts a threshold value in specific internal stress below which lump formation should occur and which all our lump-forming simulations satisfy. Thus, detection of such a modulation would provide a constraint on both mass-ratio and magnetic flux piercing the accretion flow.

Supermassive black hole binaries are likely to accrete interstellar gas through a circumbinary disk. Shortly before merger, the inner portions of this circumbinary disk are subject to general relativistic effects. To study this regime, we approximate the spacetime metric of close orbiting black holes by superimposing two boosted Kerr-Schild terms. After demonstrating the quality of this approximation, we carry out very long-term general relativistic magnetohydrodynamic simulations of the circumbinary disk. We consider black holes with spin dimensionless parameters of magnitude 0.9, in one simulation parallel to the orbital angular momentum of the binary, but in another anti-parallel. These are contrasted with spinless simulations. We find that, for a fixed surface mass density in the inner circumbinary disk, aligned spins of this magnitude approximately reduce the mass accretion rate by 14% and counter-aligned spins increase it by 45%, leaving many other disk properties unchanged.

Tidal disruption events (TDEs) taking place in active galactic nuclei (AGNs) are different from ordinary TDEs. In these events, the returning tidal debris stream drills through the pre-existing AGN accretion disk near the stream pericenter, destroying the inner disk in the process, and then intersects with the disk a second time at radii ranging from a few to hundreds of times the pericenter distance. The debris dynamics of such TDEs, and hence their appearance, are distinct from ordinary TDEs. Here we explore the observational signatures of this "second impact" of the stream with the disk. Strong shocks form as the dilute stream is stopped by the denser disk. Compton cooling of the shocked material produces hard X-rays, even soft gamma-rays, with most of the energy emitted between ~10 keV and 1 MeV. The luminosity follows the mass-return rate, peaking between ~$10^{42}$ and $10^{44}$ erg/s. The X-ray hardness and the smoothness of the light curve provide possible means for distinguishing the second impact from ordinary AGN flares, which exhibit softer spectra and more irregular light curves.

We present a formulation for a local cooling function to be employed in the diffuse, hot corona region of 3D GRMHD simulations of accreting black holes. This new cooling function calculates the cooling rate due to inverse Compton scattering by considering the relevant microphysics in each cell in the corona and approximating the radiation energy density and Compton temperature there by integrating over the thermal seed photon flux from the disk surface. The method either assumes ion and electron temperatures are equal (1T), or calculates them separately (2T) using an instantaneous equilibrium approach predicated on the actual relevant rate equations (Coulomb and Compton). The method is shown to be consistent with a more detailed ray-tracing calculation where the bulk of the cooling occurs, but is substantially less costly to perform. As an example, we apply these methods to a \textscharm3d simulation of a $10 M_\odot$, non-spinning black hole, accreting at nominally 1\% the Eddington value. Both 1T and 2T approaches lead to increased radiative efficiency and a larger fraction of total cooling in the corona as compared to the original target-temperature cooling function used by \textscharm3d, especially in the 1T case. Time-averaged post-processing reveals that the continuum spectral observations predicted from these simulations are qualitatively similar to actual X-ray binary data, especially so for the 1T approach which yields a harder power-law component ($\Gamma = 2.25$) compared to the 2T version ($\Gamma = 2.53$)

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 of the debris follows highly eccentric orbits for a significant time, many properties of the observed optical/UV emission can be explained by the scale of those eccentric orbits and the shocks embedded in the debris flow near orbital apocenter. In this picture, soft X-ray emission at early times results from the smaller amount of debris mass deflected into a compact accretion disc by weak shocks near the stellar pericenter. A general proposal for the near-constancy of the ultraviolet/optical color temperatures is provided, by linking it to incomplete thermalization of radiation in the atmosphere of the emitting region. We also briefly discuss the radio signals from the interaction of unbound debris and jets with the black hole environment.

The flare produced when a star is tidally disrupted by a supermassive black hole holds potential as a diagnostic of both the black hole mass and the star mass. We propose a new method to realize this potential based upon a physical model of optical/UV light production in which shocks near the apocenters of debris orbits dissipate orbital energy, which is then radiated from that region. Measurement of the optical/UV luminosity and color temperature at the peak of the flare leads directly to the two masses. The black hole mass depends mostly on the temperature observed at peak luminosity, while the mass of the disrupted star depends mostly on the peak luminosity. We introduce \sc TDEmass, a method to infer the black hole and stellar masses given these two input quantities. Using \sc TDEmass, we find, for 21 well-measured events, black hole masses between $5\times 10^5$ and $10^7 M_\odot$ and disrupted stars with initial masses between 0.6 and $13M_\odot$. An open-source \sc python-based tool for \sc TDEmass is available at https://github.com/taehoryu/TDEmass.git.

Tidal disruption events involve numerous physical processes (fluid dynamics, magnetohydrodynamics, radiation transport, self-gravity, general relativistic dynamics) in highly nonlinear ways, and, because TDEs are transients by definition, frequently in non-equilibrium states. For these reasons, numerical solution of the relevant equations can be an essential tool for studying these events. In this chapter, we present a summary of the key problems of the field for which simulations offer the greatest promise and identify the capabilities required to make progress on them. We then discuss what has been---and what cannot be---done with existing numerical methods. We close with an overview of what methods now under development may do to expand our ability to understand these events.

The black hole of an active galactic nucleus is encircled by an accretion disk. The surface density of the disk is always too low to affect the tidal disruption of a star, but it can be high enough that a vigorous interaction results when the debris stream returns to pericenter and punches through the disk. Shocks excited in the disk dissipate the kinetic energy of the disk interior to the impact point and expedite inflow toward the black hole. Radiatively efficient disks with luminosity $\gtrsim10^{-3}$ Eddington have a high enough surface density that the initial stream-disk interaction leads to energy dissipation at a super-Eddington rate. Because of the rapid inflow, only part of this dissipated energy emerges as radiation, while the rest is advected into the black hole. Dissipation, inflow, and cooling balance to keep the bolometric luminosity at an Eddington-level plateau whose duration is tens of days, with an almost linear dependence on stellar mass. After the plateau, the luminosity decreases in proportion to the disk surface density, with a power-law index between $-3$ and $-2$ at earlier times, and possibly a steeper index at later times.

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 $0.15~{\rm M}_\odot$ to $10~{\rm M}_\odot$. We find that, relative to the traditional order-of-magnitude estimate $r_{\rm t}$, the physical tidal radius of low-mass stars ($M_{\star} \lesssim 0.7~ {\rm M}_\odot$) is larger by tens of percent, while for high-mass stars ($M_{\star} \gtrsim1~ {\rm M}_\odot$) it is smaller by a factor 2--2.5. The traditional estimate of the range of energies found in the debris is $\approx 1.4\times$ too large for low-mass stars, but is a factor $\sim 2$ too small for high-mass stars; in addition, the energy distribution for high-mass stars has significant wings. For all stars undergoing tidal encounters, we find that mass-loss continues for many stellar vibration times because the black hole's tidal gravity competes with the instantaneous stellar gravity at the star's surface until the star has reached a distance from the black hole $\sim O(10)r_{\rm t}$.

Using a suite of fully relativistic hydrodynamic simulations applied to main-sequence stars with realistic internal density profiles, we examine full and partial tidal disruptions across a wide range of black hole mass ($10^{5}\leq M_{\rm BH}/\mathrm{M}_{\odot}\leq 5\times 10^{7}$) and stellar mass ($0.3 \leq M_{\star} /\mathrm{M}_{\odot}\leq 3$) as larger $M_{\rm BH}$ leads to stronger relativistic effects. For fixed $M_{\star}$, as $M_{\rm BH}$ increases, the ratio of the maximum pericenter distance yielding full disruptions ($\mathcal{R}_{\rm t}$) to its Newtonian prediction rises rapidly, becoming triple the Newtonian value for $M_{\rm BH} = 5\times10^{7}~{\rm M}_\odot$, while the ratio of the energy width of the stellar debris for full disruptions to the Newtonian prediction decreases steeply, resulting in a factor of two correction at $M_{\rm BH} = 5 \times 10^7~{\rm M}_\odot$. We find that for partial disruptions, the fractional remnant mass for a given ratio of the pericenter to $\mathcal{R}_{\rm t}$ is higher for larger $M_{\rm BH}$. These results have several implications. As $M_{\rm BH}$ increases above $\sim 10^7~{\rm M}_\odot$, the cross section for complete disruptions is suppressed by competition with direct capture. However, the cross section ratio for partial to complete disruptions depends only weakly on $M_{\rm BH}$. The relativistic correction to the debris energy width delays the time of peak mass-return rate and diminishes the magnitude of the peak return rate. For $M_{\rm BH} \gtrsim 10^7~{\rm M}_\odot$, the $M_{\rm BH}$-dependence of the full disruption cross section and the peak mass-return rate and time is influenced more by relativistic effects than by Newtonian dynamics.

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 cross section and the characteristic energy width of the debris. Moreover, the full disruption cross section is almost independent of $M_*$ for $M_*/M_\odot \lesssim 3$. Independent of $M_*$, relativistic effects increase the critical pericenter distance for full disruptions by up to a factor $\sim 3$ relative to the Newtonian prediction. The probability of a direct capture is also independent of $M_*$; at $M_{BH}/M_\odot \simeq 5 \times 10^6$ this probability is equal to that of a complete disruption. The width of the debris energy distribution $\Delta E$ can differ from the standard estimate by factors from 0.35 to 2, depending on $M_*$ and $M_{BH}$, implying a corresponding change in the characteristic mass-return timescale. The "frozen-in approximation" is inconsistent with $\Delta E$, and mass-loss continues over a long span of time. We provide analytic forms, suitable for use in both event rate estimates and parameter inference, to describe all these trends. For partial disruptions, we find a nearly-universal relation between the star's angular momentum and the fraction of $M_*$ remaining. Within the "empty loss-cone" regime, partial disruptions must precede full disruptions. These partial disruptions can drastically affect the rate and appearance of subsequent total disruptions.

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 the prograde direction and are hotter than main sequence stars of the same mass. Their specific orbital energy is $\simeq10^{-3}\times$ that of the debris, but of either sign with respect to the black hole potential, while their specific angular momentum is close to that of the original star. Even for strong encounters, remnants have speeds at infinity relative to the black hole potential $\lesssim 300$ km s$^{-1}$, so they are unable to travel far out into the galactic bulge. The remnants most deeply bound to the black hole go through a second tidal disruption event upon their first return to pericenter; if they have not thermally relaxed, they will be completely disrupted.

Tidal disruption events (TDEs), events in which a star passes very close to a supermassive black hole, are generally imagined as leading either to the star's complete disruption or to its passage directly into the black hole. In the former case it is widely believed that in all cases the bound portion of the debris quickly "circularizes" due to relativistic apsidal precession, i.e., forms a compact accretion disk, and emits a flare of standardized lightcurve and spectrum. We show here that TDEs are more diverse and can be grouped into several distinct categories on the basis of stellar pericenter distance $r_p$; we calculate the relative frequency of these categories. In particular, because rapid circularization requires $r_p \lesssim 10r_g$ ($r_g \equiv GM_{\rm BH}/c^2$), it can happen in only a minority of total disruptions, $\lesssim 1/4$ when the black hole has mass $M_{\rm BH} = 10^6 M_\odot$. For larger pericenter distances, $10 < r_p/r_g < 27$ (for $M_{\rm BH}=10^6M_\odot$), main sequence stars are completely disrupted, but the bound debris orbits are highly eccentric and possess semimajor axes $\sim 100\times$ the scale of the expected compact disk. Partial disruptions with fractional mass-loss $\gtrsim 10\%$ should occur with a rate similar to that of total disruptions; for fractional mass-loss $\gtrsim 50\%$, the rate is $\approx 1/3$ as large. Partial disruptions -- which must precede total disruptions when the stars' angular momenta evolve in the "empty loss-cone" regime -- change the orbital energy by factors $\gtrsim O(1)$. Remnants of partial disruptions are in general far from thermal equilibrium. Depending on the orbital energy of the remnant and conditions within the stellar cluster surrounding the SMBH, it may return after hundreds or thousands of years and be fully disrupted, or it may rejoin the stellar cluster.

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 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 the prograde direction and are hotter than MS stars of the same mass. Their specific orbital energy is $\simeq10^{-3}\times$ that of the debris (but of either sign with respect to the black hole potential) while their specific angular momentum is close to that of the original star. Even for strong encounters, remnants have speeds at infinity relative to the black hole potential $\lesssim 300$ km s$^{-1}$, so they are unable to travel far out into the galactic bulge. Remnants bound to the black hole can possibly go through a second tidal disruption event.

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. We consider eight different stellar masses, from $0.15~{\rm M}_\odot$ to $10~{\rm M}_\odot$. In the first paper (Ryu et al. 2019a), 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. We find that, relative to the traditional order-of-magnitude estimate $r_{\rm t}$, the physical tidal radius of low-mass stars is larger by tens of percent, while for high-mass stars ($M_{\star} \gtrsim1~ {\rm M}_\odot$) it is smaller by a factor $2-2.5$. The traditional estimate of the range of energies found in the debris is approximately accurate for low-mass stars, but is a factor $\sim 2$ too small for high-mass stars; in addition, the energy distribution for high-mass stars has significant wings. For all stars undergoing tidal encounters, we find that mass-loss continues for a long time because the ${\it instantaneous}$ tidal radius, the distance out to which the black hole's tidal gravity competes with the instantaneous stellar gravity at the star's surface, stays comparable to the distance to the black hole until the star has reached $O(10)~r_{\rm t}$. These findings indicate significant failings in the popular "frozen-in" approximation.

A star is tidally disrupted by a supermassive black hole when their separation is shorter than the "tidal radius". This quantity is often estimated on an order-of-magnitude basis without reference to the star's internal structure. Using MESA models for main sequence stars and fully general relativistic dynamics, we find the physical tidal radius for complete disruption $\cal{R}_t$ for a $10^6M_\odot$ black hole (BH). We find that across a factor $\sim20$ in stellar mass $M_*$, i.e., $0.15M_{\odot}\leq M_*\leq3M_\odot$, $\cal{R}_t\sim27\times$(BH's gravitational radius). When comparing $\cal{R}_t$ with the commonly used order-of-magnitude estimate $r_t$, we find that $\cal{R}_t\sim1.05-1.45r_t$ for $0.15M_\odot\leq M_*\leq0.5M_\odot$, but between $0.5 M_\odot$ and $1 M_\odot$, $\cal{R}_t$ drops to $\sim 0.45r_t$, and it remains at this value up to $10 M_\odot$. The near-constancy of $\cal{R}_t$ implies a weaker dependence of the full disruption rate on $M_*$ than when predicted with $r_t$. The characteristic energy width of the debris $\Delta E$ ranges from $\sim1.2\Delta\cal{E}$ for low-mass stars to $\sim 0.35\Delta\cal{E}$ for higher-mass stars, where $\Delta\cal{E}=GM_{\rm BH}R_*/\cal{R}_t^{2}$. We present analytic fits for the $M_*$ dependence of $\cal{R}_t$ and $\Delta E$; these fits lead to analytic expressions for the time of peak mass fallback rate and the maximal mass fallback rate. Our results also bear on the fraction of events leading to fast or slow circularization, as well as on the character of the tidal event occurring when the remnant of a partial disruption returns to the black hole. Using a semi-analytic model, we show that $\cal{R}_t$ is primarily determined by the star's central density rather than its mean density. For high-mass stars, the full disruption rate is roughly 1/4 the partial disruption rate, while this ratio is close to unity for low-mass stars.

In this paper we continue the first ever study of magnetized mini-disks coupled to circumbinary accretion in a supermassive binary black hole (SMBBH) approaching merger reported in Bowen et al. 2018. We extend this simulation from 3 to 12 binary orbital periods. We find that relativistic SMBBH accretion acts as a resonant cavity, where quasi-periodic oscillations tied to the the frequency at which the black hole's orbital phase matches a non-linear $m=1$ density feature, or ``lump'', in the circumbinary accretion disk permeate the system. The rate of mass accretion onto each of the mini-disks around the black holes is modulated at the beat frequency between the binary frequency and the lump's mean orbital frequency, i.e., $\Omega_{\rm beat} = \Omega_{\rm bin} - \bar{\Omega}_{\rm lump}$, while the total mass accretion rate of this equal-mass binary is modulated at two different frequencies, $\gtrsim \bar{\Omega}_{\rm lump}$ and $\approx 2 \Omega_{\rm beat}$. The instantaneous rotation rate of the lump itself is also modulated at two frequencies close to the modulation frequencies of the total accretion rate, $\bar{\Omega}_{\rm lump}$ and $2 \Omega_{\rm beat}$. Because of the compact nature of the mini-disks in SMBBHs approaching merger, the inflow times within the mini-disks are comparable to the period on which their mass-supply varies, so that their masses---and the accretion rates they supply to their black holes---are strongly modulated at the same frequency. In essence, the azimuthal symmetry of the circumbinary disk is broken by the dynamics of orbits near a binary, and this $m=1$ asymmetry then drives quasi-periodic variation throughout the system, including both accretion and disk-feeding. In SMBBHs approaching merger, such time variability could introduce distinctive, increasingly rapid, fluctuations in their electromagnetic emission.

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 TDEs in AGNs, we simulated a suite of stream--disk collisions with various mass current ratios. The collision excites shocks in the disk, leading to inflow and energy dissipation orders of magnitude above Eddington; however, much of the radiation is trapped in the inflow and advected into the black hole, so the actual bolometric luminosity may be closer to Eddington. The emergent spectrum may not be thermal, TDE-like, or AGN-like. The rapid inflow causes the disk interior to the impact point to be depleted within a fraction of the mass return time. If the stream is heavy enough to penetrate the disk, part of the outgoing material eventually hits the disk again, dissipating its kinetic energy in the second collision; another part becomes unbound, emitting synchrotron radiation as it shocks with surrounding gas.

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 faster and wider. A tidal disruption event whose periapse distance is a factor of 7 smaller than the tidal radius can account for the radio emission observed in ASASSN-14li. This model also allows us to obtain a more accurate estimate for the gas density around the centre of the host galaxy of ASASSN-14li.

We describe results from a new technique for the prediction of complete, self-consistent X-ray spectra from three-dimensional General Relativistic magnetohydrodynamic (GRMHD) simulations of black hole accretion flows. Density and cooling rate data from a HARM3D GRMHD simulation are processed by both an improved version of the Monte Carlo radiation transport code PANDURATA (in the corona) and the Feautrier solver PTRANSX (in the disk), with XSTAR subroutines. The codes are run in a sequential but iterative fashion to achieve globally energy-conserving and self-consistent radiation fields, temperature maps, and photoionization equilibria. The output is the X-ray spectrum as seen by a distant observer. For the example cases we consider here---a non-rotating $10 M_\odot$ black hole with solar abundances, accreting at 0.01, 0.03, 0.1, or 0.3 Eddington---we find spectra resembling actual observations of stellar-mass black holes in the soft or steep power-law state: broad thermal peaks (at 1-3 keV), steep power-laws extending to high energy ($\Gamma$ = 2.7-4.5), and prominent, asymmetric Fe K$\alpha$ emission lines with equivalent widths in the range 40-400 eV (larger EW at lower accretion rates). By starting with simulation data, we obviate the need for parameterized descriptions of the accretion flow geometry---no a priori specification of the corona's shape or flux, or the disk temperature or density, etc., are needed. Instead, we apply the relevant physical principles to simulation output using appropriate numerical techniques; this procedure allows us to calculate inclination-dependent spectra after choosing only a small number of physically meaningful parameters: black hole mass and spin, accretion rate, and elemental abundances.

Spectropolarimetry is a powerful technique that has provided critical support for the geometric unification model of local active galactic nuclei. In this paper, we present optical (rest-frame UV) Keck spectropolarimetry of five luminous obscured (Type 2) and extremely red quasars (ERQs) at z~2.5. Three objects reach polarization fractions of >10% in the continuum. We propose a model in which dust scattering is the dominant scattering and polarization mechanism in our targets, though electron scattering cannot be completely excluded. Emission lines are polarized at a lower level than is the continuum. This suggests that the emission-line region exists on similar spatial scales as the scattering region. In three objects we detect an intriguing 90 degree swing in the polarization position angle as a function of line-of-sight velocity in the emission lines of Ly-alpha, CIV and NV. We interpret this phenomenon in the framework of a geometric model with an equatorial dusty scattering region in which the material is outflowing at several thousand km/sec. Emission lines may also be scattered by dust or resonantly. This model explains several salient features of observations by scattering on scales of a few tens of pc. Our observations provide a tantalizing view of the inner region geometry and kinematics of high-redshift obscured and extremely red quasars. Our data and modeling lend strong support for toroidal obscuration and powerful outflows on the scales of the UV emission-line region, in addition to the larger scale outflows inferred previously from the optical emission-line kinematics.

We present the first fully relativistic prediction of the electromagnetic emission from the surrounding gas of a supermassive binary black hole system approaching merger. Using a ray-tracing code to post-process data from a general relativistic 3-d MHD simulation, we generate images and spectra, and analyze the viewing angle dependence of the light emitted. When the accretion rate is relatively high, the circumbinary disk, accretion streams, and mini-disks combine to emit light in the UV/EUV bands. We posit a thermal Compton hard X-ray spectrum for coronal emission; at high accretion rates, it is almost entirely produced in the mini-disks, but at lower accretion rates it is the primary radiation mechanism in the mini-disks and accretion streams as well. Due to relativistic beaming and gravitational lensing, the angular distribution of the power radiated is strongly anisotropic, especially near the equatorial plane.

We present the first magnetohydrodynamic simulation in which a circumbinary disk around a relativistic binary black hole feeds mass to individual accretion disks ("mini-disks") around each black hole. Mass flow through the accretion streams linking the circumbinary disk to the mini-disks is modulated quasi-periodically by the streams' interaction with a nonlinear $m=1$ density feature, or "lump", at the inner edge of the circumbinary disk: the stream supplying each mini-disk comes into phase with the lump at a frequency $0.74$ times the binary orbital frequency. Because the binary is relativistic, the tidal truncation radii of the mini-disks are not much larger than their innermost stable circular orbits; consequently, the mini-disks' inflow times are shorter than the conventional estimate and are comparable to the stream modulation period. As a result, the mini-disks are always in inflow disequilibrium, with their masses and spiral density wave structures responding to the stream's quasi-periodic modulation. The fluctuations in each mini-disk's mass are so large that as much as $75\%$ of the total mini-disk mass can be contained within a single mini-disk. Such quasi-periodic modulation of the mini-disk structure may introduce distinctive time-dependent features in the binary's electromagnetic emission.

Eccentric disks arise in such astrophysical contexts as tidal disruption events, but it is unknown whether the magnetorotational instability (MRI), which powers accretion in circular disks, operates in eccentric disks as well. We examine the linear evolution of unstratified, incompressible MRI in an eccentric disk orbiting a point mass. We consider vertical modes of wavenumber $k$ on a background flow with uniform eccentricity $e$ and vertical Alfvén speed $v_\mathrm A$ along an orbit with mean motion $n$. We find two mode families, one with dominant magnetic components, the other with dominant velocity components; the former is unstable at $(1-e)^3f^2\lesssim3$, where $f\equiv kv_\mathrm A/n$, the latter at $e\gtrsim0.8$. For $f^2\lesssim3$, MRI behaves much like in circular disks, but the growth per orbit declines slowly with increasing $e$; for $f^2\gtrsim3$, modes grow by parametric amplification, which is resonant for $0<e\ll1$. MRI growth and the attendant angular momentum and energy transport happen chiefly near pericenter, where orbital shear dominates magnetic tension.

Reverberation observations have uncovered an Fe K\alpha fluorescence line in the tidal disruption event (TDE) Swift J1644+57 (Kara et al. 2016). The discovery paper used the lag spectrum to argue that the X-ray continuum source was located very close to the blackhole (~30 gravitational radii) and moved sub-relativistically. We reanalyze the lag spectrum, pointing out that dilution effects cause it to indicate a geometric scale an order of magnitude larger than previously inferred. If the X-ray continuum is produced by a relativistic jet, as suggested by rapid variability, high luminosity and hard spectrum, this larger scale predicts an Fe ionization state consistent with efficient K\alpha production. Moreover, the momentum of the jet radiation impinging on the surrounding accretion flow on this larger scale accelerates a layer of gas to speeds ~0.1-0.2c, consistent with the blueshifted line profile. Implications of our results on the global picture of jetted TDEs are discussed. A power-law \gamma/X-ray spectrum may be produced by external UV-optical photons being repetitively inverse-Compton scattered by cold electrons in the jet, although our model for the K\alpha reverberation does not depend on the jet radiation mechanism (magnetic reconnection in a Poynting jet is still a viable mechanism). The non-relativistic wind driven by jet radiation may explain the late-time radio rebrightening in Swift J1644+57. This energy injection may also cause the thermal UV-optical emission from jetted TDEs to be systematically brighter than in non-jetted ones.

Near-Eddington radiation from active galactic nuclei (AGNs) has significant dynamical influence on the surrounding dusty gas, plausibly furnishing AGNs with geometrically thick obscuration. We investigate this paradigm with radiative magnetohydrodynamics simulations. The simulations solve the magnetohydrodynamics equations simultaneously with the infrared (IR) and ultraviolet (UV) radiative transfer (RT) equations; no approximate closure is used for RT. We find that our torus, when given a suitable sub-Keplerian angular momentum profile, spontaneously evolves toward a state in which its opening angle, density distribution, and flow pattern change only slowly. This "steady" state lasts for as long as there is gas resupply toward the inner edge. The torus is best described as a mid-plane inflow and a high-latitude outflow. The outflow is launched from the torus inner edge by UV radiation and expands in solid angle as it ascends; IR radiation continues to drive the wide-angle outflow outside the central hole. The dusty outflow obscures the central source in soft X-rays, the IR, and the UV over three quarters of solid angle, and each decade in column density covers roughly equal solid angle around the central source; these obscuration properties are similar to what observations imply.

We present a "multipatch" infrastructure for numerical simulation of fluid problems in which sub-regions require different gridscales, different grid geometries, different physical equations, or different reference frames. Its key element is a sophisticated client-router-server framework for efficiently linking processors supporting different regions ("patches") that must exchange boundary data. This infrastructure may be used with a wide variety of fluid dynamics codes; the only requirement is that their primary dependent variables be the same in all patches, e.g., fluid mass density, internal energy density, and velocity. Its structure can accommodate either Newtonian or relativistic dynamics. The overhead imposed by this system is both problem- and computer cluster architecture-dependent. Compared to a conventional simulation using the same number of cells and processors, the increase in runtime can be anywhere from negligible to a factor of a few; however, one of the infrastructure's advantages is that it can lead to a very large reduction in the total number of zone-updates.

We present the first exploration of relativistic gas dynamics in the immediate vicinity of binary black holes as the system inspirals close to merger in the gravitational radiation-driven regime. We focus on 2D hydrodynamical studies of comparable-mass, non-spinning systems. Relativistic effects alter the dynamics of gas in this environment in several ways. Because the gravitational potential between the two black holes becomes shallower than in the Newtonian regime, the mini-disks stretch toward the L1 point and the amount of gas passing back and forth between the mini-disks increases sharply with decreasing binary separation. This "sloshing" is quasi-periodically modulated at $2$ and $2.75$ times the binary orbital frequency, corresponding to timescales of hours to days for supermassive binary black holes. In addition, relativistic effects add an $m=1$ component to the tidally-driven spiral waves in the disks that are purely $m=2$ in Newtonian gravity; this component becomes dominant when the separation is $\lesssim 100$ gravitational radii. Both the sloshing and the spiral waves have the potential to create distinctive radiation features that may uniquely mark supermassive binary black holes in the relativistic regime.

When a circumbinary disk surrounds a binary whose secondary's mass is at least $\sim 10^{-2}\times$ the primary's mass, a nearly empty cavity with radius a few times the binary separation is carved out of the disk. Narrow streams of material pass from the inner edge of the circumbinary disk into the domain of the binary itself, where they eventually join onto the small disks orbiting the members of the binary. Using data from 3-d MHD simulations of this process, we determine the luminosity of these streams; it is mostly due to weak laminar shocks, and is in general only a few percent of the luminosity of adjacent regions of either the circumbinary disk or the "mini-disks". This luminosity therefore hardly affects the deficit in the thermal continuum predicted on the basis of a perfectly dark gap region.

Stars that pass within the Roche radius of a supermassive black hole will be tidally disrupted, yielding a sudden injection of gas close to the black hole horizon which produces an electromagnetic flare. A few dozen of these flares have been discovered in recent years, but current observations provide poor constraints on the bolometric luminosity and total accreted mass of these events. Using images from the Wide-field Infrared Survey Explorer (WISE), we have discovered transient 3.4 micron emission from several previously known tidal disruption flares. The observations can be explained by dust heated to its sublimation temperature due to the intense radiation of the tidal flare. From the break in the infrared light curve we infer that this hot dust is located ~0.1 pc from the supermassive black hole. Since the dust has been heated by absorbing UV and (potentially) soft X-ray photons of the flare, the reprocessing light curve yields an estimate of the bolometric flare luminosity. For the flare PTF-09ge, we infer that the most likely value of the luminosity integrated over frequencies at which dust can absorb photons is $8\times 10^{44}$ erg/s, with a factor of 3 uncertainty due to the unknown temperature of the dust. This bolometric luminosity is a factor ~10 larger than the observed black body luminosity. Our work is the first to probe dust in the nuclei of non-active galaxies on sub-parsec scales. The observed infrared luminosity implies a covering factor ~1% for the nuclear dust in the host galaxies.

We present first results from a new technique for the prediction of Fe K$\alpha$ profiles directly from general relativistic magnetohydrodynamic (GRMHD) simulations. Data from a GRMHD simulation are processed by a Monte Carlo global radiation transport code, which determines the X-ray flux irradiating the disk surface and the coronal electron temperature self-consistently. With that irradiating flux and the disk's density structure drawn from the simulation, we determine the reprocessed Fe K$\alpha$ emission from photoionization equilibrium and solution of the radiation transfer equation. We produce maps of the surface brightness of Fe K$\alpha$ emission over the disk surface, which---for our example of a $10 M_\odot$, Schwarzschild black hole accreting at $1\%$ the Eddington value---rises steeply one gravitational radius outside the radius of the innermost stable circular orbit and then falls $\propto r^{-2}$ at larger radii. We explain these features of the Fe K$\alpha$ radial surface brightness profile as consequences of the disk's ionization structure and an extended coronal geometry, respectively. We also present the corresponding Fe K$\alpha$ line profiles as would be seen by distant observers at several inclinations. Both the shapes of the line profiles and the equivalent widths of our predicted K$\alpha$ lines are qualitatively similar to those typically observed from accreting black holes. Most importantly, this work represents a direct link between theory and observation: in a fully self-consistent way, we produce observable results---iron fluorescence line profiles---from the theory of black hole accretion with almost no phenomenological assumptions.

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 black hole mass ($10^{6.5} M_{\odot}$) yield: quantitative agreement with the optical/UV luminosity, lightcurve, and color temperature; approximate agreement with the somewhat uncertain soft X-ray spectrum and lightcurve; and quantitative agreement with the radio luminosity, spectrum and lightcurve. Equipartition analysis of the radio data implies that the radio-emitting region expands with a constant speed, and its magnitude is comparable to the speed expected for the unbound stellar ejecta. Both facts provide strong support to our model. We find that the disruption event took place in mid-September 2014. Two independent parameters, the magnitude and logarithmic radial gradient of the ambient gas density near the black hole, must be fit to the data to explain the radio emission; their inferred values are comparable to those found near both Sgr A* and the TDE candidate Swift J1644.

We present the results of a new series of global 3D relativistic magneto-hydrodynamic (MHD) simulations of thin accretion disks around spinning black holes. The disks have aspect ratios of $H/R\sim 0.05$ and spin parameters $a/M=0, 0.5, 0.9$, and $0.99$. Using the ray-tracing code Pandurata, we generate broad-band thermal spectra and polarization signatures from the MHD simulations. We find that the simulated spectra can be well fit with a simple, universal emissivity profile that better reproduces the behavior of the emission from the inner disk, compared to traditional analyses carried out using a Novikov-Thorne thin disk model. Lastly, we show how spectropolarization observations can be used to convincingly break the spin-inclination degeneracy well-known to the continuum fitting method of measuring black hole spin.

Radio emission from radio-quiet quasars may be due to star formation in the quasar host galaxy, to a jet launched by the supermassive black hole, or to relativistic particles accelerated in a wide-angle radiatively-driven outflow. In this paper we examine whether radio emission from radio-quiet quasars is a byproduct of star formation in their hosts. To this end we use infrared spectroscopy and photometry from Spitzer and Herschel to estimate or place upper limits on star formation rates in hosts of ~300 obscured and unobscured quasars at z<1. We find that low-ionization forbidden emission lines such as [NeII] and [NeIII] are likely dominated by quasar ionization and do not provide reliable star formation diagnostics in quasar hosts, while PAH emission features may be suppressed due to the destruction of PAH molecules by the quasar radiation field. While the bolometric luminosities of our sources are dominated by the quasars, the 160 micron fluxes are likely dominated by star formation, but they too should be used with caution. We estimate median star formation rates to be 6-29 Msun/year, with obscured quasars at the high end of this range. This star formation rate is insufficient to explain the observed radio emission from quasars by an order of magnitude, with log(L_radio, observed/L_radio, SF)=0.6-1.3 depending on quasar type and star formation estimator. Although radio-quiet quasars in our sample lie close to the 8-1000 micron infrared / radio correlation characteristic of the star-forming galaxies, both their infrared emission and their radio emission are dominated by the quasar activity, not by the host galaxy.

Substantial evidence points to dusty, geometrically thick tori obscuring the central engines of active galactic nuclei (AGNs), but so far no mechanism satisfactorily explains why cool dust in the torus remains in a puffy geometry. Near-Eddington infrared (IR) and ultraviolet (UV) luminosities coupled with high dust opacities at these frequencies suggest that radiation pressure on dust can play a significant role in shaping the torus. To explore the possible effects of radiation pressure, we perform three-dimensional radiative hydrodynamics simulations of an initially smooth torus. Our code solves the hydrodynamics equations, the time-dependent multi-angle group IR radiative transfer (RT) equation, and the time-independent UV RT equation. We find a highly dynamic situation. IR radiation is anisotropic, leaving primarily through the central hole. The torus inner surface exhibits a break in axisymmetry under the influence of radiation and differential rotation; clumping follows. In addition, UV radiation pressure on dust launches a strong wind along the inner surface; when scaled to realistic AGN parameters, this outflow travels at $\sim 5000 (M/10^7 M_\odot)^{1/4} [L_\mathrm{UV}/(0.1 L_\mathrm E)]^{1/4} \mathrm{km}\,\mathrm s^{-1}$ and carries $\sim 0.1 (M/10^7 M_\odot)^{3/4} [L_\mathrm{UV}/(0.1 L_\mathrm E)]^{3/4} M_\odot\,\mathrm{yr}^{-1}$, where $M$, $L_\mathrm{UV}$, and $L_\mathrm E$ are the mass, UV luminosity, and Eddington luminosity of the central object respectively.

Models for tidal disruption events (TDEs) in which a supermassive black hole disrupts a star commonly assume that the highly eccentric streams of bound stellar debris promptly form a circular accretion disk at the pericenter scale. However, recent numerical simulations (Shiokawa et al., 2015) demonstrated that dissipation via hydrodynamical shocks is insufficient to circularize debris, and the flow retains its initial semi-major axis scale throughout the first ~10 orbits of the event. The bolometric peak luminosity of most TDE candidates, a few x 10^44 erg/s, implies that we observe only ~1% of the energy expected from radiatively efficient accretion. Motivated by these results, (Piran et al., 2015) suggested that the observed optical TDE emission is powered by shocks at the apocenter between freshly infalling material and earlier arriving matter. This model explains the small radiated energy, the low temperature, and the large radius implied by the observations as well as the t^-5/3 light curve. However the question of the system's low bolometric efficiency remains unanswered. We suggest that the high orbital energy and low angular momentum of the flow make it possible for magnetic stresses to reduce the matter's already small angular momentum to the point at which it can fall ballistically into the SMBH before circularization. As a result, the efficiency is only ~1--10% of a standard accretion disk's efficiency. Thus, the intrinsically high eccentricity of the tidal debris naturally explains why most TDE candidates are fainter than expected.

Using only physical mechanisms, i.e., 3D MHD with no phenomenological viscosity, we have simulated the dynamics of a moderately thin accretion disk subject to torques whose radial scaling mimics those produced by lowest-order post-Newtonian gravitomagnetism. In this simulation, we have shown how, in the presence of MHD turbulence, a time-steady transition can be achieved between an inner disk region aligned with the equatorial plane of the central mass's spin and an outer region orbiting in a different plane. The position of the equilibrium orientation transition is determined by a balance between gravitomagnetic torque and warp-induced inward mixing of misaligned angular momentum from the outer disk. If the mixing is interpreted in terms of diffusive transport, the implied diffusion coefficient is ~(0.6--0.8)c_s^2/Omega for sound speed c_s and orbital frequency Omega. This calibration permits estimation of the orientation transition's equilibrium location given the central mass, its spin parameter, and the disk's surface density and scaleheight profiles. However, the alignment front overshoots before settling into an equilibrium, signaling that a diffusive model does not fully represent the time-dependent properties of alignment fronts under these conditions. Because the precessional torque on the disk at the alignment front is always comparable to the rate at which misaligned angular momentum is brought inward to the front by warp-driven radial motions, no break forms between the inner and outer portions of the disk in our simulation. Our results also raise questions about the applicability to MHD warped disks of the traditional distinction between "bending wave" and "diffusive" regimes.

We consider the evolution of a supermassive black hole binary (SMBHB) surrounded by a retrograde accretion disk. Assuming the disk is exactly in the binary plane and transfers energy and angular momentum to the binary via direct gas accretion, we calculate the time evolution of the binary's semi-major axis $a$ and eccentricity $e$. Because the gas is predominantly transferred when the binary is at apocenter, we find the eccentricity grows rapidly while maintaining constant $a(1+e)$. After accreting only a fraction of the secondary's mass, the eccentricity grows to nearly unity; from then on, gravitational wave emission dominates the evolution, preserving constant $a(1-e)$. The high-eccentricity waveforms redistribute the peak gravitational wave power from the nHz to $\mu$Hz bands, substantially affecting the signal that might be detected with pulsar timing arrays. We also estimate the torque coupling binaries of arbitrary eccentricity with obliquely aligned circumbinary disks. If the outer edge of the disk is not an extremely large multiple of the binary separation, retrograde accretion can drive the binary into the gravitational wave-dominated state before these torques align the binary with the angular momentum of the mass supply.

When an accretion disk surrounds a binary rotating in the same sense, the binary exerts strong torques on the gas. Analytic work in the 1D approximation indicated that these torques sharply diminish or even eliminate accretion from the disk onto the binary. However, recent 2D and 3D simulational work has shown at most modest diminution. We present new MHD simulations demonstrating that for binaries with mass ratios of 1 and 0.1 there is essentially no difference between the accretion rate at large radius in the disk and the accretion rate onto the binary. To resolve the discrepancy with earlier analytic estimates, we identify the small subset of gas trajectories traveling from the inner edge of the disk to the binary and show how the full accretion rate is concentrated onto them.

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 \citepShiokawa+2015 have revealed that the circularization scale is close to the scale of the most-bound initial orbits, $\sim 10^3 M_{BH,6.5}^{-2/3} R_g \sim 10^{15} M_{BH,6.5}^{1/3}$~cm from the black hole, and the corresponding circularization energy dissipation rate is $\sim 10^{44} M_{BH,6.5}^{-1/6}$~erg/s. We suggest that the energy liberated during circularization, rather then energy liberated by accretion onto the black hole, powers the observed optical TDE candidates. The observed rise times, luminosities, temperatures, emission radii, and line widths seen in these TDEs \citep[e.g.][]Arcavi+2014 are all more readily explained in terms of heating associated with circularization than in terms of accretion.

We study how the matter dispersed when a supermassive black hole tidally disrupts a star joins an accretion flow. Combining a relativistic hydrodynamic simulation of the stellar disruption with a relativistic hydrodynamics simulation of the tidal debris motion, we track such a system until ~80% of the stellar mass bound to the black hole has settled into an accretion flow. Shocks near the stellar pericenter and also near the apocenter of the most tightly-bound debris dissipate orbital energy, but only enough to make the characteristic radius comparable to the semi-major axis of the most-bound material, not the tidal radius as previously thought. The outer shocks are caused by post-Newtonian effects, both on the stellar orbit during its disruption and on the tidal forces. Accumulation of mass into the accretion flow is non-monotonic and slow, requiring ~3--10x the orbital period of the most tightly-bound tidal streams, while the inflow time for most of the mass may be comparable to or longer than the mass accumulation time. Deflection by shocks does, however, remove enough angular momentum and energy from some mass for it to move inward even before most of the mass is accumulated into the accretion flow. Although the accretion rate rises sharply and then decays roughly as a power-law, its maximum is ~0.1x the previous expectation, and the duration of the peak is ~5x longer than previously predicted. The geometric mean of the black hole mass and stellar mass inferred from a measured event timescale is therefore ~0.2x the value given by classical theory.

We present the results of local, vertically stratified, radiation MHD shearing box simulations of MRI turbulence appropriate for the hydrogen ionizing regime of dwarf nova and soft X-ray transient outbursts. We incorporate the frequency-integrated opacities and equation of state for this regime, but neglect non-ideal MHD effects and surface irradiation, and do not impose net vertical magnetic flux. We find two stable thermal equilibrium tracks in the effective temperature versus surface mass density plane, in qualitative agreement with the S-curve picture of the standard disk instability model. We find that the large opacity at temperatures near $10^4$K, a corollary of the hydrogen ionization transition, triggers strong, intermittent thermal convection on the upper stable branch. This convection strengthens the magnetic turbulent dynamo and greatly enhances the time-averaged value of the stress to thermal pressure ratio $\alpha$, possibly by generating vertical magnetic field that may seed the axisymmetric magnetorotational instability, and by increasing cooling so that the pressure does not rise in proportion to the turbulent dissipation. These enhanced stress to pressure ratios may alleviate the order of magnitude discrepancy between the $\alpha$-values observationally inferred in the outburst state and those that have been measured from previous local numerical simulations of magnetorotational turbulence that lack net vertical magnetic flux.

Observations indicate that most massive galaxies contain a supermassive black hole, and theoretical studies suggest that when such galaxies have a major merger, the central black holes will form a binary and eventually coalesce. Here we discuss two spectral signatures of such binaries that may help distinguish them from ordinary AGN. These signatures are expected when the mass ratio between the holes is not extreme and the system is fed by a circumbinary disk. One such signature is a notch in the thermal continuum that has been predicted by other authors; we point out that it should be accompanied by a spectral revival at shorter wavelengths and also discuss its dependence on binary properties such as mass, mass ratio, and separation. In particular, we note that the wavelength $\lambda_n$ at which the notch occurs depends on these three parameters in such a way as to make the number of systems displaying these notches $\propto \lambda_n^{16/3}$; longer wavelength searches are therefore strongly favored. A second signature, first discussed here, is hard X-ray emission with a Wien-like spectrum at a characteristic temperature $\sim 100$ keV produced by Compton cooling of the shock generated when streams from the circumbinary disk hit the accretion disks around the individual black holes. We investigate the observability of both signatures. The hard X-ray signal may be particularly valuable as it can provide an indicator of black hole merger a few decades in advance of the event.

When matter orbits around a central mass obliquely with respect to the mass's spin axis, the Lense-Thirring effect causes it to precess at a rate declining sharply with radius. Ever since the work of Bardeen & Petterson (1975), it has been expected that when a fluid fills an orbiting disk, the orbital angular momentum at small radii should then align with the mass's spin. Nearly all previous work has studied this alignment under the assumption that a phenomenological "viscosity" isotropically degrades fluid shears in accretion disks, even though it is now understood that internal stress in flat disks is due to anisotropic MHD turbulence. In this paper we report a pair of matched simulations, one in MHD and one in pure (non-viscous) HD in order to clarify the specific mechanisms of alignment. As in the previous work, we find that disk warps induce radial flows that mix angular momentum of different orientation; however, we also show that the speeds of these flows are generically transonic and are only very weakly influenced by internal stresses other than pressure. In particular, MHD turbulence does not act in a manner consistent with an isotropic viscosity. When MHD effects are present, the disk aligns, first at small radii and then at large; alignment is only partial in the HD case. We identify the specific angular momentum transport mechanisms causing alignment and show how MHD effects permit them to operate more efficiently. Lastly, we relate the speed at which an alignment front propagates outward (in the MHD case) to the rate at which Lense-Thirring torques deliver angular momentum at smaller radii.

Recent studies of accretion onto supermassive black hole binaries suggest that much, perhaps most, of the matter eventually accretes onto one hole or the other. If so, then for binaries whose inspiral from ~1 pc to 0.001 - 0.01 pc is driven by interaction with external gas, both the binary orbital axis and the individual black hole spins can be reoriented by angular momentum exchange with this gas. Here we show that, unless the binary mass ratio is far from unity, the spins of the individual holes align with the binary orbital axis in a time few-100 times shorter than the binary orbital axis aligns with the angular momentum direction of the incoming circumbinary gas; the spin of the secondary aligns more rapidly than that of the primary by a factor ~(m_1/m_2)^1/2>1. Thus the binary acts as a stabilizing agent, so that for gas-driven systems, the black hole spins are highly likely to be aligned (or counteraligned if retrograde accretion is common) with each other and with the binary orbital axis. This alignment can significantly reduce the recoil speed resulting from subsequent black hole merger.

Global disk simulations provide a powerful tool for investigating accretion and the underlying magnetohydrodynamic turbulence driven by the magneto-rotational instability (MRI). Using them to predict accurately quantities such as stress, accretion rate, and surface brightness profile requires that purely numerical effects, arising from both resolution and algorithm, be understood and controlled. We use the flux-conservative Athena code to conduct a series of experiments on disks having a variety of magnetic topologies to determine what constitutes adequate resolution. We develop and apply several resolution metrics: Qz and Qphi, the ratio of the grid zone size to the characteristic MRI wavelength, alpha_mag, the ratio of the Maxwell stress to the magnetic pressure, and the ratio of radial to toroidal magnetic field energy. For the initial conditions considered here, adequate resolution is characterized by Qz > 15, Qphi > 20, alpha_mag = 0.45, and a field energy ratio of 0.2. These values are associated with > 35 zones per scaleheight, a result consistent with shearing box simulations. Numerical algorithm is also important. Use of the HLLE flux solver or second-order interpolation can significantly degrade the effective resolution compared to the HLLD flux solver and third-order interpolation. Resolution at this standard can be achieved only with large numbers of grid zones, arranged in a fashion that matches the symmetries of the problem and the scientific goals of the simulation.

In this document, we describe the scientific potential of blazar observations with a X-ray polarimetry mission like GEMS (Gravity and Extreme Magnetism SMEX). We describe five blazar science investigations that such a mission would enable: (i) the structure and the role of magnetic fields in AGN jets, (ii) analysis of the polarization of the synchrotron X-ray emission from AGN jets, (iii) discrimination between synchrotron self-Compton and external Compton models for blazars with inverse Compton emission in the X-ray band, (iv) a precision study of the polarization properties of the X-ray emission from Cen-A, (v) tests of Lorentz Invariance based on X-ray polarimetric observations of blazars. We conclude with a discussion of a straw man observation program and recommended accompanying multiwavelength observations.

Orbiting disks may exhibit bends due to a misalignment between the angular momentum of the inner and outer regions of the disk. We begin a systematic simulational inquiry into the physics of warped disks with the simplest case: the relaxation of an unforced warp under pure fluid dynamics, i.e. with no internal stresses other than Reynolds stress. We focus on the nonlinear regime in which the bend rate is large compared to the disk aspect ratio. When warps are nonlinear, strong radial pressure gradients drive transonic radial motions along the disk's top and bottom surfaces that efficiently mix angular momentum. The resulting nonlinear decay rate of the warp increases with the warp rate and the warp width, but, at least in the parameter regime studied here, is independent of the sound speed. The characteristic magnitude of the associated angular momentum fluxes likewise increases with both the local warp rate and the radial range over which the warp extends; it also increases with increasing sound speed, but more slowly than linearly. The angular momentum fluxes respond to the warp rate after a delay that scales with the square-root of the time for sound waves to cross the radial extent of the warp. These behaviors are at variance with a number of the assumptions commonly used in analytic models to describe linear warp dynamics.