A tidal disruption event (TDE) occurs when a star wanders close enough to a black hole to be disrupted by its tidal force. The debris of a tidally disrupted star are expected to form an accretion disc around the supermassive black hole. The light curves of these events sometimes show a quasi-periodic modulation of the flux that can be associated with the precession of the accretion disc due to the Lense-Thirring ("frame-dragging") effect. Since the initial star orbit is in general inclined with respect to the black hole spin, this misalignment combined with the Lense-Thirring effect leads to a warp in the disc. In this paper we provide a simple model of the system composed by a thick and narrow accretion disc surrounding a spinning supermassive black hole, with the aim to: (a) compute the expected precession period as a function of the system parameters, (b) discuss the conditions that have to be satisfied in order to have rigid precession, (c) investigate the alignment process, highlighting how different mechanisms play a role leading the disc and the black hole angular momenta into alignment.

We investigate the dynamics of a nonzero mass, circular orbit planet around an eccentric orbit binary for various values of the binary eccentricity, binary mass fraction, planet mass, and planet semi-major axis by means of numerical simulations. Previous studies investigated the secular dynamics mainly by approximate analytic methods. In the stationary inclination state, the planet and binary precess together with no change in relative tilt. For both prograde and retrograde planetary orbits, we explore the conditions for planetary orbital libration versus circulation and the conditions for stationary inclination. As was predicted by analytic models, for sufficiently high initial inclination, a prograde planet's orbit librates about the stationary tilted state. For a fixed binary eccentricity, the stationary angle is a monotonically decreasing function of the ratio of the planet-to-binary angular momentum j. The larger j, the stronger the evolutionary changes in the binary eccentricity and inclination. We also calculate the critical tilt angle that separates the circulating from the librating orbits for both prograde and retrograde planet orbits. The properties of the librating orbits and stationary angles are quite different for prograde versus retrograde orbits. The results of the numerical simulations are in very good quantitative agreement with the analytic models. Our results have implications for circumbinary planet formation and evolution.

The immense tidal forces of massive black holes can rip apart stars that come too close to them. As the resulting stellar debris spirals inwards, it heats up and emits x-rays when near the black hole. Here, we report the discovery of an exceptionally stable 131-second x-ray quasi-periodicity from a black hole after it disrupted a star. Using a black hole mass indicated from host galaxy scaling relations implies that, (1) this periodicity originates from very close to the black hole's event horizon, and (2) the black hole is rapidly spinning. Our findings suggest that other disruption events with similar highly sensitive observations likely also exhibit quasi-periodicities that encode information about the fundamental properties of their black holes.

We analyse the evolution of a mildly inclined circumbinary disc that orbits an eccentric orbit binary by means of smoother particle hydrodynamic (SPH) simulations and linear theory. We show that the alignment process of an initially misaligned circumbinary disc around an eccentric orbit binary is significantly different than around a circular orbit binary and involves tilt oscillations. The more eccentric the binary, the larger the tilt oscillations and the longer it takes to damp these oscillations. A circumbinary disc that is only mildly inclined may increase its inclination by a factor of a few before it moves towards alignment. The results of the SPH simulations agree well with those of linear theory. We investigate the properties of the circumbinary disc/ring around KH 15D. We determine disc properties based on the observational constraints imposed by the changing binary brightness. We find that the inclination is currently at a local minimum and will increase substantially before setting to coplanarity. In addition, the nodal precession is currently near its most rapid rate. The recent observations that show a reappearance of Star B impose constraints on the thickness of the layer of obscuring material. Our results suggest that disc solids have undergone substantial inward drift and settling towards to disc midplane. For disc masses ∼ 0.001M ⊙ , our model indicates that the level of disc turbulence is low α ≪ 0.001. Another possibility is that the disc/ring contains little gas.

We investigate the formation and evolution of misaligned accretion discs around the secondary component of a binary through mass transfer driven by Kozai-Lidov oscillations of the circumprimary disc's eccentricity and inclination. We perform SPH simulations to study the amount of mass transferred to the secondary star as a function of both the disc and binary parameters. For the range of parameters we explore, we find that increasing the disc aspect ratio, viscosity parameter and initial inclination as well as decreasing the binary mass ratio leads to larger amount of mass transfer, up to a maximum of about ten per cent of the initial mass of the primary disc. The circumsecondary disc forms with a high eccentricity and a high inclination and is also able to undergo KL oscillations. The circumsecondary disc oscillations have a shorter period than those in the disc around the primary. We find that some of the material that escapes the Roche-lobe of the two components forms a misaligned circumbinary accretion disc. This study has implications for disc evolution in young binary star systems.