P. B. Ivanov

A fully relativistic twisted disc around a slowly rotating Kerr black hole: derivation of dynamical equations and the shape of stationary configurations

In this paper we derive equations describing the dynamics and stationary configurations of a twisted fully relativistic thin accretion disc around a slowly rotating black hole. We assume that the inclination angle of the disc is small and that the standard relativistic generalization of the α model of accretion discs is valid when the disc is flat. We find that similar to the case of non-relativistic twisted discs the disc dynamics and stationary shapes can be determined by a pair of equations formulated for two complex variables describing the orientation of the disc rings and velocity perturbations induced by the twist. We analyse analytically and numerically the shapes of stationary twisted configurations of accretion discs having non-zero inclinations with respect to the black hole equatorial plane at large distances r from the black hole. It is shown that the stationary configurations depend on two parameters – the viscosity parameter α and the parameter , where δ* is the opening angle (δ*∼h/r, where h is the disc half-thickness and r is large) of a flat disc and a is the black hole rotational parameter. When a > 0 and the shapes depend drastically on the value of α. When α is small the disc inclination angle oscillates with radius with amplitude and radial frequency of the oscillations dramatically increasing towards the last stable orbit, Rms. When α has a moderately small value the oscillations do not take place but the disc does not align with the equatorial plane at small radii. The disc inclination angle either is increasing towards Rms or exhibits a non-monotonic dependence on the radial coordinate. Finally, when α is sufficiently large the disc aligns with the equatorial plane at small radii. When a < 0 the disc aligns with the equatorial plane for all values of α. The results reported here may have implications for determining the structure and variability of accretion discs close to Rms as well as for modelling of emission spectra coming from different sources, which are supposed to contain black holes.

A unified normal mode approach to dynamic tides and its application to rotating Sun-like stars

We determine the response of a uniformly rotating star to tidal perturbations due to a companion. General periodic orbits and parabolic flybys are considered. We evaluate energy and angular momentum exchange rates as a sum of contributions from normal modes allowing for dissipative processes. We consider the case when the response is dominated by the contribution of an identifiable regular spectrum of low frequency modes, such as gravity modes and evaluate it in the limit of very weak dissipation. Our formalism may be applied both to Sun-like stars with radiative cores and convective envelopes and to more massive stars with convective cores and radiative envelopes. We provide general expressions for transfer of energy and angular momentum valid for an orbit with any eccentricity. Detailed calculations are made for Sun-like stars in the slow rotation regime where centrifugal distortion is neglected in the equilibrium and the traditional approximation is made for the normal modes. We use both a WKBJ procedure and direct numerical evaluation which are found to be in good agreement for regimes of interest. Finally we use our formalism to determine the evolution time scales for an object, in an orbit of small eccentricity, around a Sun-like star in which the tidal response is assumed to occur. Systems with either no rotation or synchronous rotation are considered. Only rotationally modified gravity modes are taken into account under the assumption that wave dissipation occurs close to the stellar centre.

Dynamical tides in exoplanetary systems containing hot Jupiters: Confronting theory and observations

We are grateful to G. I. Ogilvie for his important remarks and suggestions. SVC and PBI were supported in part by RFBR grants 15-02-08476 and 16-02-01043, by programme 7 of the Presidium of Russian Academy of Sciences and also by Grant of the President of the Russian Federation for Support of the Leading Scientific Schools NSh-6595.2016.2.

Physical constraints on multi-dimensional cosmological models

In this work we investigate the possibility of inflation and dynamical reduction in a multi-dimensional cosmology. General considerations lead us to consider the most natural spatially flat and initially isotropic hydrodynamical model with two phenomenological phase transitions. We find that the baryonic asymmetry generation never occurs in such models. We conclude that extra dimensions probably never evolved in a classical way, being always quantum in nature.

A Quasi-Stationary Twisted Disk Formed as a Result of a Tidal Disruption Event

Abstract In this note we briefly review the main results of our recent study of the formation of misaligned accretion disks after the tidal disruption of stars by rotating supermassive black holes. Since the accretion rates in such disks initially exceed the Eddington limit they are initially advection dominated. Assuming the α model for the disk viscosity implies that the disk can become thermally unstable when the accretion rate is comparable to, or smaller than, the Eddington value, while still being radiation pressure dominated. It then undergoes cyclic transitions between high and low states. During these transitions the aspect ratio varies from ~1 to ~10−3, which is reflected in changes in the degree of disk misalignment at the stream impact location. For maximal black hole rotation and sufiociently large values of the viscosity parameter, α ≳ 0.01–0.1, the ratio of the disk inclination to that of the initial stellar orbit is estimated to be 0.1–0.2 in the advection dominated state, while reaching order unity in the low state. Misalignment decreases with decrease of α, but increases as the black hole rotation parameter decreases. Thus, it is always significant when the latter is small.

On the formation of a quasi-stationary twisted disc after a tidal disruption event

MXG acknowledges support through Leopoldina fellowship programme (fellowship number LPDS 2009-50). Simulations were performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service, provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and funding from the Science and Technology Facilities Council. MXG also acknowledges the computing time granted (NIC project number 8163) on the supercomputer JUROPA at Julich Supercomputing Centre (JSC). PBI was supported in part by RFBR grants 15-02-08476 and 16-02-01043 and also by Grant of the President of the Russian Federation for Support of the Leading Scientific Schools NSh-6595.2016.2.

The evolution of a supermassive retrograde binary embedded in an accretion disk

Abstract In this note we discuss the main results of a study of a massive binary with unequal mass ratio, q, embedded in an accretion disk, with its orbital rotation being opposed to that of the disk. When the mass ratio is sufficiently large, a gap opens in the disk, but the mechanism of gap formation is very different from the prograde case. Inward migration occurs on a timescale of tev ~ Mp/Ṁ, where Mp is the mass of the less massive component (the perturber), and Ṁ is the accretion rate. When q ≪ 1, the accretion takes place mostly onto the more massive component, with the accretion rate onto the perturber being smaller than, or of order of, q1/3 Ṁ. However, this rate increases when supermassive binary black holes are considered and gravitational wave emission is important. We estimate a typical duration of time for which the accretion onto the perturber and gravitational waves could be detected.