Ladislav Subr

Enhanced activity of massive black holes by stellar capture assisted by a self-gravitating accretion disc

Aims. We study the probability of close encounters between stars from a nuclear cluster and a massive black hole (10 4 MM• 10 8 M� ). The gravitational field of the system is dominated by the black hole in its sphere of influence. It is further modified by the cluster mean field (a spherical term) and a gaseous disc/torus (an axially symmetric term) causing a secular evolution of stellar orbits via Kozai oscillations. Intermittent phases of high eccentricity increase the chance that stars become damaged inside the tidal radius of the central hole. Such events can produce debris and lead to recurring episodes of enhanced accretion activity. Methods. We introduce an effective loss cone and associate it with tidal disruptions during the high-eccentricity phases of the Kozai cycle. By numerical integration of the trajectories forming the boundary of the loss cone, we determine its shape and volume. We also include the effect of a relativistic advance of the pericentre. Results. The potential of the disc has the efffect of enlarging the loss cone, therefore, the predicted number of tidally disrupted stars should grow by factor of � 10 2 . On the other hand, the effect of the cluster mean potential, together with the relativistic pericentre advance, act against the eccentricity oscillations. In the end we expect the tidal disruption events to be approximately ten times more frequent in comparison with the model in which the three effects - the cluster mean field, the relativistic pericentre advance, and the Kozai mechanism - are all ignored. The competition of different influences suppresses the predicted star-disruption rate as the black hole mass increases. Hence, the process under consideration is more important for intermediate-mass black holes, M• � 10 4 M� .

The warped young stellar disc in the Galactic centre

Aims. Within the central parsec of the Galaxy, several dozen young stars orbiting a central supermassive black hole are observed. A subset of these stars forms a coherently rotating disc. Other observations reveal a massive molecular torus that lies at a radius ∼ 1.5 pc from the centre. In this paper we consider the gravitational influence of the molecular torus upon the stars of the stellar disc. Methods. We derive an analytical formula for the rate of precession of individual stellar orbits and we show that it is highly sensitive to the orbital semi-major axis and inclination with respect to the plane of the torus, as well as to the mass of the torus. Results. Assuming that both the stellar disc and the molecular torus are stable on the timescale ≥6 Myr, we constrain the mass of the torus and its inclination with respect to the young stellar disc. We further suggest that all young stars observed in the Galactic centre may have a common origin in a single coherently rotating structure with an opening angle ≤5°, which was partially destroyed (warped) during its lifetime by the gravitational influence of the molecular torus.

A new method to create initially mass segregated star clusters in virial equilibrium

Mass segregation stands as one of the most robust features of the dynamical evolution of self-gravitating star clusters. In this paper we formulate parametrized models of mass segregated star clusters in virial equilibrium. To this purpose we introduce mean interparticle potentials for statistically described unsegregated systems and suggest a single-parameter generalization of its form which gives a mass segregated state. We describe an algorithm for construction of appropriate star cluster models. Their stability over several crossing-times is verified by following the evolution by means of direct N-body integration.

Variable Line Profiles Due to Non-Axisymmetric Patterns in an Accretion Disc around a Rotating Black Hole

We have explored spectral line profiles due to spiral patterns in accretion discs around black holes. A parametrization was employed for the shape and emissivity of spiral waves, which can be produced by non-axisymmetric perturbations affecting the disc density and ionization structure. The effects of the light-travel time, energy shift, and gravitational focusing near to a rotating black hole were taken into account. A high-resolution ray-tracing code was used to follow the time variations of the synthetic line profile. A variety of expected spectral features were examined and the scheme applied to a broad iron line observed in MCG-6-30-15.

On highly eccentric stellar trajectories interacting with a self-gravitating disc in Sgr A

We propose that Kozais phenomenon is responsible for the long-term evolution of stellar orbits near a supermassive black hole. We pursue the idea that this process may be driven by a fossil accretion disc in the centre of our Galaxy, causing the gradual orbital decay of stellar trajectories, while setting some stars on highly elliptic orbits. We evolve model orbits that undergo repetitive transitions across the disc over the period of 10 7 years. We assume that the disc mass is small compared to the central black hole, and its gravitational field comparatively weak, yet non-zero, and we set the present values of orbital parameters of the model star consistent with those reported for the S2 star in Sagittarius A*. We show how a model trajectory decays and circularizes, but at some point the mean eccentricity is substantially increased by Kozais resonance. In consequence the orbital decay of highly eccentric orbits is accelerated. A combination of an axially symmetric gravitational field and dissipative environment can provide a mechanism explaining the origin of stars on highly eccentric orbits tightly bound to the central black hole. In the context of other S-stars, we can conclude that an acceptable mass of the disc (i.e., M d < I per cent of the black hole mass) is compatible with their surprisingly young age and small pericentre distances, provided these stars were formed at r ≤ 10 5 gravitational radii.

Star-disc interactions in a galactic centre and oblateness of the inner stellar cluster

The structure of a quasi-stationary stellar cluster is modelled assuming that it is embedded in the gravitational field of a supermassive black hole. The gradual orbital decay of stellar trajectories is caused by the dissipative interaction with an accretion disc. The gravitational field of the disc is constructed and its effect on the cluster structure is taken into account as an axially symmetric perturbation. Attention is focused on a circumnuclear region (r < 10 4 gravitational radii) where the effects of the central black hole and the disc dominate over the influence of an outer galaxy. It is shown how the stellar system becomes gradually flattened towards the disc plane. For certain combinations of the model parameters, a toroidal structure is formed by a fraction of stars. Growing anisotropy of stellar velocities as well as their segregation occur. The mass function of the inner cluster is modified and it progressively departs from the asymptotic form assumed in the outer cluster. A new stationary distribution can be characterized in terms of velocity dispersion of the stellar sample in the central region of the modified cluster.

The coupling of a young stellar disc with the molecular torus in the Galactic Centre

The Galactic Centre hosts, according to observations, a number of early-type stars. About one half of those which are orbiting the central supermassive black hole on orbits with projected radii ≳0.03 pc form a coherently rotating disc. Observations further reveal a massive gaseous torus and a significant population of late-type stars. In this paper, we investigate, by means of numerical N-body computations, the orbital evolution of the stellar disc, which we consider to be initially thin. We include the gravitational influence of both the torus and the late-type stars, as well as the self-gravity of the disc. Our results show that, for a significant set of system parameters, the evolution of the disc leads, within the lifetime of the early-type stars, to a configuration compatible with the observations. In particular, the disc naturally reaches a specific - perpendicular - orientation with respect to the torus, which is indeed the configuration observed in the Galactic Centre. We, therefore, suggest that all the early-type stars may have been born within a single gaseous disc.

TWO-BODY RELAXATION DRIVEN EVOLUTION OF THE YOUNG STELLAR DISK IN THE GALACTIC CENTER

The center of our Galaxy hosts almost two hundred very young stars, a subset of which is orbiting the central supermassive black hole (SMBH) in a relatively thin disk-like structure. First analyses indicated a power-law surface density profile of the disk, ?R ? with ? = ?2. Recently, however, doubts about this profile arose. In particular, it now seems to be better described by a sort of broken power law. By means of both analytical arguments and numerical N-body modeling, we show that such a broken power-law profile is a natural consequence of the two-body relaxation of the disk. Due to the small relative velocities of the nearby stars in co-planar Keplerian orbits around the SMBH, two-body relaxation is effective enough to affect the evolution of the disk on timescales comparable to its estimated age. In the inner, densest part of the disk, the profile becomes rather flat (? ?1) while the outer parts keep imprints of the initial state. Our numerical models show that the observed projected surface density profile of the young stellar disk can result from two-body relaxation driven evolution of a disk with initial single power-law profile with ?2 ? ?1.5. In addition, we suggest that two-body relaxation may have caused a significant radial migration of the S-stars toward the central SMBH, thus playing an important role in their formation scenario.

Secular theory of the orbital evolution of the young stellar disc in the Galactic Centre

We investigate the orbital evolution of a system of N mutually interacting stars on initially circular orbits around the dominating central mass. We include the perturbative influence of a distant axisymmetric source and an extended spherical potential. In particular, we focus on the case when the secular evolution of orbital eccentricities is suppressed by the spherical perturbation. By means of standard perturbation methods, we derive semi-analytic formulae for the evolution of normal vectors of the individual orbits. We find its two qualitatively different modes. Either the orbits interact strongly and, under such circumstances, become dynamically coupled, precessing synchronously in the potential of the axisymmetric perturbation, or, if their mutual interaction is weaker, the orbits precess independently, interchanging periodically their angular momentum, which leads to oscillations of inclinations. We argue that these processes may have been fundamental to the evolution of the disc of young stars orbiting the supermassive black hole in the centre of the Milky Way.

THE PROPERTIES OF HYPERVELOCITY STARS AND S-STARS ORIGINATING FROM AN ECCENTRIC DISK AROUND A SUPERMASSIVE BLACK HOLE

Hypervelocity stars (HVSs), which are observed in the Galactic halo, are believed to be accelerated to large velocities by a process of tidal disruption of binary stars passing close to the supermassive black hole (SMBH) which resides in the center of the Galaxy. It is, however, still unclear where these relatively young stars were born and what dynamical process pushed them to nearly radial orbits around the SMBH. In this paper we investigate the possibility that the young binaries originated from a thin eccentric disk, similar to the one currently observed in the Galactic center. By means of direct N-body simulations, we follow the dynamical evolution of an initially thin and eccentric disk of stars with a 100% binary fraction orbiting around the SMBH. Such a configuration leads to Kozai–Lidov oscillations of orbital elements, bringing a considerable number of binaries to the close vicinity of the black hole. Subsequent tidal disruption of these binaries accelerates one of their components to velocities well above the escape velocity from the SMBH, while the second component becomes tightly bound to the SMBH. We describe the main kinematic properties of the escaping and tightly bound stars within our model, and compare them qualitatively to the properties of the observed HVSs and S-stars, respectively. The most prominent feature is strong anisotropy in the directions of the escaping stars, which is observed for Galactic HVSs but has not yet been explained.