Effect of angular momentum distribution on gravitational loss-cone instability in stellar clusters around massive BH

Small perturbations in spherical and thin disk stellar clusters surrounding massive a black hole are studied. Due to the black hole, stars with sufficiently low angular momentum escape from the system through the loss cone. We show that stability properties of spherical clusters crucially depend on whether the distribution of stars is monotonic or non-monotonic in angular momentum. It turns out that only non-monotonic distributions can be unstable. At the same time the instability in disk clusters is possible for both types of distributions.Comment: 14 pages, 7 figures, submitted to MNRA

Gravitational Loss-Cone Instability in Stellar Systems with Retrograde Orbit Precession

We study spherical and disk clusters in a near-Keplerian potential of galactic centers or massive black holes. In such a potential orbit precession is commonly retrograde, i.e. direction of the orbit precession is opposite to the orbital motion. It is assumed that stellar systems consist of nearly radial orbits. We show that if there is a loss cone at low angular momentum (e.g., due to consumption of stars by a black hole), an instability similar to loss-cone instability in plasma may occur. The gravitational loss-cone instability is expected to enhance black hole feeding rates. For spherical systems, the instability is possible for the number of spherical harmonics $l \ge 3$. If there is some amount of counter-rotating stars in flattened systems, they generally exhibit the instability independently of azimuthal number $m$. The results are compared with those obtained recently by Tremaine for distribution functions monotonically increasing with angular momentum. The analysis is based on simple characteristic equations describing small perturbations in a disk or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analyzing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose-Nyquist criterion for disk and spherical gravitational systems.Comment: Accepted to Monthly Notices of the Royal Astronomical Society; typos adde

Formation Mechanisms for Spirals in Barred Galaxies

We consider a scenario of formation of the spiral structure in barred galaxies. This scenario includes the new non-resonant mechanism of elongation of spirals, due to the characteristic behaviour of the gravitational potential beyond the principal spiral arms

Short Wavelength Analysis of the Evolution of Perturbations in a Two-component Cosmological Fluid

The equations describing a two-component cosmological fluid with linearized density perturbations are investigated in the small wavelength or large $k$ limit. The equations are formulated to include a baryonic component, as well as either a hot dark matter (HDM) or cold dark matter (CDM) component. Previous work done on such a system in static spacetime is extended to reveal some interesting physical properties, such as the Jeans wavenumber of the mixture, and resonant mode amplitudes. A WKB technique is then developed to study the expanding universe equations in detail, and to see whether such physical properties are also of relevance in this more realistic scenario. The Jeans wavenumber of the mixture is re-interpreted for the case of an expanding background spacetime. The various modes are obtained to leading order, and the amplitudes of the modes are examined in detail to compare to the resonances observed in the static spacetime results. It is found that some conclusions made in the literature about static spacetime results cannot be carried over to an expanding cosmology.Comment: 42 pages, 12 figure

Resolving Gas Dynamics in the Circumnuclear Region of a Disk Galaxy in a Cosmological Simulation

Using a hydrodynamic adaptive mesh refinement code, we simulate the growth and evolution of a galaxy, which could potentially host a supermassive black hole, within a cosmological volume. Reaching a dynamical range in excess of 10 million, the simulation follows the evolution of the gas structure from super-galactic scales all the way down to the outer edge of the accretion disk. Here, we focus on global instabilities in the self-gravitating, cold, turbulence-supported, molecular gas disk at the center of the model galaxy, which provide a natural mechanism for angular momentum transport down to sub-pc scales. The gas density profile follows a power-law scaling as r^-8/3, consistent with an analytic description of turbulence in a quasi-stationary circumnuclear disk. We analyze the properties of the disk which contribute to the instabilities, and investigate the significance of instability for the galaxy's evolution and the growth of a supermassive black hole at the center.Comment: 16 pages (includes appendix), submitted to ApJ. Figures here are at low resolution; for higher resolution version, download http://casa.colorado.edu/~levinerd/ms.pd

Self-gravitating fragmentation of eccentric accretion disks

We consider the effects of eccentricity on the fragmentation of gravitationally unstable accretion disks, using numerical hydrodynamics. We find that eccentricity does not affect the overall stability of the disk against fragmentation, but significantly alters the manner in which such fragments accrete gas. Variable tidal forces around an eccentric orbit slow the accretion process, and suppress the formation of weakly-bound clumps. The "stellar" mass function resulting from the fragmentation of an eccentric disk is found to have a significantly higher characteristic mass than that from a corresponding circular disk. We discuss our results in terms of the disk(s) of massive stars at ~0.1pc from the Galactic Center, and find that the fragmentation of an eccentric accretion disk, due to gravitational instability, is a viable mechanism for the formation of these systems.Comment: 9 pages, 7 figures. Accepted for publication in Ap

On the Possibility of Development of the Explosion Instability in a Two-Component Gravitating System

We obtain an expression for the energy of the density wave propagating in a multicomponent gravitating medium in the form well known from electrodynamics. Using the above, the possibility of "triple production" of the quasi-particles, or waves, with their energies summing up to zero, in a non-equilibrium medium is demonstrated. That kind of resonance wave interaction is shown to result in the development of an explosion instability. By the method developed in plasma physics, the characteristic time of the instability is evaluated.Comment: 15 pages, 3 figures, accepted for publication (JETP

Algebraic damping in the one-dimensional Vlasov equation

We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation evolving according to the linearized Vlasov equation decays algebraically with the exponent -2 and a well defined frequency. The theoretical results are successfully tested against numerical $N$-body simulations, corresponding to the full Vlasov dynamics in the large $N$ limit, in the case of the Hamiltonian mean-field model. For this purpose, we use a weighted particles code, which allows us to reduce finite size fluctuations and to observe the asymptotic decay in the $N$-body simulations.Comment: 26 pages, 8 figures; text slightly modified, references added, typos correcte