Density waves in the shearing sheet I. Swing amplification

The shearing sheet model of a galactic disk is studied anew. The theoretical description of its dynamics is based on three building blocks: Stellar orbits, which are described here in epicyclic approximation, the collisionless Boltzmann equation determining the distribution function of stars in phase space, and the Poisson equation in order to take account of the self-gravity of the disk. Using these tools I develop a new formalism to describe perturbations of the shearing sheet. Applying this to the unbounded shearing sheet model I demonstrate again how the disturbances of the disk evolve always into `swing amplified' density waves, i.e. spiral-arm like, shearing density enhancements, which grow and decay while the wave crests swing by from leading to trailing orientation. Several examples are given how such `swing amplification' events are incited in the shearing sheet.Comment: small corrections, uses new A&A style fil

Kinematic Density Waves in Accretion Disks

When thin accretion disks around black holes are perturbed, the main restoring force is gravity. If gas pressure, magnetic stresses, and radiation pressure are neglected, the disk remains thin as long as orbits do not intersect. Intersections would result in pressure forces which limit the growth of perturbations. We find that a discrete set of perturbations is possible for which orbits remain non-intersecting for arbitrarily long times. These modes define a discrete set of frequencies. We classify all long-lived perturbations for arbitrary potentials and show how their mode frequencies are related to pattern speeds computed from the azimuthal and epicyclic frequencies. We show that modes are concentrated near radii where the pattern speed has vanishing radial derivative. We explore these modes around Kerr black holes as a possible explanation for the high-frequency quasi-periodic oscillations of black hole binaries such as GRO J1655-40. The long-lived modes are shown to coincide with diskoseismic waves in the limit of small sound speed. While the waves have long lifetime, they have the wrong frequencies to explain the pairs of high-frequency quasi-periodic oscillations observed in black hole binaries.Comment: 28 pages, 6 figures; extended comparison with diskoseismology; added reference to astro-ph/060368

Finite element modelling of perturbed stellar systems

I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and suitable interpolating functions. General expressions are then introduced for the Hamiltonian and phase space distribution functions of the stars that visit a given element. Using the weighted residual form of Poisson's equation, I derive the Galerkin projection of the perturbed collisionless Boltzmann equation, and assemble the global evolutionary equations of nodal distribution functions. The FEM is highly adaptable to all kinds of potential and density profiles, and it can deal with density clumps and initially non-axisymmetric systems. I use ring elements of non-uniform widths, choose linear and quadratic interpolation functions in the radial direction, and apply the FEM to the stability analysis of the cutout Mestel disc. I also integrate the forced evolutionary equations and investigate the disturbances of a stable stellar disc due to the gravitational field of a distant satellite galaxy. The performance of the FEM and its prospects are discussed.Comment: 11 pages, three figures, accepted for publication by MNRA

Stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs

We construct aligned and unaligned stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs (SIDs) coupled by gravity. In comparison with SID problems studied earlier, there exist three possible classes of stationary solutions allowed by more dynamic freedoms. Our exact global perturbation solutions and critical points are valuable for testing numerical magnetohydrodynamic codes. For galactic applications, our model analysis contains more realistic elements and offer useful insights for structures and dynamics of disc galaxies consisting of stars and magnetized gas.Comment: 25 pages, 31 figures, accepted by Monthly Notices of Royal Astronomical Society, style files include

Outline of the Unified Theory of Spiral and Bar-like Structures in Galaxies

This paper presents a new approach to studying galactic structures. They are considered as the low-frequency normal modes in a disc of orbits precessing at different angular speeds. Such a concept is an adequate alternative to the commonly used approach of treating the disc as a set of individual stars rotating at near-circular orbits around the centre. The problem of determining the normal modes is reduced to a simple integral equation in the form of the classical eigen-value problem, where the eigen-value is directly equal to the pattern speed of the mode, $\Omega_p$. An examination of the general properties of the basic integral equation shows that two types of solutions exist, bar-like and spiral. The numerical solutions of both types are obtained. The characteristic pattern speeds are of the order of the mean orbit precession speed, although for the bar-modes $\Omega_p$ can markedly exceed the maximum precessing speed of orbits. It is shown that the bar-mode grows due to the immediate action of its gravitational field on the stars at the resonance regions. As for the spiral mode, its excitation is probably due to the inner Lindblad resonance that can promote mode growth.Comment: 19 pages, 10 figures, 1 tabl

A new approach to the problem of modes in the Mestel disk

We examine the modes admitted by the Mestel disk, a disk with a globally flat rotation curve. In contrast to previous analyses of this problem by Zang (\cite{1976PhDT........26Z}) and Evans & Read (\cite{1998MNRAS.300...83E}, \cite{1998MNRAS.300..106E}), we approximate the orbits to obtain almost closed expressions for the kernel of the integral equation governing the behaviour of the modes. Otherwise we, like them, follow Kalnajs' programme to simultaneously solve the Boltzmann and Poisson equations. We investigate the modes admitted by both the self-consistent and a cut-out Mestel disk, the difference being that in the latter, a part of the matter in the disk is immobilised. This breaks the self-similarity and produces a pronouncedly different picture, both technically and in terms of the disk properties. The self-consistent disk is governed by a Cauchy integral equation, the cut-out disk by an integral equation that can be treated as a Fredholm equation of the second kind. In general, our approximation reproduces the results of the previous works remarkably well, yielding quantities mostly within 5% of the values reported by Zang and Evans & Read and thus also the basic result that in a ``standard'' cut-out disk, only one-armed modes are unstable at the limit of axisymmetric stability. In the self-consistent disk, relatively compact expressions for the kernel allow an intuitive understanding of most of the properties of neutral (non-rotating, non-growing) modes there. We finally show that self-consistent Mestel disks do not admit growing or rotating modes in this sort of stellar-dynamical analysis.Comment: 10 pages, 1 figure; accepted for publication in A&

Interplay between Stellar Spirals and the ISM in Galactic Disks

We propose a new dynamical picture of galactic stellar and gas spirals, based on hydrodynamic simulations in a `live' stellar disk. We focus especially on spiral structures excited in a isolated galactic disk without a stellar bar. Using high-resolution, 3-dimensional N-body/SPH simulations, we found that the spiral features of the gas in galactic disks are formed by essentially different mechanisms from the galactic shock in stellar density waves. The stellar spiral arms and the interstellar matter on average corotate in a galactic potential at any radii. Unlike the stream motions in the galactic shock, the interstellar matter flows into the local potential minima with irregular motions. The flows converge to form dense gas clouds/filaments near the bottom of the stellar spirals, whose global structures resemble dust-lanes seen in late-type spiral galaxies. The stellar arms are non-steady; they are wound and stretched by the galactic shear, and thus local densities of the arm change on a time scale of ~ 100 Myrs, due to bifurcating or merging with other arms. This makes the gas spirals associated with the stellar arms non-steady. The association of dense gas clouds are eventually dissolved into inter-arm regions with non-cirucular motions. Star clusters are formed from the cold, dense gases, whose ages are less than ~30 Myrs, and they are roughly associated with the background stellar arms without a clear spatial offset between gas spiral arms and distribution of young stars.Comment: 13 pages, 12 figures, accepted by ApJ. Higher resolution of ms.pdf is available at http://d.pr/Nvjk A targzipped Supplementary movies is available at http://d.pr/TV6

Patterns in the Outer Parts of Galactic Disks

This paper describes test particle simulations of the response of the outer parts of Galactic disks to barring and spiral structure. Simulations are conducted for cold Mestel disks and warm quasi-exponential disks with completely flat rotation curves, subjected to pure quadrupoles and logarithmic spirals. Even though the starting velocity distributions are smooth, the end-points of the bar simulations show bimodality and multi-peaked structures at locations near the outer Lindblad resonance (OLR), although spirality can make this smoother. The growth of a bar may cause the disk isophotes to become boxy at the OLR, as stars accummulate particularly along the minor axis. The growth of a bar is also accompanied by substantial heating of the disk stars near the OLR. For the growth of a $10^{10} M_{\rm \odot}$ bar, the radial velocity dispersion is typically quadrupled for initially cold disks (initial \sigmau $\sim 10$ \kms), and typically doubled for disks with final \sigmau $\sim 45$ \kms. Simulations performed of the growth and dissolution of bars give very similar results, demonstrating that the heat once given to disk stars is very difficult to remove.Comment: 14 pages, 19 figure

Dynamical friction force exerted on spherical bodies

We present a rigorous calculation of the dynamical friction force exerted on a spherical massive perturber moving through an infinite homogenous system of field stars. By calculating the shape and mass of the polarization cloud induced by the perturber in the background system, which decelerates the motion of the perturber, we recover Chandrasekhar's drag force law with a modified Coulomb logarithm. As concrete examples we calculate the drag force exerted on a Plummer sphere or a sphere with the density distribution of a Hernquist profile. It is shown that the shape of the perturber affects only the exact form of the Coulomb logarithm. The latter converges on small scales, because encounters of the test and field stars with impact parameters less than the size of the massive perturber become inefficient. We confirm this way earlier results based on the impulse approximation of small angle scatterings.Comment: 5 pages, 2 figures, accepted in MNRA