E. V. Polyachenko

Gas motions in the plane of the spiral galaxy NGC 3631

The velocity field of the nearly face-on galaxy NGC 3631, derived from observations in the H alpha line and the HI radio line, is analysed to study perturbations related to the spiral structure of the galaxy. We confirm our previous conclusion that the line-of-sight velocity field gives evidence of the wave nature of the observed two-armed spiral structure. Fourier analysis of the observed velocity field is used to determine the location of corotation of the spiral structure of this galaxy, and the radius of corotation R_c is found to be about 42 arcsec, or 3.2 kpc. The vector velocity field of the gas in the plane of the disc is restored, and taking into account that we previously investigated vertical motions, we now have a full 3D gaseous velocity field of the galaxy. We show clear evidence of the existence of two anticyclonic and four cyclonic vortices near corotation in a frame of reference rotating with the spiral pattern. The centres of the anticyclones lie between the observed spiral arms. The cyclones lie close to the observed spirals, but their centres are shifted from the maxima in brightness.

Giant cyclones in gaseous discs of spiral galaxies

Abstract We report the detection of giant cyclonic vortices in the gaseous disc of the spiral galaxy NGC 3631 in the reference frame rotating with the spiral pattern. A presence of such structures was predicted by the authors for galaxies, where the radial gradient of the perturbed velocity exceeds that of the rotational velocity. This situation really takes place in NGC 3631.

Notes on the stability threshold for radially anisotropic polytropes

We discuss some contradictions found in the literature concerning the problem of stability of collisionless spherical stellar systems, which are the simplest anisotropic generalization of the well-known polytrope models. Their distribution function F(E, L) is a product of powerlaw functions of the energy E and angular momentum L, i.e. F ∝ L −s (− E) q . On the one hand, calculation of the growth rates in the framework of linear stability theory and N-body simulations shows that these systems become stable when the parameter s characterizing the velocity anisotropy of the stellar distribution is lower than some finite threshold value, s < scrit. On the other hand, Palmer & Papaloizou showed that the instability remains up to the isotropic limit s = 0. Using our method of determining the eigenmodes for stellar systems, we show that the growth rates in weakly radially anisotropic systems are indeed positive, but decrease exponentially as the parameter s approaches zero, i.e. γ ∝ exp(−s∗/s). In fact, for systems with a finite lifetime this means stability.

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

We study the small perturbations in spherical and thin disc stellar clusters surrounding a massive black hole. Because of the black hole, stars with sufficiently low angular momentum escape from the system through the loss cone. We show that the 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, instability in disc clusters is possible for both types of distribution.

On the nature of the radial orbit instability in spherically symmetric collisionless stellar systems

We consider a two-parametric family of radially anisotropic models with non-singular density distribution in the centre. If highly eccentric orbits are locked near the centre, the characteristic growth rate of the instability is much less than the Jeans and dynamic frequencies of the stars (slow modes). The instability occurs only for even spherical harmonics and the perturbations are purely growing (aperiodic). On the contrary, if all orbits nearly reach the outer radius of the sphere, both even and odd harmonics are unstable. Unstable odd modes oscillate having characteristic frequencies of the order of the dynamical frequencies (fast modes). Unstable even harmonics contain a single aperiodic mode and several oscillatory modes, the aperiodic mode being the most unstable. The question of the nature of the radial orbit instability (ROI) is revisited. Two main interpretations of ROI were suggested in the literature. The first one refers to the classical Jeans instability associated with the lack of velocity dispersion of stars in the transverse direction. The second one refers to Lynden-Bells orbital approach to bar formation in disc galaxies, which implies slowness and bi-symmetry of the perturbation. Oscillatory modes, odd spherical harmonics modes, and non-slow modes found in one of the models show that the orbital interpretation is not the only possible.

On the bar formation mechanism in galaxies with cuspy bulges

We show by numerical simulations that a purely stellar dynamical model composed of an exponential disc, a cuspy bulge, and an NFW halo with parameters relevant to the Milky Way Galaxy is subject to bar formation. Taking into account the finite disc thickness, the bar formation can be explained by the usual bar instability, in spite of the presence of an inner Lindblad resonance, that is believed to damp any global modes. The effect of replacing the live halo and bulge by a fixed external axisymmetric potential (rigid models) is studied. It is shown that while the e-folding time of bar instability increases significantly (from 250 to 500 Myr), the bar pattern speed remains almost the same. For the latter, our average value of 55 km/s/kpc agrees with the assumption that the Hercules stream in the solar neighbourhood is an imprint of the bar--disc interaction at the outer Lindblad resonance of the bar. Vertical averaging of the radial force in the central disc region comparable to the characteristic scale length allows us to reproduce the bar pattern speed and the growth rate of the rigid models, using normal mode analysis of linear perturbation theory in a razor thin disc. The strong increase of the e-folding time with decreasing disc mass predicted by the mode analysis suggests that bars in galaxies similar to the Milky Way have formed only recently.

Equilibrium models of radially anisotropic spherical stellar systems with softened central potentials

We study a new class of equilibrium two-parametric distribution functions of spherical stellar systems with a radially anisotropic velocity distribution of stars. The models are less singular counterparts of the so-called generalized polytropes, widely used in the past in works on equilibrium and the stability of gravitating systems. The offered models, unlike the generalized polytropes, have finite density and potential in the centre. The absence of the singularity is necessary for proper consideration of the instability of the radial orbit, which is the most important instability in spherical stellar systems. We provide a comparison of the main observed parameters (i.e. potential, density, anisotropy) predicted by the present models and by other popular equilibrium models.

On the Instability of Weakly Radially Anisotropic Star Clusters

We discuss contradictions existing in the literature in the problem on the stability of collisionless spherical stellar systems, which are the simplest anisotropic generalization of the well-known polytropic models. On the one hand, calculations of the growth rates within the framework of a linear stability theory and N-body simulations suggest that these systems should become stable when the parameter s characterizing the degree of anisotropy of the stellar velocity distribution becomes lower than some critical value scrit > 0. On the other hand, according to Palmer and Papaloizou, the growth rate should be nonzero up to the isotropic limit s = 0. Using our method of determining the eigenmodes of stellar systems, we show that even though the mode growth rates in weakly radially anisotropic systems of this type are nonzero, they are exponentially small, i.e., decrease as γ ∝ exp(−a/s) when s → 0. For slightly radially anisotropic systems with a finite lifetime, this actually implies stability.

Slow modes in stellar systems with nearly harmonic potentials: I. Spoke approximation, radial orbit instability

Using a consistent perturbation theory for collisionless disk-like and spherical star clusters, we construct a theory of slow modes for systems having an extended central region with a nearly harmonic potential due to the presence of a fairly homogeneous (on the scales of the stellar system) heavy, dynamically passive halo. In such systems, the stellar orbits are slowly precessing, centrally symmetric ellipses (2: 1 orbits). Depending on the density distribution in the system and the degree of halo inhomogeneity, the orbit precession can be both prograde and retrograde, in contrast to systems with 1: 1 elliptical orbits where the precession is unequivocally retrograde. In the first paper, we show that in the case where at least some of the orbits have a prograde precession and the stellar distribution function is a decreasing function of angular momentum, an instability that turns into the well-known radial orbit instability in the limit of low angular momenta can develop in the system. We also explore the question of whether the so-called spoke approximation, a simplified version of the slow mode approximation, is applicable for investigating the instability of stellar systems with highly elongated orbits. Highly elongated orbits in clusters with nonsingular gravitational potentials are known to be also slowly precessing 2: 1 ellipses. This explains the attempts to use the spoke approximation in finding the spectrum of slow modes with frequencies of the order of the orbit precession rate. We show that, in contrast to the previously accepted view, the dependence of the precession rate on angular momentum can differ significantly from a linear one even in a narrow range of variation of the distribution function in angular momentum. Nevertheless, using a proper precession curve in the spoke approximation allows us to partially “rehabilitate” the spoke approach, i.e., to correctly determine the instability growth rate, at least in the principal (O(αT−1/2) order of the perturbation theory in dimensionless small parameter αT, which characterizes the width of the distribution function in angular momentum near radial orbits.

Effects of galaxy–satellite interactions on bar formation

Aims. We aim to show how encounters with low-mass satellite galaxies may alter the bar formation in a Milky Way-like disc galaxy. Methods. We use high-resolution N-body simulations of a disc galaxy prone to mild bar instability. For realistic initial conditions of satellites, we take advantage of cosmological simulations of Milky Way-like dark matter haloes. Results. The satellites may have a significant impact on the time of bar formation. Some runs with satellites demonstrate a delay, while others show an advancement in bar formation compared to the isolated run, with such time differences reaching