Restoring the full velocity field in the gaseous disk ofthe spiral galaxy NGC 157

We analyse the line-of-sight velocity field of ionized gas in the spiral galaxy NGC 157 which has been obtained in the H\alpha emission at the 6m telescope of SAO RAS. The existence of systematic deviations of the observed gas velocities from pure circular motion is shown. A detailed investigation of these deviations is undertaken by applying a Fourier analysis of the azimuthal distributions of the line-of-sight velocities at different distances from the galactic center. As a result of the analysis, all the main parameters of the wave spiral pattern are determined: the corotation radius, the amplitudes and phases of the gas velocity perturbations at different radii, and the velocity of circular rotation of the disk corrected for the velocity perturbations due to spiral arms. At a high confidence level, the presence of the two giant anticyclones in the reference frame rotating with the spiral pattern is shown; their sizes and the localization of their centers are consistent with the results of the analytic theory and of numerical simulations. Besides the anticyclones, the existence of cyclones in residual velocity fields of spiral galaxies is predicted. In the reference frame rotating with the spiral pattern these cyclones have to reveal themselves in galaxies where a radial gradient of azimuthal residual velocity is steeper than that of the rotation velocity (abridged).Comment: 23 pages including 25 eps-figures. Accepted for publication in A&

Spectral density asymptotics for Gaussian and Laguerre β\beta-ensembles in the exponentially small region

The first two terms in the large $N$ asymptotic expansion of the $\beta$ moment of the characteristic polynomial for the Gaussian and Laguerre $\beta$-ensembles are calculated. This is used to compute the asymptotic expansion of the spectral density in these ensembles, in the exponentially small region outside the leading support, up to terms $o(1)$ . The leading form of the right tail of the distribution of the largest eigenvalue is given by the density in this regime. It is demonstrated that there is a scaling from this, to the right tail asymptotics for the distribution of the largest eigenvalue at the soft edge.Comment: 19 page

Elliptical motions of stars in close binary systems

Motions of stars in close binary systems with a conservative mass exchange are examined. It is shown that Paczynski-Huang model widely used now for obtaining the semi-major axis variation of a relative stars orbit is incorrect, because it brings about large mistakes. A new model suitable for elliptical orbits of stars is proposed. Both of reactive and attractive forces between stars and a substance of the flowing jet are taken into account. A possibility of a mass exchange at presence of accretion disk is considere

Dynamic stabilization of non-spherical bodies against unlimited collapse

We solve equations, describing in a simplified way the newtonian dynamics of a selfgravitating nonrotating spheroidal body after loss of stability. We find that contraction to a singularity happens only in a pure spherical collapse, and deviations from the spherical symmetry stop the contraction by the stabilising action of nonlinear nonspherical oscillations. A real collapse happens after damping of the oscillations due to energy losses, shock wave formation or viscosity. Detailed analysis of the nonlinear oscillations is performed using a Poincar\'{e} map construction. Regions of regular and chaotic oscillations are localized on this map.Comment: MNRAS, accepted, 7 pages, 9 figure

A generic C1C^1 map has no absolutely continuous invariant probability measure

Let $M$ be a smooth compact manifold (maybe with boundary, maybe disconnected) of any dimension $d \ge 1$. We consider the set of $C^1$ maps $f:M\to M$ which have no absolutely continuous (with respect to Lebesgue) invariant probability measure. We show that this is a residual (dense $G_\delta) set in the$C^1$ topology. In the course of the proof, we need a generalization of the usual Rokhlin tower lemma to non-invariant measures. That result may be of independent interest.Comment: 12 page

The Radial Orbit Instability in Collisionless N-Body Simulations

Using a suite of self-gravitating, collisionless N-body models, we systematically explore a parameter space relevant to the onset and behavior of the radial orbit instability (ROI), whose strength is measured by the systemic axis ratios of the models. We show that a combination of two initial conditions, namely the velocity anisotropy and the virial ratio, determines whether a system will undergo ROI and exactly how triaxial the system will become. A third initial condition, the radial shape of the density profile, plays a smaller, but noticeable role. Regarding the dynamical development of the ROI, the instability a) begins after systems collapse to their most compact configuration and b) evolves fastest when a majority of the particles have radially anisotropic orbits while there is a lack of centrally-concentrated isotropic orbits. We argue that this is further evidence that self-reinforcing torques are the key to the onset of the ROI. Our findings support the idea that a separate orbit instability plays a role in halting the ROI.Comment: accepted for publication in ApJ. 9 figures in emulateapj styl

Mechanisms of the Vertical Secular Heating of a Stellar Disk

We investigate the nonlinear growth stages of bending instability in stellar disks with exponential radial density profiles.We found that the unstable modes are global (the wavelengths are larger than the disk scale lengths) and that the instability saturation level is much higher than that following from a linear criterion. The instability saturation time scales are of the order of one billion years or more. For this reason, the bending instability can play an important role in the secular heating of a stellar disk in the $z$ direction. In an extensive series of numerical $N$-body simulations with a high spatial resolution, we were able to scan in detail the space of key parameters (the initial disk thickness $z_0$, the Toomre parameter $Q$, and the ratio of dark halo mass to disk mass $M_{\rm h} / M_{\rm d}$). We revealed three distinct mechanisms of disk heating in the $z$ direction: bending instability of the entire disk, bending instability of the bar, and heating on vertical inhomogeneities in the distribution of stellar matter.Comment: 22 pages including 8 figures. To be published in Astronomy Letters (v.29, 2003

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