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

Stationary orbits of satellites of disk galaxies

The satellite of an S-galaxy will experience opposing dynamical-friction forces from the stars of the disk and the halo. If these forces are in balance, the satellite may travel in a stable, near-circular orbit whose radius, for a wide range of physical parameters, should be limited to a zone 1.2 to 1.4 times the disk radius, much as is observed. The idea is very simple. The dynamical friction acting on a small satellite, moving through a stellar galactic halo, makes this satellite slow down. On the other hand, a stellar disk, rotating faster than a satellite, makes it speed up. But the density distributions in radius for disk's and halo's stars in real flat galaxies are quite different (respectively, exponential and power-law). Moreover, the observational data show that the exponential profile for disk's surface density drops abruptly at some radius (r sub d). So it is natural to expect that a stationary orbit could be near the edge of a disk (where two effects are mutually compensated)

COLLEGE ATTENDANCE RATIONAL CHOICE: MODELING AND EMPIRICAL ESTIMATIONS

Previous findings of economic literature pointed out that there is significant correlation of family characteristics and family background with an individual’s rational choice of education. However, variable of abilities was omitted. This study develops and estimates the model of rational choice of college attendance with respect to agent’s individual and family characteristics as well as abilities to meet college requirements. Paper concludes significant impact of an individual’s cognitive abilities on his rational educational choice. Additional finding is that gender of individual has dual effect on his educational choice. First is negative via income mechanism. And the second is positive via motivation mechanism to compensate an income gap

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-Bell's 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.Comment: 11 pages, 6 figures; Accepted to MNRA

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.Comment: 13 pages, 15 figures, submitted to MNRAS Dec 2015, accepted Jul 29, 201