The influence of central black holes on the dynamical evolution of bars in disk galaxies is examined. In particular, we use numerical simulation to estimate the minimum mass black hole (BH) needed to destroy a bar. Initially, bars form in the disks via dynamical instability. Thereafter, once a bar is fully developed, a BH is adiabatically added at the center of the disk. To mitigate the global effects of gravitational softening, Poisson's equation for the disk is solved by expanding the density and potential of the galaxy in a set of basis functions.Our results indicate that a bar can be completely destroyed in a time much smaller than a Hubble time if the central mass exceeds about 0.5% of the disk mass. Since the implied minimum BH mass for bar destruction is of order 10 8.5 M ⊙ for a typical disk galaxy, this process should not be a rare phenomenon. The bar amplitude decreases gradually with time after the BH is added, and the rate at which the bar is destroyed increases with increasing BH mass. This suggests that bar destruction arises from scattering of stars that support the bar as they pass close to the center.

A recent observation with the Hipparcos satellite and some numerical simulations imply that the interaction between an oblate halo and a disc is inappropriate for the persistence of galactic warps. Then, we have compared the time evolution of galactic warps in a prolate halo with that in an oblate halo. The haloes were approximated as fixed potentials, while the discs were represented by N-body particles. We have found that the warping in the oblate halo continues to wind up, and finally disappears. On the other hand, for the prolate halo model, the precession rate of the outer disc increases when the precession of the outer disc recedes from that of the inner disc, and vice versa. Consequently, the warping in the prolate halo persisted to the end of the simulation by retaining the alignment of the line of nodes of the warped disc. Therefore, our results suggest that prolate haloes could sustain galactic warps. The physical mechanism of the persistence of warp is discussed on the basis of the torque between a halo and a disc and that between the inner and outer regions of the disc.Comment: 8 pages, 8 figures. Accepted for publication in MNRA

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First, we have ensured that spherical nonrotating collisionless systems collapse with almost retaining spherical configurations during initial contraction phases even if they are allowed to collapse three-dimensionally. Next, on the assumption of spherical symmetry, we examine the evolution of velocity dispersions with collapse for the systems which have uniform or power-law density profiles with Maxwellian velocity distributions by integrating the collisionless Boltzmann equation directly. The results show that as far as the initial contraction phases are concerned, the radial velocity dispersion never grows faster than the tangential velocity dispersion except at small radii where the nearly isothermal nature remains, irrespective of the density profiles and virial ratios. This implies that velocity anisotropy as an initial condition should be a poor indicator for the radial orbit instability. The growing behavior of the velocity dispersions is briefly discussed from the viewpoint that phase space density is conserved in collisionless systems.

It is shown that the cuspy density distributions observed in the cores of elliptical galaxies can be realized by dissipationless gravitational collapse. The initial models consist of power‐law density spheres such as ρ∝r−1 with anisotropic velocity dispersions. Collapse simulations are carried out by integrating the collisionless Boltzmann equation directly, on the assumption of spherical symmetry. From the results obtained, the extent of constant density cores, formed through violent relaxation, decreases as the velocity anisotropy increases radially, and practically disappears for extremely radially anisotropic models. As a result, the relaxed density distributions become more cuspy with increasing radial velocity anisotropy. It is thus concluded that the velocity anisotropy could be a key ingredient for the formation of density cusps in a dissipationless collapse picture. The velocity dispersions increase with radius in the cores according to the nearly power‐law density distributions. The power‐law index, n, of the density profiles, defined as ρ∝r−n, changes from n≈2.1 at intermediate radii to a shallower power than n≈2.1 toward the centre. This density bend can be explained from our postulated local phase‐space constraint that the phase‐space density accessible to the relaxed state is determined at each radius by the maximum phase‐space density of the initial state.