Towards the Unified Theory of Galactic Bar-Modes

The arguments in favor of the unified formation mechanism for both slow (Lynden-Bell's) bars and common fast bars are given. This mechanism consists in a certain instability that is akin to the well-known radial orbit instability; it is caused by the mutual attraction and alignment of axes of precessing star orbits (up to now, such a way of formation was considered only for slow bars). The general theory of the low-frequency modes of a disk consisting of precessing orbits (at different angular velocities) is presented. The problem of determining these modes is reduced to the integral equations of a rather simple structure. The characteristic pattern speeds ($\Omega_p$) of the low-frequency modes are of order of the mean orbit precession speeds ($\bar\Omega_{pr}$). The bar-modes also belong to this type of modes. The slow bars have $\Omega_p \approx \bar\Omega_{pr}$; for the fast bars, $\Omega_p$ may far exceed even the maximum precessing speed of disk orbits (however, $\Omega_p$ remains to be of order of these precessing speeds). The possibility of such an excess of $\Omega_p$ over $\Omega_{pr}^{\max}$ is connected with the effect of ``repelling'' orbits that tend to move in the direction opposite to that they are being pushed. The preliminary analysis of the orbit precession patterns for a number of typical potentials is given. It is noted that the maximum radius of the ``attracting'' circular orbits ($r_c$) may be used as a reasonable estimate of a bar length.