Motion of a rigid body in a tidal field. An application to elliptical galaxies in clusters (Q1270703)

The authors investigate the motion, near the equilibrium configuration, of an initially spinless rigid body subject to an external tidal field. Two cases are considered: when the center of mass of the body is at rest at the equilibrium point of the field generated by a generic mass distribution, and when it is placed on a circular orbit subject to a spherically symmetric potential. In both cases the authors consider the corresponding linear system and the (linear) stability, and obtain the frequencies from this linearization. The results are applied to the problem of alignment of galaxies in clusters. The authors compare radially aligned configurations found through \(N\)-body simulations which are equilibrium positions. The study of orbital times leads the authors to the conclusion that for realistic parameters the stellar orbital times are shorter than the oscillatory times around the equilibrium configurations of the galaxies in the cluster. They discuss the possible resonances between stellar orbits inside the galaxy and the oscillations of the galaxy as a whole, as a mechanism of collisionless evaporation of stars.