Radial alignment of elliptical galaxies by the tidal force of a cluster of galaxies

Unlike the random radial orientation distribution of field elliptical galaxies, galaxies in a cluster are expected to point preferentially towards the center of the cluster, as a result of the cluster's tidal force on its member galaxies. In this work an analytic model is formulated to simulate this effect. The deformation time scale of a galaxy in a cluster is usually much shorter than the time scale of change of the tidal force; the dynamical process of the tidal interaction within the galaxy can thus be ignored. An equilibrium shape of a galaxy is then assumed to be the surface of equipotential, which is the sum of the self-gravitational potential of the galaxy and the tidal potential of the cluster at this location. We use a Monte-Carlo method to calculate the radial orientation distribution of these galaxies, by assuming the NFW mass profile of the cluster and the initial ellipticity of field galaxies. The radial angles show a single peak distribution centered at zero. The Monte-Carlo simulations also show that a shift of the reference center from the real cluster center weakens the anisotropy of the radial angle distribution. Therefore, the expected radial alignment cannot be revealed if the distribution of spatial position angle is used instead of that of radial angle. The observed radial orientations of elliptical galaxies in cluster Abell~2744 are consistent with the simulated distribution.