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.
