Energy evolution in the progenitor of galaxy shells: a semi-analytical model

A shell galaxy is a peculiar elliptical galaxy hosting stellar arcs braceing it from both sides. As remnants of a disrupted galaxy during merging, the arcs reveal the phase space density of its progenitor. Here a host elliptical is targetted by a tangentially anisotropic dwarf galaxy on a nearly radial orbit, and we investigate the changes in energy and angular momentum of the progenitor’s particles before and after its intrusion, and determine the merging timescale from the observables of the present-day arcs. In our semi-analytical framework The dwarf galaxy is modeled in a series of simulations, either numerically as self-interacting N-bodies (except that dynamical friction is neglected as our dwarf is only 1% of the host galaxy mass) or semi-analytically as test particles in two static but radially-merging Plummer/Hernquist potential wells. Results show that our semi-analytical test particle runs not only reproduce the number of shells and their positions as well as the N-body simulations, but also accurately match the evolutions of energies and angular momenta of the particles. Finally the merging timescale is accurately estimated in our semi-analytical model from the positions of the shells.