Dynamics of merging: Post-merger mixing and relaxation of an Illustris
  galaxy
  During the merger of two galaxies, the resulting system undergoes violent
relaxation and seeks stable equilibrium. However, the details of this evolution
are not fully understood. Using Illustris simulation, we probe two physically
related processes, mixing and relaxation. Though the two are driven by the same
dynamics---global time-varying potential for the energy, and torques caused by
asymmetries for angular momentum---we measure them differently. We define
mixing as the redistribution of energy and angular momentum between particles
of the two merging galaxies. We assess the degree of mixing as the difference
between the shapes of their N(E)s, and their N(L^2)s. We find that the
difference is decreasing with time, indicating mixing. To measure relaxation,
we compare N(E) of the newly merged system to N(E) of a theoretical prediction
for relaxed collisionless systems, DARKexp, and witness the system becoming
more relaxed, in the sense that N(E) approaches DARKexp N(E). Because the
dynamics driving mixing and relaxation are the same, the timescale is similar
for both. We measure two sequential timescales: a rapid, 1 Gyr phase after the
initial merger, during which the difference in N(E) of the two merging halos
decreases by ~80%, followed by a slow phase, when the difference decreases by
~50% over ~8.5 Gyrs. This is a direct measurement of the relaxation timescale.
Our work also draws attention to the fact that when a galaxy has reached Jeans
equilibrium it may not yet have reached a fully relaxed state given by DARKexp,
in that it retains information about its past history. This manifests itself
most strongly in stars being centrally concentrated. We argue that it is
particularly difficult for stars, and other tightly bound particles, to mix
because they have less time to be influenced by the fluctuating potential, even
across multiple merger events.
