  Many active matter systems, mostly on the microscopic scale, are well
approximated as overdamped, meaning that any inertial momentum is immediately
dissipated by the environment. On the other hand, especially for macroscopic
active systems but also for many mesoscopic ones the time scale of inertial
motion can become large enough to be relevant for the dynamics. This raises the
question how collective dynamics in active matter is influenced by inertia. In
this article we implement and study an underdamped active phase field crystal
model. We focus on how the collective dynamics changes with the time scale of
inertial motion. While the state diagram stays unaltered in this modification,
the relaxation time scale towards the steady state considerably increases with
particle mass. Our numerical results suggest that transiently stable rotating
clusters of density peaks act as defects which need to decay before the final
state of global collective motion forms. We extract the formation and decay
times quantitatively. Finally, we give a physical intuition for the formation
and decay of rotating clusters to qualitatively explain how the extracted times
depend on mass.
