  We present the dynamical evolution of the dark matter's relaxation response
to galaxies and their connection to the astrophysical properties as simulated
in the IllustrisTNG suite of cosmological hydrodynamical simulations. Our
results show that the radially-dependent linear relaxation relation model from
our previous work is applicable at least from redshift $z=5$. We focus on the
offset parameter $q_0$, which characterizes the relaxation of dark matter
shells without changing the enclosed mass. We perform multiple time-series
analyses to determine the possible causal connections between the relaxation
mechanism and astrophysical processes such as star formation and associated
feedback processes, as well as feedback due to active galactic nuclei. We show
that star formation activity significantly influences the halo relaxation
response throughout its evolutionary history, with essentially immediate
effects in the inner haloes and delayed effects of 2 to 3 Gyr in the outer
regions. Metal content shows a weaker connection to relaxation than star
formation rates, but the accumulated wind from feedback processes exhibits a
stronger correlation. These findings enhance our understanding of halo
relaxation mechanisms. Our estimates of the time-scales relevant for dark
matter relaxation can potentially improve the description of halo profiles in
existing baryonification schemes and semi-analytical galaxy formation models.
Our results also show how the relaxation response of dark haloes can probe the
evolutionary history of the galaxies they host.
