Abstract
We investigate the impact of a galaxy's merger history on its system of
satellites using the new \textsc{vintergatan-gm} suite of zoom-in
hydrodynamical simulations of Milky Way-mass systems. The suite simulates five
realizations of the same halo with targeted `genetic modifications' (GMs) of a
$z \approx 2$ merger, but resulting in the same halo mass at $z=0$. We find
that differences in the satellite stellar mass functions last for 2.25-4.25 Gyr
after the $z \approx 2$ merger; specifically, the haloes that have undergone
smaller mergers host up to 60% more satellites than those of the larger merger
scenarios. However, by $z=0$ these differences in the satellite stellar mass
functions have been erased. The differences in satellite numbers seen soon
after the mergers are driven by several factors, including the timings of major
mergers, the masses and satellite populations of the central and merging
systems, and the subsequent extended history of minor mergers. The results
persist when measured at fixed central stellar mass rather than fixed time,
implying that a host's recent merger history can be a significant source of
scatter when reconstructing its dynamical properties from its satellite
population.