Modelling the tightest relation between galaxy properties and dark
  matter halo properties from hydrodynamical simulations of galaxy formation
  We investigate how a property of a galaxy correlates most tightly with a
property of its host dark matter halo, using state-of-the-art hydrodynamical
simulations of galaxy formation EAGLE, Illustris, and IllustrisTNG. Unlike most
of the previous work, our analyses focus on all types of galaxies, including
both central and satellite galaxies. We find that the stellar mass of a galaxy
at the epoch of the peak circular velocity with an evolution correction gives
the tightest such correlation to the peak circular velocity $V_{\rm peak}$ of
the galaxy's underling dark matter halo. The evolution of galaxy stellar mass
reduces rather than increases scatter in such a relation. We also find that one
major source of scatter comes from star stripping due to the strong
interactions between galaxies. Even though, we show that the size of scatter
predicted by hydrodynamical simulations has a negligible impact on the
clustering of dense $V_{\rm peak}$-selected subhalo from simulations, which
suggests that even the simplest subhalo abundance matching (SHAM), without
scatter and any additional free parameter, can provide a robust prediction of
galaxy clustering that can agree impressively well with the observations from
the SDSS main galaxy survey.
