How gas flows shape the stellar-halo mass relation in the EAGLE
  simulation
  The difference in shape between the observed galaxy stellar mass function and
the predicted dark matter halo mass function is generally explained primarily
by feedback processes. Feedback can shape the stellar-halo mass (SHM) relation
by driving gas out of galaxies, by modulating the first-time infall of gas onto
galaxies (i.e., preventative feedback), and by instigating fountain flows of
recycled wind material. We present and apply a method to disentangle these
effects for hydrodynamical simulations of galaxy formation. We build a model of
linear coupled differential equations that by construction reproduces the flows
of gas onto and out of galaxies and haloes in the EAGLE cosmological
simulation. By varying individual terms in this model, we isolate the relative
effects of star formation, ejection via outflow, first-time inflow and wind
recycling on the SHM relation. We find that for halo masses $M_{200} < 10^{12}
\, \mathrm{M_\odot}$ the SHM relation is shaped primarily by a combination of
ejection from galaxies and haloes, while for larger $M_{200}$ preventative
feedback is also important. The effects of recycling and the efficiency of star
formation are small. We show that if, instead of $M_{200}$, we use the
cumulative mass of dark matter that fell in for the first time, the evolution
of the SHM relation nearly vanishes. This suggests that the evolution is due to
the definition of halo mass rather than to an evolving physical efficiency of
galaxy formation. Finally, we demonstrate that the mass in the circum-galactic
medium is much more sensitive to gas flows, especially recycling, than is the
case for stars and the interstellar medium.
