The co-evolution of molecular hydrogen and the grain size distribution
  in an isolated galaxy
  Understanding the evolution of dust and molecular hydrogen (H$_2$) is a
critical aspect of galaxy evolution, as they affect star formation and the
spectral energy distribution of galaxies. We use the
$N$-body/smoothed-particle-hydrodynamics code {\sc Gadget-4} to compute the
evolution of dust and H$_2$ in a suite of numerical simulations of an isolated
Milky-Way-like galaxy. The evolution of the full grain size distribution (GSD)
is solved by sampling the grain size on a logarithmically spaced grid with 30
bins. The evolution of a primordial chemistry network with twelve species is
solved consistently with the hydrodynamic evolution of the system, including
star formation, metal and energy ejections from stars into the interstellar
medium through supernova feedback and stellar winds. The formation model for
H$_2$ considers the GSD and photo-dissociation through the UV radiation of
young stars. We identify the processes needed for producing a sizeable amount
of H$_2$, verify that the resulting star formation law in the later stages of
galaxy evolution is consistent with observations of local spirals, and show
that our model manages to produce a galactic molecular gas fraction in line
with observations of Milky-Way-like galaxies. We stress the importance of the
co-evolution of the GSD and H$_2$, as models assuming a fixed MRN shape for the
GSD overestimate the production of H$_2$ in regimes where the dust abundance is
dominated by large grains and underestimate it in the regime where the dust is
dominated by small grains, both of which are realized in simulations of dust
evolution.
