The Atomic to Molecular Transition and its Relation to the Scaling
  Properties of Galaxy Disks in the Local Universe
  We extend existing semi-analytic models of galaxy formation to track atomic
and molecular gas in disk galaxies. Simple recipes for processes such as
cooling, star formation, supernova feedback, and chemical enrichment of the
stars and gas are grafted on to dark matter halo merger trees derived from the
Millennium Simulation. Each galactic disk is represented by a series of
concentric rings. We assume that surface density profile of infalling gas in a
dark matter halo is exponential, with scale radius r_d that is proportional to
the virial radius of the halo times its spin parameter $\lambda$. As the dark
matter haloes grow through mergers and accretion, disk galaxies assemble from
the inside out. We include two simple prescriptions for molecular gas formation
processes in our models: one is based on the analytic calculations by Krumholz,
McKee & Tumlinson (2008), and the other is a prescription where the H_2
fraction is determined by the kinematic pressure of the ISM. Motivated by the
observational results of Leroy et al. (2008), we adopt a star formation law in
which $\Sigma_{SFR}\propto\Sigma_{H_2}$ in the regime where the molecular gas
dominates the total gas surface density, and $\Sigma_{SFR}\propto
\Sigma_{gas}^2$ where atomic hydrogen dominates. We then fit these models to
the radial surface density profiles of stars, HI and H_2 drawn from recent high
resolution surveys of stars and gas in nearby galaxies. We explore how the
ratios of atomic gas, molecular gas and stellar mass vary as a function of
global galaxy scale parameters, including stellar mass, stellar surface
density, and gas surface density. We elucidate how the trends can be understood
in terms of three variables that determine the partition of baryons in disks:
the mass of the dark matter halo, the spin parameter of the halo, and the
amount of gas recently accreted from the external environment.
