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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 $λ$. 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 $Σ_{SFR}\proptoΣ_{H_2}$ in the regime where the molecular gas dominates the total gas surface density, and $Σ_{SFR}\propto Σ_{gas}^2$ 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.