The atomic-to-molecular transition and its relation to the scaling properties of galaxy discs in the local Universe

We extend the existing semi-analytic models of galaxy formation to track atomic and molecular gas in disc 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 disc is represented by a series of concentric rings. We assume that the surface density profile of an infalling gas in a dark matter halo is exponential, with scale radius rd 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, disc 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, and the other is a prescription where the H2 fraction is determined by the pressure of the interstellar medium (ISM). Motivated by the observational results of Leroy et al., we adopt a star formation law in which forumla in the regime where the molecular gas dominates the total gas surface density, and forumla where atomic hydrogen dominates. We then fit these models to the radial surface density profiles of stars, H I and H2 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 discs: the mass of the dark matter halo, the spin parameter of the halo and the amount of gas recently accreted from the external environment.Jian Fu thanks the Joint Program between Chinese Academic of Sciences and Max-Planck-Gesellschaft for the chance of visiting the Max-Planck-Institut fur Astrophysik, and Deutsche Forschungs- ¨ gemeinschaft for the extra support. He also thanks the support from the National Science Foundation of the Key Project No. 10833005, the Group Innovation Project No. 10821302, and by 973 programme No. 2007CB815402. Guinevere Kauffmann thanks Reinhard Genzel for conversations that inspired this work. Mark Krumholz acknowledges support from the Alfred P. Sloan Foundation, the National Science Foundation through grant AST-0807739, NASA through ATFP grant NNX09AK31G and NASA through the Spitzer Space Telescope Theoretical Research Program, provided by a contract issued by the Jet Propulsion Laboratory