The relation between mid-plane pressure and molecular hydrogen in
  galaxies: Environmental dependence
  Molecular hydrogen (H2) is the primary component of the reservoirs of cold,
dense gas that fuel star formation in our galaxy. While the H2 abundance is
ultimately regulated by physical processes operating on small scales in the
interstellar medium (ISM), observations have revealed a tight correlation
between the ratio of molecular to atomic hydrogen in nearby spiral galaxies and
the pressure in the mid-plane of their disks. This empirical relation has been
used to predict H2 abundances in galaxies with potentially very different ISM
conditions, such as metal-deficient galaxies at high redshifts. Here, we test
the validity of this approach by studying the dependence of the pressure -- H2
relation on environmental parameters of the ISM. To this end, we follow the
formation and destruction of H2 explicitly in a suite of hydrodynamical
simulations of galaxies with different ISM parameters. We find that a pressure
-- H2 relation arises naturally in our simulations for a variety of dust-to-gas
ratios or strengths of the interstellar radiation field in the ISM. Fixing the
dust-to-gas ratio and the UV radiation field to values measured in the solar
neighborhood results in fair agreement with the relation observed in nearby
galaxies with roughly solar metallicity. However, the parameters (slope and
normalization) of the pressure -- H2 relation vary in a systematical way with
ISM properties. A particularly strong trend is the decrease of the
normalization of the relation with a lowering of the dust-to-gas ratio of the
ISM. We show that this trend and other properties of the pressure -- H2
relation are natural consequences of the transition from atomic to molecular
hydrogen with gas surface density.
