  We present a detailed description of a phenomenological H2 formation model
and local star formation prescription based on the density of molecular (rather
than total) gas. Such approach allows us to avoid the arbitrary density and
temperature thresholds typically used in star formation recipes. We present
results of the model based on realistic cosmological simulations of high-z
galaxy formation for a grid of numerical models with varied dust-to-gas ratios
and interstellar far UV (FUV) fluxes. Our results show that both the
atomic-to-molecular transition on small, ~10 pc scales and the
Kennicutt-Schmidt (KS) relation on ~kpc scales are sensititive to the
dust-to-gas ratio and the FUV flux. The atomic-to-molecular transition as a
function of gas density or column density has a large scatter but is rather
sharp and shifts to higher densities with decreasing dust-to-gas ratio and/or
increasing FUV flux. Consequently, star formation is concentrated to higher gas
surface density regions, resulting in steeper slope and lower amplitude of the
KS relation at a given gas surface density, in less dusty and/or higher FUV
flux environments. These trends should have a particularly strong effect on the
evolution of low-mass, low surface brightness galaxies which typically have low
dust content and anemic star formation, but are also likely to be important for
evolution of the Milky Way-sized systems. We parameterize the dependencies
observed in our simulations in convenient fitting formulae, which can be used
to model the dependence of the KS relation on the dust-to-gas ratio and FUV
flux in semi-analytic models and in cosmological simulations that do not
include radiative transfer and H2 formation.
