Environmental Dependence of the Kennicutt-Schmidt Relation in Galaxies

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 an approach allows us to avoid the arbitrary density and temperature thresholds typically used in star formation recipes in galaxy formation simulations. 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, tens-of-parsec scales and the Kennicutt-Schmidt (K-S) relation on large, kiloparsec scales are sensitive 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 K-S relation at a given Σ_H, in less dusty and/or higher FUV flux environments. We parameterize the dependences observed in our simulations in convenient fitting formulae, which can be used to model the dependence of the K-S 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. Finally, we show that ionized gas can contribute a significant fraction of the total gas surface density in environments typical for high-redshift galaxies.