HOW UNIVERSAL IS THE $\Sigma _{\rm SFR}\hbox{--}\Sigma _{\rm H_2}$ RELATION?

Abstract

It is a well-established empirical fact that the surface density of the star formation rate, ΣSFR, strongly correlates with the surface density of molecular hydrogen, \Sigma _{H_2}, at least when averaged over large (~kpc) scales. Much less is known, however, about whether (and how) the \Sigma _SFR{--}\Sigma _H_2 relation depends on environmental parameters, such as the metallicity or the UV radiation field in the interstellar medium (ISM). Furthermore, observations indicate that the scatter in the \Sigma _SFR{--}\Sigma _H_2 relation increases rapidly with decreasing averaging scale. How the scale-dependent scatter is generated and how one recovers a tight ~ kpc scale \Sigma _SFR{--}\Sigma _H_2 relation in the first place is still largely debated. Here, these questions are explored with hydrodynamical simulations that follow the formation and destruction of H2, include radiative transfer of UV radiation, and resolve the ISM on ~60 pc scales. We find that within the considered range of H2 surface densities (10-100 M sun pc-2), the \Sigma _SFR{--}\Sigma _H_2 relation is steeper in environments of low-metallicity and/or high-radiation fields (compared to the Galaxy), that the star formation rate (SFR) at a given H2 surface density is larger, and the scatter is increased. Deviations from a "universal" \Sigma _SFR{--}\Sigma _H_2 relation should be particularly relevant for high-redshift galaxies or for low-metallicity dwarfs at z ~ 0. We also find that the use of time-averaged SFRs produces a large, scale-dependent scatter in the \Sigma _SFR{--}\Sigma _H_2 relation. Given the plethora of observational data expected from upcoming surveys such as ALMA, the scale-scatter relation may indeed become a valuable tool for determining the physical mechanisms connecting star formation and H2 formation.