The Kennicutt-Schmidt Star Formation Relation at z~2

Recent observations of excited CO emission lines from z~2 disc galaxies have shed light on the Kennicutt-Schmidt relation at high-z via observed SFR-CO (J=2-1) and (J=3-2) relations. Here, we describe a novel methodology for utilising these observations of high-excitation CO to derive the underlying Schmidt (SFR-rho^N) relationship. To do this requires an understanding of the potential effects of differential CO excitation with SFR. If the most heavily star-forming galaxies have a larger fraction of their gas in highly excited CO states than the lower SFR galaxies, then the observed molecular SFR-CO^alpha index, alpha, will be less than the underlying (volumetric) Schmidt index, N. Utilising a combination of SPH models of galaxy evolution and molecular line radiative transfer, we present the first calculations of CO excitation in z~2 disc galaxies with the aim of developing a mapping between various observed SFR-CO relationships and the underlying Schmidt relation. We find that even in relatively luminous z~2 discs, differential excitation does indeed exist, resulting in alpha < N for highly excited CO lines. This means that an observed (e.g.) SFR-CO (J=3-2) relation does not map linearly to SFR-H2 relation. We utilise our model results to provide a mapping from alpha to N for the range of Schmidt indices N=1-2. By comparing to recent observational surveys, we find that the observed SFR-CO (J=2-1) and SFR-CO (J=3-2) relations suggest that an underlying SFR rho^1.5 relation describes z~2 disc galaxies.