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 SFR ∝ ρN relation at high z via observed SFR– COJ=2−1 and SFR– COJ=3−2 relations. Here, we describe a novel methodology for utilizing these observations of high-excitation CO to derive the underlying Schmidt (SFR∝ ρN) 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 Kennicutt–Schmidt index, α, will be less than the underlying SFR ∝ ρN index, N. Utilizing 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 SFR ∝ ρN relation. We find that even in relatively luminous z ∼ 2 discs, differential excitation does indeed exist, resulting in α < N for highly excited CO lines. This means that an observed (e.g.) SFR– COJ=3−2 relation does not map linearly to a SFR– H2 relation. We utilize our model results to provide a mapping from α to N for the range of Schmidt indices N = 1–2. By comparing to recent observational surveys, we find that the observed SFR– α COJ=2−1 and SFR– α COJ=3−2 relations suggest that an underlying SFR ∝ ρ1.5 relation describes z ∼ 2 disc galaxies.