The Kennicutt-Schmidt star formation relation at z ∼ 2

Recent observations of excited CO emission lines from z similar to 2 disc galaxies have shed light on the SFR proportional to N relation at high z via observed Sigma(SFR)-Sigma alpha(COJ=2-1) and Sigma(SFR)-Sigma alpha(COJ=3-2) relations. Here, we describe a novel methodology for utilizing these observations of high-excitation CO to derive the underlying Schmidt (SFR proportional to 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 Kennicutt-Schmidt index, alpha, will be less than the underlying SFR proportional to N 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 similar to 2 disc galaxies with the aim of developing a mapping between various observed Sigma(SFR)-Sigma alpha(CO) relationships and the underlying SFR proportional to N relation. We find that even in relatively luminous z similar to 2 discs, differential excitation does indeed exist, resulting in alpha < N for highly excited CO lines. This means that an observed (e.g.) Sigma(SFR)-Sigma alpha(COJ=3-2) relation does not map linearly to a Sigma(SFR)-Sigma alpha(H2) relation. We utilize 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 and Sigma(SFR)-Sigma alpha(COJ=3-2) relations suggest that an underlying SFR proportional to 1.5 relation describes z similar to 2 disc galaxies.