  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.
