  We present high spatial resolution (0.4", ~3.5 kpc) PdBI interferometric data
on three ultra-luminous infrared galaxies (ULIRGs) at z~2: two submillimetre
galaxies and one submillimetre faint star forming radio galaxy. The three
galaxies have been ro- bustly detected in CO rotational transitions, either
12CO(J=4-3) or 12CO(J=3-2), allowing their sizes and gas masses to be
accurately constrained. These are the highest spatial resolution observations
observed to date (by a factor of ~2) for intermediate-excitation CO emission in
z~2 ULIRGs. The galaxies appear extended over several resolution elements,
having a mean radius of 3.7 kpc. High-resolution (0.3") combined MERLIN-VLA
observations of their radio continua allow an analysis of the star formation
behaviour of these galaxies, on comparable spatial scales to that of the CO
observations. This 'matched beam' approach sheds light on the spatial
distribution of both molecular gas and star formation, and we can therefore
calculate accurate star formation rates and gas surface densities: this allows
us to place the three systems in the context of a Kennicutt-Schmidt (KS)-style
star formation law. We find a difference in size between the CO and radio
emission regions, and as such we suggest that using the spatial extent of the
CO emission region to estimate the surface density of star formation may lead
to error. This size difference also causes the star formation efficiencies
within systems to vary by up to a factor of 5. We also find, with our new
accurate sizes, that SMGs lie significantly above the KS relation, indicating
that stars are formed more efficiently in these extreme systems than in other
high-z star forming galaxies.
