High Resolution Imaging of PHIBSS z~2 Main Sequence Galaxies in CO J=1-0

We present Karl G. Jansky Very Large Array observations of the CO J=1-0 transition in a sample of four $z\sim2$ main sequence galaxies. These galaxies are in the blue sequence of star-forming galaxies at their redshift, and are part of the IRAM Plateau de Bure HIgh-$z$ Blue Sequence Survey (PHIBSS) which imaged them in CO J=3-2. Two galaxies are imaged here at high signal-to-noise, allowing determinations of their disk sizes, line profiles, molecular surface densities, and excitation. Using these and published measurements, we show that the CO and optical disks have similar sizes in main-sequence galaxies, and in the galaxy where we can compare CO J=1-0 and J=3-2 sizes we find these are also very similar. Assuming a Galactic CO-to-H$_2$ conversion, we measure surface densities of $\Sigma_{mol}\sim1200$ M$_\odot$pc$^{-2}$ in projection and estimate $\Sigma_{mol}\sim500-900$ M$_\odot$pc$^{-2}$ deprojected. Finally, our data yields velocity-integrated Rayleigh-Jeans brightness temperature line ratios $r_{31}$ that are approximately unity. In addition to the similar disk sizes, the very similar line profiles in J=1-0 and J=3-2 indicate that both transitions sample the same kinematics, implying that their emission is coextensive. We conclude that in these two main sequence galaxies there is no evidence for significant excitation gradients or a large molecular reservoir that is diffuse or cold and not involved in active star-formation. We suggest that $r_{31}$ in very actively star-forming galaxies is likely an indicator of how well mixed the star formation activity and the molecular reservoir are.