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.
