Resolved CO(1-0) Emission and Gas Properties in Luminous Dusty Star-forming Galaxies at z=2-4

We present the results of a survey of CO(1-0) emission in 14 infrared luminous dusty star-forming galaxies (DSFGs) at 2 < z < 4 with the NSF's Karl G. Jansky Very Large Array. All sources are detected in (CO)-C-12(1-0), with an angular resolution of similar to 1 ''. Seven sources show extended and complex structure. We measure CO luminosities of (mu)L '(CO(1-0)) = 0.4-2.9 x 10(11) K km s(-1) pc(2), and molecular gas masses of (mu)M-H2 = 1.3-8.6 x 10(11) M-?, where (mu) is the magnification factor. The derived molecular gas depletion times of t(dep) = 40-460 Myr, cover the expected range of both normal star-forming galaxies and starbursts. Compared to the higher -J CO transitions previously observed for the same sources, we find CO temperature brightness ratios of r(32/10) = 0.4-1.4, r(43/10) = 0.4-1.7, and r(54/10) = 0.3-1.3. We find a wide range of CO spectral line energy distributions (SLEDs), in agreement with other high -z DSFGs, with the exception of three sources that are most comparable to Cloverleaf and APM08279+5255. Based on radiative transfer modeling of the CO SLEDs we determine densities of n(H2) = 0.3 -8.5 x 10(3) cm(-3) and temperatures of T-K = 100-200 K. Lastly, four sources are 2 detected in the continuum, three have radio emission consistent with their infrared-derived star formation rates, while HerBS-70E requires an additional synchrotron radiation component from an active galactic nucleus. Overall, we find that even though the sample is similarly luminous in the infrared, by tracing the CO(1-0) emission a diversity of galaxy and excitation properties are revealed, demonstrating the importance of CO(1-0) observations in combination to higher -J transitions.