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We present an analysis of the relationship between the CO-H$_{2}$ conversionfactor ($\alpha_{\rm CO}$) and total mass surface density ($\Sigma_{\rm tot}$)in star-forming galaxies at $z < 1.5$. Our sample, which is drawn from the IRAMPlateau de Bure HIgh-$z$ Blue Sequence Survey (PHIBSS) and the CO LegacyDatabase for GASS (COLD GASS), includes 'normal,' massive star-forming galaxiesthat dominate the evolution of the cosmic star formation rate (SFR) at thisepoch and probe the $\Sigma_{\rm tot}$ regime where the strongest variation in$\alpha_{\rm CO}$ is observed. We constrain $\alpha_{\rm CO}$ via existing COobservations, measurements of the star formation rate, and an assumed moleculargas depletion time ($t_{\rm dep}$=$M_{\rm gas}$/SFR) --- the latter two ofwhich establish the total molecular gas mass independent of the observed COluminosity. For a broad range of adopted depletion times, we find that$\alpha_{\rm CO}$ is independent of total mass surface density, with littledeviation from the canonical Milky Way value. This runs contrary to a scenarioin which $\alpha_{\rm CO}$ decreases as surface density increases within theextended clouds of molecular gas that potentially fuel clumps of star formationin $z\sim1$ galaxies, similar to those observed in local ULIRGs. Instead, ourresults suggest that molecular gas, both at $z\sim0$ and $z\sim1$, is primarilyin the form of self-gravitating molecular clouds. While CO observations suggesta factor of $\sim3$ reduction in the average molecular gas depletion timebetween $z \sim 0$ and $z\sim1$, we find that, for typical galaxies, thestructure of molecular gas and the process of star formation at $z \sim 1$ isotherwise remarkably similar to that observed in local star-forming systems.

PHIBSS: Exploring the Dependence of the CO-H$_2$ Conversion Factor on Total Mass Surface Density at ${\it z} < 1.5$