  We measure the radial profile of the 12CO(1-0) to H_2 conversion factor (Xco)
in NGC 628. The H\alpha emission from the VENGA integral field spectroscopy is
used to map the star formation rate surface density (\Sigma_{SFR}). We estimate
the molecular gas surface density (\Sigma_{H2}) from \Sigma_{SFR} by inverting
the molecular star formation law (SFL), and compare it to the CO intensity to
measure Xco. We study the impact of systematic uncertainties by changing the
slope of the SFL, using different SFR tracers (H\alpha vs. far-UV plus 24\mu
m), and CO maps from different telescopes (single-dish and interferometers).
The observed Xco profile is robust against these systematics, drops by a factor
of 2 from R~7 kpc to the center of the galaxy, and is well fit by a gradient
\Delta log(Xco)=0.06\pm0.02 dex kpc^-1. We study how changes in Xco follow
changes in metallicity, gas density, and ionization parameter. Theoretical
models show that the gradient in Xco can be explained by a combination of
decreasing metallicity, and decreasing \Sigma_{H2} with radius. Photoelectric
heating from the local UV radiation field appears to contribute to the decrease
of Xco in higher density regions. Our results show that galactic environment
plays an important role at setting the physical conditions in star forming
regions, in particular the chemistry of carbon in molecular complexes, and the
radiative transfer of CO emission. We caution against adopting a single Xco
value when large changes in gas surface density or metallicity are present.
