Vz-GAL Dusty Star-Forming Galaxies: Revisiting the CO-H2 Conversion Factor Tension

The CO luminosity-to-H 2 mass conversion factor (alpha CO) remains a debated uncertainty in determining molecular gas masses of high-redshift dusty star-forming galaxies (DSFGs). Dynamical mass constraints have often favored alpha CO=0.8 M (K km s-1 pc squared)-1, whereas dust- and radiative-transfer-based methods imply higher values. We revisit this ``tension" using the largest homogeneous sample of 21 unlensed z about1-4 DSFGs, with securely measured luminosities from the VLA survey and resolved (about 0.1) ALMA 1 mm dust continuum imaging. For 12 galaxies with robust modeling constraints, we derive molecular gas masses using dust spectral energy distribution modeling and the TUNER LVG framework, adopting a solar-metallicity gas-to-dust mass ratio of 100. Although not fully independent due to shared assumptions on dust properties, these approaches yield mutually consistent gas masses corresponding to alpha CO about1.5-11.5, with a median near the Galactic alpha CO=4.3. Isotropic virial dynamical masses agree with these gas masses when realistic molecular gas sizes are adopted, while our proposed ``mixed" (rotating, pressure-supported, thick-disk) estimator systematically underestimates dynamical masses, producing low alpha CO limits. Using GN20 (z=4.055) as a case study, we show that resolved gas geometry and kinematics reconcile the discrepancy with LVG-derived alpha CO. Our results suggest that current data do not require alpha CO=0.8, and intermediate to near-Galactic values remain dynamically viable given uncertainties in gas geometry, dust properties, and gas-to-dust ratios. Further progress in calibrating alpha CO in the early universe will require resolved molecular gas observations, physically motivated ISM modeling, and stringent constraints on dust properties.