We use Atacama Large Millimeter Array (ALMA) observations of four submillimeter galaxies (SMGs) at z ~ 2–3 to investigate the spatially resolved properties of the interstellar medium (ISM) at scales of 1–5 kpc (0farcs1–0farcs6). The velocity fields of our sources, traced by the 12CO(J = 3–2) emission, are consistent with disk rotation to the first order, implying average dynamical masses of ~3 × 1011 M⊙ within two half-light radii. Through a Bayesian approach we investigate the uncertainties inherent to dynamically constraining total gas masses. We explore the covariance between the stellar mass-to-light ratio and CO-to-H2 conversion factor, α CO, finding values of αCO=1.1−0.7+0.8 for dark matter fractions of 15%. We show that the resolved spatial distribution of the gas and dust continuum can be uncorrelated to the stellar emission, challenging energy balance assumptions in global SED fitting. Through a stacking analysis of the resolved radial profiles of the CO(3–2), stellar, and dust continuum emission in SMG samples, we find that the cool molecular gas emission in these sources (radii ~5–14 kpc) is clearly more extended than the rest-frame ~250 μm dust continuum by a factor >2. We propose that assuming a constant dust-to-gas ratio, this apparent difference in sizes can be explained by temperature and optical depth gradients alone. Our results suggest that caution must be exercised when extrapolating morphological properties of dust continuum observations to conclusions about the molecular gas phase of the interstellar medium (ISM)
