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Measuring protoplanetary disk gas surface density profiles with ALMA

The gas and dust are spatially segregated in protoplanetary disks due to the vertical settling and radial drift of large grains. A fuller accounting of the mass content and distribution in disks therefore requires spectral line observations. We extend the modeling approach presented in Williams & Best (2014) to show that gas surface density profiles can be measured from high fidelity 13CO integrated intensity images. We demonstrate the methodology by fitting ALMA observations of the HD 163296 disk to determine a gas mass, Mgas = 0.048 solar masse, and accretion disk characteristic size Rc = 213au and gradient gamma = 0.39. The same parameters match the C18O 2--1 image and indicates an abundance ratio [13CO]/[C18O] of 700 independent of radius. To test how well this methodology can be applied to future line surveys of smaller, lower mass T Tauri disks, we create a large 13CO 2--1 image library and fit simulated data. For disks with gas masses 3-10 Jupiter masses at 150pc, ALMA observations with a resolution of 0.2-0.3 arcseconds and integration times of about 20 minutes allow reliable estimates of Rc to within about 10au and gamma to within about 0.2. Economic gas imaging surveys are therefore feasible and offer the opportunity to open up a new dimension for studying disk structure and its evolution toward planet formation.