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It is key to constrain the gas surface density distribution, Sigma_gas, asfunction of disk radius in protoplanetary disks. In this work we investigate ifspatially resolved observations of rarer CO isotopologues may be good tracersof Sigma_gas. Physical-chemical models with different input Sigma_gas(R) arerun. The input disk surface density profiles are compared with the simulated13CO intensity radial profiles to check if and where the two follow each other.There is always an intermediate region in the disk where the slope of the 13COradial emission profile and Sigma_gas(R) coincide. At small radii the lineradial profile underestimates Sigma_gas, as 13CO emission becomes opticallythick. The same happens at large radii where the column densities become toolow and 13CO is not able to efficiently self-shield. If the gas surface densityprofile is a simple power-law of the radius, the input power-law index can beretrieved within 20% uncertainty if one choses the proper radial range. Ifinstead Sigma_gas(R) follows the self-similar solution for a viscously evolvingdisk, retrieving the input power-law index becomes challenging, in particularfor small disks. Nevertheless, it is found that the power-law index can be inany case reliably fitted at a given line intensity contour around 6 K km/s, andthis produces a practical method to constrain the slope of Sigma_gas(R).Application of such a method is shown in the case study of the TW Hya disk.Spatially resolved 13CO line radial profiles are promising to probe the disksurface density distribution, as they directly trace Sigma_gas(R)profile atradii well resolvable by ALMA. There, chemical processes like freeze-out andisotope selective photodissociation do not affect the emission, and, assumingthat the volatile carbon does not change with radius, no chemical model isneeded when interpreting the observations.

Probing the protoplanetary disk gas surface density distribution with $^{13}$CO emission