Left: Radial profile of the ¹³CO data (in black) with three models that vary R_c and γ, that are convolved with a Gaussian beam similar to the observations. Parameters that are changed with respect to the fiducial model used in the main text are denoted in the legend. The shaded region marks the 1σ uncertainty on the azimuthal average of the data. Right: Radial profile of the ¹³CO (orange) and C¹⁸O emission (blue) in DR Tau. The dotted lines are a linear fit in log-log space. The fit is only performed in the pivot region (bold dotted line), where the line is optically thin but with enough column density to efficiently self-shield. The shaded regions mark the 1σ uncertainty on the azimuthal average of the data.