Predicted line ratio (left) and gas temperature (right) at the height where the ¹³CO J = 6−5 (solid) and J =2−1 (dotted) transitions become optically thick for different gas cavity depths (no drop to a factor of 0.001, colors) in the Herbig disk models (top) and Τ Tauri models (bottom). We note the different temperature scales for the two types of stars. If the transitions are optically thin, the midplane temperature is shown, as that is the region that optically thin CO lines trace in the gas cavity. The dotted horizontal line in the left panels indicates the theoretical maximum value for the line ratio if both ¹³CO lines are optically thick and emit from the same disk layer.