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We use high angular and spectral resolution (${\sim} 1''$ & 0.1 km s -1 ) images in $^{12}{\rm CO}$, $^{13}{\rm CO}$ $J=2\!\rightarrow\! 1$, $J=1\!\rightarrow\! 0$ and ${\rm C}^{18}{\rm O}$ $J=2\!\rightarrow\! 1$ coming from the IRAM interferometer to probe the vertical temperature distribution in the disk of DM Tau. We investigate here a new method based on the different opacities of the CO isotopomers to sample the temperature disk structure at various vertical scales inside the disk. Typically, the $^{12}{\rm CO}$ transitions are sampling at 2–4 scale heights, while the $^{13}{\rm CO}$ data are more likely tracing 1 scale height for the $J=2$–1, and the disk mid-plane for the $J=1$–0 line. At the disk scale at which the IRAM observations are sensitive ($R\geq 50$–60 AU), the analysis reveals a vertical temperature gradient. The outer layers where τ ($^{12}{\rm CO}$ $J=2\!\rightarrow\! 1$ $) \simeq 1$ are warmer (${\sim} 30$ K) than the inner layers probed by $^{13}{\rm CO}$ and ${\rm C}^{18}{\rm O}$ data (${\sim} 13$–20 K). These findings are consistent with the structure expected for flared irradiated disks around TTauri stars. We also observe that the outer radius of the disk is smaller in $^{13}{\rm CO}$ and ${\rm C}^{18}{\rm O}$ than in $^{12}{\rm CO}$. These differences in truncation radius are in agreement with photodissociation effects. We also note that the dynamical mass determination from CO is weakly affected by the temperature gradient.

Structure of the DM Tau Outer Disk: Probing the vertical kinetic temperature gradient