Probing the structure of protoplanetary disks:: a comparative study of DM Tau, LkCa 15, and MWC 480

Context. The physical structure of proto-planetary disks is not yet well constrained by current observations. Millimeter interferometry is an essential tool to investigate young disks. Aims. We study the vertical and radial temperature distribution in a few well-known disks from an observational perspective. The surface density distribution of CO and HCO+ and the scale-height are also investigated. Methods. We report CO observations at sub-arcsecond resolution with the IRAM array of the disks surrounding MWC 480, LkCa 15, and DM Tau, and simultaneous measurements of HCO+ J = 1 -> 0. To derive the disk properties, we fit a standard disk model in which all parameters are power laws of the distance to the star to the data. Possible biases associated with the method are detailed and explained. We compare the properties of the observed disks with similar objects. Results. We find evidence for a vertical temperature gradient in the disks of MWC 480 and DM Tau, as in AB Aur, but not in LkCa 15. The disk temperatures increase with stellar effective temperature. Except for AB Aur, the bulk of the CO gas is at temperatures smaller than 17 K, below the condensation temperature on grains. We find the scale height of the CO distribution to be larger ( by 50%) than the expected hydrostatic scale height. The total amount of CO and the isotopologue ratio depends globally on the star. The more UV luminous objects appear to have more CO, but there is no simple dependency. The [(CO)-C-13]/[HCO+] ratio is similar to 600, with substantial variations between sources, and with radius. The temperature behavior is consistent with expectations, but published chemical models have difficulty reproducing the observed CO quantities. Changes in the slope of the surface density distribution of CO, compared to the continuum emission, suggest a more complex surface density distribution than is usually assumed in models. Vertical mixing seems an important chemical agent, as does photo-dissociation by the ambient UV radiation at the disk's outer edge.