A dual-frequency sub-arcsecond study of proto-planetary disks at mm wavelengths: First evidence for radial variations of the dust properties

(Abridged) We attempt to characterize the radial distribution of dust in disks around a sample of young stars from an observational point of view, and, when possible, in a model-independent way, by using parametric laws. We used the IRAM PdBI interferometer to provide very high angular resolution (down to 0.4" in some sources) observations of the continuum at 1.3 mm and 3 mm around a sample of T Tauri stars in the Taurus-Auriga region. The sample includes single and multiple systems, with a total of 23 individual disks. We used track-sharing observing mode to minimize the biases. We fitted these data with two kinds of models: a "truncated power law" model and a model presenting an exponential decay at the disk edge ("viscous" model). ect evidence for tidal truncation is found in the multiple systems. The temperature of the mm-emitting dust is constrained in a few systems. Unambiguous evidence for large grains is obtained by resolving out disks with very low values of the dust emissivity index Beta. In most disks that are sufficiently resolved at two different wavelengths, we find a radial dependence of Beta, which appears to increase from low values (as low as 0) at the center to about 1.7 -- 2 at the disk edge. The same behavior could apply to all studied disks. It introduces further ambiguities in interpreting the brightness profile, because the regions with apparent Beta = 0 can also be interpreted as being optically thick when their brightness temperature is high enough. Despite the added uncertainty on the dust absorption coefficient, the characteristic size of the disk appears to increase with a higher estimated star age. These results provide the first direct evidence of the radial dependence of the grain size in proto-planetary disks.