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Transition disks are protoplanetary disks with inner depleted dust cavitiesand excellent candidates to investigate the dust evolution under the existenceof a pressure bump. A pressure bump at the outer edge of the cavity allows dustgrains from the outer regions to stop their rapid inward migration towards thestar and efficiently grow to millimetre sizes. Dynamical interactions withplanet(s) have been one of the most exciting theories to explain the clearingof the inner disk. We look for evidence of the presence of millimetre dustparticles in transition disks by measuring their spectral index with new andavailable photometric data. We investigate the influence of the size of thedust depleted cavity on the disk integrated millimetre spectral index. Wepresent the 3mm photometric observations carried out with PdBI of fourtransition disks: LkHa330, UXTauA, LRLL31, and LRLL67. We use available valuesof their fluxes at 345GHz to calculate their spectral index, as well as thespectral index for a sample of twenty transition disks. We compare theobservations with two kind of models. In the first set of models, we considercoagulation and fragmentation of dust in a disk in which a cavity is formed bya massive planet located at different positions. The second set of modelsassumes disks with truncated inner parts at different radius and with power-lawdust size distributions, where the maximum size of grains is calculatedconsidering turbulence as the source of destructive collisions. We show thatthe integrated spectral index is higher for transition disks than for regularprotoplanetary disks. For transition disks, the probability that the measuredspectral index is positively correlated with the cavity radius is 95%. Highangular resolution imaging of transition disks is needed to distinguish betweenthe dust trapping scenario and the truncated disk case.

Millimetre spectral indices of transition disks and their relation to the cavity radius