A multi-wavelength analysis for interferometric (sub-)mm observations of protoplanetary disks Radial constraints on the dust properties and the disk structure

Context. The growth of dust grains from sub-μm to mm and cm size is the first step towards the formation of planetesimals. Theoretical models of grain growth predict dust properties to change as a function of disk radius, mass, age and other physical conditions. High angular resolution observations at several (sub-)mm wavelengths constitute the ideal tool to directly probe the bulk of dust grains and to investigate the radial distribution of their properties. Aims. We lay down the methodology for a multi-wavelength analysis of (sub-)mm and cm continuum interferometric observations to constrain self-consistently the disk structure and the radial variation of the dust properties. The computational architecture is massively parallel and highly modular. Methods. The analysis is based on the simultaneous fit in the uv-plane of observations at several wavelengths with a model for the disk thermal emission and for the dust opacity. The observed flux density at the different wavelengths is fitted by posing constraints on the disk structure and on the radial variation of the grain size distribution. Results. We apply the analysis to observations of three protoplanetary disks (AS 209, FT Tau, DR Tau) for which a combination of spatially resolved observations in the range „0.88mm to „10mm is available (from SMA, CARMA, and VLA). In these disks we find evidence of a decrease in the maximum dust grain size, amax, with radius. We derive large amax values up to 1 cm in the inner disk 15 AU ď R ď 30 AU and smaller grains with amax „ 1 mm in the outer disk (R Á 80 AU). Our analysis of the AS 209 protoplanetary disk confirms previous literature results showing amax decreasing with radius. Conclusions. Theoretical studies of planetary formation through grain growth are plagued by the lack of direct information on the radial distribution of the dust grain size. In this paper we develop a multi-wavelength analysis that will allow this missing quantity to be constrained for statistically relevant samples of disks and to investigate possible correlations with disk or stellar parameters.