A multi-wavelength analysis for interferometric (sub-)mm observations of
  protoplanetary disks: radial constraints on the dust properties and the disk
  structure
  Theoretical models of grain growth predict dust properties to change as a
function of protoplanetary disk radius, mass, age and other physical
conditions. 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. 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. 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), finding evidence of a decreasing maximum
dust grain size (a_max) with radius. We derive large a_max values up to 1 cm in
the inner disk between 15 and 30 AU and smaller grains with a_max~1 mm in the
outer disk (R > 80AU). 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.
