C2D Spitzer-IRS spectra of disks around T Tauri stars V. Spectral decomposition

(Abridged) Dust particles evolve in size and lattice structure in protoplanetary disks, due to coagulation, fragmentation and crystallization, and are radially and vertically mixed in disks. This paper aims at determining the mineralogical composition and size distribution of the dust grains in disks around 58 T Tauri stars observed with Spitzer/IRS. We present a spectral decomposition model that reproduces the IRS spectra over the full spectral range. The model assumes two dust populations: a warm component responsible for the 10μm emission arising from the disk inner regions and a colder component responsible for the 20-30μm emission, arising from more distant regions. We show evidence for a significant size distribution flattening compared to the typical MRN distribution, providing an explanation for the usual boxy 10μm feature profile generally observed. We reexamine the crystallinity paradox, observationally identified by Olofsson et al. (2009), and we find a simultaneous enrichment of the crystallinity in both the warm and cold regions, while grain sizes in both components are uncorrelated. Our modeling results do not show evidence for any correlations between the crystallinity and either the star spectral type, or the X-ray luminosity (for a subset of the sample). The size distribution flattening may suggests that grain coagulation is a slightly more effective process than fragmentation in disk atmospheres, and that this imbalance may last over most of the T Tauri phase. This result may also point toward small grain depletion via strong stellar winds or radiation pressure in the upper layers of disk. The non negligible cold crystallinity fractions suggests efficient radial mixing processes in order to distribute crystalline grains at large distances from the central object, along with possible nebular shocks in outer regions of disks that can thermally anneal amorphous grains.