Formation and Evolution of the Dust in Galaxies. III. The Disk of the   Milky Way
  Models of chemical evolution of galaxies including the dust are nowadays required to decipher the high-z universe. In a series of three papers we have tackled the problem and set a modern chemical evolution model. In the first paper (Piovan et al., 2011a) we revised the condensation coefficients for the elements that typically are present in the dust. In the second paper (Piovan et al., 2011b) we have implemented the dust into the Padova chemical model and tested it against the observational data for the Solar Neighbourhood. In this paper we extend it to the whole Disk of the Milky Way (MW). The Disk is used as a laboratory to analyze the spatial and temporal behaviour of (i) several dust grain families with the aid of which we can describe the ISM, (ii) the abundances in the gas, dust, and total ISM of the elements present in the dust and (iii) the depletion of the same elements. The temporal evolution of the dust and gas across the Disk is calculated under the effect of radial flows and a central Bar. The gradients of the abundances of C, N, O, Mg, Si, S, Ca and Fe in gas and dust across the Disk are derived as a function of time. The theoretical gradients nicely reproduce those derived from Cepheids, OB stars, Red Giants and HII regions. This provides the backbone for the companion processes of dust formation and evolution across the Disk. We examine in detail the contributions to dust by AGB stars, SNae and grain accretion in the ISM at different galacto-centric distances. Furthermore, we examine the variation of the ratio silicates/carbonaceous grains with time and position in the Disk. Finally, some hints about the depletion of the elements in regions of high and low SFR (inner and outer Disk) are presented. The results obtained make it possible to extend the model to other astrophysical situations or different theoretical models like the chemo-dynamical N-Body simulations. 
L. Piovan, C. Chiosi, E. Merlin, T. Grassi, R. Tantalo, U. Buonomo and   L. P. Cassar\`a
astro-ph.GA astro-ph.CO astro-ph.SR