Models of the dust structures around Vega-excess stars

We present models of the submillimetre dust emission around four Ve,oa-exce ss stars. The results are adjusted to fit simultaneously the spectral energ y distribution from millimetre through to optical wavelengths, as well as t he submillimetre image. The combination of spatially resolved images with c ontinuum fluxes over a range of wavelengths can remove some of the previous ambiguities in estimating the dust emission characteristics and circumstel lar distributions. Fomalhaut shows the brightest and best-resolved submillimetre image, and so gives the most unambiguous fit. Both the imaging and photometric results c an best be modelled by an edge-on thick torus, of inner radius 100 au, oute r radius 140 au and thickness similar to 120 au. The observed sharp outer b oundary cannot be fitted by a reasonable power-law density distribution. Fu rthermore, inside 100 au the density also drops abruptly, by at least a fac tor of 10. The structures of Vega and epsilon Eri are also best modelled by radially t hin rings rather than discs, in both cases viewed almost pole-on. However, there are clearly clumps :in their morphologies which cannot be explained b y simple axisymmetric models. The submillimetre disc in beta Pic can be adequately fitted by the same mod el as that used to account for the extended structure seen in scattered lig ht. However, the additional southwestern emission component, if it lies in the beta Pic system, must have a dust mass comparable to that of the whole visible disc. In all cases, the spectral energy distribution can be fitted by a single ri ng or disc-like structure. Grain sizes of a few tens of mu m and beta = 0.8 -1.1 provide the best fits, and we place limits on the dust size distributi on. The dust temperatures are too low and there is too much temperature variati on between the sources for grain sublimation to be effective at creating th e central holes. All rings are dominated by grain-grain collisions, and we discuss methods of coating and sustaining the observed structures. Most lik ely they arise from a mechanism such as planet shepherding The outer cut-of f may arise in a similar way, although external stripping of material is no t discounted.