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Disk Radii and Grain Sizes in Herschel-Resolved Debris Disks

(Abridged) The radii of debris disks and the sizes of their dust grains are tracers of the formation mechanisms and physical processes operating in these systems. We use a sample of 34 debris disks spatially resolved in various Herschel programs to constrain them. While we modeled disks with both warm and cold components, we focus our analysis only on the cold outer disks, i.e. Kuiper-belt analogs. The disk radii derived from the resolved images reveal a large dispersion, but no significant trend with the stellar luminosity, which argues against ice lines as a dominant player in setting the debris disk sizes. Fixing the disk radii to those inferred from the resolved images, we model the spectral energy distributions to determine the dust temperatures and the grain size distributions. While the dust temperature systematically increases towards earlier spectral types, its ratio to the blackbody temperature at the disk radius decreases with the stellar luminosity. This is explained by an increase of typical grain sizes towards more luminous stars. The sizes are compared to the radiation pressure blowout limit $s_\text{blow}$ that is proportional to the stellar luminosity-to-mass ratio and thus also increases towards earlier spectral classes. The grain sizes in the disks of G- to A-stars are inferred to be several times $s_\text{blow}$ at all stellar luminosities, in agreement with collisional models of debris disks. The sizes, measured in the units of $s_\text{blow}$, appear to decrease with the luminosity, which may be suggestive of the disk's stirring level increasing towards earlier-type stars.