Abstract

We have confronted the predictions of the steady state collisional evolution model with the results of the searches for cold debris disks around AFGKM type stars conducted with Spitzer and, more recently, with the Herschel DEBRIS program. We used a novel technique to determine the parameters of the disk population evolved with this model over the star ages in fitting, not the detection frequencies in these surveys, but the shape of the distribution of the fractional dust luminosities observed. In this approach, we stipulate that the initial disk mass distribution is bimodal and that only high-mass collisionally-dominated disks are detected. The best determined parameter of the model is the diameter Dc of the largest planetesimals in the collisional cascade of the model. It ranges between 2 and 60 km, consistently for disks around both A- and FGK-type stars. It is remarkable that this range is consistent with the break found at around 30km in the Kuiper belt objects size distribution. This break separates the subpopulations of the largest primordial objects from the eroded planetesimals. Finally, we make the assumption that the same disk population surrounds the M-dwarfs that have been searched and we study to what degree the apparently less frequent debris disks around this type of stars is consistent with the model.

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