Are debris discs self-stirred?

This paper aims to consider the evidence that debris discs are self-stirred by the formation of Pluto-size objects. A semi-analytical model for the dust produced during self-stirring is developed and applied to the statistics for A-stars. We show that there is no significant statistical difference between fractional excesses of A stars less than or similar to 50 Myr old, and therefore focus on reproducing the broad trends, the 'rise and fall' of the fraction of stars with excesses that the pre-stirred model of Wyatt et al. does not predict. Using a population model, we find that the statistics and trends can be reproduced with a self-stirring model of planetesimal belts with radius distribution N(r) alpha r(-0.8) between 15-120 au, with width dr = r/2. Discs must have this 15 au minimum radius in order to show a peak in disc fraction, rather than a monotonic decline. However, the marginal significance of the peak in the observations means that models with smaller minimum radii also formally fit the data. Populations of extended discs with fixed inner and/or outer radii fail to fit the statistics, due mainly to the slow 70 mu m evolution as stirring moves further out in the disc. This conclusion, that debris discs are narrow belts rather than extended discs, is independent of the significance of 24 mu m trends for young A-stars. Although the rise and fall is naturally explained by self-stirring, we show that the statistics can also be reproduced with a model in which discs are stirred by secular perturbations from a nearby eccentric planet. Detailed imaging, which can reveal warps, sharp edges and offsets in individual systems, is the best way to characterize the stirring mechanism. From a more detailed look at beta Pictoris Moving Group and TW Hydrae Association A-stars, we find that the disc around beta Pictoris is likely the result of secular stirring by the proposed planet at similar to 10 au; the structure of the HR 4796A disc also points to sculpting by a planet. The two other stars with discs, HR 7012 and eta Tel, possess transient hot dust, though the outer eta Tel disc is consistent with a self-stirred origin. We suggest that planet formation provides a natural explanation for the belt-like nature of debris discs, with inner regions cleared by planets that may also stir the disc, and the outer edges set by where planetesimals can form.