2018MNRAS.479.3300K

When a protoplanetary disc loses gas, it leaves behind planets and one or more planetesimal belts. The belts get dynamically excited, either by planets ('planet stirring') or by embedded big planetesimals ('self-stirring'). Collisions between planetesimals become destructive and start to produce dust, creating an observable debris disc. Following Kenyon & Bromley, it is often assumed that self-stirring starts to operate as soon as the first ∼1000\hboxkm sized embedded 'Plutos' have formed. However, state-of-the-art pebble concentration models robustly predict planetesimals between a few \hboxkm and ∼200\hboxkm in size to form in protoplanetary discs rapidly, before then slowly growing into Pluto-sized bodies. We show that the time-scale, on which these planetesimals excite the disc sufficiently for fragmentation, is shorter than the formation time-scale of Plutos. Using an analytic model based on the Ida & Makino theory, we find the excitation time-scale to be T_ excite_ ~100 x_ m_^–1 M_*^–3/2 a^3\hboxMyr, where x_m is the total mass of a protoplanetary disc progenitor in the units of the Minimum-Mass Solar Nebula, a is its radius in the units of 100\hboxau, and M_* is the stellar mass in solar masses. These results are applied to a set of 23 debris discs that have been well resolved with ALMA or SMA. We find that the majority of these discs are consistent with being self-stirred. However, three large discs around young early-type stars do require planets as stirrers. These are 49 Cet, HD 95086, and HR 8799, of which the latter two are already known to have planets.