Dust production in debris discs: constraints on the smallest grains

The surface energy constraint puts a limit on the smallest fragment $s_{surf}$ that can be produced after a collision. Based on analytical considerations, this mechanism has been recently identified as been potentially able to prevent the production of small dust grains in debris discs and cut off their size distribution at sizes larger than the blow-out size. We numerically investigate the importance of this effect to find under which conditions it can leave a signature in the small-size end of a disc's particle size distribution (PSD). An important part of this work is to map out, in a disc at steady-state, what is the most likely collisional origin for micron-sized grains, in terms of the sizes of their collisional progenitors. We implement, for the first time, the surface energy constraint into a collisional evolution code. We consider a debris disc extending from 50 to 100AU and 2 different stellar types. We also consider two levels of stirring in the disc: dynamically "hot" (e=0.075) and "cold" (e=0.01). For all cases, we derive $s_{surf}$ maps as a function of target and projectile sizes, $s_t$ and $s_p$, and compare them to equivalent maps for the dust-production rate. We then compute disc-integrated PSDs and estimate the imprint of the surface energy constraint. We find that the ($s_p$,$s_t$) regions of high $s_{surf}$ values do not coincide with those of high dust production rate. As a consequence, the surface energy constraint has generally a weak effect on the system's PSD. The maximum $s_{surf}$-induced depletion of $\mu$m-sized grains is $\sim 30$% and is obtained for a sun-like star and a dynamically hot case. For the e=0.01 cases, the surface energy effect is negligible compared to the massive small grain depletion induced by another mechanism: the natural imbalance between dust production and destruction rates in low-stirring discs identified by Thebault&Wu(2008).