Low strength and a shared size distribution connect the hot and cold Kuiper belt populations

Understanding how the observed size distribution of Kuiper Belt objects emerged from the primordial planetesimal population remains a major challenge in planetary science. In particular, the similarity between the size distributions of dynamically hot and cold populations in the 100 - 400 km range calls for a unified explanation. Motivated by this observational constraint and by theoretical models of pebble accretion, we model the coupled dynamical and collisional evolution of the trans-planetary disc under the early instability scenario. Here we show that a common planetesimal formation mechanism operating up to about 400 km and modulated by an exponential taper shape, combined with a transition to a shallow power law distribution in the inner disc, can reproduce the current size-frequency distributions of cold and hot populations. This outcome requires assuming that planetesimals were weaker to impacts than previously thought. Our results connect formation models with current observations, thereby constraining the early conditions of the Solar System and the properties of planetesimals.