OSSOS finds an Exponential Cutoff in the Size Distribution of the Cold Classical Kuiper belt

Abstract

The cold main classical Kuiper Belt consists of those non-resonant small solar system bodies with low orbital inclinations and orbital semi-major axes between 42.4 and 47.7 au. These objects likely formed \textit{in situ} and the population has experienced minimal collisional modification since formation. Using the Outer Solar System Origins Survey (OSSOS) ensemble sample and characterization, combined with constraints from deeper surveys and supported by evidence from the Minor Planet Center catalog and the Deep Ecliptic Survey, we determine the absolute magnitude $H_r$ distribution of the cold classical belt from $H_r\simeq5$ to 12 (roughly diameters of 400 km to 20 km). We conclude that the cold population's $H_r$ distribution exhibits an exponential cutoff at large sizes. Exponential cutoffs at large sizes are not a natural outcome of pair-wise particle accretion but exponentially tapered power-law size distributions are a feature of numerical simulations of planetesimal formation via a streaming instability. Our observation of an exponential cutoff agrees with previous observational inferences that no large objects ($D \gtrsim 400$ km) exist in the cold population. We note that the asymptotic slope of the $H_r$ distribution is consistent with $\alpha \sim 0.4$ and this asymptotic slope is also found in streaming instability modelling of planetesimal formation and is thus not necessarily associated with achieving collisional equilibrium. Studies of the transneptunian region are providing the parameters that will enable future streaming-instability studies to determine the initial conditions of planetesimal formation in the $\approx$45 au region of the Sun's protoplanetary disk.