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We measure the absolute magnitude, $H$, distribution, $dN(H) \propto10^{\alpha H}$ of the scattering Trans-Neptunian Objects (TNOs) as a proxy fortheir size-frequency distribution. We show that the H-distribution of thescattering TNOs is not consistent with a single-slope distribution, but musttransition around $H_g \sim 9$ to either a knee with a shallow slope or to adivot, which is a differential drop followed by second exponentialdistribution. Our analysis is based on a sample of 22 scattering TNOs drawnfrom three different TNO surveys, the Canada-France Ecliptic Plane Survey(CFEPS, Petit et al. 2011), Alexandersen et al. (2014), and the Outer SolarSystem Origins Survey (OSSOS, Bannister et al. 2016), all of which provide wellcharacterized detection thresholds, combined with a cosmogonic model for theformation of the scattering TNO population. Our measured absolute magnitudedistribution result is independent of the choice of cosmogonic model. Based onour analysis, we estimate that number of scattering TNOs is (2.4-8.3)$\times10^5$ for $H_r < 12$. A divot $H$-distribution is seen in a variety offormation scenarios and may explain several puzzles in Kuiper Belt science. Wefind that a divot $H$-distribution simultaneously explains the observedscattering TNO, Neptune Trojan, Plutino, and Centaur $H$-distributions whilesimultaneously predicting a large enough scattering TNO population to act asthe sole supply of the Jupiter-Family Comets.

OSSOS II: A Sharp Transition in the Absolute Magnitude Distribution of the Kuiper Belt's Scattering Population