OSSOS. VIII. The Transition Between Two Size Distribution Slopes in the Scattering Disk

TL;DR

This study analyzes the size distribution of scattering trans-Neptunian Objects using the largest sample to date, revealing a transition between two slopes and supporting a break in the distribution, which refines understanding of the distant small-body population.

Contribution

It provides the first detailed constraints on the size distribution break and slopes of scattering TNOs using a large, sensitive dataset, confirming the need for a broken power-law model.

Findings

A broken power-law better fits the data than a single slope.

The transition occurs around H=7.7 to 8.3, with different slopes.

The intrinsic population estimates are approximately 3 million for H<12.

Abstract

The scattering trans-Neptunian Objects (TNOs) can be measured to smaller sizes than any other distant small-body population. We use the largest sample yet obtained, 68 discoveries, primarily by the Outer Solar System Origins Survey (OSSOS), to constrain the slope of its luminosity distribution, with sensitivity to much fainter absolute $H$ magnitudes than previous work. Using the analysis technique in Shankman et al. (2016), we confirm that a single slope for the $H$-distribution is not an accurate representation of the scattering TNOs and Centaurs, and that a break in the distribution is required, in support of previous conclusions. A bright-end slope of $\alpha_b=0.9$ transitioning to a faint-end slope $\alpha_f$ of 0.4-0.5 with a differential number contrast $c$ from 1 (a knee) to 10 (a divot) provides an acceptable match to our data. We find that break magnitudes $H_b$ of 7.7 and 8.3, values both previously suggested for dynamically hot Kuiper belt populations, are equally non-rejectable for a range of $\alpha_f$ and $c$ in our statistical analysis. Our preferred divot $H$-distribution transitions to $\alpha_f=0.5$ with a divot of contrast $c=3$ at $H_b=8.3$, while our preferred knee $H$-distribution transitions to $\alpha_f=0.4$ at $H_b=7.7$. The intrinsic population of scattering TNOs required to match the OSSOS detections is $3\times10^6$ for $H_r<12$, and $9\times10^4$ for $H_r<8.66$ ($D\gtrsim100$~km), with Centaurs having an intrinsic population two orders of magnitude smaller.