# Reconstructing the size distribution of the primordial Main Belt

## TL;DR

This study estimates the primordial size distribution of main-belt asteroids by analyzing the pristine zone, removing family members, and using simulations to infer an upper bound on the original size distribution slope.

## Contribution

It introduces a novel method to isolate primordial asteroids and constrains the initial size distribution slope of the main belt asteroids.

## Key findings

- Primordial size distribution slope q ≈ -1.
- Upper bound for slope q = -1.43.
- No evidence of large primordial asteroid families in middle or pristine zones.

## Abstract

In this work we aim to constrain the slope of the size distribution of main-belt asteroids, at their primordial state. To do so we turn out attention to the part of the main asteroid belt between 2.82 and 2.96~AU, the so-called "pristine zone", which has a low number density of asteroids and few, well separated asteroid families. Exploiting these unique characteristics, and using a modified version of the hierarchical clustering method we are able to remove the majority of asteroid family members from the region. The remaining, background asteroids should be of primordial origin, as the strong 5/2 and 7/3 mean-motion resonances with Jupiter inhibit transfer of asteroids to and from the neighboring regions. The size-frequency distribution of asteroids in the size range $17<D(\rm{km})<70$ has a slope $q\simeq-1$. Using Monte-Carlo methods, we are able to simulate, and compensate for the collisional and dynamical evolution of the asteroid population, and get an upper bound for its size distribution slope $q=-1.43$. In addition, applying the same 'family extraction' method to the neighboring regions, i.e. the middle and outer belts, and comparing the size distributions of the respective background populations, we find statistical evidence that no large asteroid families of primordial origin had formed in the middle or pristine zones.