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 ( 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 .