Weak S-type asteroids compared to C-type explain the observed size distribution of the main belt

The main belt, the region between the orbits of Mars and Jupiter, is home to more than 1 million asteroids. These asteroids form orbital groups, (i.e., asteroid families formed by collisions) and also spectral groups (taxonomies) with different chemical compositions, in particular carbonaceous (C-types) and silicate (S-types). In this paper, we extend the existing main-belt collisional model by finding the appropriate strength-versus-size dependence (also known as the scaling law) for these two groups. We used color indices and geometric albedos of 56 and 72 spectroscopically confirmed C- and S-types (control samples), along with statistical methods on 1,065,034 asteroids, to assign C-, S-, or other types. This allowed us to construct observed size-frequency distributions (SFDs) for several subpopulations constrained by either semimajor axis (inner, middle, outer) or taxonomy (C, S, other). Then we used a Monte Carlo collisional model to compute the long-term collisional evolution (4.5 billion years) and derive synthetic SFDs. Our best-fit scaling laws indicate that S-types must be weaker below approximately 0.2, than C-types to explain the deficiency of asteroids in the inner part of the main belt near (and below) the observational limit. This may correspond to differences in chemical composition or material porosity. Future research will focus on the scaling laws of asteroids with rare or "extreme" taxonomies (e.g., V, M).