Eccentricity distribution in the main asteroid belt

TL;DR

This study analyzes the eccentricity distribution of over 64,000 main belt asteroids, revealing differences between proper and osculating eccentricities and suggesting a late dynamical excitation event affecting the inner belt.

Contribution

It provides a detailed analysis of asteroid eccentricities, highlighting the dependence on heliocentric distance and proposing a model for the inner belt's excitation history.

Findings

Proper eccentricities deviate from Rayleigh distribution, especially in the inner belt.

Eccentricities are independent of asteroid size but vary with heliocentric distance.

Inner belt eccentricities suggest a late dynamical excitation event.

Abstract

The observationally complete sample of the main belt asteroids now spans more than two orders of magnitude in size and numbers more than 64,000 (excluding collisional family members). We undertook an analysis of asteroids' eccentricities and their interpretation with simple physical models. We find that Plummer's (1916) conclusion that the asteroids' eccentricities follow a Rayleigh distribution holds for the osculating eccentricities of large asteroids, but the proper eccentricities deviate from a Rayleigh distribution: there is a deficit of eccentricities smaller than $\sim0.1$ and an excess of larger eccentricities. We further find that the proper eccentricities do not depend significantly on asteroid size but have strong dependence on heliocentric distance: the outer asteroid belt follows a Rayleigh distribution, but the inner belt is strikingly different. Eccentricities in the inner belt can be modeled as a vector sum of a primordial eccentricity vector of random orientation and magnitude drawn from a Rayleigh distribution of parameter $\sim0.06$, and an excitation of random phase and magnitude $\sim0.13$. These results imply that a late dynamical excitation of the asteroids occurred, it was independent of asteroid size, it was stronger in the inner belt than in the outer belt. We discuss implications for the primordial asteroid belt and suggest that the observationally complete sample size of main belt asteroids is large enough that more sophisticated model-fitting of the eccentricities is warranted and could serve to test alternative theoretical models of the dynamical excitation history of asteroids and its links to the migration history of the giant planets.