  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.
