  From the results of a comprehensive asteroid population evolution model, we
conclude that the YORP-induced rotational fission hypothesis can be consistent
with the observed population statistics of small asteroids in the main belt
including binaries and contact binaries. The foundation of this model is the
asteroid rotation model of Marzari et al. (2011), which incorporates both the
YORP effect and collisional evolution. This work adds to that model the
rotational fission hypothesis and the binary evolution model of Jacobson &
Scheeres (2011). The asteroid population evolution model is highly constrained
by these and other previous works, and therefore it has only two significant
free parameters: the ratio of low to high mass ratio binaries formed after
rotational fission events and the mean strength of the binary YORP (BYORP)
effect. We successfully reproduce characteristic statistics of the small
asteroid population: the binary fraction, the fast binary fraction,
steady-state mass ratio fraction and the contact binary fraction. We find that
in order for the model to best match observations, rotational fission produces
high mass ratio ($> 0.2$) binary components with four to eight times the
frequency as low mass ratio ($< 0.2$) components, where the mass ratio is the
mass of the secondary component divided by the mass of the primary component.
This is consistent with post-rotational fission binary system mass ratio being
drawn from either a flat or a positive and shallow distribution, since the high
mass ratio bin is four times the size of the low mass ratio bin; this is in
contrast to the observed steady-state binary mass ratio, which has a negative
and steep distribution. This can be understood in the context of the
BYORP-tidal equilibrium hypothesis, which predicts that low mass ratio binaries
survive for a significantly longer period of time than high mass ratio systems.
