We model the long-term evolution of the Hilda collisional family located in
the 3/2 mean-motion resonance with Jupiter. Its eccentricity distribution
evolves mostly due to the Yarkovsky/YORP effect and assuming that: (i) impact
disruption was isotropic, and (ii) albedo distribution of small asteroids is
the same as for large ones, we can estimate the age of the Hilda family to be
4−1+0Gyr. We also calculate collisional activity in the J3/2
region. Our results indicate that current collisional rates are very low for a
200\,km parent body such that the number of expected events over Gyrs is much
smaller than one.
The large age and the low probability of the collisional disruption lead us
to the conclusion that the Hilda family might have been created during the Late
Heavy Bombardment when the collisions were much more frequent. The Hilda family
may thus serve as a test of orbital behavior of planets during the LHB. We
tested the influence of the giant-planet migration on the distribution of the
family members. The scenarios that are consistent with the observed Hilda
family are those with fast migration time scales ≃0.3Myr to
3Myr, because longer time scales produce a family that is depleted
and too much spread in eccentricity. Moreover, there is an indication that
Jupiter and Saturn were no longer in a compact configuration (with period ratio
PS/PJ>2.09) at the time when the Hilda family was created