In the Nice model , the late heavy bombardment ( LHB ) is related to an orbital instability of giant planets which causes a fast dynamical dispersion of a transneptunian cometary disk .
We study effects produced by these hypothetical cometary projectiles on main-belt asteroids .
In particular , we want to check whether the observed collisional families provide a lower or an upper limit for the cometary flux during the LHB .

We present an updated list of observed asteroid families as identified in the space of synthetic proper elements by the hierarchical clustering method , colour data , albedo data and dynamical considerations and we estimate their physical parameters .
We selected 12 families which may be related to the LHB according to their dynamical ages .
We then used collisional models and N-body orbital simulations to gain insight into the long-term dynamical evolution of synthetic LHB families over 4 { Gyr } .
We account for the mutual collisions between comets , main-belt asteroids , and family members , the physical disruptions of comets , the Yarkovsky/YORP drift in semimajor axis , chaotic diffusion in eccentricity/inclination , or possible perturbations by the giant-planet migration .

Assuming a “ standard ” size-frequency distribution of primordial comets , we predict the number of families with parent-body sizes D _ { PB } \geq 200 { km } – created during the LHB and subsequent \simeq 4 { Gyr } of collisional evolution – which seems consistent with observations .
However , more than 100 asteroid families with D _ { PB } \geq 100 { km } should be created at the same time which are not observed .
This discrepancy can be nevertheless explained by the following processes : i ) asteroid families are efficiently destroyed by comminution ( via collisional cascade ) , ii ) disruptions of comets below some critical perihelion distance ( q \lesssim 1.5 { AU } ) are common .

Given the freedom in the cometary-disruption law , we can not provide stringent limits on the cometary flux , but we can conclude that the observed distribution of asteroid families does not contradict with a cometary LHB .