Constraining the cometary flux through the asteroid belt during the late heavy bombardment

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 trans-Neptunian 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 >= 200 km - created during the LHB and subsequent similar or equal to 4 Gyr of collisional evolution - which seems consistent with observations. However, more than 100 asteroid families with D-PB >= 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 less than or similar to 1.5 AU) are common. Given the freedom in the cometary-disruption law, we cannot 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.