  Numerical simulations of asteroid break-ups, including both the fragmentation
of the parent body and the gravitational interactions between the fragments,
have allowed us to reproduce successfully the main properties of asteroid
families formed in different regimes of impact energy, starting from a
non-porous parent body. In this paper, using the same approach, we concentrate
on a single regime of impact energy, the so-called catastrophic threshold
usually designated by Q*D, which results in the escape of half of the target's
mass. Thanks to our recent implementation of a model of fragmentation of porous
materials, we can characterize Q*D for both porous and non-porous targets with
a wide range of diameters. We can then analyze the potential influence of
porosity on the value of Q*D, and by computing the gravitational phase of the
collision in the gravity regime, we can characterize the collisional outcome in
terms of the fragment size and ejection speed distributions, which are the main
outcome properties used by collisional models to study the evolutions of the
different populations of small bodies. We also check the dependency of Q*D on
the impact speed of the projectile. In the strength regime, which corresponds
to target sizes below a few hundreds of meters, we find that porous targets are
more difficult to disrupt than non-porous ones. In the gravity regime, the
outcome is controlled purely by gravity and porosity in the case of porous
targets. In the case of non-porous targets, the outcome also depends on
strength. We then propose some power-law relationships between Q*D and both
target's size and impact speed that can be used in collisional evolution
models.
