On collisional capture rates of irregular satellites around the gas-giant planets and the minimum mass of the solar nebula

We investigate the probability that an inelastic collision of planetesimals within the Hill sphere of the Jovian planets could explain the presence and orbits of observed irregular satellites. Capture of satellites via this mechanism is highly dependent on not only the mass of the protoplanetary disc, but also the shape of the planetesimal size distribution. We performed 2000 simulations for integrated time intervals ∼2 Myr and found that, given the currently accepted value for the minimum mass solar nebula and planetesimal number density based upon the Nesvorný et al. and Charnoz & Morbidelli size distribution dN∼D −3.5 dD, the collision rates for the different Jovian planets range between ∼0.6 and ≳170 Myr−1 for objects with radii 1 km ≤r≤ 10 km. Additionally, we found that the probability that these collisions remove enough orbital energy to yield a bound orbit was ≲10−5 and had very little dependence on the relative size of the planetesimals. Of these collisions, the collision energy between two objects was ≳103 times the gravitational binding energy for objects with radii ∼100 km. We find that capturing irregular satellites via collisions between unbound objects can only account for ∼0.1 per cent of the observed population, hence this cannot be the sole method of producing irregular satellites.