The effects of ablation on the cross section of planetary envelopes at capturing planetesimals

Abstract

We explore the cross section of giant planet envelopes at capturing planetesimals of different sizes. For this purpose we employ two sets of realistic planetary envelope models (computed assuming for the protoplanetary nebula masses of 10 and 5 times the mass of the minimum mass solar nebula), account for drag and ablation effects and study the trajectories along which planetesimals move. The core accretion of these models has been computed in the oligarchic growth regime [Fortier, A., Benvenuto, O.G., Brunini, A., 2007. Astron. Astrophys. 473, 311 322], which has also been considered for the velocities of the incoming planetesimals. This regime predicts velocities larger that those used in previous studies of this problem. As the rate of ablation is dependent on the third power of velocity, ablation is more important in the oligarchic growth regime. We compute energy and mass deposition, fractional ablated masses and the total cross section of planets for a wide range of values of the critical parameter of ablation. In computing the total cross section of the planet we have included the contributions due to mass deposited by planetesimals moving along unbound orbits. Our results indicate that, for the case of small planetary cores and low velocities for the incoming planetesimals, ablation has a negligible impact on the capture cross section in agreement with the results presented in Inaba and Ikoma [Inaba, S., Ikoma, M., 2003. Astron. Astrophys. 410, 711 723]. However for the case of larger cores and high velocities of the incoming planetesimals as predicted by the oligarchic growth regime, we find that ablation is important in determining the planetary cross section, being several times larger than the value corresponding ignoring ablation. This is so regardless of the size of the incoming planetesimals.