The growth of Jupiter and Saturn and the capture of Trojans

We have studied the capture of planetesimals in Trojan-type orbits by a growing proto-planet. The change of the gravity field due to the mass growth causes a significant fraction of planetesimals orbiting nearby to be trapped as Trojans of the proto-planet. After a planetesimal is captured on a Trojan-type orbit, the libration amplitude of its critical argument is consistently reduced by the further mass growth of the proto-planet. The dynamical mechanism is discussed and the characteristics of the Trojan population captured by Jupiter during its growth are analysed. We find an interesting mechanism which could explain the observed high inclination Trojans. The synergy of a Kozai secular resonance with the growth of Jupiter's mass generates high inclination Trojans from low inclination-high eccentricity planetesimals orbiting near the growing proto-planet. The libration amplitudes of the model Trojans trapped by the mass-growth of Jupiter are higher compared to those of the observed Trojans. A possible mechanism that decreases the libration amplitudes of the model population is collisional evolution. We also show that the simultaneous formation of Jupiter and Saturn strongly inhibits the capture of planetesimals as Saturn Trojans. The interference of the 1:1 resonance with a secular resonance and, in some cases, also with the 5:2 resonance with Jupiter (Innanen and Mikkola, 1989), generates instability and causes the ejection of most Saturn Trojans out of resonance before the end of Saturn's mass growth.