Planetary migration and the effects of mean motion resonances on Jupiteris Trojan asteroids

We present results of several numerical simulations of fictitious Trojan asteroids under different resonant configurations of the outer planets, especially between Jupiter and Saturn. Although the present outer solar system is not locked in mean motion resonances, such commensurabilities may have been temporarily attained in the past if current theories of planetary migration are correct. By studying the evolution of Trojan-like test particles under these conditions, it is possible to obtain information related to the maximum variation of the semimajor axes of the two major Jovian planets, as well as insights on the duration of the migration itself. Results show that the 2S: 1J and 5S: 2J Jupiter-Saturn resonances introduce large instabilities in the Trojan region. In the case of 2S: 1J, a few thousand years are sufficient to expel all particles initially in tadpole orbits. For 5S: 2J, these may survive for up to 10(6) yr. The 7S: 3J commensurability, on the other hand, is much less disruptive. These results seem to indicate that the observed presence of the Jovian Trojans is compatible with a planetary migration as proposed by Han & Malhotra, in which the orbital distance between Jupiter and Saturn did not vary by more about 1 AU. Larger variations of the semimajor axes seem unlikely.