A general model of resonance capture in planetary systems: first- and second-order resonances

摘要: Mean motion resonances are a common feature of both our own Solar system and extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semimajor axes change, for instance they migrate through protoplanetary disc. We use Hamiltonian model to thoroughly investigate the capture behaviour first- second-order resonances. Using this method, all same order described by one equation, with applications specific appropriate scaling. focus on limit where body is massless test particle other massive planet. quantify how probability into depends relative migration rate planet particle, particle's eccentricity. Resonant fails high rates, has decreasing higher eccentricities, although certain peaks at finite More planets particles eccentricities rates. also calculate libration amplitudes offset centres captured particles, change eccentricity if does not occur. Libration larger initial The allows complete description as it successively encounters several Data files containing integration grid output will available online. discuss implications scenarios: (i) Planet gas discs trapping or planetesimals resonances: we find that, classical prescriptions Type I migration, possible, lower mass those further from star should trap objects first-order closer than star. For fast enough no its suggest that present amplitude may signature epoch capture, suggesting (e.g. HD 128311). (ii) debris disc: resulting dynamical structure strongly planetesimal Translating spatial structure, expect clumpiness decrease significant level e ≲ 0.01 non-existent ≳ 0.1. (iii) Dust Poynting-Robertson (PR) drag: predict Mars have resonant ring zodiacal cloud, ≲25 per cent Earth, consistent published upper limits ring. To summarize, allow quick interpretation properties Kuiper Belt Objects, synthetic images disc structures quickly generated, which useful predicting interpreting made Atacama Large Millimeter Array (ALMA), Darwin/Terrestrial Finder (TPF) similar missions. (Less)