A&A 605, A72 (2017) DOI: 10.1051/0004-6361/201630022 Astronomy c ESO 2017 Astrophysics& AMD-stability and the classification of planetary systems? J. Laskar and A. C. Petit ASD/IMCCE, CNRS-UMR 8028, Observatoire de Paris, PSL, UPMC, 77 Avenue Denfert-Rochereau, 75014 Paris, France e-mail:
[email protected] Received 7 November 2016 / Accepted 23 January 2017 ABSTRACT We present here in full detail the evolution of the angular momentum deficit (AMD) during collisions as it was described in Laskar (2000, Phys. Rev. Lett., 84, 3240). Since then, the AMD has been revealed to be a key parameter for the understanding of the outcome of planetary formation models. We define here the AMD-stability criterion that can be easily verified on a newly discovered planetary system. We show how AMD-stability can be used to establish a classification of the multiplanet systems in order to exhibit the planetary systems that are long-term stable because they are AMD-stable, and those that are AMD-unstable which then require some additional dynamical studies to conclude on their stability. The AMD-stability classification is applied to the 131 multiplanet systems from The Extrasolar Planet Encyclopaedia database for which the orbital elements are sufficiently well known. Key words. chaos – celestial mechanics – planets and satellites: dynamical evolution and stability – planets and satellites: formation – planets and satellites: general 1. Introduction motion resonances (MMR, Wisdom 1980; Deck et al. 2013; Ramos et al. 2015) could justify the Hill-type criteria, but the The increasing number of planetary systems has made it nec- results on the overlap of the MMR island are valid only for close essary to search for a possible classification of these planetary orbits and for short-term stability.