AMD-stability of Planetary Systems

Due to the increasing large number of discovered planetary systems, it becomes important to set up some framework for a rapid understanding of the dynamics of the discovered systems, without the need of computer intensive numerical simulations. This has been the goal of our recent work on AMD-stability.

In a planetary system, the AMD (Angular Momentum Deficit) is the difference between the planar circular angular momentum and the total angular momentum. This quantity is conserved between collisions in the average system, and decreases during collisions.

This leads to the concept of AMD-stability. A planetary system is AMD-stable if the AMD in the system is not sufficient to allow collisions. The advantage of this notion is that it becomes possible to verify very quickly whether a newly discovered planetary system is stable or potentially unstable, without any numerical integration of the equations of motion. These principles have been applied to the 131 multiple planetary systems of the exoplanet.eu database whose orbital elements are sufficiently well determined (Laskar and Petit, 2017a).

AMD-stability, based on the secular evolution, addresses to long time stability, in absence of mean motion resonances. On the other hand, criterions for short term stability have been established on the basis of Hill radius (Marchal & Bozis 1982; Gladman 1993; Pu & Wu 2015) or on the overlap of mean motion resonances ( Wisdom 1980; Duncan et al. 1989; Mustill & Wyatt 2012; Deck et al. 2013). Both long and short time scales can be combined owing some modification of the AMD-stability criterion (Petit, Laskar & Boué, 2017b). Finally, Hill stability can be expressed in a very effective and simple way in the AMD framework ( Petit, Laskar, Boué, 2018).

Ref: Laskar, J. and Petit, A.C., 2017a, AMD-stability and the classification of planetary systems, A&A, 605, A72 Petit, A.C. Laskar, J. and Boué, G., 2017b, AMD-stability in presence of first order mean motion resonances, A&A, 607, A35 Petit, A.C. Laskar, J. and Boué, G., 2018, Hill stability in the AMD framework, A&A, 617, A93