Nekhoroshev Estimates for the Survival Time of Tightly Packed Planetary Systems
Abstract
Nbody simulations of nonresonant, tightly packed planetary systems have found that their survival time (I.e., time to first close encounter) grows exponentially with their interplanetary spacing and planetary masses. Although this result has important consequences for the assembly of planetary systems by giant collisions and their longterm evolution, this underlying exponential dependence is not understood from first principles, and previous attempts based on orbital diffusion have only yielded powerlaw scalings. We propose a different picture, where large deviations of the system from its initial conditions is due to a few slowly developing highorder resonances. Thus, we show that the survival time of the system T can be estimated using a heuristic motivated by Nekhoroshev's theorem, and obtain a formula for systems away from overlapping twobody meanmotion resonances as T/P={c_{1} a/∆a \exp (c_{2} ∆a/a/μ,SUP>1/4), where P is the average Keplerian period, a is the average semimajor axis, ∆a ≪ a is the difference between the semimajor axes of neighboring planets, μ is the planettostar mass ratio, and c_{1} and c_{2} are dimensionless constants. We show that this formula is in good agreement with numerical Nbody experiments for c_{1} = 5 × 10^{4} and c_{2} = 8.
 Publication:

The Astrophysical Journal
 Pub Date:
 March 2020
 DOI:
 10.3847/20418213/ab75dc
 arXiv:
 arXiv:1907.06660
 Bibcode:
 2020ApJ...892L..11Y
 Keywords:

 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 accepted for publication in the Astrophysical Journal