The self gravity effect on the orbital stability of Twotinos

TL;DR

This paper uses N-body simulations to analyze how self-gravity impacts the orbital stability of Twotinos, revealing that their total mass is significantly reduced by self-gravity and planetary perturbations, affecting models of solar system evolution.

Contribution

It provides a new formula for the timescale of Twotino instability considering self-gravity, and concludes the primordial mass was much lower than previously thought.

Findings

Half of Twotinos become unstable in a timescale given by the new formula.

The total mass of Twotinos is reduced to about 0.01 Earth masses.

Self-gravity and planetary perturbations significantly influence Twotino stability.

Abstract

We investigate how the self gravity changes the orbital stability of Twotinos using N-body simulations in which the gravitational interaction between planetesimals are fully calculated. We show the timescale in which the half of Twotinos becomes unstable, t_{half}, obey the formula, t_{half} = 4 \times 106(Mtot0.1M\oplus)-1(mp7.6 \times 1023g)-1(hi2i1/20.002)(years), if we assume the primordial planetesimals disk have the power low surface mass density, \Sigma = \Sigma_0 \times r-2/3. Where Mtot, mp, hi2i1/2 are the total mass of large bodies of Twotinos, the maximum mass of planetesimals, and the inclination dispersion. With this formulae, we conclude the total mass of Twotinos is reduced to the order of 0.01 M\oplus by the self gravity and secular perturbation of the Planets even if there was huge mass such as several order of the earth mass in 1:2 MMR of Neptune at the early age of the solar system. These results will invoke reexamination to many previous works which tried to explain the dynamical evolution of TNOs.