Locations of stationary/periodic solutions in mean motion resonances according to properties of dust grains

TL;DR

This paper analytically and numerically investigates stationary and periodic solutions of dust grains in mean motion resonances, considering Poynting-Robertson effect and stellar wind, revealing conditions for long-term capture and specific orbital configurations.

Contribution

It provides a combined analytical and numerical framework for identifying stationary solutions in dust grain resonances, including effects of stellar forces and shifts from exact resonance.

Findings

Stationary solutions are periodic and can have shifted semimajor axes.

Numerical and analytical results for semimajor axis shifts are in excellent agreement.

Stationary solutions correspond to specific distributions of dust particle pericenters.

Abstract

The equations of secular evolution for dust grains in mean motion resonances with a planet are solved for stationary points. This is done including both Poynting-Robertson effect and stellar wind. The solutions are stationary in semimajor axis, eccentricity, and resonant angle, but allow the pericentre to advance. The semimajor axis of stationary solutions can be slightly shifted from the exact resonant value. The periodicity of the stationary solutions in a reference frame orbiting with the planet is analytically proved. The existence of periodic solutions in mean motion resonances means that analytical theory enables for dust particles also infinitely long capture times. The stationary solutions are periodic motions to which the eccentricity asymptotically approaches and around which the libration occurs. Using numerical integration of equation of motion are successfully found initial conditions corresponding to the stationary solutions. Numerically and analytically determined shifts of the semimajor axis form the exact resonance for the stationary solutions are in excellent agreement. The stationary solutions can be plotted by locations of pericenters in the reference frame orbiting with the planet. The pericenters are distributed in the space according to properties of dust particles.