Locations of stationary/periodic solutions in mean motion resonances according to properties of dust grains
arXiv:1505.03987 · doi:10.1093/mnras/stw894
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.
13 pages, 6 figures, 1 table, accepted to MNRAS
References in corpus (7)
- Probing for Exoplanets Hiding in Dusty Debris Disks: Disk Imaging, Characterization, and Exploration with HST/STIS Multi-Roll Coronagraphy
- A narrow, edge-on disk resolved around HD 106906 with SPHERE
- Predictions for Shepherding Planets in Scattered Light Images of Debris Disks
- The effect of Poynting-Robertson drag on the triangular Lagrangian points
- Capture and evolution of dust in planetary mean-motion resonances: a fast, semi-analytic method for generating resonantly trapped disk images
- On the stability of dust orbits in mean motion resonances with considered perturbation from an interstellar wind
- Positions of equilibrium points for dust particles in the circular restricted three-body problem with radiation