Other
Scientific paper
Sep 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999dda....31.0804s&link_type=abstract
American Astronomical Society, DDA meeting #31, #08.04
Other
Scientific paper
N-body simulations of the final stages of planet formation fail to form massive planets in the outer solar system unless a strong "drag" force is applied to damp the orbital eccentricites and inclinations of the largest planetesimals. A physical mechanism that could provide an effective drag is the excitation of collective gravitational waves in the disk of planetesimals. For example, Ward and Hahn (1998) have suggested that the planet Neptune could damp its orbital eccentricity by exciting apsidal waves in the Kuiper belt. I will describe a new numerical method for modeling the self-consistent dynamical interaction between a planet and an apsidal wave that can be inserted into an N-body simulation of planetary accretion. The most straight-forward method of simulating the wave would be to divide the disk into a collection of precessing wires that interact gravitationally with each other as well as with the planet. This is essentially the formalism described by Tremaine (1998) in his theory of "resonant relaxation." For linear waves, this method would require a large matrix multiplication each time step, where the dimension of the matrix is determined by the number of wires required to resolve the wave. A more efficient method is to approximate the solution of the wave equation with a truncated series of Chebyshev polynomials and use the collocation method to evaluate the gravitational interactions within the disk. Chebyshev polynomials are attractive because (1) they are eigenfunctions of the gravitational interaction operator for uniform density disks and (2) a much smaller number of polynomials (compared to wires) is required to resolve a given wave pattern in the disk. I will present the results of a simulation using the Chebyshev collocation method to model the dynamical evolution of a planet that is simultaneously excited by another planet and damped by an apsidal wave in the disk.
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