The osteology of spiral structure generated by major planets in proto-planetary disks. (arXiv:1910.11167v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Sanders_R/0/1/0/all/0/1">R.H. Sanders</a>
Here I describe numerical calculations of the motion of particles in a disk
about a solar-mass object perturbed by a planet on a circular orbit with mass
greater than 0.001 of the stellar mass. A simple algorithm for simulating bulk
viscosity is added to the ensemble of particles and the response of the disk is
followed for several planet rotation periods. Spiral structure forms near the
inner Lindblad resonance (2-1) and extends to the planetary orbit radius
(co-rotation). As for gaseous disks on a galactic scale perturbed by a weak
rotating bar-like distortion, this is shown to be related to the appearance of
two perpendicular families of periodic orbits near the resonance combined with
dissipation which inhibits the crossing of streamlines. Spiral density
enhancements result from the crowding of streamlines due to the gradual shift
between families. The results, such as the dependence of pitch-angle on radius
and the asymmetry of the spiral features, resemble those of sophisticated
calculations that include more physical effects. This illustrates that the
fundamental process of spiral formation via interaction with planets in such
disks is due to orbital motion in a perturbed Keplerian field combined with
dissipation.
Here I describe numerical calculations of the motion of particles in a disk
about a solar-mass object perturbed by a planet on a circular orbit with mass
greater than 0.001 of the stellar mass. A simple algorithm for simulating bulk
viscosity is added to the ensemble of particles and the response of the disk is
followed for several planet rotation periods. Spiral structure forms near the
inner Lindblad resonance (2-1) and extends to the planetary orbit radius
(co-rotation). As for gaseous disks on a galactic scale perturbed by a weak
rotating bar-like distortion, this is shown to be related to the appearance of
two perpendicular families of periodic orbits near the resonance combined with
dissipation which inhibits the crossing of streamlines. Spiral density
enhancements result from the crowding of streamlines due to the gradual shift
between families. The results, such as the dependence of pitch-angle on radius
and the asymmetry of the spiral features, resemble those of sophisticated
calculations that include more physical effects. This illustrates that the
fundamental process of spiral formation via interaction with planets in such
disks is due to orbital motion in a perturbed Keplerian field combined with
dissipation.
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