A Mechanism of Exciting Planetary Inclination and Eccentricity through a Residual Gas Disk

Abstract

Accordling to the theory of Kozai resonance, the initial mutual inclination between a small body and a massive planet in an outer circular orbit is as high as $\sim 39.2^{\circ }$ for pumping the eccentricity of the inner small body. Here we show that, with the presence of a residual gas disk outside two planetary orbits, the inclination can be reduced as low as a few degrees. The presence of disk changes the nodal precession rates and directions of the planet orbits. At the place where the two planets achieve the same nodal processing rate, vertical secular resonance would occur so that mutual inclination of the two planets will be excited, which might trigger the Kozai resonance between the two planets further. However, in order to pump an inner Jupiter-like planet, the conditions required for the disk and the outer planet are relatively strict. We develop a set of evolution equations, which can fit the N-body simulation quite well but be integrated within a much shorter time. By scanning the parameter spaces using the evolution equations, we find that, a massive planet ($10M_J$) at 30AU with $6^o$ inclined to a massive disk ($50M_J$) can finally enter the Kozai resonance with an inner Jupiter around the snowline. And a $20^{\circ }$ inclination of the outer planet is required for flipping the inner one to a retrograde orbit. In multiple planet systems, the mechanism can happen between two nonadjacent planets, or inspire a chain reaction among more than two planets. This mechanism could be the source of the observed giant planets in moderate eccentric and inclined orbits, or hot-Jupiters in close-in, retrograde orbits after tidal damping.

36 pages, 10 figures, Accepted for publication in ApJ

References in corpus (6)

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• TTV-determined Masses for Warm Jupiters and their Close Planetary Companions
• The effect of orbital damping during planet migration on the Inclination and Eccentricity Distributions of Neptune Trojans
• Secular resonances between bodies on close orbits II: prograde and retrograde orbits for irregular satellites
• Super-earths and mini-neptunes follow different orbital period-eccentricity relations