SIMBAD references

According 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 ∼39.°2 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 to as low as a few degrees. The presence of the 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 (VSR) occurs so that the mutual inclination of the two planets will be excited, which might further trigger the Kozai resonance between the two planets. 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 can be integrated within a much shorter time. By scanning the parameter spaces using the evolution equations, we find that a massive planet (10 M_J) at 30 AU with an inclination of 6° to a massive disk (50 M_J) can finally enter the Kozai resonance with an inner Jupiter around the snowline. An inclination of 20° of the outer planet to the disk is required for flipping the inner one to a retrograde orbit. In multiple planet systems, the mechanism can happen between two nonadjacent planets or can 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.