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A Secular Resonant Origin for the Loneliness of Hot Jupiters

  • Authors: Christopher Spalding, and Konstantin Batygin

2017 The Astronomical Journal 154 93.

  • Provider: AAS Journals

Caption: Figure 2.

The time evolution of the nodal regression frequencies for both planets as the host star contracts. The requirement to turn a giant planet–super Earth system into an apparently lonely giant is that ﹩{\nu }_{2}\lt {\nu }_{1}﹩ (i.e., the red line is above the blue line) at the point when the disk dissipates, such that a point is crossed where the two frequencies are roughly commensurate. As argued in the text, this will always happen as the giant grows, but can be bypassed due to planet–disk interactions. If this is the picture dominating the hot Jupiter–warm Jupiter distribution, we would expect to see more hot Jupiters with companions around faster-rotating, massive stars and a gradual drop in companion fraction toward smaller semimajor axes. Parameters used in this illustrative figure are ﹩{m}_{1}/{M}_{\star }={10}^{-3},{m}_{2}/{M}_{\star }={10}^{-5},{a}_{1}=0.04\,{\rm{au}},{a}_{2}\,=0.1\,{\rm{au}},{P}_{\star }=3\,{\rm{days}}﹩ around a solar mass star. Resonance is encountered at ﹩t=2.86\,{\rm{Myr}}﹩.

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