Last couple years I missed this one: the HD 45364 system. 34.35 ±0.04 parsecs from here, in the southern "Bigger Dog" constellation, its star shines 0.637 L⊙. In 2009 its two known planets were seen to orbit at 3:2 resonance like Neptune and its plutini. (It was actually the first resonance raised to publication.) Zhexing Li, Stephen Kane and three others were curious what another decade of study might offer.
They went with a dynamical model, which is of course better than Kepler (meant for a two-body system only) and feasible for these narrow bounds. Their equations echo more Laplace:
φb = 3λc - 2λb + ϖb φc = 3λc - 2λb + ϖc
... but integrated numerically. They say the resonance is impermanent; the planets librate. It looks like 3:2 now but will shift, then shift back. That is the stability here. Eccentricity changes too, b 0-0.07 and c 0-0.03. Ah! Milankovitch. Which is about the limit of interplanetary interreactions, compare lately Gliese 1153 = HD 104067.
All this constrains the planets' mutual ratio of mass. It actually cuts the mass of c, which is unusual given that radial mass when not transiting is always given in M sini. They are considered 0.19 and 0.55 Mj. The angles i are such that sini approaches 1. That is: each planet orbit wobbles into edge-on to us some of the time.
As to how these giants got to the inner system: they were thought to be migrates from further-out. Two models allow for arrival into the quasiresonance here. Keeping in mind we still own no constraints on radius therefore density / composition.
The authors see space for exomoons; as migrates, these planets had space to accrete Jupiter-like menageries of rock and ice, before rolling inbound. At 0.9 AU, c's maximum eccentricity is 0.03; this half-Jovian cuts into the inner sector of the HZ where our Earth would be. Such moons as exist might include Iolikes, a rocky Ganymede around b, and an ice Ganymede around c which becomes a watermoon.
Li et al. suggest we keep watching this space for when b and maybe also c transit/s, as at least b should soon. With any moons.
If c does own a moon free of its planet's tides, that brings up habitability; although, I don't hold hopes for its internal magnet, being certainly tidally-locked and small. But: more HZ stretches beyond 0.9 AU. The authors think planets could survive here too. Nothing here has budged the Milankovitch dance; so if anything is out to 5 AU / 10 year period, it's not Jovian. But most likely is that even small planets will be migrates - therefore, I think, little Neptunes. Hycean.
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