Fig. 6

Top row: analytical maps constructed for Kepler-305 as explained in Sect. 3.2. Panel a: we plot the quantity , which represents how close the system is now to some resonant equilibrium point, for different mass ratios m1 ∕m2 and m2 ∕m3 (each point in this plot is constructed by repeating the procedure described in Fig. 5). We notice that
changes verylittle with the mass ratios, and is of the order of ~0.002. Comparing with Fig. 9, we see that this can be the case by pure chance only in ~ 15% of randomly generated systems close to the 3:2–2:1 mean motion resonance chain. Panel b: we show a map of the quantity
representing the equilibrium orbital configuration that is selected at each fixed value of m1 ∕m2 and m2 ∕m3 by imposing (a3∕a1)|eq ≡ (a3∕a1)|obs. Bottom row: numerical maps constructed for Kepler-305 as explained in Sect. 3.3. We show numerical maps of
in panel c and
in panel d, analogous to the analytical plots above (over a slightly smaller range of mass ratios for simplicity). These are intended to validate the analytical maps, and show very good agreement between corresponding panels.
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