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Fig. 6

image

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 m1m2 and m2m3 (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 m1m2 and m2m3 by imposing (a3a1)|eq ≡ (a3a1)|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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