Effect of the initial value of ϖ_b − ϖ_c on the subsequent tidal evolution of a system. Panels a and b: ϖ_b(0) − ϖ_c(0) = 180° (Case I); panels c and d: ϖ_b(0) − ϖ_c(0) = 90° (Case II). The red dot and blue cross in panel a indicate the initial and current state, respectively, of Kepler-419. Panels e and f: valuesof a_b and e_b at t_end = 10⁸ yr (solid black curves), t_end = 10⁹ yr (dashed blue curves), and t_end = 2.3 × 10⁹ yr (the estimated age of the system; dot-dashed red curves) as functions of the initial value of ϖ_b − ϖ_c, which show that for a range of initial relative orientations, planet b can sustain a high value of e_b because it spends most of its time with a periastron distance which is too high for significant circularisation to occur. Panel g: evolution of planet b’s periastron distance, p_b, for Case I (blue) and Case II (red), the latter showing escape from libration and hence a permanently low value of p_b. Panel h: average value of p_b, ⟨p_b ⟩, as a functionof ϖ_b(0) − ϖ_c(0). Angles are in degrees.