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Fig. 8

image

Logarithm of critical eccentricity eAR (top panels) and associated normalised final-rotation period ProtP (bottom panels) as functions of logarithms of orbital period (horizontal axis) and ocean depth (vertical axis), for σR = 10−5 s−1 (left) and σR = 10−6 s−1 (right). The calculated critical eccentricity is such that the final-rotation period satisfies the condition ProtP ≤ 0.95 to retain solely asynchronous states clearly separated from the synchronisation. In the eccentricity maps (top panels), the yellow colour designates the region of the non-resonant regime, where the critical eccentricity is high (log10 eAR ≈−0.6). Conversely, the blue shades designate the regions where eAR is low owing to the resonances of the oceanic tidal response. In the final-rotation maps, the yellow colour designates states that are close to synchronisation, while the dark blue colour corresponds to the 3/2 spin-orbit resonance, induced by the degree-3 eccentricity term. Values of parameters used for the solid part are given by Table 1. In both cases, the stellar mass is M = 0.09 M, the initial rotation rate is , and 10 Hough modes are taken into account in the calculation of the tidal response.

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