that limit cycles could occur on outer edge exoplanets as initially predicted

That limit cycles could occur on outer edge

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that limit cycles could occur on outer edge exoplanets, as initially predicted in 1D studies [ 79 ]. Geosciences 2018 , 8 , x FOR PEER REVIEW 9 of 48 outpace volcanic outgassing, the planet freezes instead. The process of cycling into and out of such warm conditions is called a “limit cycle” (Figure 4). Planets that receive low levels of stellar insolation, like those near the outer edge of the habitable zone, and with low enough CO 2 outgassing rates, are susceptible to these unstable climates [78,79]. Limit cycle frequency is a strong function of the soil CO 2 pressure and the volcanic outgassing flux [79]. Recent 3D calculations [80] also confirm that limit cycles could occur on outer edge exoplanets, as initially predicted in 1D studies [79]. Figure 4. Maximum surface temperature (black curve) and pCO 2 level (green curve) for an Earth-like planet with a volcanic outgassing rate 10% of that of Earth’s orbiting a G-star ( A ) and F-star ( B ) for S EFF = 0.7. Transient periods of warming during which temperatures exceeding the freezing point of water (dashed line) are followed by extended periods of global glaciation (adapted from Haqq-Misra et al. [79]). Haqq-Misra et al. [79] argued that this mechanism decreases HZ width on planets with low volcanic outgassing rates. Although it may be possible that limit cycles occur on some exoplanets [76,80], this particular result is a direct prediction of the carbonate–silicate cycle and does not depend on the occurrence of limit cycles. This can be demonstrated by employing a recent weathering rate parameterization [81] and assuming that volcanic outgassing and weathering rates are equal at steady state (Equation (5)): A B Figure 4. Maximum surface temperature (black curve) and pCO 2 level (green curve) for an Earth-like planet with a volcanic outgassing rate 10% of that of Earth’s orbiting a G-star ( A ) and F-star ( B ) for S EFF = 0.7. Transient periods of warming during which temperatures exceeding the freezing point of water (dashed line) are followed by extended periods of global glaciation (adapted from Haqq-Misra et al. [ 79 ]). Haqq-Misra et al. [ 79 ] argued that this mechanism decreases HZ width on planets with low volcanic outgassing rates. Although it may be possible that limit cycles occur on some exoplanets [ 76 , 80 ], this particular result is a direct prediction of the carbonate–silicate cycle and does not depend on the occurrence of limit cycles.
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Geosciences 2018 , 8 , 280 10 of 48 This can be demonstrated by employing a recent weathering rate parameterization [ 81 ] and assuming that volcanic outgassing and weathering rates are equal at steady state (Equation (5)): W W EARTH = pCO 2 p EARTH β e [ k act ( T sur f - 288 )] h 1 + k run ( T sur f - 288 ) i 0.65 (5) Here, W is the weathering rate, k act is an activation energy (0.09), T surf is surface temperature, k run is a runoff efficiency factor (0.045), and β is the dependence of p CO 2 on W . W earth and P earth are the soil weathering rates and soil pCO 2 values, respectively, for the Earth. As predicted for planets that have an operational carbonate–silicate cycle, this parameterization assumes that weathering and volcanic outgassing rates scale with pressure. I assume soil
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