I assume soil pCO 2 is 30 times that of the atmosphere following the lierature

I assume soil pco 2 is 30 times that of the

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volcanic outgassing rates scale with pressure. I assume soil pCO 2 is 30 times that of the atmosphere, following the lierature [ 78 ]. I also use a β of 0.35, which is consistent with experimental measurements for silicate rocks [ 82 84 ]. According to Figure 2 , the CO 2 partial pressure at the outer edge is 8 bar and S EFF is 0.36 ( d = 1/0.36 = 1.67 AU; from Equation (3)), which requires a volcanic outgassing rate ~4 times that of Earth’s to maintain a mean surface temperature of 273 K (according to Equation (5)). At a S EFF of 0.6, d is ( 1/0.6 ) ~1.3 AU, which corresponds to an atmospheric CO 2 partial pressure of ~0.08 bar (Figure 2 ). To support the same mean surface temperature of 273 K, the volcanic outgassing rate would only need to be ~1/5 as high, and lower than the Earth’s (Earth’s higher mean surface temperature requires larger volcanic outgassing rates). Thus, irrespective of the existence of limit cycles, planets with low volcanic outgassing rates can only support low atmospheric CO 2 pressures, requiring the planets to be closer to their stars to maintain warm surface conditions. Likewise, planets with high volcanic outgassing rates are located farther away at the same mean surface temperature, which is consistent with carbonate–silicate cycle predictions [ 33 ]. Although the possibility of limit cycles on some outer edge exoplanets remains intriguing, and would require observations to confirm, limit cycles likely did not occur on our planet because volcanic outgassing rates and solar insolation are both thought to have been high enough to support warm stable climates [ 76 ]. It is important to note that limit cycles should not be equated with snowball Earth episodes, which are temporary excursions into a globally frozen state thought to have occurred a few times throughout Earth’s history [ 85 , 86 ]. Whereas limit cycles are caused by energy fluctuations in the cycling of CO 2 , other external factors, including life, may have been the trigger for snowball Earth events. For instance, methanogenic production of CH 4 may have helped combat the faint young Sun problem on the early Earth until oxygen levels rose, which would have caused anaerobic methanogens to perish or become confined to restricted habitats [ 87 ]. These limit cycles have also been proposed as a possible transient warming mechanism for early Mars [ 78 ]. However, recent studies argue that limit cycles are unlikely to have occurred on early Mars for several reasons. First, observations of ancient terrains reveal no evidence of widespread glaciation [ 68 , 88 , 89 ], which is crucial for this mechanism. It is also difficult to transiently warm a very icy early Mars because melting the highly-reflective ice would require atmospheric CO 2 pressures that exceed available paleopressure constraints (e.g., [ 90 92 ]). At high enough ice cover, the atmosphere can collapse [ 68 , 93 ]. Moreover, Batalha et al. [ 78 ] had assumed a linear dependence between silicate weathering and the dissolution of H+ in ground water, which made their model especially susceptible to limit cycles. However, silicate rocks exhibit a fractional order dependence [ 82 84 ], which greatly
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