Equation 10 is also multiplied by the conversion factor for Gyr to seconds B

Equation 10 is also multiplied by the conversion

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Equation (10) is also multiplied by the conversion factor for Gyr to seconds (B). Alternatively, the above equation could be rewritten with a reference escape flux that sums the mass flux contributions of H and O atoms (e.g., [ 113 , 114 , 187 ]) . Moreover, infrared coolants, which are not present in any of these simpler models (ibid), would also lower escape rates. Despite the above caveats, this equation is sufficient for the illustrative purposes shown below. If we assume that Venus was in a runaway greenhouse state between t = 1 and 7 Myr and t = 20–50 Myr, according to one model prediction (Figure 4 in Ramirez and Kaltenegger [ 51 ]), Equation (10) predicts that ~3 × 10 23 moles of H 2 (1 Earth ocean contains 7.8 × 10 22 moles of H 2 ) or ~4 Earth oceans could have been lost. In contrast, if Earth was in a runaway greenhouse state, this may have
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Geosciences 2018 , 8 , 280 22 of 48 occurred only briefly in the very beginning ( t = 1–2 Myr). Although Earth may have lost ~1 Earth ocean during this time, the Ramirez and Kaltenegger [ 51 ] model predicts that Earth was not in a runaway greenhouse state during the final stages of accretion when most of the water was delivered (e.g., [ 179 ]). In comparison, water losses for planets orbiting pre-main-sequence M-stars will be much higher than those for our solar system because M-star super-luminosity can last hundreds of millions of years to over 2 billion years, which can trigger runaway greenhouse conditions of comparable duration ([ 51 ]; Figures 10 and 11 ). Depending on the model assumptions (e.g., heating efficiency, flux partitioning) and stellar EUV flux parameterization used (e.g., [ 186 , 188 ]), young M-star planets that later settle into the main-sequence HZ can lose up to a few tens to several hundreds of Earth oceans of water (e.g., [ 51 , 114 , 183 , 189 191 ]). Geosciences 2018 , 8 , x FOR PEER REVIEW 22 of 48 Figure 11. The pre-main-sequence habitable zone for an M8. A planet originally located at 0.03 AU undergoes a runaway greenhouse for ~100 Myr before settling near the outer edge of the habitable zone at the start of the main-sequence. Based on work from Ramirez and Kaltenegger [51]. 8.2. The Ultimate Fate of Worlds during the Post-Main-Sequence As main-sequence stars evolve onto the post-main-sequence, stellar luminosity increases by a few orders of magnitude and the habitable zone sweeps outward, the opposite of what occurs during the pre-main-sequence (e.g., [130,131]). For example, our Sun is expected to become up to 3000 times brighter at the end of the red giant branch (RGB) phase as compared with today [131]. For more massive stars, the post-main-sequence luminosity increase is somewhat less, increasing ~1000× for a F1 star from the beginning of the main-sequence to the peak of the RGB (ibid). Stellar EUV fluxes are low during the post-main-sequence so hydrodynamic escape is no longer a major concern during this time [131]. However, post-main-sequence habitability faces other serious challenges. As a star brightens to become a red giant, the star gradually loses its mass, and high stellar winds are emitted, which erode planetary atmospheres throughout the stellar system (e.g., [192,193]).
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