Analytical investigation of the decrease in the size of the habitable zone due to limited CO${}_2$ outgassing rate

Abstract

The habitable zone concept is important because it focuses the scientific search for extraterrestrial life and aids the planning of future telescopes. Recent work has shown that planets near the outer edge of the habitable zone might not actually be able to stay warm and habitable if CO${}_2$ outgassing rates are not large enough to maintain high CO${}_2$ partial pressures against removal by silicate weathering. In this paper I use simple equations for the climate and CO${}_2$ budget of a planet in the habitable zone that can capture the qualitative behavior of the system. With these equations I derive an analytical formula for an effective outer edge of the habitable zone, including limitations imposed by the CO${}_2$ outgassing rate. I then show that climate cycles between a Snowball state and a warm climate are only possible beyond this limit if the weathering rate in the Snowball climate is smaller than the CO${}_2$ outgassing rate (otherwise stable Snowball states result). I derive an analytical solution for the climate cycles including a formula for their period in this limit. This work allows us to explore the qualitative effects of weathering processes on the effective outer edge of the habitable zone, which is important because weathering parameterizations are uncertain.

accepted at ApJ

References in corpus (6)

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• GCM Simulations of Unstable Climates in the Habitable Zone
• Habitable Snowballs: Temperate Land Conditions, Liquid Water, and Implications for CO${}_2$ Weathering
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• High pCO${}_2$ reduces sensitivity to CO${}_2$ perturbations on temperate, Earth-like planets throughout most of habitable zone
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• The Effect of Seafloor Weathering on Planetary Habitability
• The Drake Equation as a Function of Spectral Type and Time
• Carbon cycle instability for high-$\mathrm{C}{\mathrm{O}}_2$ exoplanets: Implications for habitability
• Simple Stochastic Modeling of Snowball Probability Throughout Earth History
• Snowball Bistability Vanishes at Moderate Orbital Eccentricity
• Earth-Like: An education & outreach tool for exploring the diversity of planets like our own
• Not Earth-like Yet Temperate? More Generic Climate Feedback Configurations Still Allow Temperate Climates in Habitable Zone Exo-Earth Candidates
• The Onset of a Globally Ice-covered State for a Land Planet
• Seafloor Weathering and Stochastic Outgassing Unlikely to Significantly Shorten the Future Lifespan of Earth's Terrestrial Biosphere
• Climate uncertainties caused by unknown land distribution on habitable M-Earths