A Mathematical Model of Circumstellar and Circumplanetary Habitable Zones Accounting for Multiple Heat Sources

Abstract

The habitable zone is the range of orbital radii at which a celestial body’s temperature is conducive to liquid water. It is influenced by factors including stellar radiation and tidal heating. The ability to predict exoplanetary habitability can improve understanding of the range of orbital parameters that may allow life to develop and survive.

I combine elements of mathematical models developed in the literature to determine energy contributions by stellar radiation and tidal heating, producing a Maple 18 model accounting for both circumstellar and circumplanetary habitability. Using input star, planet, and moon properties, the model outputs calculated temperatures for both the planet and moon, as well as coloured maps representing the habitable zone.

Using this model, I assess the effect on the habitable zone when tidal heating is considered in addition to stellar radiation, giving a better understanding of how these factors influence habitability. Specifically, tidal heating may pushes both edges of the habitable zone outward, but whether the habitable zone size changes is unclear. Additionally, it is expected that accounting for the circumplanetary habitable zone will expand the overall habitable zone.

By synthesizing a single model from existing literature models, a more accurate prediction of exoplanetary system habitability may be obtained, allowing scientists to better determine which exoplanets are more likely to have life and target these for further study. The model is therefore applied to existing exoplanet data to demonstrate this application of the model in predicting exoplanet and exomoon temperatures.