Do Rocky Planets around M Stars Have Atmospheres? A Statistical Approach to the Cosmic Shoreline

Answering the question "do rocky exoplanets around M stars have atmospheres?" is a key science goal of the JWST mission, with 500 hours of Director's Discretionary Time (DDT) awarded to address it. Theoretically, the so-called "Cosmic Shoreline" may not hold around M stars due to their harsher XUV environment, possibly resulting in most rocky planets lacking significant atmospheres -- a hypothesis that remains to be statistically tested through judicious target selection. We identify target selection as a combinatorial optimization problem ("knapsack problem"). We develop a statistical framework to test population-level hypotheses from observations and combine a formation and evolution model, 1D-RCE atmosphere model, and genetic algorithm to simulate populations and find the optimal set of observations. We find that, firstly, if all rocky planets around M stars are indeed bare rocks, JWST can efficiently place an upper bound on the atmosphere occurrence rates to less than 1 in 8, even without optimized target selection, but further improvements to the constraint are cost-prohibitive. Secondly, if the Cosmic Shoreline hypothesis (XUV or bolometric) holds true for M stars, strong evidence ($Δ$BIC>5) can be found within ~500 observing hours using the optimal strategy of a "wide and shallow" approach. Our statistical framework can be directly applied to upcoming observations to robustly identify the Cosmic Shoreline and to optimize target selection for determining other trends in exoplanet atmosphere observations, including those from future missions.