2020ApJ...891..155F

We model the long-term X-ray and ultraviolet (XUV) luminosity of TRAPPIST-1 to constrain the evolving high-energy radiation environment experienced by its planetary system. Using a Markov Chain Monte Carlo (MCMC) method, we derive probabilistic constraints for TRAPPIST-1's stellar and XUV evolution that account for observational uncertainties, degeneracies between model parameters, and empirical data of low-mass stars. We constrain TRAPPIST-1's mass to m_* = 0.089 ± 0.001 M_☉ and find that its early XUV luminosity likely saturated at log₁₀(L_XUV/L_bol)=-3.03_–0.12^+0.23. From the posterior distribution, we infer that there is a ∼40% chance that TRAPPIST-1 is still in the saturated phase today, suggesting that TRAPPIST-1 has maintained high activity and L_XUV/L_bol ≃ 10^–3 for several gigayears. TRAPPIST-1's planetary system therefore likely experienced a persistent and extreme XUV flux environment, potentially driving significant atmospheric erosion and volatile loss. The inner planets likely received XUV fluxes ∼10³-10⁴ times that of the modern Earth during TRAPPIST-1's ∼1 Gyr long pre-main-sequence phase. Deriving these constraints via MCMC is computationally nontrivial, so scaling our methods to constrain the XUV evolution of a larger number of M dwarfs that harbor terrestrial exoplanets would incur significant computational expenses. We demonstrate that approxposterior, an open source Python machine learning package for approximate Bayesian inference using Gaussian processes, accurately and efficiently replicates our analysis using 980 times less computational time and 1330 times fewer simulations than MCMC sampling using emcee. We find that approxposterior derives constraints with mean errors on the best-fit values and 1σ uncertainties of 0.61% and 5.5%, respectively, relative to emcee.