# On The XUV Luminosity Evolution of TRAPPIST-1

## TL;DR

This study models the long-term XUV luminosity evolution of TRAPPIST-1 using Bayesian methods, revealing its sustained high activity and implications for planetary atmospheric erosion, while demonstrating a more efficient inference technique with approxposterior.

## Contribution

We develop a Bayesian framework to constrain TRAPPIST-1's XUV evolution and introduce approxposterior, a machine learning tool that significantly reduces computational costs.

## Key findings

- TRAPPIST-1's XUV luminosity likely remained saturated for several Gyrs.
- Inner planets received XUV fluxes 1000-10,000 times Earth's during pre-main sequence.
- Approxposterior accurately replicates MCMC results with much less computational effort.

## Abstract

We model the long-term XUV luminosity of TRAPPIST-1 to constrain the evolving high-energy radiation environment experienced by its planetary system. Using Markov Chain Monte Carlo (MCMC), 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 $m_{\star} = 0.089 \pm{0.001}$ M$_{\odot}$ and find that its early XUV luminosity likely saturated at $\log_{10}(L_{XUV}/L_{bol}) = -3.03^{+0.23}_{-0.12}$. From the posterior distribution, we infer that there is a ${\sim}40\%$ chance that TRAPPIST-1 is still in the saturated phase today, suggesting that TRAPPIST-1 has maintained high activity and $L_{XUV}/L_{bol} \approx 10^{-3}$ for several Gyrs. 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 ${\sim}10^3 - 10^4\times$ that of the modern Earth during TRAPPIST-1's ${\sim}1$ Gyr-long pre-main sequence phase. Deriving these constraints via MCMC is computationally non-trivial, 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 $1\sigma$ uncertainties of $0.61\%$ and $5.5\%$, respectively, relative to emcee.