A Coupled Analysis of Atmospheric Mass Loss and Tidal Evolution in XUV Irradiated Exoplanets: the TRAPPIST-1 Case Study

Abstract: Exoplanets residing close to their stars can experience evolution of both their physical structures and their orbits due to the influence of their host stars. In this work, we present a coupled analysis of dynamical tidal dissipation and atmospheric mass loss for exoplanets in XUV irradiated environments. As our primary application, we use this model to study the TRAPPIST-1 system, and place constraints on the interior structure and orbital evolution of the planets. We start by reporting on a UV continuum flux measurement (centered around $\sim1900$ Angstroms) for the star TRAPPIST-1, based on 300 ks of Neil Gehrels Swift Observatory data, and which enables an estimate of the XUV-driven thermal escape arising from XUV photo-dissociation for each planet. We find that the X-ray flaring luminosity, measured from our X-ray detections, of TRAPPIST-1 is 5.6 $\times$10$^{-4} L_{}$, while the full flux including non-flaring periods is 6.1 $\times$10$^{-5} L_{}$, when $L_{*}$ is TRAPPIST-1's bolometric luminosity. We then construct a model that includes both atmospheric mass-loss and tidal evolution, and requires the planets to attain their present-day orbital elements during this coupled evolution. We use this model to constrain the ratio $Q'=3Q/2k_{2}$ for each planet. Finally, we use additional numerical models implemented with the Virtual Planet Simulator \texttt{VPLanet} to study ocean retention for these planets using our derived system parameters.