Differentiating Modern and Prebiotic Earth Scenarios for TRAPPIST-1e: High-resolution Transmission Spectra and Predictions for JWST

The TRAPPIST-1 system is a priority target for terrestrial exoplanet characterization. TRAPPIST-1e, residing in the habitable zone, will be observed during the JWST GTO Program. Here, we assess the prospects of differentiating between prebiotic and modern Earth scenarios for TRAPPIST-1e via transmission spectroscopy. Using updated TRAPPIST-1 stellar models from the Mega-MUSCLES survey, we compute self-consistent model atmospheres for a 1 bar prebiotic Earth scenario and two modern Earth scenarios (1 and 0.5 bar eroded atmosphere). Our modern and prebiotic high-resolution transmission spectra (0.4 - 20 $\mu$m at $R \sim$ 100,000) are made available online. We conduct a Bayesian atmospheric retrieval analysis to ascertain the molecular detectability, abundance measurements, and temperature constraints achievable for both scenarios with JWST. We demonstrate that JWST can differentiate between our prebiotic and modern Earth scenarios within 20 NIRSpec Prism transits via CH$_4$ abundance measurements. However, JWST will struggle to detect O$_3$ for our modern Earth scenario to $> 2\,\sigma$ confidence within the nominal mission lifetime ($\sim$ 80 transits over 5 years). The agnostic combination of N$_2$O and/or O$_3$ offers better prospects, with a predicted detection significance of $2.7\,\sigma$ with 100 Prism transits. We show that combining MIRI LRS transits with Prism data provides little improvement to atmospheric constraints compared to observing additional Prism transits. Though biosignatures will be challenging to detect for TRAPPIST-1e with JWST, the abundances for several important molecules - CO$_2$, CH$_4$, and H$_2$O - can be measured to a precision of $\lesssim$ 0.7 dex (a factor of 5) within a 20 Prism transit JWST program.