tokens: is undetected in one scenario, an upper limit on its abundance can suffice to disfavour biological production for certain molecules. Fig. 7 shows the posterior distributions for the mixing ratio of each molecule from our retrievals. A 10 Prism transit campaign suffices to constrain the CO 2 and CH 4 abundances of the modern Earth to within an order of magnitude (0.78 dex and 0.85 dex, respectively); for the prebiotic Earth only CO 2 is constrained (0.62 dex). An increase to 20 Prism transits offers two new results: (i) an order of magnitude constraint on the H 2 O abundance for the prebiotic Earth (0.70 dex); and (ii) a upper limit on the prebiotic Earth CH 4 abundance in tension with the confidence interval of the modern Earth CH 4 abundance. The latter is a diagnostic difference between the modern and prebiotic scenarios accessible with only 20 transits. A further increase to 100 Prism transits offers dramatic improvements: constraints on the CO 2 , H 2 O, and CH 4 abundances to ∼ a factor of 2 (0.3 dex), and an order of magnitude constraint on the modern Earth N 2 O abundance (0.78 dex). Constraints on the O 3 abundance of the modern Earth can be obtained, to within an order of magnitude, with either 100 Prism + 100 MIRI transits (0.63 dex), or 200 Prism transits (0.59 dex). However, 200 Prism transits result in significantly better constrained abundances for the other molecules. As above, we recommend additional Prism transits instead of dividing time between the Prism and MIRI. Figure 7. Retrieved atmospheric composition from simulated JWST observations of TRAPPIST-1e. The predicted mixing ratio constraints for CO 2 , H 2 O, CH 4 , N 2 O, and O 3 for the 1 bar modern Earth (green) and prebiotic Earth (orange) are shown by the marginalized posterior histograms. Each row corresponds to a different JWST observing campaign, ranging from 10 NIRSpec Prism transits (top) to 200 Prism transits (bottom). Various combinations of NIRSpec Prism + MIRI LRS transits are also included. Predicted detection significances for each molecule are annotated (green text for the modern Earth; orange text for the prebiotic Earth). Abundance constraints (error bars) are overlaid, with the interval annotated where constraints 1 dex are possible. For non-detections, abundance upper limits are shown (vertical lines with arrows). The prebiotic and Modern scenarios can first be distinguished with 20 Prism transits via the CH 4 abundance (the prebiotic upper limit precludes the modern abundance). Similarly, the N 2 O abundance can be differentiated with 200 Prism transits. Even 200 Prism transits (or 100 Prism + 100 MIRI transits) are insufficient to distinguish the O 3 abundances. O 2 is unconstrained in all cases. Adding MIRI data slightly increases the detection significances of O 3 , but adding the same quantity of Prism transits produces tighter constraints on all other atmospheric parameters. Our analysis demonstrates that the most effective way to
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