Transiting compact multi-planet systems provide many unique opportunities to characterize the planets, including studies of size distributions, mean densities, orbital dynamics, and atmospheric compositions. The relatively short orbital periods in these systems ensure that events requiring specific orbital locations of the planets (such as primary transit and secondary eclipse points) occur with high frequency. The orbital motion and associated phase variations of the planets provide a means to constrain the atmospheric compositions through measurement of their albedos. Here we describe the expected phase variations of the TRAPPIST-1 system and times of superior conjunction when the summation of phase effects produce maximum amplitudes. We also describe the infrared flux emitted by the TRAPPIST-1 planets and the influence on the overall phase amplitudes. We further present the results from using the global circulation model ROCKE-3D to model the atmospheres of TRAPPIST-1e and TRAPPIST-1f assuming modern Earth and Archean atmospheric compositions. These simulations are used to calculate predicted phase curves for both reflected light and thermal emission components. We discuss the detectability of these signatures and the future prospects for similar studies of phase variations for relatively faint M stars.
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