  We explore the occurrence and detectability of planet-planet occultations
(PPOs) in exoplanet systems. These are events during which a planet occults the
disk of another planet in the same system, imparting a small photometric signal
as its thermal or reflected light is blocked. We focus on the planets in
TRAPPIST-1, whose orbital planes we show are aligned to within 0.3 degrees at
90% confidence. We present a photodynamical model for predicting and computing
PPOs in TRAPPIST-1 and other systems for various assumptions of the planets'
atmospheric states. When marginalizing over the uncertainties on all orbital
parameters, we find that the rate of PPOs in TRAPPIST-1 is about 1.4 per day.
We investigate the prospects for detection of these events with the James Webb
Space Telescope, finding that ~10-20 occultations per year of b and c should be
above the noise level at 12-15 microns. Joint modeling of several of these PPOs
could lead to a robust detection. Alternatively, observations with the proposed
Origins Space Telescope should be able to detect individual PPOs at high
signal-to-noise. We show how PPOs can be used to break transit timing variation
degeneracies, imposing strong constraints on the eccentricities and masses of
the planets, as well as to constrain the longitudes of nodes and thus the
complete three-dimensional structure of the system. We further show how
modeling of these events can be used to reveal a planet's day/night temperature
contrast and construct crude surface maps. We make our photodynamical code
available on github.
