  Multiple planet systems provide an ideal laboratory for probing exoplanet
composition, formation history and potential habitability. For the TRAPPIST-1
planets, the planetary radii are well established from transits (Gillon et al.,
2016, Gillon et al., 2017), with reasonable mass estimates coming from transit
timing variations (Gillon et al., 2017, Wang et al., 2017) and dynamical
modeling (Quarles et al., 2017). The low bulk densities of the TRAPPIST-1
planets demand significant volatile content. Here we show using
mass-radius-composition models, that TRAPPIST-1f and g likely contain
substantial ($\geq50$ wt\%) water/ice, with b and c being significantly drier
($\leq15$ wt\%). We propose this gradient of water mass fractions implies
planets f and g formed outside the primordial snow line whereas b and c formed
inside. We find that compared to planets in our solar system that also formed
within the snow line, TRAPPIST-1b and c contain hundreds more oceans worth of
water. We demonstrate the extent and timescale of migration in the TRAPPIST-1
system depends on how rapidly the planets formed and the relative location of
the primordial snow line. This work provides a framework for understanding the
differences between the protoplanetary disks of our solar system versus M
dwarfs. Our results provide key insights into the volatile budgets, timescales
of planet formation, and migration history of likely the most common planetary
host in the Galaxy.
