  A leading model for the origin of super-Earths proposes that planetary
embryos migrate inward and pile up on close-in orbits. As large embryos are
thought to preferentially form beyond the snow line, this naively predicts that
most super-Earths should be very water-rich. Here we show that the
shortest-period planets formed in the migration model are often purely rocky.
The inward migration of icy embryos through the terrestrial zone accelerates
the growth of rocky planets via resonant shepherding. We illustrate this
process with a simulation that provided a match to the Kepler-36 system of two
planets on close orbits with very different densities. In the simulation, two
super-Earths formed in a Kepler-36-like configuration; the inner planet was
pure rock while the outer one was ice-rich. We conclude from a suite of
simulations that the feeding zones of close-in super-Earths are likely to be
broad and disconnected from their final orbital radii.
