  We explore scenarios for the origin of two different density planets in the
Kepler 36 system in adjacent orbits near the 7:6 mean motion resonance. We find
that fine tuning is required in the stochastic forcing amplitude, the migration
rate and planet eccentricities to allow two convergently migrating planets to
bypass mean motion resonances such as the 4:3, 5:4 and 6:5, and yet allow
capture into the 7:6 resonance. Stochastic forcing can eject the system from
resonance causing a collision between the planets, unless the disk inducing
migration and stochastic forcing is depleted soon after resonance capture.
  We explore a scenario with approximately Mars mass embryos originating
exterior to the two planets and migrating inwards toward two planets. We find
that gravitational interactions with embryos can nudge the system out of
resonances. Numerical integrations with about a half dozen embryos can leave
the two planets in the 7:6 resonance. Collisions between planets and embryos
have a wide distribution of impact angles and velocities ranging from
accretionary to disruptive. We find that impacts can occur at sufficiently high
impact angle and velocity that the envelope of a planet could have been
stripped, leaving behind a dense core. Some of our integrations show the two
planets exchanging locations, allowing the outer planet that had experienced
multiple collisions with embryos to become the innermost planet. A scenario
involving gravitational interactions and collisions with embryos may account
for both the proximity of the Kepler 36 planets and their large density
contrast.
