  Formation of the planets in the Kepler-36 system is modeled by detailed
numerical simulations according to the core-nucleated accretion scenario. The
standard model is updated to include the dissolution of accreting rocky
planetesimals in the gaseous envelope of the planet, leading to substantial
enrichment of the envelope mass in heavy elements and a non-uniform composition
with depth. For Kepler-36 c, models involving in situ formation and models
involving orbital migration are considered. The results are compared with
standard formation models. The calculations include the formation (accretion)
phase, as well as the subsequent cooling phase, up to the age of Kepler-36 (7
Gyr). During the latter phase, mass loss induced by stellar XUV radiation is
included. In all cases, the results fit the measured mass, 7.84 M$_\oplus$, and
radius, 3.68 R$_\oplus$, of Kepler-36 c. Two parameters are varied to obtain
these fits: the disk solid surface density at the formation location, and the
"efficiency" factor in the XUV mass loss rate. The updated models are hotter
and therefore less dense in the silicate portion of the planet and in the
overlying layers of H/He, as compared with standard models. The lower densities
mean that only about half as much H/He is needed to be accreted to fit the
present-day mass and radius constraints. For Kepler-36 b, an updated in situ
calculation shows that the entire H/He envelope is lost, early in the cooling
phase, in agreement with observation.
