  Studies of high-multiplicity, tightly-packed planetary systems suggest that
dynamical instabilities are common and affect both the orbits and planet
structures, where the compact orbits and typically low densities make physical
collisions likely outcomes. Since the structure of many of these planets is
such that the mass is dominated by a rocky core, but the volume is dominated by
a tenuous gas envelope, the sticky-sphere approximation, used in dynamical
integrators, may be a poor model for these collisions. We perform five sets of
collision calculations, including detailed hydrodynamics, sampling mass ratios
and core mass fractions typical in Kepler Multis. In our primary set of
calculations, we use Kepler-36 as a nominal remnant system, as the two planets
have a small dynamical separation and an extreme density ratio. We use an
N-body code, Mercury 6.2, to integrate initially unstable systems and study the
resultant collisions in detail. We use these collisions, focusing on grazing
collisions, in combination with realistic planet models created using gas
profiles from Modules for Experiments in Stellar Astrophysics and core profiles
using equations of state from Seager et al. (2007), to perform hydrodynamic
calculations, finding scatterings, mergers, and even a potential planet-planet
binary. We dynamically integrate the remnant systems, examine the stability,
and estimate the final densities, finding the remnant densities are sensitive
to the core masses, and collisions result in generally more stable systems. We
provide prescriptions for predicting the outcomes and modeling the changes in
mass and orbits following collisions for general use in dynamical integrators.
