  The discovery of Jupiter-mass planets in close orbits about their parent
stars has challenged models of planet formation. Recent observations have shown
that a number of these planets have highly inclined, sometimes retrograde
orbits about their parent stars, prompting much speculation as to their origin.
It is known that migration alone cannot account for the observed population of
these misaligned hot Jupiters, which suggests that dynamical processes after
the gas disc dissipates play a substantial role in yielding the observed
inclination and eccentricity distributions. One particularly promising
candidate is planet-planet scattering, which is not very well understood in the
non-linear regime of tides. Through three-dimensional hydrodynamical
simulations of multi-orbit encounters, we show that planets that are scattered
into an orbit about their parent stars with closest approach distance being
less than approximately three times the tidal radius are either destroyed or
completely ejected from the system. We find that as few as 5 and as many as 18
of the currently known hot Jupiters have a maximum initial apastron for
scattering that lies well within the ice line, implying that these planets must
have migrated either before or after the scattering event that brought them to
their current positions. If stellar tides are unimportant $(Q_\ast \gtrsim
10^7)$, disk migration is required to explain the existence of the hot Jupiters
present in these systems. Additionally, we find that the disruption and/or
ejection of Jupiter-mass planets deposits a Sun's worth of angular momentum
onto the host star. For systems in which planet-planet scattering is common, we
predict that planetary hosts have up to a 35% chance of possessing an obliquity
relative to the invariable plane of greater than 90 degrees.
