  Dynamical instabilities among giant planets are thought to be nearly
ubiquitous, and culminate in the ejection of one or more planets into
interstellar space. Here we perform N-body simulations of dynamical
instabilities while accounting for torques from the galactic tidal field. We
find that a fraction of planets that would otherwise have been ejected are
instead trapped on very wide orbits analogous to those of Oort cloud comets.
The fraction of ejected planets that are trapped ranges from 1-10%, depending
on the initial planetary mass distribution. The local galactic density has a
modest effect on the trapping efficiency and the orbital radii of trapped
planets. The majority of Oort cloud planets survive for Gyr timescales. Taking
into account the demographics of exoplanets, we estimate that one in every
200-3000 stars could host an Oort cloud planet. This value is likely an
overestimate, as we do not account for instabilities that take place at early
enough times to be affected by their host stars' birth cluster, or planet
stripping from passing stars. If the Solar System's dynamical instability
happened after birth cluster dissolution, there is a ~7% chance that an ice
giant was captured in the Sun's Oort cloud.
