  Planetary systems with sufficiently small orbital spacings can experience
planetary mergers and ejections. The branching ratio of mergers vs ejections
depends sensitively on the treatment of planetary close encounters. Previous
works have adopted a simple "sticky-sphere" prescription, whose validity is
questionable. We apply both smoothed particle hydrodynamics and $N$-body
integrations to investigate the fluid effects in close encounters between gas
giants and the long-term evolution of closely-packed planetary systems.
Focusing on parabolic encounters between Jupiter-like planets with $M_J$ and
$2M_J$, we find that quick mergers occur when the impact parameter $r_p$ (the
pericenter separation between the planets) is less than $2R_J$, and the merger
conserved 97% of the initial mass. Strong tidal effects can affect the
"binary-planet" orbit when $r_p$ is between $2R_J$ and $4R_J$. We quantify
these effects using a set of fitting formulae that can be implemented in
$N$-body codes. We run a suite of $N$-body simulations with and without the
formulae for systems of two giant planets initially in unstable, nearly
circular coplanar orbits. The fluid (tidal) effects significantly increase the
branching ratio of planetary mergers relative to ejections by doubling the
effective collision radius. While the fluid effects do not change the
distributions of semi-major axis and eccentricity of each type of remnant
planets (mergers vs surviving planets in ejections), the overall orbital
properties of planet scattering remnants are strongly affected due to the
change in the branching ratio. We also find that the merger products have broad
distributions of spin magnitudes and obliquities.
