In planetary systems with sufficiently small inter-planet spacing, close encounters can lead to planetary collisions/mergers or ejections. We study the spin property of the merger products of two giant planets in a statistical manner using numerical simulations and analytical modeling. Planetary collisions lead to rapidly rotating objects and a broad range of obliquities. We find that, under typical conditions for two-planet scatterings, the distributions of spin magnitude $S$ and obliquity $\Theta_{ \rm SL}$ of the merger products have simple analytical forms: $f_{ S} \propto S$ and $f_{ \cos\Theta_{ \rm SL}} \propto (1-\cos^2\Theta_{ \rm SL})^{ -1/2}$. Though parameter studies, we determine the regime of validity for the analytical distributions of spin and obliquity. Since planetary mergers is a major outcome of planet-planet scatterings, observational search for the spin/obliquity signatures of exoplanets would provide important constraints on the dynamical history of planetary systems.
Categories: astro-ph.EP