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Planetary Spin and Obliquity from Mergers

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 $Θ_{\rm SL}$ of the merger products have simple analytical forms: $f_{S} \propto S$ and $f_{\cosΘ_{\rm SL}} \propto (1-\cos^2Θ_{\rm SL})^{-1/2}$. 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.