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 ${\theta }_{\mathrm{SL}}$ of the merger products have simple analytical forms: fS ∝ S and ${f}_{\cos {\theta }_{\mathrm{SL}}}\propto {(1-{\cos }^{2}{\theta }_{\mathrm{SL}})}^{-1/2}$. Through parameter studies, we determine the regime of validity for the analytical distributions of spin and obliquity. Since planetary mergers are 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.