Spin and Obliquity Distributions of Low-mass Planets Shaped by Dynamical Instability

Exoplanetary systems hosting multiple low-mass planets are thought to have experienced dynamical instability, during which planet-planet collisions and mergers occur; these collisions can impart substantial amount of angular momentum to the merger remnants, changing the obliquities of the resulting planets significantly. In this work, we carry out a series of $N$-body experiments to investigate the spin magnitude $(|\vec{S}|)$ and obliquity $(\theta_{\rm SL})$ distributions of low-mass exoplanets that have gone through planetary collisions. In our fiducial super-Earth (with $m=3M_{\oplus}$, $R=1.3R_{\oplus}$) and mini-Neptune systems (with $m=9M_{\oplus}$, $R=2.5R_{\oplus}$), the collision products follow a nearly uniform distribution in $\cos{\theta_{\rm SL}}$ and the spin-magnitude distribution is approximately linear in $|\vec{S}|$. Parameter studies and theoretical analysis show that increasing planetary radii or masses, or decreasing the initial planet-planet mutual inclinations, tend to polarize the obliquity distribution toward alignment or anti-alignment (i.e., excess probability near $\cos{\theta_{\rm SL}}=\pm1$). Experiments with initially two-planet and three-planet systems produce qualitatively similar outcomes, suggesting that the trends in this study may generalize to systems with higher planetary multiplicities.