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

Abstract 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 a 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 (∣ S ∣) and obliquity ( θ SL ) distributions of low-mass exoplanets that have gone through planetary collisions. In our fiducial super-Earth (with m = 3 M ⊕ , R = 1.3 R ⊕ ) and mini-Neptune systems (with m = 9 M ⊕ , R = 2.5 R ⊕ ), the collision products follow a nearly uniform distribution in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>cos</mml:mi> <mml:msub> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">SL</mml:mi> </mml:mrow> </mml:msub> </mml:math> , and the spin magnitude distribution is approximately linear in ∣ 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 antialignment (i.e., excess probability near <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>cos</mml:mi> <mml:msub> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">SL</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> </mml:math> ). 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.