On the Secular Dynamics of Putative Astrophysical Disk in the Outer Solar System

The trans-Neptunian scattered disk exhibits unexpected dynamical structure, ranging from an extended dispersion of perihelion distance to a clustered distribution in orbital angles. Self-gravity of the scattered disk has been proposed in the literature as an alternative mechanism to Planet Nine for sculpting the orbital architecture of the trans-Neptunian region. The numerics of this hypothesis hitherto have been limited to N=O(100) super-particle simulations with no resolution of the motion of the giant planets, which are instead captured in the orbit-averaged (quadrupolar) potential through an enhanced J2 moment of the central body. Such simulations reveal the onset of collective dynamical behaviour — termed the “inclination instability” — wherein orbital circularisation occurs at the expense of coherent excitation of the inclination. Here, we report N=O(10⁴) GPU-accelerated simulations of a self-gravitating scattered disk (across a range of disk masses spanning 5 Me to 40 Me) that self-consistently account for intra-particle interactions as well as Neptune’s perturbations. Our numerical experiments show that even under the most favourable conditions, the inclination instability never ensues; instead, due to scattering, the disk depletes. While our calculations show that a transient lopsided structure can emerge within the first few hundreds of Myr, the terminal outcomes of these calculations systematically reveal a scattered disk that is free of any orbital clustering.