Steeper Scattered Disks Buckle Faster

Disks of low-mass bodies scattered by giant planets to large semi-major axis and constant periapsis orbits are vulnerable a buckling instability. This instability exponentially grows orbital inclinations, raises distances, coherently tilts resulting in clustering arguments periapsis. The dynamically hot system is then susceptible the formation lopsided mode. Here we show that timescale decreases as radial surface density population becomes more centrally dense, i.e., steeper disks buckle faster. Accounting for differential apsidal precession driven planets, find $\sim\!10\,M_\oplus$ sufficient primordial disk trans-Neptunian region have been unstable if $dN \propto a^{-2.5} da$.