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Giant Planet Influence on the Collective Gravity of a Primordial Scattered Disk

Axisymmetric disks of high eccentricity, low mass bodies on near-Keplerian orbits are unstable to an out-of-plane buckling. This "inclination instability" exponentially grows the orbital inclinations, raises perihelia distances and clusters in argument of perihelion. Here we examine the instability in a massive primordial scattered disk including the orbit-averaged gravitational influence of the giant planets. We show that differential apsidal precession induced by the giant planets will suppress the inclination instability unless the primordial mass is $\gtrsim 20$ Earth masses. We also show that the instability should produce a "perihelion gap" at semi-major axes of hundreds of AU, as the orbits of the remnant population are more likely to have extremely large perihelion distances ($\mathcal{O}(100~\rm{AU})$) than intermediate values.