Giant Planet Influence on the Collective Gravity of a Primordial Scattered Disk
Abstract
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 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 (O(100~AU)) than intermediate values.