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 perihelion distances, and clusters in the 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 semimajor axes of hundreds of astronomical units, as the orbits of the remnant population are more likely to have extremely large perihelion distances ( ) than intermediate values.