Dynamical evolution induced by planet nine

High-inclination dynamics induced by Planet Nine involves coupled modulation of two degrees of freedom with no clear symmetry, is intrinsically non-adiabatic, is difficult to model integrably, and is primarily driven by a well-defined octupole-level secular harmonic.

“Unlike the eccentricity-perihelion and inclination-node evolution described above, high-inclination dynamics induced by Planet Nine involves coupled modulation of two degrees of freedom (related to e and i ), with no clear symmetry inherent to the motion. Moreover, even in the simplified simulations of Batygin and Morbidelli (2017); Li et al. (2018), no discernible separation of timescales mat”

In a simplified 2D model with an effective quadrupole moment and Planet Nine as the only direct perturber, all KBOs that are not phase-protected are dynamically unstable, resulting in a fully resonant orbital distribution of distant KBOs.

“By restricting all orbital motion to a common plane, this physical setup renders all KBOs that are not phase-protected dynamically unstable, resulting in a fully resonant orbital distribution of distant KBOs.”

A radically excited distribution of Centaur inclinations is a natural outcome of Planet Nine induced evolution and constitutes a tantalizing line of evidence that points to Planet Nine's existence.

“As discussed further below, a radically excited distribution of Centaur inclinations is a natural outcome of Planet Nine induced evolution, and constitutes a tantalizing line of evidence that points to Planet Nine's existence (Batygin and Brown 2016b; Batygin and Morbidelli 2017; Becker et al. 2018; see also Gomes et al. 2015).”

Secular interactions are dominantly responsible for sculpting the observed distribution of long-period KBOs.

“it is secular interactions that are dominantly responsible for sculpting the actual observed distribution of long-period KBOs (Batygin and Morbidelli, 2017).”

The existence of an additional, multi-Earth mass planetary member of the solar system-Planet Nine-can successfully resolve the theoretical tension posed by the anomalous structure of the distant Kuiper belt.

“A series of recent studies (Batygin and Brown, 2016a,b; Batygin and Morbidelli, 2017; Millholland and Laughlin, 2017; Becker et al., 2017; Hadden et al., 2018; Khain et al., 2018a; C´ aceres & Gomes, 2018; Li et al., 2018) have demonstrated that the existence of an additional, multi-Earth mass planetary member of the solar system Planet Nine - can successfully resolve this theoretical tension.”

The orbit-flipping behavior of distant objects induced by Planet Nine is almost always triggered at the minimum of the KBO eccentricity cycle.

“the orbitflipping behavior of distant objects induced by Planet Nine is almost always triggered at the minimum of the KBO eccentricity cycle (which translates to a maximum in ; Batygin and Morbidelli 2017).”

This finding is quantitatively consistent with analytical estimates, wherein ̄a_c is interpreted as the minimum semi-major axis at which Hamiltonian (9) possesses an elliptic equilibrium at $ = 180 deg.

“This finding is quantitatively consistent with analytical estimates, wherein ¯ a c is interpreted as the minimum semi-major axis at which Hamiltonian (9) possess an elliptic equilibrium at $ = 180 deg (Batygin and Morbidelli, 2017).”

Secular dynamics embedded within P9 MMRs have a very similar phase-space topology to the purely secular phase-space portraits computed using Hamiltonian (9).

“Batygin and Morbidelli (2017) demonstrated that secular dynamics embedded within P9 MMRs have a very similar phase-space topology to the purely secular phase-space portraits computed using Hamiltonian (9).”