Shaping of the inner Oort cloud by Planet Nine

We present a numerical simulation of the dynamical interaction between the proposed Planet Nine and a debris disk around the Sun for $4\mathrm{G}\mathrm{y}\mathrm{r}$, accounting for the secular perturbation of the four giant planets in two scenarios: (a) an initially thin circular disk around the Sun (b) inclined and eccentric disk. We show, in both scenarios, that Planet Nine governs the dynamics in between $1000-5000\mathrm{A}\mathrm{U}$ and forms spherical structure in the inner part ($\sim 1000\mathrm{A}\mathrm{U}$) and inclined disk. This structure is the outcome of mean motion resonances and secular interaction with Planet Nine. We compare the morphology of this structure with the outcome from a fly-by encounter of a star with the debris disk and show distinct differences between the two cases. We predict that this structure serves as a source of comets and calculate the resulting comet production rate to be detectable.