  The scattered disk is a vast population of trans-Neptunian minor bodies that
orbit the sun on highly elongated, long-period orbits. The stability of
scattered disk objects is primarily controlled by a single parameter - their
perihelion distance. While the existence of a perihelion boundary that
separates chaotic and regular motion of long-period orbits is well established
through numerical experiments, its theoretical basis as well as its semi-major
axis dependence remain poorly understood. In this work, we outline an
analytical model for the dynamics of distant trans-Neptunian objects and show
that the orbital architecture of the scattered disk is shaped by an infinite
chain of $2:j$ resonances with Neptune. The widths of these resonances increase
as the perihelion distance approaches Neptune's semi-major axis, and their
overlap drives chaotic motion. Within the context of this picture, we derive an
analytic criterion for instability of long-period orbits, and demonstrate that
rapid dynamical chaos ensues when the perihelion drops below a critical value,
given by
$q_{\rm{crit}}=a_{\rm{N}}\,\big(\ln((24^2/5)\,(m_{\rm{N}}/M_{\odot})\,(a/a_{\rm{N}})^{5/2})\big)^{1/2}$.
This expression constitutes a boundary between the "detached" and actively
"scattering" sub-populations of distant trans-Neptunian minor bodies.
Additionally, we find that within the stochastic layer, the Lyapunov time of
scattered disk objects approaches the orbital period, and show that the
semi-major axis diffusion coefficient is approximated by
$\mathcal{D}_a\sim(8/(5\,\pi))\,(m_{\rm{N}}/M_{\odot})\,\sqrt{\mathcal{G}\,M_{\odot}\,a_{\rm{N}}}\,\exp\big[-(q/a_{\rm{N}})^2/2\big]$.
We confirm our results with numerical simulations and highlight the connections
between scattered disk dynamics and the Chirikov Standard Map. Implications of
our results for the long-term evolution of the distant solar system are
discussed.
