Title: The Eccentric Kozai-Lidov mechanism for Outer Test Particle,
Abstract: The secular approximation of the hierarchical three body systems has been
proven to be very useful in addressing many astrophysical systems, from
planets, stars to black holes. In such a system two objects are on a tight
orbit, and the tertiary is on a much wider orbit. Here we study the dynamics of
a system by taking the tertiary mass to zero and solve the hierarchical three
body system up to the octupole level of approximation. We find a rich dynamics
that the outer orbit undergoes due to gravitational perturbations from the
inner binary. The nominal result of the precession of the nodes is mostly
limited for the lowest order of approximation, however, when the octupole-level
of approximation is introduced the system becomes chaotic, as expected, and the
tertiary oscillates below and above 90deg, similarly to the non-test particle
flip behavior (e.g., Naoz 2016). We provide the Hamiltonian of the system and
investigate the dynamics of the system from the quadrupole to the octupole
level of approximations. We also analyze the chaotic and quasi-periodic orbital
evolution by studying the surfaces of sections. Furthermore, including general
relativity, we show case the long term evolution of individual debris disk
particles under the influence of a far away interior eccentric planet. We show
that this dynamics can naturally result in retrograde objects and a puffy disk
after a long timescale evolution (few Gyr) for initially aligned configuration.