Title: Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth,
Abstract: We use a secular model to describe the non-resonant dynamics of
trans-Neptunian objects in the presence of an external ten-earth-mass
perturber. The secular dynamics is analogous to an "eccentric Kozai mechanism"
but with both an inner component (the four giant planets) and an outer one (the
eccentric distant perturber). By the means of Poincaré sections, the cases of
a non-inclined or inclined outer planet are successively studied, making the
connection with previous works. In the inclined case, the problem is reduced to
two degrees of freedom by assuming a non-precessing argument of perihelion for
the perturbing body.
The size of the perturbation is typically ruled by the semi-major axis of the
small body: we show that the classic integrable picture is still valid below
about 70 AU, but it is progressively destroyed when we get closer to the
external perturber. In particular, for a>150 AU, large-amplitude orbital flips
become possible, and for a>200 AU, the Kozai libration islands are totally
submerged by the chaotic sea. Numerous resonance relations are highlighted. The
most large and persistent ones are associated to apsidal alignments or
anti-alignments with the orbit of the distant perturber.