Chaos in the inert Oort cloud

Abstract

Context. Distant trans-Neptunian objects are subject to planetary perturbations and galactic tides. The former decrease with the distance, while the latter increase. In the intermediate regime where they have the same order of magnitude (the 'inert Oort cloud'), both are weak, resulting in very long evolution timescales. To date, three observed objects can be considered to belong to this category. Aims. We aim to provide a clear understanding of where this transition occurs, and to characterise the long-term dynamics of small bodies in the intermediate regime: relevant resonances, chaotic zones (if any), and timescales at play. Methods. The different regimes are explored analytically and numerically. We also monitored the behaviour of swarms of particles during 4.5 Gyrs in order to identify which of the dynamical features are discernible in a realistic amount of time.Results. There exists a tilted equilibrium plane (Laplace plane) about which orbits precess. The dynamics is integrable in the low and high semi-major axis regimes, but mostly chaotic in between. From about 800 to 1100 astronomical units (au), the chaos covers almost all the eccentricity range. The diffusion timescales are large, but not to the point of being indiscernible in a 4.5 Gyrs duration: the perihelion distance can actually vary from tens to hundreds of au. Orbital variations are damped near the ecliptic (where previous studies focussed), but favoured in specific ranges of inclination corresponding to well-defined resonances. Moreover, starting from uniform distributions, the orbital angles cluster after 4.5 Gyrs for semi-major axes larger than 500 au, because of a very slow differential precession. Conclusions. Even if it is characterised by very long timescales, the inert Oort cloud mostly features chaotic regions; it is therefore much less inert than it appears. Orbits can be considered inert over 4.5 Gyrs only in small portions of the space of orbital elements, which include (90377) Sedna and 2012VP113. Effects of the galactic tides are discernible down to semi-major axes of about 500 au. We advocate including the galactic tides in simulations of distant trans-Neptunian objects, especially when studying the formation of detached bodies or the clustering of orbital elements.

Long-term orbital dynamics of trans-Neptunian objects

“…(11) and (29) with respect to the secular semi-major axis of the small body. Adapted from Saillenfest et al (2019). would dramatically change the dynamical structure described in this section, and turn the weakly-perturbed intermediate regime between the Kuiper belt and the Oort cloud into a very active dynamical region.…”

“…The other conversion formulas can be found in Saillenfest et al (2019). Expressed in the ecliptic reference frame, the Hamiltonian function M G V becomes…”

“…6, we will neglect the radial component of the galactic tides, dropping one degree of freedom. However, contrary to Saillenfest et al (2019), we will keep the hexadecapolar planetary contribution in order to resolve better the regime of low semi-major axes, where ε P 4 ε G V (see Fig. 13).…”

“…1, all dynamical regions are linked, allowing small bodies to switch between very distinct kinds of dynamics. For instance, a trans-Neptunian object initially evolving smoothly in an isolated mean-motion resonance can be transferred to the unstable scattering region, where its semi-major axis can grow Saillenfest et al (2019). Hypothetical planets beyond Neptune are not taken into account in this picture.…”

“…Below the black level, the region can be considered inert. Contrary toSaillenfest et al (2019), the hexadecapolar planetary term is included.…”