Resonances near the orbit of 2003 VB$_{12}$ (Sedna)

Abstract

2003 VB$_{12}$ (Sedna) is as much distinguished by its considerable size as by its extremely unusual orbit, which has perihelion at about $q=76$ AU with semi-major axis $a=533$ AU (Brown et al. 2004, JPL Horizons). Thus it is effectively decoupled from both Neptune and the Galactic tide (Fernandez 1997). Brown et al. (2004) and Morbidelli & Levison (2004) maintain that only scattering by a so-far-unobserved “Planet X” or by an errant star could produce such a high-perihelion orbit for a scattered-disk KBO. While a close encounter is plausible, given the Sun's likely birth in an open cluster, such an interaction would profoundly disturb the Oort cloud and would require fundamental revision to the present theories of its formation.

Although the planets cannot significantly affect VB$_{12}$'s orbit through close approaches, resonant perturbations could conceivably produce secular effects on it. To explore this possibility, we have numerically integrated test particles with $480 < a < 580$ AU and a fixed $q=76$ AU. Including the four giant planets, but ignoring the Kuiper Belt and the inner Oort Cloud, as well as the Galactic tide, we find multiple resonances, some of which perturb significantly the test particles' eccentricity more strongly than the leading secular terms. We identify these resonances as variants of the very high-order ($n_N > 60 \n$) mean-motion commensurabilities between Neptune and VB$_{12}$. Although unprecedented, these extremely high-order resonances can be significant due to VB$_{12}$'s very high eccentricity ($e=0.86$). Even powers of eccentricity beyond sixty are still on the order of $10^{-4}$, which is comparable to the strength of low-order resonances involving near-circular orbits. We extrapolate the possible long-term drift rate and estimate the likelihood of such resonances producing an “inner Oort cloud” population consistent with VB$_{12}$ over the age of the Solar System. Finally we discuss how planetary migration and the Kuiper-Belt's depletion might have affected VB$_{12}$'s putative resonance.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html