The curiously warped mean plane of the Kuiper belt

Abstract

We measured the mean plane of the Kuiper belt as a function of semi-major axis. For the classical Kuiper belt as a whole (the non-resonant objects in the semi-major axis range 42--48~au), we find a mean plane of inclination $i_m=1.8^{\circ }$${}_{-0.4^{\circ }}^{+0.7^{\circ }}$ and longitude of ascending node ${\Omega }_m=77^{\circ }$${}_{-14^{\circ }}^{+18^{\circ }}$ (in the J2000 ecliptic-equinox coordinate system), in accord with theoretical expectations of the secular effects of the known planets. With finer semi-major axis bins, we detect a statistically significant warp in the mean plane near semi-major axes 40--42~au. Linear secular theory predicts a warp near this location due to the ${\nu }_{18}$ nodal secular resonance, however the measured mean plane for the 40.3-42~au semi-major axis bin (just outside the ${\nu }_{18}$) is inclined $\sim 13^{\circ }$ to the predicted plane, a nearly 3-$\sigma$ discrepancy. For the more distant Kuiper belt objects of semi-major axes in the range 50--80~au, the expected mean plane is close to the invariable plane of the solar system, but the measured mean plane deviates greatly from this: it has inclination $i_m=9.1^{\circ }$${}_{-3.8^{\circ }}^{+6.6^{\circ }}$ and longitude of ascending node ${\Omega }_m=227^{\circ }$${}_{-44^{\circ }}^{+18^{\circ }}$. We estimate this deviation from the expected mean plane to be statistically significant at the $\sim 97-99\%$ confidence level. We discuss several possible explanations for this deviation, including the possibility that a relatively close-in ($a\lesssim 100$~au), unseen small planetary-mass object in the outer solar system is responsible for the warping.

This version corrects an error in Figure 7 and typographical errors in some equations in Appendix D (changes accepted as an erratum in AJ)

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