The Plane of the Kuiper Belt

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Abstract
We present a robust method for measuring the effective plane of the Kuiper belt. The derived plane has an inclination with respect to the ecliptic of 1.86 and an ascending node of 81.6, with a1 error in pole position of the plane of 0.37. The plane of the Kuiper belt is inconsistent with the invariable plane, the plane of Jupiter, and the plane of Neptune at the greater than 3 level. Using linear secular perturbation theory, we show that the plane of the Kuiper belt is expected to oscillate about the position of the invariable plane with a period of 1.9 million years and an amplitude of 1.2. The present predicted position of the plane of the Kuiper belt has an inclination with respect to the ecliptic of 1.74 and an ascending node of 86.7, within 0.20 of our measured position. The orbital distributions of bodies in the Kuiper belt hold important clues to the formation and evolution of the outer solar system (Morbidelli & Brown 2004). One important dy- namical property of the Kuiper belt that has yet to be exploited is its overall plane. The plane of the Kuiper belt is affected by the total angular momentum of the solar system, recent stellar encounters, and unseen distant masses in the outer solar sys- tem. Early observers of the Kuiper belt implicitly assumed that the plane of the Kuiper belt was the plane of the ecliptic and that the peak concentration of objects would therefore be in the ecliptic (Jewitt & Luu 1995; Irwin, Tremaine, & ú Zytkow 1995; Gladman et al. 1998; Chiang & Brown 1999). Several authors subsequently suggested that the invariable plane—the plane of the average angular momentum of the solar system—is more appropriately considered the plane of the Kuiper belt (Hahn 2000; Levison & Stern 2001; Allen, Bernstein, & Malhotra 2002). Despite the importance for searches and interpretations of knowing the correct plane, no accurate measure of the po- sition of the plane of the Kuiper belt has been made. The only attempt to date at extracting a measurement of the plane has been from Collander-Brown et al. (2003), who examined the average angular momentum of subsets of known Kuiper belt objects but concluded that the plane's position could not be accurately determined in that manner. We present here a new and robust method for determining the plane of the Kuiper belt that makes optimal use of the discovery information from all known Kuiper belt objects. We then examine outer solar system dynamics to determine the expected plane of the Kuiper belt given perturbations from all presently known planetary bodies. We finally conclude with a discussion of the comparison between the measured and expected plane of the Kuiper belt and the implications for the outer solar system.

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