The Inclination Distribution of the Kuiper Belt

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Abstract
We develop a general method for determining the unbiased inclination distribution of the Kuiper belt using only the inclination and latitude of discovery of known Kuiper belt objects (KBOs). These two parameters are well determined for each discovered object, so we can use all 379 known KBOs (as of 2001 January 1)—without knowing the object's precise orbit, area, detection efficiency, or the latitudinal coverage of the survey that found the object—to determine the inclination distribution. We find that a natural analytic form for the inclination distribution is a sine of the inclination multiplied by a Gaussian. The inclination distribution of all KBOs is well fitted by sin i multiplied by a sum of two Gaussians with widths 26 and 15° ± 1°. For this inclination distribution, the Kuiper belt has an effective area of 8100 deg2 and a FWHM of 12.5° ± 3.5° in latitude. The inclination distribution of the different dynamical classes appear different. The Plutinos are well fit by sin i mulitplied by a single Gaussian of width 102, the classical KBOs cannot be fit to a single Gaussian but are well fit by sin i multiplied by the sum of two Gaussians of widths 22 and 17° ± 3°, and the scattered KBOs are poorly fit by sin i multiplied by a single Gaussian of width 20° ± 4°. The poor fit of the scattered objects is possibly a result of limitations of the method in dealing with large eccentricities. The effective areas of the Plutinos, classical KBOs, and scattered KBOs are 9300 ± 1800, 6100 ± 2100, and 17000 ± 3000 deg2, respectively. The FWHMs are 23° ± 5°, 68, and 44° ± 10°, respectively. In all cases, the inclinations of the Kuiper belt objects appear larger than expected from dynamical simulations of possible perturbations.