The Deep Ecliptic Survey: A Search for Kuiper Belt Objects and Centaurs. II. Dynamical Classification, the Kuiper Belt Plane, and the Core Population

The Deep Ecliptic Survey (DES)-a search optimized for the discovery of Kuiper belt objects (KBOs) with the Blanco and Mayall 4 m telescopes at the Cerro Tololo Inter-American Observatory and Kitt Peak National Observatory-has covered 550 deg² from its inception in 1998 through the end of 2003. This survey has a mean 50% sensitivity at VR magnitude 22.5. We report here the discoveries of 320 designated KBOs and Centaurs for the period 2000 March through 2003 December and describe improvements to our discovery and recovery procedures. Our data and the data products needed to reproduce our analyses in this paper are available through the NOAO survey database. Here we present a dynamical classification scheme, based on the behavior of orbital integrations over 10 Myr. The dynamical classes, in order of testing, are ``Resonant,'' ``Centaur,'' ``Scattered-Near,'' ``Scattered-Extended,'' and ``Classical.'' (These terms are capitalized when referring to our rigorous definitions.) Of the 382 total designated KBOs discovered by the DES, a subset of 196 objects have sufficiently accurate orbits for dynamical classification. Summary information is given for an additional 240 undesignated objects also discovered by the DES from its inception through the end of 2003. The number of classified DES objects (uncorrected for observational bias) are Classical, 96; Resonant, 54; Scattered-Near, 24; Scattered-Extended, 9; and Centaur, 13. We use subsets of the DES objects (which can have observational biases removed) and larger samples to perform dynamical analyses on the Kuiper belt. The first of these is a determination of the Kuiper belt plane (KBP), for which the Classical objects with inclinations less than 5° from the mean orbit pole yield a pole at R.A.=273.92d+/-0.62d and decl.=66.70d+/-0.20d (J2000), consistent with the invariable plane of the solar system. A general method for removing observational biases from the DES data set is presented and used to find a provisional magnitude distribution and the distribution of orbital inclinations relative to the KBP. A power-law model fit to the cumulative magnitude distribution of all KBOs discovered by the DES in the VR filter yields an index of 0.86+/-0.10 (with the efficiency parameters for the DES fitted simultaneously with the population power law). With the DES sensitivity parameters fixed, we derive power-law indices of 0.74+/-0.05, 0.52+/-0.08, and 0.74+/-0.15, respectively, for the Classical, Resonant, and Scattered classes. Plans for calibration of the DES detection efficiency function and DES magnitudes are discussed. The inclination distribution confirms the presence of ``hot'' and ``cold'' populations; when the geometric sini factor is removed from the inclination distribution function, the cold population shows a concentrated ``core'' with a full width at half-maximum of approximately 4.6d, while the hot population appears as a ``halo,'' extending beyond 30°. The inclination distribution is used to infer the KBO distribution in the sky, as a function of latitude relative to the KBP. This inferred latitude distribution is reasonably consistent with the latitude distribution derived from direct observation, but the agreement is not perfect. We find no clear boundary between the Classical and Scattered classes either in their orbital inclinations with respect to the KBP or in their power-law indices in their respective magnitude distributions. This leaves open the possibility that common processes have shaped the distribution of orbital parameters for the two classes.