Keck Pencil-Beam Survey for Faint Kuiper Belt Objects

Abstract

We present the results of a pencil-beam survey of the Kuiper Belt using the Keck 10 m telescope. A single 0.01 deg^2 field is imaged 29 times for a total integration time of 4.8 hr. Combining exposures in software allows the detection of Kuiper Belt objects (KBOs) having visual magnitude m_V ≾ 27.9. Two new KBOs are discovered. One object having m_V = 25.5 lies at a probable heliocentric distance R ≈ 33 AU. The second object at m_V = 27.2 is located at R ≈ 44 AU. Both KBOs have diameters of about 50 km, assuming comet-like albedos of 4%. Data from all surveys are pooled to construct the luminosity function from m_R = 20 to 27. The cumulative number of objects per square degree, Σ(<m_R), is fitted to a power law of the form log_(10) Σ = α(m_R - 23.5), where the slope α = 0.52 ± 0.02. Differences between slopes reported in the literature are due mainly to which survey data are incorporated in the fit and not to the method of analysis. The luminosity function is consistent with a power-law size distribution for objects having diameters s = 50–500 km within 50 AU; dN ∝ s^(-q) ds, where the differential size index q = 3.6 ± 0.1. We estimate to order of magnitude that 0.2 M_⊕ and 1 × 10^(10) comet progenitors lie between 30 and 50 AU. Though our inferred size index nearly matches that derived by Dohnanyi, it is unknown whether catastrophic collisions are responsible for shaping the size distribution. Impact strengths may increase strongly with size from 50 to 500 km, whereas the derivation by Dohnanyi assumes impact strength to be independent of size. Collisional lifetimes of KBOs having diameters 50–500 km exceed the age of the solar system by at least 2 orders of magnitude in the present-day Belt, assuming bodies consist of solid, cohesive rock. Implications of the absence of detections of classical KBOs beyond 50 AU are discussed.