Pencil - Beam Searches for Faint

Motivated by a desire to understand the size distribution of objects in the Kuiper belt, an observing program has been conducted at the CFHT and Palomar 5-m telescopes. We have conducted pencil-beam searches for outer solar system objects to a limiting magnitude of R 26. Fields were searched using software recombinations of many short exposures shifted at diierent angular rates in order to detect objects at diiering heliocentric distances. Five new trans-neptunian objects were detected in these surveys. Our combined data set provides an estimate of 90 trans-neptunian objects per square degree brighter than ' 25:9. This estimate is a factor of 3 above the expected number of objects based on an extrapolation of previous surveys with brighter limits, and appears consistent with the hypothesis of a single power-law luminosity function for the entire trans-neptunian region. Maximum likelihood ts to all self-consistent published surveys with published eeciency functions predicts a cumulative sky density (< R) obeying log = 0.76(R-23.4) objects per square degree brighter than a given magnitude R.