Pencil-beam surveys for faint trans-Neptunian objects

Motivated by a desire to understand the size distribution of objects in the Edgeworth-Kuiper belt, an observing program has been conducted at the Palomar 5 m and Canada-France-Hawaii 3.6 m telescopes. We have conducted pencil-beam searches for outer solar system objects to a limiting magnitude of R similar to 26. The fields were searched using software recombinations of many short exposures shifted at different angular rates in order to detect objects at differing heliocentric distances. Five new trans-Neptunian objects were detected in these searches. Our combined data set provides an estimate of similar to 90 trans-Neptunian objects deg(-2) brighter than similar or equal to 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 fits to all self-consistent published surveys with published efficiency functions predicts a cumulative sky density Sigma(<R) obeying log Sigma = 0.76(R - 23.4) objects deg(-2) brighter than a given magnitude R.