The Luminosity Function of the Hot and Cold Kuiper belt Populations

Abridged. We have performed an ecliptic survey of the Kuiper belt, with an areal coverage of 8.9 square degrees to a 50% limiting magnitude of r'=24.7, and have detected 88 Kuiper belt objects, roughly half of which received follow-up one to two months after detection. Using this survey data alone, we have measured the luminosity function of the Kuiper belt, thus avoiding any biases that might come from the inclusion of other observations. We have found that the Cold population defined as having inclinations less than 5 degrees has a luminosity function slope alpha=0.82+-0.23, and is different from the Hot population, which has inclinations greater than 5 degrees and a luminosity function slope alpha=0.35+-0.21. As well, we have found that those objects closer than 38 AU have virtually the same luminosity function slope as the Hot population. This result, along with similar findings of past surveys demonstrates that the dynamically cold Kuiper belt objects likely have a steep size distribution, and are unique from all of the excited populations which have much shallower distributions. This suggests that the dynamically excited population underwent a different accretion history and achieved a more evolved state of accretion than the cold population. As well, we discuss the similarities of the Cold and Hot populations with the size distributions of other planetesimal populations. We find that while the Jupiter family comets and the scattered disk exhibit similar size distributions, a power-law extrapolation to small sizes for the scattered disk cannot account for the observed influx of comets. As well, we have found that the Jupiter Trojan and Hot populations cannot have originated from the same parent popuation, a result that is difficult to reconcile with scattering models similar to the NICE model.