The structure of the Kuiper Belt: Size distribution and radial extent

The size distribution in the Kuiper Belt records physical processes operati ng during the formation and subsequent evolution of the solar system. This paper reports a study of the apparent magnitude distribution of faint objec ts in the Kuiper Belt, obtained via deep imaging on the Canada-France-Hawai i Telescope and the ESO Very Large Telescope UT1. We find that the entire r ange of observed objects (magnitudes m(R) similar to 20-27) is well represe nted by an unbroken power law, with the number of objects per square degree brighter than magnitude R being of the form Sigma (m(R) < R) = 10(<alpha>( R-R0)), with alpha = 0.69 and R-0 = 23.5. This luminosity function's slope implies a steep size distribution in the observed range, which should "roll over" to a shallower "collisional" slope once observations extend to even fainter magnitudes and thus sample bodies whose collisional ages become les s than the age of the solar system. Our observations indicate the roll over is for diameters of less than 50 km, in agreement with collisional models. Modeling our survey gives a belt mass between 30 and 50 AU of order 0.1 M, relatively insensitive to the roll over diameter as long as the latter is greater than or similar to1 km. We report the discovery of several objects outside of 48 AU and discuss the evidence for a sharp outer edge to the tr ans-Neptunian distribution.