Observational Constraints on the “Missing Satellite” Problem from SDSS
We quantify the algorithmic detectability of stellar Milky Way satellites in data release 5 (DR5) of the Sloan Digital Sky Survey (SDSS), and use this to estimate the luminosity function of faint satellite galaxies in our halo. We develop a satellite detection algorithm based on the convolution of the DR5 star catalog with a kernel of zero net flux that is the difference of a narrow positive Gaussian and a much wider negative Gaussian, which removes the background star-count level. This permits us to assess the significance of any (positive) detection in terms of deviations of this map. The efficiency of this algorithm is tested by computing the recovery rate of a large set of mock objects added to SDSS DR5 as a function of their luminosity, size and distance from the Sun. Most of the recent Milky Way satellite discoveries, made by SDSS, are shown to lie very close to the survey’s detection limits. Calculating the maximum accessible volume Vmax for all faint detected objects makes it possible for the first time to calculate the luminosity function for the Milky Way satellite galaxies, accounting consistently and algorithmically for their detection biases. The number density of satellite galaxies continues to rise towards low luminosities, but may flatten at MV ∼ -5. Within the uncertainties the luminosity function can be described by a simple power law dN/dMV= 10 × 100.1(MV+5), spanning luminosities from MV=-2.5 all the way to the bright end. Comparing these results to several galaxy formation models, we find the predicted properties differ from the data.
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