The Detectability of Brown Dwarfs: Predictions and Uncertainties

In order to determine the likelihood for the detection of isolated brown dwarfs in ground-based observations as well as in future spaced-based astronomy missions, and in order to evaluate the significance of any detections that might be made, we must first know the expected surface density of brown dwarfs on the celestial sphere as a function of limiting magnitude, wavelength band, and Galactic latitude. It is the purpose of this paper to provide theoretical estimates of this surface density, as well as the range of uncertainty in these estimates resulting from various theoretical uncertainties. We first present theoretical cooling curves for low-mass stars that we have computed with the latest version of our stellar evolution code. We use our evolutionary results to compute theoretical brown-dwarf luminosity functions for a wide range of assumed initial mass functions and stellar birth rate functions. The luminosity functions, in turn, are utilized to compute theoretical surface density functions for brown dwarfs on the celestial sphere. We find, in particular, that for reasonable theoretical assumptions, the currently available upper bounds on the brown-dwarf surface density are consistent with the possibility that brown dwarfs contribute a substantial fraction of the mass of the Galactic disk.