Dark matter in the classical dwarf spheroidal galaxies: a robust constraint on the astrophysical factor for gamma-ray flux calculations

We present a new analysis of the relative detectability of dark matter annihilation in the Milky Way's eight classical dwarf spheroidal satellite galaxies. Ours is similar to previous analyses in that we use Markov-Chain Monte Carlo techniques to fit dark matter halo parameters to empirical velocity dispersion profiles via the spherical Jeans equation, but more general in the sense that we do not adopt priors derived from cosmological simulations. We show that even without strong constraints on the shapes of dSph dark matter density profiles (we require only that the inner profile satisfies -lim(r->0) [dlnrho/dln r] <=1), we obtain a robust and accurate constraint on the astrophysical component of a prospective dark matter annihilation signal, provided that the integration angle is approximately twice the projected half-light radius of the dSph divided by distance to the observer, alpha_int~2rh/d. Using this integration angle, which represents a compromise between maximizing prospective flux and minimizing uncertainty in the dSph's dark matter distribution, we calculate the relative detectability of the classical dSphs by ground- and space-based gamma-ray observatories