Internal dynamics and dynamical friction effects in the dwarf spheroidal galaxy in Fornax

In the Fornax dwarf spheroidal galaxy the globular clusters are distributed widely, without any significant central concentration. Oh et al. pointed out that such a distribution is paradoxical: dynamical friction effects estimated using single-component King models would have forced the globular clusters to spiral down to the center of the galaxy well within a Hubble time. This paper is devoted to a discussion of this paradox. We describe a model in which the stars of the dwarf spheroidal galaxy are embedded in a cloud of dark matter, and each of these components is specified by its own phase space distribution function. This model allows us to fit self-consistently the observed luminosity profile and the spatial variation of the velocity dispersion of the stars. This fitting yields two basic parameters, related to the central density and velocity dispersion, that characterize the phase space distribution of dark matter. The dynamical friction effects calculated on the basis of this self-consistent model are small enough that the observed spatial distribution of the globular clusters poses no difficulty, and the apparent paradox is resolved. Thus we have at hand a model for Fornax that reproduces the main observed features of this dwarf spheroidal galaxy.