Velocity dispersions of dwarf spheroidal galaxies: dark matter versus MOND

Abstract

We present predictions for the line-of-sight velocity dispersion profiles of dwarf spheroidal galaxies and compare them to observations in the case of the Fornax dwarf. The predictions are made in the framework of standard dynamical theory of spherical systems with different velocity distributions. The stars are assumed to be distributed according to Sersic laws with parameters fitted to observations. We compare predictions obtained assuming the presence of dark matter haloes (with density profiles adopted from N-body simulations) versus those resulting from Modified Newtonian Dynamics (MOND). If the anisotropy of velocity distribution is treated as a free parameter observational data for Fornax are reproduced equally well by models with dark matter and with MOND. If stellar mass-to-light ratio of $1 M_{\sun}/L_{\sun}$ is assumed, the required mass of the dark halo is $1.5 \times 10^9 M_{\sun}$, two orders of magnitude bigger than the mass in stars. The derived MOND acceleration scale is $a_0 = 2.1 \times 10^{-8}$ cm/s$^2$. In both cases a certain amount of tangential anisotropy in the velocity distribution is needed to reproduce the shape of the velocity dispersion profile in Fornax.