Dark matter in dwarf spheroidals - II. Observations and modelling of Draco

We present stellar radial velocity data for the Draco dwarf spheroidal (dSph) galaxy obtained using the AF2/WYFFOS instrument combination on the William Herschel Telescope. Our data set consists of 186 member stars, 159 of which have good quality velocities, extending to a magnitude V approximate to 19.5 with a mean velocity precision of approximate to2 km s(-1). As this survey is based on a high-precision photometric target list, it contains many more Draco members at large radii. For the first time, this allows a robust determination of the radial behaviour of the velocity dispersion in a dSph. We find statistically strong evidence of a rising velocity dispersion consistent with a dark matter halo that has a gently rising rotation curve. There is a <2 sigma signature of rotation about the long axis, inconsistent with tidal disruption as the source of the rising dispersion. By comparing our data set with earlier velocities, we find that Draco probably has a binary distribution and fraction comparable to those in the solar neighbourhood. We apply a novel maximum likelihood algorithm and fit the velocity data to a two parameter spherical model with an adjustable dark matter content and velocity anisotropy. Draco is best fit by a weakly tangentially anisotropic distribution of stellar orbits in a dark matter halo with a very slowly rising rotation law (v(circ) o proportional to r(0.17)). We are able to rule out both a mass-follows-light distribution and an extended halo with a harmonic core at the 2.5 to 3 sigma significance level, depending on the details of our assumptions about Draco's stellar binary population. Our modelling lends support to the idea that the dark matter in dwarf spheroidals is distributed in the form of massive, nearly isothermal haloes.