2002NewA....7..395W

The stellar initial mass function at high redshift is an important defining property of the first stellar systems to form and may also play a role in various dark matter problems. We here determine the faint stellar luminosity function in an apparently dark-matter-dominated external galaxy in which the stars formed at high redshift. The Ursa Minor dwarf spheroidal galaxy is a system with a particularly simple stellar population-all of the stars being old and metal-poor-similar to that of a classical halo globular cluster. A direct comparison of the faint luminosity functions of the UMi dSph and of similar metallicity, old globular clusters is equivalent to a comparison of the initial mass functions and is presented here, based on deep HST WFPC2 and STIS imaging data. We find that these luminosity functions are indistinguishable, down to a luminosity corresponding to 0.3 M☉. Our results show that the low-mass stellar IMF for stars that formed at very highredshift! is apparently invariant across environments as diverse as those of an extremely low-surface-brightness, dark-matter-dominated dwarf galaxy and a dark-matter-free, high-density globular cluster within the Milky Way.