Abstract
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
Sph 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 solar masses.
Our results show that the low-mass stellar IMF for stars that formed at very
high redshift 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.
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