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The luminosity function (LF) phi(L) of galaxies is defined as the number density of galaxies per unit luminosity L: the number of galaxies in volume dV with luminosity between L and L + dL is phi(L) dL dV.

The LF represents one of the most direct interfaces between studies of dwarf galaxies and cosmology, the two subjects of this conference. This statement follows directly from the form of the fluctuation spectrum - most plausible theories of structure formation (e.g. cold dark matter [3]) predict a fluctuation spectrum whose power spectrum |delta(k)|2 propto kn has index n ~ - 2 on scales of galaxies. This value of n simultaneously requires that low-mass systems be far more numerous than high-mass ones, so that the statistical properties of low-mass systems are a powerful probe of galaxy formation theories.

Consequently one of the most fundamental predictions of models of galaxy formation and evolution is the LF, particularly at faint magnitudes (e.g. refs. 6, 13, 48 - 50). These models generally assume a power spectrum of primordial dark matter fluctuations (say, from CDM theory) and then adopt prescriptions for the behavior of the baryonic component (specifically, things like the effects of gas dissipation, star-formation efficiencies, feedback from supernovae, and the temperature-density structure of the intergalactic medium need to be quantified).

Significant differences in the theoretical luminosity functions from different models are seen, even when similar dark matter power spectra are assumed, because of differing prescriptions for the behavior of the baryonic component. For example Babul & Ferguson [2] suggest a faint-end slope of alpha ~ - 2.6 at faint magnitudes, whereas White & Kauffmann [49] compute values more like alpha ~ - 1 for their dwarf suppression models (here alpha is the logarithmic slope of the LF: alpha = d log phi(L) / d log L). Therefore measuring alpha as accurately as possible at faint magnitudes seems like a worthwhile exercise.

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