Local extremely metal-poor (XMP) galaxies are of particular astrophysical interest since they allow us to look into physical processes characteristic of the early Universe, from the assembly of galaxy disks to the formation of stars in conditions of low metallicity. Given the luminosity-metallicity relationship, all galaxies fainter than Mr < -13 are expected to be XMPs. Therefore, XMPs should be common in galaxy surveys. However, they are not, because several observational biases hamper their detection. This work compares the number of faint XMPs in the SDSS-DR7 spectroscopic survey with the expected number, given the known biases and the observed galaxy luminosity function. The faint end of the luminosity function is poorly constrained observationally, but it determines the expected number of XMPs. Surprisingly, the number of observed faint XMPs (around 10) is over-predicted by our calculation, unless the upturn in the faint end of the luminosity function is not present in the model. The lack of an upturn can be naturally understood if most XMPs are central galaxies in their low-mass dark matter halos, which are highly depleted in baryons due to interaction with the cosmic ultraviolet background and to other physical processes. Our result also suggests that the upturn towards low luminosity of the observed galaxy luminosity function is due to satellite galaxies.
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