We determine the metallicity distribution function (MDF) of the Galactic halo by means of a sample of 1638 metal-poor stars selected from the Hamburg/ESO objective-prism survey (HES). The sample was corrected for minor biases introduced by the strate
gy for spectroscopic follow-up observations of the metal-poor candidates, namely best and brightest stars first. [...] We determined the selection function of the HES, which must be taken into account for a proper comparison between the HES MDF with MDFs of other stellar populations or those predicted by models of Galactic chemical evolution. The latter show a reasonable agreement with the overall shape of the HES MDF for [Fe/H] > -3.6, but only a model of Salvadori et al. (2007) with a critical metallicity for low-mass star formation of Z_cr = 10^{-3.4} * Z_Sun reproduces the sharp drop at [Fe/H] ~-3.6 present in the HES MDF. [...] A comparison of the MDF of Galactic globular clusters and of dSph satellites to the Galaxy shows qualitative agreement with the halo MDF, derived from the HES, once the selection function of the latter is included. However, statistical tests show that the differences between these are still highly significant. [ABSTRACT ABRIDGED]
We present the quantitative methods used for selecting candidate metal-poor stars in the Hamburg/ESO objective-prism survey (HES). The selection is based on the strength of the Ca II K line, B-V colors (both measured directly from the digital HES spe
ctra), as well as J-K colors from the 2 Micron All Sky Survey. The KP index for Ca II K can be measured from the HES spectra with an accuracy of 1.0 Angstrom, and a calibration of the HES B-V colors, using CCD photometry, yields a 1-sigma uncertainty of 0.07 mag for stars in the color range 0.3 < B-V < 1.4. These accuracies make it possible to reliably reject stars with [Fe/H] > -2.0 without sacrificing completeness at the lowest metallicities. A test of the selection using 1121 stars of the HK survey of Beers, Preston, and Shectman present on HES plates suggests that the completeness at [Fe/H] < -3.5 is close to 100% and that, at the same time, the contamination of the candidate sample with false positives is low: 50% of all stars with [Fe/H] > -2.5 and 97% of all stars with [Fe/H] > -2.0 are rejected. The selection was applied to 379 HES fields, covering a nominal area of 8853 square degrees of the southern high Galactic latitude sky. The candidate sample consists of 20,271 stars in the magnitude range 10 < B < 18. A comparison of the magnitude distribution with that of the HK survey shows that the magnitude limit of the HES sample is about 2 mag fainter. Taking the overlap of the sky areas covered by both surveys into account, it follows that the survey volume for metal-poor stars has been increased by the HES by about a factor of 10 with respect to the HK survey. We have already identified several very rare objects with the HES, including, e.g., the three most heavy-element deficient stars currently known.
