The metal abundance distribution of the oldest stellar component in the Sculptor dwarf spheroidal galaxy

Low-resolution spectroscopy obtained with FORS2 at the Very Large Telescope (VLT) has been used for the measurement of individual metal abundances ([Fe/H]) for 110 variable stars, including 107 RR Lyrae stars and one anomalous Cepheid, and to trace the metal distribution of the oldest stellar component in the Sculptor dwarf spheroidal galaxy. The RR Lyrae stars are spread over a 15 x 15 arcmin(2) area around the galaxy centre. Their metallicities have an average value of [Fe/H]=-1.83 +/- 0.03 (rms = 0.26 dex) and cover the metallicity range -2.40 < [Fe/H] < -0.85 (on the scale of Zinn & West), but there is only one variable that has [Fe/H] > -1.3. The star-to-star scatter is larger than typical errors on individual metallicities (+/- 0.15-0.16 dex) indicating a real spread in metal abundances. The radial velocities measured from the RR Lyrae spectra have a dispersion of 12.9 km s(-1). This value is consistent with the dispersion derived by Tolstoy et al. for metal-poor red giants associated with the blue horizontal branch stars in Sculptor. Along with the metallicity distribution these results suggest that most of the RR Lyrae stars in Sculptor arise from the same burst of stellar formation that produced the metal-poor component, originating the galaxy blue horizontal branch. The metal-rich red horizontal branch population found to be centrally concentrated only produced a few (if any) of the RR Lyrae stars in our sample. The spectroscopic metallicities were used along with the apparent luminosities to study the luminosity-metallicity relation followed by the RR Lyrae stars in Sculptor, for which we derive a shallow slope of 0.09 mag dex(-1). This result can be due to a high level of evolution off the zero-age horizontal branch of the RR Lyrae stars in this galaxy, again in agreement with their origin from the blue horizontal branch population.