Pulsating variable stars

Pulsating variable stars are fundamental tools to set the astronomical distance scale, and to sample different stellar populations in galaxies, through the study of the luminosity and luminosity-metallicity relation of the RR Lyrae stars; the Period-Luminosity (PL) and Period-Luminosity-Color (PLC) relations of Anomalous, Type II, and Dwarf Cepheids; the period distribution of the RR Lyrae variables, and the double-mode pulsators.

Population II variable stars and their role in establishing the astronomical distance scale have been a major field of study at the OAB since 1984 (e.g. Cacciari et al. 1987). A number of new projects have been started in more recent years (e.g. ``The VSNG project", Clementini 2003), in collaboration with researchers of the INAF-Padova, Napoli and Merate Observatories, to map out the variable star content in a number of Local Group galaxies of different morphological type.

RR Lyrae stars are excellent tracers of the oldest stellar population in galaxies (and therefore of the epoch of galaxy formation) and are the primary Population II distance indicators in the LG. Their absolute visual magnitude M$_V$(RR) sets the luminosity of the horizontal branch (HB) and its dependence on metal abundance, usually described as a linear relation: M $_{\rm V}{\rm (RR)}=\alpha \times {\rm [Fe/H]} + \beta$. The zeropoint of this relation constrains the GGC distances and absolute ages through the TO luminosity calibration, providing in turn a lower limit to the cosmic age. The slope gives clues on the GGC relative ages and on the time scale of Galactic halo formation and early evolution. There is now a growing consensus on a zero point $\beta \sim 0.6$ at [Fe/H] $=-1.5$ (Cacciari & Clementini 2003) which supports the long astronomical distance scale (see Clementini et al. 2003a). However, the slope $\alpha$ and its uniqueness are still a matter of debate, with literature values in the range from 0.30 mag/dex to 0.18-0.20 mag/dex (Cacciari 1999, Carretta et al. 2000) and empirical (Rey et al. 2000) and theoretical (Caputo et al. 2000) evidence for a non-linearity of the M$_{\rm V}$(RR)-[Fe/H] relation for GGCs.

The value of $\beta$ from the Baade-Wesselink method
People involved at OAB: Cacciari, Clementini.

The zeropoint of the luminosity-metallicity relation of the Galactic RR Lyrae stars is investigated using the Baade-Wesselink (BW) method on two RR Lyrae variables in the globular cluster M3. We are testing the effects on the technique of the most recent model atmospheres with various approximations in the treatment of convection, different values of turbulent velocity and more complete and accurate opacity tables, as well as the use of the instantaneous gravity along the pulsation cycle (Cacciari et al. 2000). We have reduced the high resolution spectra obtained with SARG@TNG and built up accurate radial velocity curves. Reduction of the IR (K-band) photometry obtained with ARNICA@TNG is in progress.

The value of $\alpha$ from metal abundances of RR Lyrae stars in the LMC and in Sculptor
People involved at OAB: Bragaglia, Clementini, Maio.

The slope of the luminosity-metallicity relation followed by RR Lyrae stars can be directly measured using a population of RR Lyrae variables all at the same distance, and spanning a suitable range in metal abundance. RR Lyrae stars in external galaxies play a key role in this respect, since they can be considered at the same distance from us, are numerous, and generally span large metallicity ranges. The slope of the luminosity-metallicity relation for RR Lyrae stars in the Large Magellanic Cloud (LMC) bar has been investigated in collaboration with Carretta, Gratton (INAF-Padova Obs.) and Di Fabrizio (INAF-TNG), using low resolution spectroscopy obtained with FORS1@VLT.

These spectroscopic data have allowed us to measure metallicities accurate to $\sim$ 0.15-0.20 dex using a revised version of the $\Delta S$ index (Preston 1959; Gratton et al. 2004) for a sample of about 100 RR Lyrae variables in the bar of the LMC. The derived metal abundances range from $-$0.27 to $-$2.12 with an average value of [Fe/H]  $=-1.48 \pm 0.03 \pm 0.06$. Individual metallicities were combined with the high quality photometric data by Clementini et al. (2003a) to determine the slope of the luminosity-metallicity relation of the LMC field RR Lyrae stars: $\Delta {\rm M}_V$(RR)/[Fe/H]  $=0.214\pm0.047$ mag/dex. This mild slope is in very good agreement with the one obtained by recent results on the HB luminosity of GCs in M31, and with results from the BW analysis of MW field RR Lyrae stars (Fernley et al. 1998), implying that the same luminosity-metallicity relation for HB stars is valid in these three different environments, and that a significant age-metallicity dependence is likely to exist in the family of the GGCs.

New observing time (10 hours FORS2@VLT service mode) obtained in 2003 has been devoted to multi-slit spectroscopy of about 150 RR Lyrae stars in the dwarf spheroidal galaxy Sculptor. The spectroscopic data have been fully reduced and their analysis is in progress. The derived metalicities will allow us to establish the luminosity-metallicity relation followed by the RR Lyrae in Sculptor. The comparison with our results for the LMC will then provide a clearcut proof on whether the slope of the luminosity-metallicity relation for RR Lyrae stars is universal, with fundamental bearings upon the entire Population II distance scale. This study is in collaboration with Gratton, Held (INAF-Padova Obs.), Ripepi (INAF-Napoli Obs.).