RR Lyrae-based calibration of the Globular Cluster Luminosity Function

We test whether the peak absolute magnitude M_V(TO) of the Globular Cluster Luminosity Function (GCLF) can be used for reliable extragalactic distance determination. Starting with the luminosity function of the Galactic Globular Clusters listed in Harris catalogue, we determine M_V(TO) either using current calibrations of the absolute magnitude M_V(RR) of RR Lyrae stars as a function of the cluster metal content [Fe/H] and adopting selected cluster samples. We show that the peak magnitude is slightly affected by the adopted M_V(RR)-[Fe/H] relation, with the exception of that based on the revised Baade-Wesselink method, while it depends on the criteria to select the cluster sample. Moreover, grouping the Galactic Globular Clusters by metallicity, we find that the metal-poor (MP) ([Fe/H]< -1.0, <[Fe/H]>~-1.6) sample shows peak magnitudes systematically brighter by about 0.36mag than those of the metal-rich (MR) ([Fe/H]> -1.0, (<[Fe/H]>~-0.6) one, in substantial agreement with the theoretical metallicity effect suggested by synthetic Globular Cluster populations with constant age and mass function. Moving outside the Milky Way, we show that the peak magnitude of the MP clusters in M31 appears to be consistent with that of Galactic clusters with similar metallicity, once the same M_V(RR)-[Fe/H] relation is used for distance determination. As for the GCLFs in other external galaxies, using Surface Brightness Fluctuations (SBF) measurements we give evidence that the luminosity functions of the blue (MP) Globular Clusters peak at the same luminosity within ~0.2mag, whereas for the red (MR) samples the agreement is within ~0.5mag even accounting for the theoretical metallicity correction expected for clusters with similar ages and mass distributions. Then, using the SBF absolute magnitudes provided by a Cepheid distance scale calibrated on a fiducial distance to Large Magellanic Cloud (LMC), we show that the M_V(TO) value of the MP clusters in external galaxies is in excellent agreement with the value of both Galactic and M31 ones, as inferred by an RR Lyrae distance scale referenced to the same LMC fiducial distance. Eventually, adopting μ₀(LMC) = 18.50mag, we derive that the luminosity function of MP clusters in the Milky Way, M31, and external galaxies peak at M_V(TO) =-7.66 +/- 0.11, - 7.65 +/- 0.19 and -7.67 +/- 0.23mag, respectively. This would suggest a value of -7.66 +/- 0.09mag (weighted mean), with any modification of the LMC distance modulus producing a similar variation of the GCLF peak luminosity.