We test whether the peak absolute magnitude M _ { V } ( TO ) of the Globular Cluster Luminosity Function ( GCLF ) can be used for reliable extragalactic distance determinations .
Starting with the luminosity function of the Galactic Globular Clusters listed in Harris catalog , 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 ( [ Fe/H ] < - 1.0 , \langle [ Fe/H ] \rangle \sim - 1.6 ) sample shows peak magnitudes systematically brighter by about 0.36 mag than those of the metal-rich ( [ Fe/H ] > - 1.0 , ( \langle [ Fe/H ] \rangle \sim - 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 metal-poor 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 determinations .
As for the GCLFs in other external galaxies , using Surface Brightness Fluctuations ( SBF ) measurements we give evidence that the luminosity functions of the blue ( metal-poor ) Globular Clusters peak at the same luminosity within \sim 0.2 mag , whereas for the red ( metal-rich ) samples the agreement is within \sim 0.5 mag 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 LMC , we show that the M _ { V } ( TO ) value of the metal-poor clusters in external galaxies is in excellent agreement with the value of both Galactic and M31 ones , as inferred by a RR Lyrae distance scale referenced to the same LMC fiducial distance .
Eventually , adopting \mu _ { 0 } ( LMC ) =18.50 mag , we derive that the luminosity function of metal-poor clusters in the Milky Way , M31 , and external galaxies peak at M _ { V } ( TO ) = - 7.66 \pm 0.11 mag , - 7.65 \pm 0.19 mag and - 7.67 \pm 0.23 mag , respectively .
This would suggest a value of - 7.66 \pm 0.09 mag ( weighted mean ) , with any modification of the LMC distance modulus producing a similar variation of the GCLF peak luminosity .