The \mv vs \fe Calibration: I. HST Color-Magnitude Diagrams of 8 Globular Clusters in M 31

Abstract

Color Magnitude Diagrams (CMDs) of individual stars in 8 Globular Clusters in M31 down to about 1 mag fainter (V$\sim 26.5$) than the Horizontal Branch have been obtained with the Hubble Space Telescope. In particular, we observed G280 and G351 with the FOC (f/96+F430W, f/96+F480LP) while the WFPC2 (F555W,F814W) frames for G1,G58,G105,G108,G219+Bo468 were retrieved from the HST archive. The cluster metallicities -\fe- range from -1.8 to -0.4. Coupled with sufficiently accurate (to $\sim\pm0.1$ mag) measures of the mean brightness of the HB --\vhb--, appropriate estimates of reddening for each cluster, and the adoption of a distance modulus to M31 of \dmo = 24.43, this has allowed us to yield a direct calibration for the mean absolute magnitude of the HB at the instability strip --\mv-- with varying \fe: M_V^{HB} = (0.13 \pm 0.07)\fe + (0.95 \pm 0.09), where the associated errors result from the adopted global errors in the measure and best fitting procedures. The slope of the derived relation is fully consistent with that predicted by the standard and canonical models ($\sim0.15$) and obtained by various ground-based observations, while it is only marginally compatible with higher values ($\sim0.30$), also obtained in the past. The zero-point, which is crucial to absolute age determinations, depends on the adopted distance to M31 and is moreover affected by an additional error due to the residual uncertainties in the \hst photometric zero-points ($\sim0.05$ mag, at least). If confirmed, such a calibration of the \mv \vs \fe relationship would imply old absolute ages ($> 16$Gyr) for the oldest Galactic globulars and fairly small age spread among those having a constant magnitude difference between the Main-Sequence Turnoff and the HB.