Photometry of the Globular Cluster M54 and the Sagittarius Dwarf Galaxy: The Age-Metallicity Relation

We present deep VI-band photometry of the globular cluster M54, a nearby field in the Sagittarius dwarf galaxy, and a control field. The color-magnitude diagrams reach well below the oldest main-sequence turnoffs, thus enabling an analysis of the galaxy's age-metallicity relation with unprecedented clarity. We also study the variable stars in the direction of M54. From 67 RR Lyrae variables, we confirm and improve on our previous estimates of the cluster horizontal branch magnitude, foreground reddening, and horizontal branch morphology. These values are used in determining the ages of M54 and the Sagittarius field populations. We confirm our previous result that M54 is the same age as Galactic globular clusters of similar metallicity. We also derive ages on a self-consistent scale for the other three globular clusters in Sagittarius. We find strong evidence for multiple episodes of star formation (or continuous star formation with a variable rate) in the field of Sagittarius. We characterize the principal episodes with the ages 11, 5, and 0.5 through 3 Gyr and with Fe/H values of -1.3, -0.7, and -0.4, respectively. On this scale, M54 has an age of 15 Gyr. Surprisingly, the age-metallicity relation we have derived for the galaxy as a whole is described quite well by a closed-box chemical evolution model. We also find that the populations associated with the Sgr field are clumped spatially around M54, and we consider several explanations for this phenomenon. We again speculate that Sagittarius is a nucleated dwarf elliptical galaxy with M54 as its nucleus.