MgAl burning chain in M 54: the globular cluster-like properties of a nuclear star cluster

In this study, we present the chemical abundances of Fe, Mg, Al, Si, and K for a sample of 233 likely member stars of M 54. All the stars were observed with the FLAMES high-resolution multi-object spectrograph mounted at the VLT. Our analysis confirmed the presence of a large metallicity range in M 54, with the majority of the stars having -1.8 < [Fe/H] < -1.0 dex and few stars with [Fe/H] > -1.0 dex. The mean value of the total sample is [Fe/H] = -1.40 (σ = 0.22 dex). A Markov Chain Monte Carlo analysis revealed that the observed spread in [Fe/H] is compatible with a non-null intrinsic iron dispersion. We also found that the metallicity distribution function and the broadening of the red giant branch of M 54 are not compatible with a single age, but instead they suggest a wide age range from ~ 13 Gyr to ~ 1 - 2 Gyr or a smaller age range if a significant He enhancement (Y ~ 0.35/0.40) is present in the most metal-rich stars. We identified among the stars in M 54 the entire pattern of anticorrelations linked to the MgAl burning cycle. In particular, the metal-rich component displays a higher level of H-burning with the presence of more extended anticorrelations than the metal-poor component. No Mg-poor ([Mg/Fe]