A new visit to the variable stars in M56 and its colour magnitude diagram structure

We present a $VI$ CCD photometric study and a membership analysis of the globular cluster M56 (NGC 6779). This produced a decontaminated CMD from field stars, which enabled a better confrontation with theoretical isochrones; Zero-Age Horizontal Branches (ZAHB) and post-ZAHB evolutionary tracks. Post He-flash evolutionary models with a He-core mass of 0.5 M$_\odot$ and envelopes of 0.04 - 0.18 M$_\odot$, cover the complete Horizontal Branch. Models with total mass $\sim$ 0.68 M$_\odot$ explain the RR Lyrae, while those with a mass $\sim$ 0.56 M$_\odot$ and a very subtle envelope, explain the Pop II cepheids with a progenitor in the blue tail of the HB. %Using the mean $(V-I)$ at minimum color curve for the RRab stars, we derived a value for the reddening of $E(B-V)$ = 0.26 $\pm$ 0.02. Based on the Fourier decomposition of the $V$ light curve of a single cluster member RRc star, we determined a metallicity of $\rm [Fe/H]_{ ZW}$ = -1.96 $\pm$ 0.09. Several independent distance determination approaches lead to a mean distance to M56 of $\big< d \big>$ = 9.4 $\pm$ 0.4 kpc. Finally, we report 5 new variables: 1 SX Phe, 3 EB, and 1 RRc.