The globular cluster M10: Reassessment of stellar membership, distance and age using its variable and HB stars

Time-series VI CCD photometry of the globular cluster M10 (NGC 6254) is employed to perform a detailed identification, inspection of their light curves, their classification and their cluster membership, of all the known variables reported up to 2018. The membership analysis is based on the Gaia-DR2 positions and proper motions. The metallicity of the cluster is estimated based on the sole RRc star known in the cluster. The Fourier decomposition of its light curve leads to [Fe/H]ZW=-1:59 $\pm$ 0:23 dex. The mean cluster distance, estimated by several independent methods is 5.0 $\pm$ 0.3 kpc. A multi-approach search in a region of about 10x10 arcmin2 around the cluster revealed three new variables, one SX Phe (V35) and two sinusoidal variables on the red giant branch of unclear classification (V36,V37). Modelling the HB stars is very sensitive to the stellar hydrogen shell mass, which surrounds the 0.50 M$_\odot$ helium core. To match the full stretch of the HB population, a range of total mass of 0.56 to 0.62 M$_\odot$ is required. These models support a distance of 5.35 kpc and an age of about 13 Gyrs, and hints to some individual variation of the mass loss on the uppper RGB, perhaps caused by the presence of closed magnetic field in red giants.