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.
