NGC 6712: the variable star population of a tidally disrupted globular
  cluster
  We present an analysis of $\emph{VI}$ CCD time series photometry of globular
cluster NGC 6712. Our main goal is to study the variable star population as
indicators of the cluster mean physical parameters. We employed the Fourier
decomposition of RR Lyrae light curves to confirm that $[\rm Fe/H]_{UVES} =
-1.0 \pm 0.05$ is a solid estimate. We estimated the reddening to the cluster
as $E(B-V)$ = 0.35 $\pm$ 0.04 from the RRab stars colour curves. The distance
to the cluster was estimated using three independent methods which yielded a
weighted mean distance $\big < d \big>$ = 8.1 $\pm$ 0.2 kpc. The distribution
of RRab and RRc stars on the HB shows a clear segregation around the first
overtone red edge of the instability strip, which seems to be a common feature
in OoI-type cluster with a very red horizontal branch. We carried out a
membership analysis of 60,447 stars in our FoV using the data from $Gaia$-DR2
and found 1529 likely members; we possess the light curves of 1100 among the
member stars. This allowed us to produce a clean colour-magnitude diagram,
consistent with an age of 12 Gyrs, and enabled us to discover close unresolved
contaminants for several variable stars. From the proper motion analysis we
found evidence of non-member stars in the FoV of the cluster being tidally
affected by the gravitational pull of the bulge of the Galaxy. We found that
the RRab variable V6, shows a previously undetected Blazhko effect. Finally, we
report sixteen new variables of the EW-type (9) and SR-type (7).
