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CCD \emph{VI} time-series of the extremely metal poor globular cluster M92: revisiting its variable star population

We present an analysis of \emph{VI} CCD time-series photometry of the Oo II type globular cluster M92. The variable star population of the cluster is studied with the aim of revising their classifications, identifications, frequency spectra and to select indicators of the parental cluster metallicity and distance. The Fourier decomposition of RR Lyrae light curves lead to the estimation of mean [Fe/H]$_{\rm spec}=-2.20\pm 0.18$, and distance of $8.3\pm0.2$ kpc. Four new variables are reported; one RRd (V40), a multimode SX Phe (V41), a SR (V42) and one RRc (F1) that is most likely not a cluster member. The AC nature of V7 is confirmed. The double mode nature of the RRc star V11 is not confirmed and its amplitude modulations are most likely due to the Blazhko effect. Two modes are found in the known RRc variable V13. It is argued that the variable V30, previously classified as RRab is, in fact, an BL Her-type star not belonging to the cluster. Making use of the $Gaia$-DR2 proper motions, we identified 5012 stars in the field of the cluster, that are very likely cluster members, and for which we possess photometry, enabling the production of a refined Colour-Magnitude Diagram. This also allowed us to identify a few variable stars that do not belong to the cluster. The RR Lyrae pulsation modes on the HB are cleanly separated by the first overtone red edge, a common feature in all Oo II type clusters.