NGC 1261: A time-series \emph{VI} study of its variable stars

Time-series \emph{VI} CCD photometry of the globular cluster NGC 1261 is employed to study its variable star population. A membership analysis of most variables based on Gaia~DR2 proper motions and colours, was performed prior to the estimation of the mean cluster distance and metallicity. For the member RR Lyrae, their light curves were Fourier decomposed to calculate their individual values of distance, [Fe/H], radius and mass. The $I$-band P-L for RR Lyrae stars was also employed. Our best estimates of the metallicity and distance of this Oo I cluster are [Fe/H]$_{\rm ZW}$=$-1.42 \pm 0.05$ dex and $d=17.2 \pm 0.4$ kpc. No mixture of fundamental and first overtone RR Lyrae stars in the either-or or bimodal region is seen in this cluster, as it seems to be the rule for Oo~I clusters with a red horizontal branch. A multi-approach search in a region of about 10$\times$10 arcmin$^2$ around the cluster revealed no new variable stars within the limitations of our CCD photometry.