A detailed census of variable stars in the globular cluster NGC 6333 (M9) from CCD differential photometry

We report CCD $V$ and $I$ time-series photometry of the globular cluster NGC 6333 (M9). The technique of difference image analysis has been used, which enables photometric precision better than 0.05 mag for stars brighter than $V \sim 19.0$ mag, even in the crowded central regions of the cluster. The high photometric precision has resulted in the discovery of two new RRc stars, three eclipsing binaries, seven long-term variables and one field RRab star behind the cluster. A detailed identification chart and equatorial coordinates are given for all the variable stars in the field of our images of the cluster. Our data together with literature $V$-data obtained in 1994 and 1995 allowed us to refine considerably the periods for all RR Lyrae stars. The nature of the new variables is discussed. We argue that variable V12 is a cluster member and an Anomalous Cepheid. Secular period variations, double mode pulsations and/or the Blazhko-like modulations in some RRc variables are addressed. Through the light curve Fourier decomposition of 12 RR Lyrae stars we have calculated a mean metallicity of [Fe/H]$_{\rm ZW}$=$-1.70 \pm 0.01{\rm(statistical)} \pm 0.14{\rm(systematic)}$ or [Fe/H]$_{UVES}=-1.67 \pm 0.01{\rm(statistical)} \pm 0.19{\rm(systematic)}$.Absolute magnitudes, radii and masses are also estimated for the RR Lyrae stars. A detailed search for SX Phe stars in the Blue Straggler region was conducted but none were discovered. If SX Phe exist in the cluster then their amplitudes must be smaller than the detection limit of our photometry. The CMD has been corrected for heavy differential reddening using the detailed extinction map of the cluster of Alonso-Garc\'ia et al. (2012). This has allowed us to set the mean cluster distance from two independent estimates; from the RRab and RRc absolute magnitudes, we find $8.04\pm 0.19$ kpc and $7.88\pm0.30$ kpc respectively.