Variable stars in NGC 4147 revisited: RR Lyrae stars new CCD VI photometry and physical parameters

We have calculated the physical parameters of the RR Lyrae stars in the globular cluster NGC~4147 via the Fourier decomposition of their light curves, using new data and well-established semi-empirical calibrations and zero points. The mean metallicity and distance estimated using the RRc stars are [Fe/H]$_{ZW}=-1.72\pm0.15$ and $19.05\pm0.46$ kpc respectively. The star V18, whose variability has been previously in dispute, is confirmed to be a variable of the SR type with a period of about 24.8d, and it has been used to get and independent distance estimate of the cluster. It is observed that the RRab and RRc stars do not share the inter-mode region in the horizontal branch. The cluster can be classified as of intermediate Oosterhoff type. Its horizontal branch structure and metallicity make a good case for extragalactic origin. It follows the distribution of Oo~I type globular clusters in the $M_V-$[Fe/H] plane, as depicted from the RRc stars.