Precise distances from OGLE-IV member RR Lyrae stars in six bulge globular clusters

Context. RR Lyrae stars are useful standard candles allowing one to derive accurate distances for old star clusters. Based on the recent catalogues from OGLE-IV and Gaia Early Data Release 3 (EDR3), the distances can be improved for a few bulge globular clusters. Aims. The aim of this work is to derive an accurate distance for the following six moderately metal-poor, relatively high-reddening bulge globular clusters: NGC 6266, NGC 6441, NGC 6626, NGC 6638, NGC 6642, and NGC 6717. Methods. We combined newly available OGLE-IV catalogues of variable stars containing mean I magnitudes, with Clement's previous catalogues containing mean V magnitudes, and with precise proper motions from Gaia EDR3. Astrometric membership probabilities were computed for each RR Lyrae, in order to select those compatible with the cluster proper motions. Applying luminosity-metallicity relations derived from BaSTI $\alpha$-enhanced models (He-enhanced for NGC 6441 and canonical He for the other clusters), we updated the distances with relatively low uncertainties. Results. Distances were derived with the I and V bands, with a $5-8\%$ precision. We obtained 6.6 kpc, 13.1 kpc, 5.6 kpc, 9.6 kpc, 8.2 kpc, and 7.3 kpc for NGC 6266, NGC 6441, NGC 6626, NGC 6638, NGC 6642, and NGC 6717, respectively. The results are in excellent agreement with the literature for all sample clusters, considering the uncertainties. Conclusions. The present method of distance derivation, based on recent data of member RR Lyrae stars, updated BaSTI models, and robust statistical methods, proved to be consistent. A larger sample of clusters will be investigated in a future work.