2015A&A...577A..99N

ω Centauri (NGC 5139) contains many variable stars of different types and, in particular, more than one hundred RR Lyrae stars. This enabled gathering a homogeneous sample (in terms of instrument, image quality, and time coverage) of high-quality near-infrared (NIR) RR Lyrae light curves by performing an extensive time-series campaign aimed at this object. We have conducted a variability survey of ω Cen in the NIR, using ESO's 4.1m Visible and Infrared Survey Telescope for Astronomy (VISTA). This is the first paper of a series describing our results. ω Cen was observed using VIRCAM mounted on VISTA. A total of 42 epochs in J and 100 epochs in K_S were obtained, distributed over a total timespan of 352 days. Point-spread function photometry was performed using DAOPHOT in the inner and DoPhot in the outer regions of the cluster. Periods of the known variable stars were improved when necessary using an ANOVA analysis. We collected an unprecedented homogeneous and complete NIR catalog of RR Lyrae stars in the field of ω Cen, allowing us to study for the first time all the RR Lyrae stars associated with the cluster, except for four stars that are located far away from the cluster center. We derived membership status, subclassifications between RRab and RRc subtypes, periods, amplitudes, and mean magnitudes for all the stars in our sample. Additionally, four new RR Lyrae stars were discovered, two of which are very likely cluster members. We also discuss here the distribution of ω Cen stars in the Bailey (period-amplitude) diagram. We provide reference lines in this plane for both Oosterhoff Type I (OoI) and Oosterhoff Type II (OoII) components in J and K_S. We clarify the status of many (candidate) RR Lyrae stars that have been reported as unclear in previous studies. This includes stars with anomalous positions in the color-magnitude diagram, uncertain periods or/and variability types, and possible field interlopers. We conclude that ω Cen hosts a total of 88 RRab and 101 RRc stars, which makes for a grand total of 189 probable members. We confirm that most RRab stars in the cluster appear to belong to an OoII component, as previously found using visual data.