Ground-based CCD astrometry with wide field imagers III. WFI@2.2m proper-motion catalog of the globular cluster ω Centauri

Context. omega Centauri is the most well studied Galactic Globular Cluster because of its numerous puzzling features: significant dispersion in metallicity, multiple populations, triple main-sequence, horizontal branch morphology, He-rich population(s), and extended star-formation history. Intensive spectroscopic follow-up observing campaigns targeting stars at different positions in the color-magnitude diagram promises to clarify some of these peculiarities. Aims. To be able to target cluster members reliably during spectroscopic surveys and both spatial and radial distributions in the cluster outskirts without including field stars, a high quality proper-motion catalog of omega Cen and membership probability determination are required. The only available wide field proper-motion catalog of omega Cen is derived from photographic plates, and only for stars brighter than B similar to 16. Using ESO archive data, we create a new, CCD-based, proper-motion catalog for this cluster, extending to B similar to 20. Methods. We used high precision astrometric software developed specifically for data acquired by WFI@2.2m telescope and presented in the first paper of this series. We demonstrated previously that a 7 mas astrometric precision level can be achieved with this telescope and camera for well exposed stars in a single exposure, assuming an empirical PSF and a local transformation approach in measuring star displacements. Results. We achieved a good cluster-field separation with a temporal base-line of only four years. We corrected our photometry for sky-concentration effects. We provide calibrated photometry for UBVRCIC wide-band data plus narrow-band filter data centered on H-alpha for almost 360 000 stars. We confirm that the omega Cen metal-poor and metal-rich components have the same proper motion, and demonstrate that the metal-intermediate component in addition exhibits the same mean motion as the other RGB stars. We provide membership probability determinations for published omega Cen variable star catalogs. Conclusions. Our catalog extends the proper-motion measurements to fainter than the cluster turn-off luminosity, and covers a wide area (similar to 33' x 33') around the center of omega Cen. Our catalog is electronically available to the astronomical community.