We present an extensive photometry on HB, RGB, and MSTO stars in Omega Cen. The central regions of the cluster were covered with a mosaic of F435W, F625W, and F658N-band data collected with ACS/HST. The outer reaches were covered with a large set of U,B,V,I-band data collected with the WFI@2.2m ESO/MPI telescope. The final catalogue includes ~1.7 million stars. We identified ~3,200 likely HB stars and ~12,500 stars brighter than the subgiant branch and fainter than the RGB bumps. The HB morphology changes with the radial distance. The relative number of extreme HB stars decreases from ~30% to ~21% when moving from the center toward the outer regions of the cluster, while the fraction of less hot HB stars increases from ~62% to ~72%. We performed a detailed comparison between observed ratios of different stellar tracers and predictions based on canonical evolutionary models with a primordial helium (Y=0.23) content and metal abundances (Z=0.0002,0.001) that bracket the observed spread in metallicity of Omega Cen stars. We found that the empirical star counts of HB stars are on average larger (30%-40%) than predicted. Moreover, the rate of HB stars is 43% larger than the MSTO rate. The discrepancy between the rate of HB compared with the rate of RG and MSTO stars supports the evidence that we are facing a true excess of HB stars. The same comparison was performed by assuming a mix of stellar populations made with 70% of canonical stars and 30% of He-enhanced stars. The discrepancy between theory and observations decreases by a factor of two when compared with rates predicted by canonical He content models, but still 15%-25% (Y=0.42) and 15%-20% (Y=0.33) higher than observed. Furthermore, the ratio between HB and MSTO star counts are ~24% (Y=0.42) and 30% (Y=0.33) larger than predicted lifetime ratios.
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