We present new sets of nonlinear, time-dependent convective hydrodynamical models of RR Lyrae stars assuming two metal (Z=0.0005, Z=0.001) and three helium abundances (Y=0.24, 0.30, 0.38). For each chemical composition we constructed a grid of fundamental (FU) and first overtone (FO) models covering a broad range of stellar masses and luminosities. To constrain the impact of the helium content on RR Lyrae properties, we adopted two observables --period distribution, luminosity amplitudes-- that are independent of distance and reddening. The current predictions confirm that the helium content has a marginal effect on the pulsation properties. The key parameter causing the difference between canonical and He-enhanced observables is the luminosity. We compared current predictions with the sample of 189 RR Lyrae stars in omega Cen and we found that the period range of He-enhanced models is systematically longer than observed. These findings apply to metal-poor and metal-intermediate He-enhanced models. To further constrain the impact of He-enhanced structures on the period distribution we also computed a series of synthetic HB models and we found that the predicted period distribution, based on a Gaussian sampling in mass, agrees quite well with observations. This applies not only to the minimum fundamentalized period of RR Lyrae stars (0.39 vs 0.34 day), but also to the fraction of Type II Cepheids (2% vs 3%). We also computed a series of synthetic HB models assuming a mixed HB population in which the 80% is made of canonical HB structures, while the 20% is made of He-enhanced (Y=0.30) HB structures. We found that the fraction of Type II Cepheids predicted by these models is almost a factor of two larger than observed (5% vs 3%). This indicates that the fraction of He-enhanced structures in omega Cen cannot be larger than 20%.
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