  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%.
