In our recent investigation of the Oosterhoff dichotomy in the multiple population paradigm ( 36 ) , we have suggested that the RR Lyrae variables in the Oosterhoff groups I , II , and III globular clusters ( GCs ) are produced mostly by the first , second , and third generation stars ( G1 , G2 , and G3 ) , respectively .
Here we show , for the first time , that the observed dichotomies in the inner and outer halo GCs can be naturally reproduced when these models are extended to all metallicity regimes , while maintaining reasonable agreements in the horizontal-branch type versus [ Fe/H ] correlations .
In order to achieve this , however , specific star formation histories are required for the inner and outer halos .
In the inner halo GCs , the star formation commenced and ceased earlier with relatively short formation timescale between the subpopulations ( \sim 0.5 Gyr ) , while in the outer halo , the formation of G1 was delayed by \sim 0.8 Gyr with more extended timescale between G1 and G2 ( \sim 1.4 Gyr ) .
This is consistent with the dual origin of the Milky Way halo .
Despite the difference in detail , our models show that the Oosterhoff period groups observed in both outer and inner halo GCs are all manifestations of the “ population-shift ” effect within the instability strip , for which the origin can be traced back to the two or three discrete episodes of star formation in GCs .