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We present a comparative study of the Oosterhoff II cluster M2 and the Oosterhoff I cluster M3. Both have similar metallicities, [Fe/H]=-1.62 for M2 and -1.66 for M3, but very different horizontal-branch (HB) morphologies (B-R)/(B+V+R)=0.92 for M2 and 0.08 for M3. A period shift analysis and main-sequence fitting show that RRab variables in M2 are about 0.2 mag brighter than those in M3. Comparisons of the M2 period shift with Oosterhoff I clusters NGC 3201 and NGC 7006 also yield similar results, while a comparison between M2 and the Oosterhoff II cluster NGC 5986 reveals that the RR Lyrae luminosities are very similar. The luminosity difference is thought to be due to the evolutionary effect described in 1990 by Lee, Demarque, & Zinn: the M2 RRab variables have evolved away from the zero-age horizontal branch (ZAHB), while most M3 RRab variables lie near the ZAHB. A comparison of the mean period change rates of two clusters supports this hypothesis. Our relative age estimation using the difference in color between the base of giant branch and turn-off point shows that M2 is about 2 Gyr older than M3. Our result strongly suggests that the Oosterhoff dichotomy is due to age differences between Oosterhoff group I and II. This is consistent with the idea that the global second parameter is age.

We discuss the kinematic differences between Oosterhoff group I and II clusters. Our result shows that the Oosterhoff group I clusters have zero or retrograde rotation with <v_rot≥-68±56 km.s^–1 and σ_los=131±28 km.s^–1, while the Oosterhoff group II clusters have prograde rotation with <v_rot≥+94±47 km.s^–1 and σ_los=115±29 km.s^–1, confirming a similar conclusion of van den Bergh. The difference in kinematics and ages between Oosterhoff group I and II clusters suggests that they may have different origins: The Oosterhoff II clusters were formed very early in the proto-Galaxy while the Oosterhoff I clusters were formed at different locations and at a later time, and were probably merger events. The period distributions of an unbiased sample of field RRab variables with {mid}Z{mid}≤3 kpc and {mid}Z{mid}≥5 kpc indicate that they may belong to different populations, with peak periods of 0.65 and 0.55 days, respectively. If the hypothesis that the Oosterhoff dichotomy is due to evolution is correct, then this period shift among the field RR Lyrae variables suggests that the RRab population with {mid}Z{mid}≤3 kpc is somewhat older than the RRab population with {mid}Z{mid}≥5 kpc. This also suggests different formation histories.

In an appendix, we discuss that the frequently used Gaussian HB mass-dispersion rate (i.e., the mass-loss rate at the red giant branch [RGB] tip) in synthetic HB model calculations cannot fully explain the extended blue HB population and the pulsational properties of RR Lyrae variables in M2. Comparisons with synthetic HB models strongly suggests that an enhanced mass loss is required that extends the HB toward lower HB masses. We also discuss statistical effects on the metallicity estimate using P_0,min for field RRab variables reported by Castellani, Maceroni, & Tosi in 1983. Our calculations suggest that the statistical effect is sufficient to explain the apparent gradient in P_0,min without introducing a metallicity gradient.Galaxy: formatio