Theoretical Period Changes in Yellow Giant Pulsators

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Abstract
Period changes in RR Lyrae variables and Cepheids, known for more than 60 years, can possibly be explained by small changes in a helium composition gradient below the hydrogen and helium convection zones. The particular cases for the globular cluster M15 double-mode RR Lyrae variable V53 and the Cepheid Polaris are studied. For the last 80 years, the fundamental mode period of V53 has been decreasing while the overtone mode period in this same star has been increasing. The rather steady overtone mode period increase for Polaris stopped very recently, and the period now seems constant. Diffusive settling of helium in these kinds of stars has been known to be slight because of the two convection zones and the long diffusion timescale below them. But a small amount of helium settling, even before the star begins to pulsate, and then a dredge-up of just a little helium by an occasional overshooting can change surface layer structures and periods. This dredge-up can have a timescale as short as the convection turnover time, i.e., a few days. A slight helium dredge-up episode may now have temporarily stopped the decaying pulsations and period increase of Polaris. Such an episode cannot explain the double-mode V53 case, but possibly the helium composition gradient is deepened enough by matter accretion in only 80 years to explain its observed opposite period changes. Another mechanism that might be important for period changes is tidal mixing of the small composition gradients caused by occasional close encounters of stars in clusters. Significant stellar rotation would keep the surface layer composition homogeneous and not allow the anomalous period changes discussed here.

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