Do the Pulsation Properties of Red Giants Vary around their Long Secondary Period Cycle?

We have used visual and Johnson V observations from the American Association of Variable Star Observers (AAVSO) International Database, and the AAVSO VSTAR time-series package, and (O-C) analysis to investigate possible changes in the pulsation period and amplitude of the pulsating red giants U Del, EU Del, X Her, and Y Lyn around the cycle of their long secondary periods (LSPs). We find no such changes in period or amplitude. This suggests (weakly) that the process – whatever it is – that causes the LSPs does not significantly change the physical properties of the visible hemisphere of the stars as the LSP cycle proceeds.