Studies of the Long Secondary Periods in Pulsating Red Giants
  We have used systematic, sustained visual observations from the AAVSO International Database, and the AAVSO time-series analysis package VSTAR to study the unexplained "long secondary periods" (LSPs) in 27 pulsating red giants. In our sample, the LSPs range from 479 to 2967 days, and are on average 8.1 +/- 1.3 times the pulsation period. There is no evidence for more than one LSP in each star. In stars with both the fundamental and first overtone radial period present, the LSP is more often about 10 times the latter. The visual amplitudes of the LSPs are typically 0.1 magnitude and do not correlate with the LSP. The phase curves tend to be sinusoidal, but at least two are sawtooth. The LSPs are stable, within their errors, over the timespan of our data, which is typically 25,000 days. The amplitudes, however, vary by up to a factor of two or more on a timescale of roughly 20-30 LSPs. There is no obvious difference between the behavior of the carbon (C) stars and the normal oxygen (M) stars. Previous multicolor photoelectric observations showed that the LSP color variations are similar to those of the pulsation period, and of the LSPs in the Magellanic Clouds, and not like those of eclipsing stars. We note that the LSPs are similar to the estimated rotation periods of the stars, though the latter have large uncertainties. This suggests that the LSP phenomenon may be a form of modulated rotational variability. 
John R. Percy and Emily Deibert
astro-ph.SR