Volume 45 number 1 (2017)
We have used AAVSO visual and photoelectric V data, and the AAVSO time-series package VSTAR and the Lomb-Scargle time-series algorithm to determine improved pulsation periods, "long secondary periods" (LSPs), and their amplitudes in 51 shorter-period pulsating red giants in the AAVSO photoelectric photometry program, and in the AAVSO long-period variable (LPV) binocular program. As is well known, radial pulsation becomes detectable in red giants at about spectral type M0, with periods of about 20 days. We find that the LSP phenomenon is also first detectable at about M0. Pulsation and LSP amplitudes increase from near zero to about 0.1 at pulsation periods of 100 days. At longer periods, the pulsation amplitudes continue to increase, but the LSP amplitudes are generally between 0.1 and 0.2 on average. The ratios of LSP to pulsation period cluster around 5 and 10, presumably depending on whether the pulsation period is the fundamental or first overtone. The pulsation and LSP phase curves are generally close to sinusoidal, except when the amplitude is small, in which case they may be distorted by observational scatter or, in the case of the LSP amplitude, by the pulsational variability. As with longer-period stars, the LSP amplitude i ncreases and decreases by a factor of two or more, for unknown reasons, on a time scale of about 20 LSPs. The LSP phenomenon is thus present and similar in radially pulsating red giants of all periods. Its cause remains unknown.