Secular Evolution in Mira Variable Pulsations
  Stellar evolution theory predicts that asymptotic giant branch stars undergo a series of short thermal pulses that significantly change their luminosity and mass on timescales of hundreds to thousands of years. Secular changes in these stars resulting from thermal pulses can be detected as measurable changes in period if the star is undergoing Mira pulsations. The American Association of Variable Star Observers (AAVSO) International Database currently contains visual data for over 1500 Mira variables. Light curves for these stars span nearly a century in some cases, making it possible to study the secular evolution of the pulsation behavior on these timescales. In this paper, we present the results of our study of period change in 547 Mira variables using data from the AAVSO. We find non-zero rates of period change, dlnP/dt, at the 2-sigma significance level in 57 of the 547 stars, at the 3-sigma level in 21 stars, and at the level of 6-sigma or greater in eight of the 547. The latter eight stars have been previously noted in the literature, and our derived rates of period changes largely agree with published values. The largest and most statistically significant dlnP/dt are consistent with the rates of period change expected during thermal pulses on the AGB. A number of other stars exhibit non-monotonic period changes on decades-long timescales, the cause of which is not yet known. 
M.R. Templeton, J.A. Mattei, and L.A. Willson