Variability in red supergiant stars:: pulsations, long secondary periods and convection noise

We study the brightness variations of galactic red supergiant stars using long-term visual light curves collected by the American Association of Variable Star Observers over the last century. The full sample contains 48 red semiregular or irregular variable stars, with a mean time-span of observations of 61 yr. We determine periods and period variability from analyses of power density spectra and time-frequency distributions. We find two significant periods in 18 stars. Most of these periods fall into two distinct groups, ranging from a few hundred to a few thousand days. Theoretical models imply fundamental, first and possibly second overtone mode pulsations for the shorter periods. Periods greater than 1000 d form a parallel period-luminosity relation that is similar to the long secondary periods of the asymptotic giant branch stars. A number of individual power spectra shows a single mode resolved into multiple peaks under a Lorentzian envelope, which we interpret as evidence for stochastic oscillations, presumably caused by the interplay of convection and pulsations. We find a strong 1/f noise component in the power spectra that is remarkably similar in almost all stars of the sample. This behaviour fits the picture of irregular photometric variability caused by large convection cells, analogous to the granulation background seen in the Sun.