Period-luminosity (PL) relations of variable red giants in the Large (LMC) and Small Magellanic Clouds (SMC) are presented. The PL diagrams are plotted in three planes: logP-K_S, logP-W_{JK}, and logP-W_I. Fourteen PL sequences are distinguishable, a
nd some of them consist of three closely spaced ridges. Each of the sequences is fitted with a linear or quadratic function. The similarities and differences between the PL relations in both galaxies are discussed for four types of red giant variability: OGLE Small Amplitude Red Giants (OSARGs), Miras and Semiregular Variables (SRVs), Long Secondary Periods (LSPs) and ellipsoidal variables. We propose a new method of separating OSARGs from non-variable stars and SRVs. The method employs the position in the reddening-free PL diagrams and the characteristic period ratios of these multiperiodic variables. The PL relations for the LMC OSARG are compared with the calculated relations for RGB models along isochrones of relevant ages and metallicities. We also compare measured periods and amplitudes of the OSARGs with predictions based on the relations valid for less luminous solar-like pulsators. Miras and SRVs seem to follow PL relation of the same slopes in the LMC and SMC, while for LSP and ellipsoidal variables slopes in both galaxies are different. The PL sequences defined by LSP variables and binary systems overlap in the whole range of analyzed wavebands. We put forward new arguments for the binary star scenario as an explanation of the LSP variability and elaborate on it further. The measured pulsation to orbital period ratio implies nearly constant ratio of the star radius to orbital distance, R/A=0.4, as we find. Combined effect of tidal friction and mass loss enhanced by the low-mass companion may explain why such a value is preferred.
Observations of stellar activity cycles provide an opportunity to study magnetic dynamos under many different physical conditions. Space-based asteroseismology missions will soon yield useful constraints on the interior conditions that nurture such m
agnetic cycles, and will be sensitive enough to detect shifts in the oscillation frequencies due to the magnetic variations. We derive a method for predicting these shifts from changes in the Mg II activity index by scaling from solar data. We demonstrate this technique on the solar-type subgiant beta Hyi, using archival International Ultraviolet Explorer spectra and two epochs of ground-based asteroseismic observations. We find qualitative evidence of the expected frequency shifts and predict the optimal timing for future asteroseismic observations of this star.
