The Properties of Long-Period Variables in the Large Magellanic Cloud   from MACHO
  We present a new analysis of the long-period variables in the Large Magellanic Cloud (LMC) from the MACHO Variable Star Catalog. Three-quarters of our sample of evolved, variable stars have periodic light curves. We characterize the stars in our sample using the multiple periods found in their frequency spectra. Additionally, we use single-epoch Two Micron All Sky Survey measurements to construct the average infrared light curves for different groups of these stars. Comparison with evolutionary models shows that stars on the red giant branch (RGB) or the early asymptotic giant branch (AGB) often show non-periodic variability, but begin to pulsate with periods on the two shortest period-luminosity sequences (3 & 4) when they brighten to K_s ~ 13. The stars on the thermally pulsing AGB are more likely to pulsate with longer periods that lie on the next two P-L sequences (1 & 2), including the sequence associated with the Miras in the LMC. The Petersen diagram and its variants show that multi-periodic stars on each pair of these sequences (3 & 4, and 1 & 2) typically pulsate with periods associated only with that pair. The periods in these multi-periodic stars become longer and stronger as the star evolves. We further constrain the mechanism behind the long secondary periods (LSPs) seen in half of our sample, and find that there is a close match between the luminosity functions of the LSP stars and all of the stars in our sample, and that these star's pulsation amplitudes are relatively wavelength independent. Although this is characteristic of stellar multiplicity, the large number of these variables is problematic for that explanation. 
Oliver J. Fraser, Suzanne L. Hawley and Kem H. Cook