Ellipsoidal variability and long secondary periods in MACHO red giant stars

We present a period-luminosity-amplitude analysis of 5899 red giant and binary stars in the Large Magellanic Cloud, using publicly available observations of the MACHO Project. For each star, we determined new periods, which were double-checked in order to exclude aliases and false periods. The period-luminosity (P-L) relations confirm the existence of a short-period, small-amplitude P-L sequence at periods shortward of sequence A. We point out that the widely accepted sequence of eclipsing binaries between sequences C and D, known as sequence E, does not exist. The correct position for sequence E is at periods a factor of 2 greater, and the few stars genuinely lying between sequences C and D are underluminous Mira variables, presumably enshrouded in dust. The true sequence E overlaps with the sequence of long secondary periods (LSPs; sequence D), and their P-L relation is well described by a simple model assuming Roche geometry. The amplitudes of LSPs have properties that are different from both the pulsations and the ellipsoidal variations, but they are more similar to the former than the latter, arguing for pulsation rather than binarity as the origin of the LSP phenomenon.