Pulsation modes of long-period variables in the period-luminosity plane

We present a phenomenological analysis of long-period variables (LPVs) in the Large Magellanic Cloud with the aim of detecting pulsation modes associated with different period-luminosity (PL) relations. Among brighter LPVs, we discover a group of triple-mode semi-regular variables with the fundamental, first-overtone, and second-overtone modes simultaneously excited, which fall on PL sequences C, C′, and B, respectively. The mode identification in the fainter red giants is more complicated. We demonstrate that the fundamental-mode pulsators partly overlap with the first-overtone modes. We show a possible range of fundamental mode and first overtone periods in the PL diagram.