Investigating the Light Curves of 5 Long Period Variable Stars: A Study Cross-Harmonics using VStar, MESA, and GYRE

Abstract: Long Period Variables (LPVs) are Asymptotic Giant Branch stars with periods >100 days. Around one third to half of LPVs display a Long Secondary Period (LSP) that is 5-10 times the length of the main periods. The exact cause of LSPs are unknown, with one potential explanation lying in cross-harmonics caused by the interaction of two simultaneously occurring periods. In this paper, we use the Fourier analysis software VStar to examine the visual range photometric light curves obtained through the American Association of Variable Star Observers of a sample of 5 stars. We find that one star, V CVn, displays a secondary period over 20 times the length of its main period, inconsistent with traditional LSPs. To test if cross-harmonics can result in an LSP or VCVn's extra-long secondary period, we then construct evolutionary tracks and pulsation models of LPVs using Modules for Evolution in Stellar Astrophysics (MESA) and GYRE. After examining the interactions of the fundamental pulsation mode and the first 4 overtones with each other, we do not find evidence that LSPs or V CVn's extra-long secondary period could be caused by cross-harmonics.