Phase Offsets Between the Minimum Light and Radial Velocity in Long Secondary Period Stars

Abstract

Long secondary periods (LSPs), observed in a substantial fraction of luminous red giants, remain one of the longstanding problems in red giant variability. Previous studies have found a systematic phase relation between their photometric and radial velocity (RV) variations. We investigate this relation using ASAS-SN photometry and Gaia RV curves for 983 LSP stars, and compare it with other types of Long Period Variables. We confirm that LSP stars have a relatively narrow distribution of phase offsets between the phase of minimum RV and minimum light, with a mean value of $Δϕ=-0.15\pm0.10$ in phase ($-0.96\pm0.64$ rad). Interestingly, this phase offset is similar for Miras, showing that this quantity is not sufficient to distinguish LSPs from pulsational variability. However, pulsating red giants show a relation between period and RV amplitude, with the RV amplitude generally increasing toward longer periods. LSP stars deviate from this relation, showing RV amplitudes of only a few km/s despite their long periods. The stacked light and RV curves of the LSP sample also show remarkable homogeneity and a coherent phase relation. In the binary interpretation of LSPs, the observed phase offset requires the obscuring material to be shifted in orbital phase with respect to the companion, consistent with models in which a low-mass companion produces a dusty wake in the wind of the red giant.