Gaia Astrometry Disfavors a Binary Origin for Long Secondary Periods

Abstract Approximately one-third of luminous pulsating red giant stars exhibit long secondary periods (LSPs): stable photometric variability with periods of several months to years in addition to their much shorter primary pulsation cycles. Now nearly a century after their discovery, the physical origin of LSPs remains unresolved. A leading explanation invokes binarity, in which the LSP corresponds to the orbital period of a low-mass companion responsible for both the photometric variability and the radial-velocity (RV) modulation. We test this hypothesis using a nearby sample of LSP stars from the Gaia Focused Product Release, which provides multi-epoch RVs and contemporaneous optical photometry. We find that interpreting the observed RV variability as orbital motion implies companion masses narrowly distributed around M 2 ≈ 0.1 M ⊙ with separations of 1–3 au, placing them squarely in the brown dwarf desert observed around their solar-type progenitors. Assuming such companions exist, we then forward-model the astrometric signature expected in Gaia DR3 and predict systematically elevated astrometric wobble for nearby LSPs. In contrast, the observed astrometric wobble of nearby LSP stars is systematically lower than these predictions and consistent with most systems exhibiting LSPs being single. This discrepancy disfavors low-mass stellar or substellar companions as the dominant origin of LSPs in evolved stars, motivating a further exploration of alternative stellar mechanisms.