Astrometric modeling of unresolved variable binary systems. II. Application to Gaia epoch astrometry of nearby pulsating and convective red giants

Abstract

(Abbreviated) The interpretation of high-precision astrometry for intrinsically variable stars remains challenging, particularly for unresolved binary systems containing asymptotic giant branch (AGB) stars. In such systems, large-amplitude pulsations and evolving convective surface structures induce time-dependent photocentre displacements that perturb the observed orbital motion. At the same time, Gaia DR4 epoch astrometry offers the prospect of deriving accurate orbital solutions and parallaxes for nearby unresolved AGB binaries. Building upon the variability-induced mover (VIM) framework, we extend the astrometric model for unresolved evolved binaries by combining Keplerian photocentre motion, pulsation-induced flux-dependent photocentre shifts, and convection-induced photocentre motion. In the forward simulations, convection is represented either by stochastic photocentre displacements drawn from an exponential correlation function or by photocentre time series extracted from 3D radiation-hydrodynamic simulations. We then test a retrieval framework that fits the orbital and VIM signal while incorporating a red-noise covariance matrix to account for correlated astrometric residuals produced by convection. We show that Gaia epoch astrometry can recover reliable orbital and astrometric parameters for unresolved AGB binaries despite strong pulsation- and convection-induced photocentre variability. Pulsation-induced variability produces a coherent VIM signal that can be modeled jointly with the Keplerian photocentre orbit, while convection-induced photocentre motion behaves primarily as temporally correlated astrometric noise. Retrievals that ignore this correlated component lead to biased proper motions and parallaxes, whereas the inclusion of a physically motivated red-noise covariance model enables accurate recovery of the underlying orbital solution and astrometric parameters.