Dynamical plausibility of triple-assisted interaction in Be-star multiple systems

Classical Be stars are rapidly rotating B-type stars surrounded by gaseous circumstellar disks. The origin of the angular momentum required to sustain their near-critical rotation remains uncertain. Binary interaction is a promising spin-up channel, and in hierarchical multiple systems a tertiary companion may drive the secular evolution of an unresolved inner binary. We investigated whether observed Be-star multiple systems are dynamically compatible with a triple-assisted interaction scenario, in which a resolved tertiary companion excites the eccentricity of an unresolved inner binary through the Kozai--Lidov mechanism and brings it closer to an interaction regime. We combined speckle-interferometric detections, reported inner periods, and proper-motion anomalies (PMas) to construct synthetic populations of hierarchical triples. Accepted configurations were required to be dynamically stable, to evolve in the secular regime, to have a Kozai--Lidov timescale shorter than the adopted main-sequence lifetime scale, and to reach an inner-periastron interaction proxy. For the best-constrained systems, we performed refined target-specific simulations using the adopted stellar masses, distances, periods, PMa scales, and speckle separations. HD 35079 and HD 55606 provide the cleanest period-plus-speckle dynamical matches: their observed inner periods and speckle separations are simultaneously reproduced by stable, secularly active triples. HD 205329 remains dynamically plausible, but its interpretation is astrometrically cautionary because it depends on the PMa constraint. HD 41335 is a diagnostic case: the period-plus-speckle and PMa-plus-speckle constraints are viable separately, whereas the simultaneous period, PMa, and speckle constraints yield no accepted configurations under the adopted tolerances. Several PMa-plus-speckle systems, including HD 37330, HD 41600, HD 205329, and HD 71510, are observationally promising hierarchical-triple candidates, but their interpretation is more dependent on the astrometric PMa constraint. As an independent consistency check, we estimated the angular-momentum budget required to spin up the Be star and found a median fractional requirement of Δ M_ ̊m req /M under the adopted assumptions. Several observed Be-star multiple systems admit dynamically plausible Kozai--Lidov-active configurations in which a resolved tertiary companion can drive an unresolved inner binary towards interaction. These systems are therefore prime targets for continued speckle, spectroscopic, and astrometric monitoring, as well as for future binary-evolution modelling of triple-assisted Be-star spin-up.