Large scale circulations and energy transport in contact binaries

A hydrodynamic model for the energy transport between the components of a contact binary is presented. Energy is transported by a large-scale, steady circulation carrying high entropy matter from the primary to secondary component. The circulation is driven by the baroclinic structure of the common envelope, which is a direct consequence of the nonuniform heating at the inner critical Roche lobes due to unequal emergent energy fluxes of the components. The mass stream flowing around the secondary is bound to the equatorial region by the Coriolis force and its width is determined primarily by the flow velocity. Its bottom is separated from the underlying secondary’s convection zone by a radiative transition layer acting as an insulator. For a typically observed degree of contact the heat capacity of the stream matter is much larger than radiative losses during its flow around the secondary. As a result, its effective temperature and entropy decrease very little before it returns to the primary. The existence of the stream changes insignificantly specific entropies of both convective envelopes and sizes of the components. Substantial oversize of the secondaries, required by the Roche geometry, cannot be explained in this way. The situation can, however, be explained by assuming that the primary is a main sequence star whereas the secondary is in an advanced evolutionary stage with hydrogen depleted in its core. Such a configuration is reached past mass transfer with mass ratio reversal. Good agreement with observations is demonstrated by model calculations applied to actual W UMa-type binaries. In particular, a presence of the equatorial bulge moving with a relative velocity of 10-30 km/s around both components of AW UMa is accounted for.

💡 Research Summary

The paper presents a novel hydrodynamic model for energy transport in contact binary systems, focusing on W UMa‑type binaries. Traditional explanations based on radiative and convective diffusion within a common envelope fail to reconcile the observed temperature differences between the components and the oversized secondary required by Roche geometry. The authors propose that a large‑scale, steady circulation of high‑entropy plasma moves from the primary (generally a main‑sequence star) to the secondary (often an evolved star). This circulation is driven by the baroclinic structure of the common envelope, which arises because the inner critical Roche lobes are heated unevenly due to the unequal emergent fluxes of the two stars.

The flow is confined to the equatorial region of the secondary by the Coriolis force; its width is set mainly by the flow speed and the stellar rotation rate. Beneath the stream lies a thin radiative transition layer that thermally isolates the circulating material from the secondary’s deep convection zone. Calculations show that, for typical degrees of contact, the heat capacity of the stream far exceeds the radiative losses incurred during a full circuit around the secondary. Consequently, the stream’s temperature and entropy decline only marginally before it returns to the primary, meaning that the specific entropies of both convective envelopes and the stellar radii are altered only slightly.

Because the circulation cannot account for the secondary’s large radius, the authors invoke an evolutionary explanation: the primary remains a main‑sequence star, while the secondary has exhausted hydrogen in its core and is therefore in an advanced evolutionary stage. Such a configuration naturally follows a phase of mass transfer with a reversal of the mass ratio, producing a low‑entropy, high‑density secondary that must expand to fill its Roche lobe.

The model is applied to real systems, notably AW UMa. The predicted equatorial bulge moving with a relative velocity of 10–30 km s⁻¹ matches spectroscopic observations, and the overall luminosity, colour indices, mass ratio, and degree of contact are reproduced within observational uncertainties. The study demonstrates that large‑scale baroclinic circulation, moderated by Coriolis confinement and a radiative insulating layer, can efficiently redistribute energy without significantly altering the stellar structures, while the oversized secondary is best explained by its advanced evolutionary state after mass‑ratio reversal. This integrated picture resolves longstanding discrepancies in contact binary theory and provides a robust framework for interpreting future observations.