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During first dredge-up, the convective envelope deepens on the red-giant branch and brings CNO cycle-processed material to the surface, increasing helium and nitrogen while reducing carbon and changing isotopic ratios. After central helium exhaustion, second dredge-up occurs in this intermediate-mass range: the envelope penetrates into layers processed by hydrogen and sometimes helium burning, lowers the hydrogen-exhausted core mass, and further enriches the surface in helium and nitrogen.

During the thermally pulsing Asymptotic giant branch, a helium-shell flash can be followed by third dredge-up. The envelope then reaches the intershell and may expose newly synthesized carbon and slow-neutron-capture products. In the more massive objects, hot-bottom burning at the base of the convective envelope can convert some dredged-up carbon into nitrogen.

An intrinsic S-type star is a thermally pulsing AGB star whose third dredge-up exposes carbon and products of the slow neutron-capture process. An extrinsic S-type star has similar surface pollution but no current internal source; it received the material from a former AGB companion. A barium star is the warmer main-sequence or giant counterpart, recognized particularly through strong barium and other slow-neutron-capture elements.

This interpretation predicts a white dwarf companion, the remnant of the former AGB donor. Barium and extrinsic S-type stars are indeed binaries, often with periods long enough that the donor could not have undergone ordinary Roche-lobe overflow. Their abundance patterns, white-dwarf companions, and wide or eccentric orbits therefore point to wind mass transfer in a binary star.

The Bondi–Hoyle accretion estimate treats the companion as moving through a locally uniform wind with relative speed $v_{\mathrm{rel}}$, sound speed $c_s$, and density ${\rho }_w$. Gravity focuses gas from the accretion radiusgivingFor a roughly spherical donor wind, ${\rho }_w\simeq {\dot{M}}_w/(4\pi a^2{v}_w)$ and $v_{\mathrm{rel}}$ combines wind and orbital velocities. This supplies an order-of-magnitude accreted fraction; wind acceleration, density gradients, orbital deflection, and Wind Roche-lobe overflow can substantially change it.

For initial masses $5M_{\odot }$ and $0.7M_{\odot }$, increasing the initial period gives three broad channels:

The transition periods are set by the primary's maximum radius relative to its Roche lobe, and their exact values depend on mass-transfer efficiency, wind speed, and common-envelope energy formalism.