Stellar dredge-up occurs when a convective envelope penetrates into layers altered by nuclear burning and transports their material to the surface.
First dredge-up occurs as a star ascends the red-giant branch. Its deepening convective envelope exposes material processed by hydrogen burning, especially enhanced helium and nitrogen and depleted carbon.
Second dredge-up occurs after core helium exhaustion in sufficiently massive intermediate-mass stars. The convective envelope moves inward, mixes helium- and hydrogen-burning products to the surface, and reduces the hydrogen-exhausted core mass.
Third dredge-up follows a thermal pulse on the asymptotic giant branch, when the convective envelope reaches into the intershell and can carry freshly made carbon and slow-neutron-capture elements to the surface.
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