A giant star's main-sequence progenitor had the solar-system value

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Stellar structure, energy generation and evolution

Stars from the Inside, Ch Stellar evolution: from the Hayashi track to the iron core, and the ages of clusters

Problem

^{12}\mathrm{C}/^{13}\mathrm{C} = 89

. After first dredge-up has deepened its convective envelope into layers once processed by the CN cycle in its hydrogen-burning core on the main sequence, spectroscopy of its surface gives

^{12}\mathrm{C}/^{13}\mathrm{C} = 11

. ((a)) State the range of

^{12}\mathrm{C}/^{13}\mathrm{C}

that standard first dredge-up predicts for a low-mass giant, and say whether the observed value of

11

lies inside, above, or below it. ((b)) Predict what must additionally be happening in this giant if standard dredge-up alone cannot account for the observation, and state whether the responsible process is fully understood.

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