An open cluster's colour-magnitude diagram places its main-sequence turn-off at

PHYSICS · Subjective · 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

M_{\rm TO} = 2.5\,M_\odot

. Over this mass range the initial-final mass relation is well described by a straight line through two calibration points: a

1\,M_\odot

star ends as a

0.55\,M_\odot

white dwarf, and a

3\,M_\odot

star ends as a

0.70\,M_\odot

white dwarf. (a) Estimate the cluster's age from the turn-off mass, using

t_{\rm MS} \approx 10^{10}(M/M_\odot)^{-2.5}\,\mathrm{yr}

. (b) Use linear interpolation on the initial-final mass relation to predict the mass of the white dwarf the turn-off star will leave. (c) Express the mass lost by the turn-off star as a percentage of its initial mass, and state in which evolutionary phase (main sequence, red giant branch, or asymptotic giant branch superwind) most of that mass is lost, giving a reason based on the mass-loss rates quoted for each phase.

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