Someone argues: "The brightest star on the colour-magnitude diagram of open cluster…

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

Someone argues: "The brightest star on the colour-magnitude diagram of open cluster NGC 2168 has MV=−3M_V = -3 and spectral type B0, which by the mass-luminosity relation corresponds to a mass of about 15 M⊙15\,M_\odot. Using tMS≈1010(M/M⊙)−2.5 yrt_{\rm MS} \approx 10^{10}(M/M_\odot)^{-2.5}\,\mathrm{yr}, tMS=1010×15−2.5=1.15×107 yrt_{\rm MS} = 10^{10}\times15^{-2.5} = 1.15\times10^{7}\,\mathrm{yr}, so the cluster's age is 1.15×107 yr1.15\times10^{7}\,\mathrm{yr}." Find the error in this reasoning, and state the correct method for reading a cluster's age off its colour-magnitude diagram.

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