Use the main-sequence lifetime scaling

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

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

, obtained from

t \propto M/L

with

L \propto M^{3.5}

and normalised to the Sun. ((a)) Estimate the main-sequence lifetime of a

3\,M_\odot

star. ((b)) Such a star has a convective core. Suppose overshooting at the core's edge mixes in enough extra hydrogen to raise the fuel the star burns on the main sequence by

20\%

, at the same luminosity. Estimate the new lifetime, and say whether overshooting lengthens or shortens the life compared with the scaling.

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