A pre-main-sequence star of mass has

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

A pre-main-sequence star of mass

2\,M_\odot

has, at some moment before it reaches the main sequence, radius

4\,R_\odot

and luminosity

8\,L_\odot

. It generates no nuclear energy at this stage: its luminosity is supplied entirely by gravitational contraction (the gravothermal term). ((a)) Estimate its Kelvin-Helmholtz time

t_{\rm KH} = GM^2/(RL)

in years. ((b)) Compare this with the Sun's Kelvin-Helmholtz time of

3.1\times10^{7}\,\mathrm{yr}

and say, in one sentence, what the comparison implies about how close this star is to settling onto the main sequence.

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