Mestel cooling gives for white dwarfs of the same core composition and envelope opacity

PHYSICS · Subjective · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Stellar death and compact objects

Stars from the Inside, Ch White dwarfs: the relativistic polytrope, the Chandrasekhar mass and a cooling clock

Problem

Mestel cooling gives

t_{\rm cool} \propto M^{5/7}L^{-5/7}

for white dwarfs of the same core composition and envelope opacity. Mestel's law puts a

0.6\,M_\odot

carbon-oxygen white dwarf at

L = 1.0\times10^{-4}\,L_\odot

after a cooling time of

4.4\,\mathrm{Gyr}

. Use this to estimate the cooling age of a

1.0\,M_\odot

carbon-oxygen white dwarf observed at

L = 1.0\times10^{-3}\,L_\odot

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