Mestel's cooling law gives

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's cooling law gives tcool∝M5/7L−5/7t_{\rm cool} \propto M^{5/7}L^{-5/7}. A 0.6 M⊙0.6\,M_\odot carbon-oxygen white dwarf reaches L=10−4 L⊙L = 10^{-4}\,L_\odot after a cooling time of 4.4 Gyr4.4\,\mathrm{Gyr}. Using the same scaling, estimate the cooling time of a 0.9 M⊙0.9\,M_\odot white dwarf to reach L=10−3 L⊙L = 10^{-3}\,L_\odot.

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