An oxygen ( , ) layer inside a white dwarf has density and temperature

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Astrophysics & Cosmology · Stellar death and compact objects

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

Problem

An oxygen (Z=8Z=8, A=16A=16) layer inside a white dwarf has density ρ=5.0×109 kg m−3\rho = 5.0\times10^{9}\,\mathrm{kg\,m^{-3}} and temperature T=5.0×106 KT = 5.0\times10^{6}\,\mathrm{K}. Take the ion spacing as a=(3/4πni)1/3a = (3/4\pi n_i)^{1/3}, with nin_i the ion number density, and the Coulomb coupling parameter as Γ=Z2e24πϵ0 a kBT.\Gamma = \frac{Z^2 e^2}{4\pi\epsilon_0\,a\,k_BT}. Crystallisation sets in near Γ≈175\Gamma \approx 175. Compute Γ\Gamma and state whether this layer has crystallised.

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