A carbon-oxygen white dwarf has central density and .

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Quantum statistical mechanics and quantum gases · Quantum statistical mechanics and quantum gases

Stars from the Inside, Ch Pressure against gravity: the equation of state, polytropes and the Lane-Emden equation

Problem

A carbon-oxygen white dwarf has central density ρ=6×108 kg m−3\rho = 6\times10^{8}\,\mathrm{kg\,m^{-3}} and μe=2\mu_e = 2. ((a)) Compute the electron pressure using the non-relativistic degenerate formula Pe=1.00×107(ρ/μe)5/3 PaP_e = 1.00\times10^{7}(\rho/\mu_e)^{5/3}\,\mathrm{Pa}. ((b)) Compute it using the ultra-relativistic formula Pe=1.24×1010(ρ/μe)4/3 PaP_e = 1.24\times10^{10}(\rho/\mu_e)^{4/3}\,\mathrm{Pa}. ((c)) Compute x=pF/mecx = p_F/m_ec using ρ/μe=9.7×108 kg m−3\rho/\mu_e = 9.7\times10^{8}\,\mathrm{kg\,m^{-3}} at x=1x=1 and x∝(ρ/μe)1/3x \propto (\rho/\mu_e)^{1/3}, and say which of the two limits is the better approximation here.

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