A helium core inside a red giant has

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 helium core inside a red giant has ρ=5×107 kg m−3\rho = 5\times10^{7}\,\mathrm{kg\,m^{-3}}, μe=2\mu_e = 2 and temperature T=1×107 KT = 1\times10^{7}\,\mathrm{K}. ((a)) Estimate the degeneracy boundary temperature Tdeg≈1.2×103(ρ/μe)2/3 KT_{\rm deg} \approx 1.2\times10^{3}(\rho/\mu_e)^{2/3}\,\mathrm{K} for this density. ((b)) State whether this core is degenerate or an ideal gas, and by roughly what factor TdegT_{\rm deg} exceeds or falls short of the actual TT.

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