A shell in the envelope of a star of about has

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Stellar structure, energy generation and evolution

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

Problem

A shell in the envelope of a star of about 100 M⊙100\,M_\odot has ρ=10 kg m−3\rho = 10\,\mathrm{kg\,m^{-3}}, T=8×106 KT = 8\times10^{6}\,\mathrm{K} and mean molecular weight μ=0.62\mu = 0.62. Ions and electrons are non-degenerate and fully ionised. ((a)) Compute the combined ion-plus-electron (ideal-gas) pressure Pgas=ρkBT/(μmH)P_{\rm gas} = \rho k_BT/(\mu m_H). ((b)) Compute the radiation pressure Prad=aT4/3P_{\rm rad} = aT^4/3, with a=7.566×10−16 J m−3 K−4a = 7.566\times10^{-16}\,\mathrm{J\,m^{-3}\,K^{-4}}. ((c)) Give the total pressure and the fraction contributed by radiation.

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