Near the top of a solar-type envelope

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 Energy transport and the complete stellar model

Problem

Near the top of a solar-type envelope, in the hydrogen-ionisation zone, a point has

m = 1.95\times10^{30}\,\mathrm{kg}

L = 3.83\times10^{26}\,\mathrm{W}

P = 1.0\times10^{6}\,\mathrm{Pa}

T = 2.0\times10^{4}\,\mathrm{K}

, and

\kappa = 1.0\,\mathrm{m^2\,kg^{-1}}

(the opacity is high here because hydrogen is partially ionised). ((a)) Evaluate

\nabla_{\rm rad}

at this point. ((b)) Say whether the layer is radiative or convective, taking

\nabla_{\rm ad}=0.40

as an upper bound, since partial ionisation lowers it.

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