Consider a mass shell inside a main-sequence star

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

Consider a mass shell inside a 4 M⊙4\,M_\odot main-sequence star, at the point where the mass coordinate is m=1.5 M⊙m = 1.5\,M_\odot. At this point L=250 L⊙L = 250\,L_\odot, P=3.0×1015 PaP = 3.0\times10^{15}\,\mathrm{Pa}, T=1.2×107 KT = 1.2\times10^{7}\,\mathrm{K}, and the Rosseland mean opacity is κˉ=0.030 m2 kg−1\bar\kappa = 0.030\,\mathrm{m^2\,kg^{-1}}. The gas is ideal, fully ionised and monatomic, so ∇ad=0.4\nabla_{\rm ad} = 0.4. ((a)) Evaluate ∇rad\nabla_{\rm rad} at this point. ((b)) State whether the shell is stable against convection.

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