In the convective envelope of a subgiant

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

In the convective envelope of a subgiant, at a depth where the local gravity is g=120 m s−2g = 120\,\mathrm{m\,s^{-2}}, the gas is fully ionised and behaves ideally so δ=1\delta=1, the pressure scale height is HP=2.0×107 mH_P = 2.0\times10^{7}\,\mathrm{m}, the mixing-length parameter is αMLT=1.5\alpha_{\rm MLT}=1.5 (calibrated), and mixing-length theory gives a superadiabatic excess ∇−∇ad=2.0×10−6\nabla-\nabla_{\rm ad} = 2.0\times10^{-6} there. ((a)) Find the mixing length ℓ\ell. ((b)) Use vc2≈gδ(∇−∇ad)ℓ2/(8HP)v_c^2 \approx g\delta(\nabla-\nabla_{\rm ad})\ell^2/(8H_P) to estimate the convective velocity vcv_c.

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