Two Fe I lines near arise from the same lower level and form in the same layer

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Astrophysics & Cosmology · Radiation, radiative transfer and stellar atmospheres

Stars from the Inside, Ch Radiative transfer solved: the grey atmosphere, the diffusion limit and the curve of growth

Problem

Two Fe I lines near λ=500 nm\lambda = 500\,\mathrm{nm} arise from the same lower level and form in the same layer, where the Doppler width is ΔλD=2.2×10−3 nm\Delta\lambda_D = 2.2\times10^{-3}\,\mathrm{nm}. Line A has oscillator strength fA=1.0×10−3f_A = 1.0\times10^{-3} and equivalent width WA=3.8×10−4 nmW_A = 3.8\times10^{-4}\,\mathrm{nm}; line B has fB=0.10f_B = 0.10 and WB=7.3×10−3 nmW_B = 7.3\times10^{-3}\,\mathrm{nm}. Take λ=500 nm\lambda = 500\,\mathrm{nm} for both and πre=8.85×10−15 m\pi r_e = 8.85\times10^{-15}\,\mathrm{m}. ((a)) Assuming line A lies on the linear part of the curve of growth, find the column density NN of atoms in the lower level. ((b)) Apply the same linear law to line B. Compare the two values of NN, and say which line to trust and why. ((c)) Treat line B as lying on the flat part, Wλ≈2ΔλDln⁡τ0W_\lambda \approx 2\Delta\lambda_D\sqrt{\ln\tau_0}, and estimate its line-centre optical depth τ0\tau_0. Since τ0\tau_0 is proportional to NfNf for lines from the same level, deduce τ0\tau_0 for line A, and say whether this supports the assumption of part (a).

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