The bolometric (frequency-integrated) centre-to-limb intensity profile of a star is…
PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Radiation, radiative transfer and stellar atmospheres · 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
The bolometric (frequency-integrated) centre-to-limb intensity profile of a star is measured. At disc centre (μ=1) the intensity is I(1); at μ=0.4 the measured ratio is I(0.4)/I(1)=0.76.
((a)) Using the linear limb-darkening law I(μ)/I(1)=1−u(1−μ), find the limb-darkening coefficient u implied by this measurement.
((b)) The Eddington grey atmosphere predicts I(μ)/I(1)=(2+3μ)/5, i.e. u=3/5. Compute the value this predicts for I(0.4)/I(1) and compare it with the measured ratio.
((c)) State, in one sentence, what the sign of the discrepancy implies about how steeply the frequency-integrated source function actually rises with depth compared with the grey atmosphere.