A light-curve model first assumes both stars are uniform discs
PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Celestial mechanics and planetary systems · Celestial mechanics and planetary systems
Stars from the Inside, Ch Binary stars: fitted orbits, modelled eclipses and the Roche geometry
Problem
A light-curve model first assumes both stars are uniform discs. For a system in which the smaller, cooler star passes centrally in front of the larger star, always staying entirely within its disc (a 'flat-bottomed' eclipse in the uniform-disc model, between second and third contact), predict how replacing the uniform disc of the larger star with a limb-darkened one, following the linear law I(μ)/I(1)=1−u(1−μ) with u=0.6, changes the shape of the light curve over that same interval.
((a)) State whether the flux is now lowest at mid-eclipse or at the contacts bounding this interval.
((b)) Justify this using the values of I(μ)/I(1) at the disc centre and near its limb.