An eclipsing binary in a circular orbit shows two eclipses each cycle
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
An eclipsing binary in a circular orbit shows two eclipses each cycle, both of the total kind: at each minimum, one star's disc is either wholly hidden behind, or wholly transiting in front of, the other's disc (so the same area is blocked or hidden each time). Treat both stars as spherical, uniformly bright discs, with no limb darkening. The deeper, primary minimum has a fractional flux loss of 0.50 and occurs when star A is hidden or blocked; the shallower, secondary minimum has a fractional flux loss of 0.20 and occurs when star B is hidden or blocked.
((a)) Find the surface-brightness ratio SB/SA.
((b)) A colleague argues that, because the primary minimum is deeper, star A must be the larger of the two stars. Say whether this follows, giving a one-sentence reason.