Assumptions Made in Using the Milne-Eddington Model to Obtain Residual Intensity r_ν

1.  I = I(θ), azimuthal symmetry of the intensity (equivalent to spherical symmetry of the star).

2.  Coherent, isotropic scattering.

3.  j_ν(total) = j_ν(coherent scattering) + j_ν(continuum) + j_ν(line) = (1 - ε)l_νJ_ν + κ_νB_ν(T) + εl_νB_ν(T).

4.  η_ν º l_ν/κ_ν ¹ η_ν(τ_ν) ("Milne's approximation").

5.  ε ¹ ε(τ_ν).

6.  K_ν = ⅓ J_ν ("Eddington's approximation").

7.  B_ν(τ_ν) = a_ν + b_ν (τ_ν / (1 + η_ν) (The Planck function can be adequately approximated by the two lowest order
     terms in its Taylor's Series expansion.  The independent variable is chosen to be τ_ν / (1 + η_ν) rather than τ_ν
      because it is independent of l_ν and therefore varies only slightly with ν.  τ_ν / (1+η_ν) = ò(κ_ν+ l_ν)ρ dz /(1+η_ν)  =
     òκ_ν(1+η_ν)ρ dz /(1+η_ν) = òκ_νρ dz, since η_ν is assumed independent of τ_ν and therefore of z.)

8.  dH_C /dτ_C = 0 (conservation of flux).

9.  H_C (τ_C = 0) = ½J_C (τ_C = 0).

      10.  J_ν = (2 + 3τ_ν)H_ν .