Polytropic Index n
n = 1.5
ξ₁ (surface): —
ρ_c/⟨ρ⟩: —
Mass exponent: —
Lane-Emden (1870/1907):
(1/ξ²) d/dξ[ξ² dθ/dξ] = −θⁿ
θ(0)=1, θ'(0)=0
P = Kρ^(1+1/n) (polytropic EOS)
• n=3/2: convective stars, white dwarfs (non-rel.)
• n=3: Eddington standard model, massive stars
• n=5: infinite radius (no surface)
ξ₁ = first zero of θ = stellar radius (in polytropic units)