Curve of growth
= Curve of growth
A curve of growth describes the <equivalent width> $E(m)=\int(1-e^{-m\kappa_\nu})d\nu$ as a function of absorber <mass path> or <column density>. Its weak-line limit is $E\simeq mS$. Saturation makes growth sublinear: a pure Gaussian core gives $E\sim2\Delta_D\sqrt{\log\tau_0}$, while saturated <Lorentzian line shape> wings give $E\sim2\sqrt{mS\Delta_L}$. The spectral coordinate and coefficient convention must be consistent.