 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 $E\sim 2{\Delta }_D\sqrt{\log {\tau }_0}$, while saturated Lorentzian line shape wings give $E\sim 2\sqrt{mS{\Delta }_L}$. The spectral coordinate and coefficient convention must be consistent.

The curve of growth is a concept used in various fields, such as astronomy, biology, and economics, to describe how certain quantities change in relation to time or another variable. Here are a few contexts in which the term is commonly used: 1. **Astronomy**: In astronomy, the curve of growth refers to the relationship between the strength of spectral lines of a star or other celestial object and the abundance of absorbing or emitting material.