Equivalent width

An absorption equivalent width is $W_{\lambda }=\int [1-I_{\lambda }/I_{\lambda }^0]d\lambda$, the wavelength width of a completely black interval that removes the same continuum-normalized area. For a narrow spectral line profile, small optical depth and negligible stimulated emission, the energy-density convention for Einstein coefficients gives $W_{\lambda }=h{B}_{12}{N}_1/{\nu }_{12}$. This follows by replacing $1-e^{-{\tau }_{\nu }}$ by ${\tau }_{\nu }$ and using $|d\lambda /d\nu |=c/{\nu }^2$. At redshift $z$, the observed and rest-frame values satisfy $W_{\mathrm{obs}}=(1+z)W_{\mathrm{rest}}$.