This week I’ve started looking into making measurements of spectral features using Sherpa (program in Python). Before doing this, I wanted to understand what these measurements are, visually. These three measurements are Equivalent Width, Full Width Half Maximum (FWHM), and Line-to-Continuum Flux Ratio.

Shown in the figure above is the equivalent width (W) of an absorption line. The idea is you take the total area inside the absorption line, and create a rectangular box of the same area, extending from the continuum to the 0 flux line. The width of this box is the equivalent width. This measurement is used to describe the strength of the line (the higher the value, the stronger the line)!

Shown in the above plot is the Full Width Half Maximum (FWHM) of an emission line (it’s the same idea for absorption lines). You get the peak (maximum) value of the emission line, and draw a line at the half point. The width of the spectral feature at this flux value is the FWHM. For an absorption line, it’s the half of the minimum value instead of maximum. This measurement is used to describe how broadened the spectral feature is (the higher the value, the more broadened the line)!

Shown above is a sketch I made to illustrate the line-to-continuum flux ratio. In essence, you take the ratio of the flux of the continuum (the example used in the figure is a continuum flux of 1.0) to the flux of the max (or min) value of the feature (in the example, a value of 0.3) and subtracts it from 1. This measurement is used to characterize the depth of the line compared to the continuum (the higher the value, the deeper the line)! In the example above, the value is [1 – (0.3/1)] = 0.7

As illustrated above, these measurements describe a spectral feature. To recap, the equivalent width characterizes the overall *strength* of the line, the FWHM characterizes the *width, *or how* broadened* the line is, and the line-to-continuum flux ratio characterizes the *depth* of the line! Together, you can discern what the spectral feature may be saying about the physics of the scenario or target you are observing.

-Dan