equivalent width

How do you put a single number on the strength of an absorption line? A line can be deep and narrow or shallow and broad, yet remove the same total amount of light. Astronomers want a measure of the whole bite a line takes out of the spectrum, regardless of its exact shape. That measure is the equivalent width.

The trick is a clever picture. Take all the light the line removes, and imagine sweeping it into a perfectly black, rectangular notch that goes all the way down to zero brightness. The equivalent width is how wide that black rectangle would have to be — measured in wavelength, say in nanometres or in tiny fractions of a nanometre — to remove exactly the same total amount of light as the real line. A strong line that swallows a lot of light has a large equivalent width; a faint one has a small one. It captures total strength while ignoring whether the line is deep-and-thin or shallow-and-wide.

Equivalent width is the everyday currency of quantitative spectroscopy. Because it sidesteps the messy details of a line's shape, it is robust and easy to measure, and it is the number astronomers feed into the curve of growth to work out how many atoms of an element are present. Measure the equivalent widths of many lines and, with the temperature in hand, you can reconstruct a star's full chemical recipe.