Equivalent width

The equivalent width is the strength of a spectral line. A continuum is a graph of intensity (on the y axis) versus wavelength (on the x axis). The spectral line (or line profile) is then placed on the graph. A rectangle is then put on the graph. It has the height of the continuum level (or continuum intensity). Its width is chosen so that the rectangle has the same amount of area as the area between the spectral line and the continuum level. The width of that rectangle is the equivalent width. The equivalent width is used in astronomy to compare emission lines or absorption lines.

Derivation
The area between the continuum intensity (the dotted line at the top of the graph) and the spectral line (the curve) is found with basic integral calculus. Basically, the area between two curves the integral of their difference.

Where  and  are two curves. To find the area between the continuum intensity and the spectral line, we replace  with  (this is the continuum intensity), and we replace  with  (this is the intensity of the spectrum):where  is the area between the two curves. We can make a rectangle with the same area as . We will say that this rectangle has the same height as the continuum intensity, or . The area of a rectangle is  (height times width). Using  the height and  as the width, the area becomes . Here,  is the equivalent width. Therefore,

 is unknown, so using algebra to isolate  gives this equation:

References

Other websites
Equivalent Width in the SAO Encyclopedia of Astronomy
Category:Astrophysics
Category:Spectroscopy