Equivalent width

The equivalent width (of English. Width ) is a measure of the astronomical spectroscopy for the strength of the lines in an absorption spectrum . It represents a quantity that does not depend on the properties of the apparatus used and is therefore well suited for comparing different measurements. ${\displaystyle W}$

calculation

Geometric interpretation with equal areas (red area and hatched rectangle;
the rectangle ends at the top at I ₀ )

A background source of constant intensity is assumed , which is weakened by foreground material around a certain frequency . ${\displaystyle I_{0}}$ ${\displaystyle \nu _{0}}$

In the intensity-frequency diagram, the strength of the absorption is given as the total area between the intensity of the background source and the actual intensity profile : ${\displaystyle I(\nu )}$

${\displaystyle I_{tot}=\int d\nu \,(I_{0}-I(\nu ))}$

The equivalent width then corresponds to the width of a rectangle with an area equivalent to the absorbed intensity , where the height of the rectangle is given by : ${\displaystyle I_{tot}}$ ${\displaystyle I_{0}}$

${\displaystyle W={\frac {I_{tot}}{I_{0}}}={\frac {\int d\nu \,(I_{0}-I(\nu ))}{I_{0}}}}$

units

From the calculation it can be deduced that the equivalent width is given in units of frequency (e.g. Hertz ) or in units of wavelength that is directly linked to the frequency via the speed of light (e.g. nanometers or Ångström ).

swell

• David F. Gray, The Observation and Analysis of Stellar Photospheres , Third Edition, Cambridge 2005, ISBN 0-521-85186-6