<p>The equation is dimensionally incorrect, or at least the two &quot;fluxes&quot;, represented by <span class="math-container">$F$</span> cannot have the same units.</p>
<p>Equivalent width is in units of wavelength, thus the units of <span class="math-container">$F_{\rm line}$</span> are the units of <span class="math-container">$F_{\rm cont}$</span> multiplied by a wavelength.</p>
<p>For example, <span class="math-container">$F_{\rm cont}$</span> could be in erg cm<span class="math-container">$^{-2}$</span> per Angstrom, the equivalent width would be in Angstroms and <span class="math-container">$F_{\rm line}$</span> would be in erg cm<span class="math-container">$^{-2}$</span>.</p>
<p>If <span class="math-container">$F_{\rm cont}$</span> is not expressed per unit of wavelength, then it needs to be converted to be so before multiplying it by equivalent width.</p>

CC BY-SA 4.0
2024-04-19T18:59:05.903Z
2024-04-19T18:59:05.903Z
ProfRob
<p>I have the following equation used to calculate line flux from equivalent width.</p>
<blockquote>
<p><span class="math-container">$F_{line}=EW \times F_{cont}$</span></p>
</blockquote>
<p>If <span class="math-container">$EW$</span>, the equivalent width of a line is in Angstroms, and <span class="math-container">$F_{cont}$</span>, the continuum flux density unit is in <span class="math-container">$ erg\hspace{1pt} s^{-1} cm^{-2}{Hz}^{-1}$</span>, then what would be the units of <span class="math-container">$F_{line}$</span>? From the equation the units should be <span class="math-container">$erg\hspace{1pt} s^{-1} cm^{-2}{Hz}^{-1}A$</span> but the line flux units are <span class="math-container">$erg\hspace{1pt} s^{-1} cm^{-2}A^{-1}$</span>.</p>

<units><flux>
I need clarity on the units in this flux equation
1500kook12
# I need clarity on the units in this flux equation

(Asked by: username_0 on 2024-04-19)

I have the following equation used to calculate line flux from equivalent width.

> $F\_{line}=EW \times F\_{cont}$

If $EW$, the equivalent width of a line is in Angstroms, and $F\_{cont}$, the continuum flux density unit is in $ erg\hspace{1pt} s^{-1} cm^{-2}{Hz}^{-1}$, then what would be the units of $F\_{line}$? From the equation the units should be $erg\hspace{1pt} s^{-1} cm^{-2}{Hz}^{-1}A$ but the line flux units are $erg\hspace{1pt} s^{-1} cm^{-2}A^{-1}$.

**Tags:** units, flux

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## 1 answers

### Answer by username_1 on 2024-04-19. Score: 1

The equation is dimensionally incorrect, or at least the two "fluxes", represented by $F$ cannot have the same units.

Equivalent width is in units of wavelength, thus the units of $F\_{\rm line}$ are the units of $F\_{\rm cont}$ multiplied by a wavelength.

For example, $F\_{\rm cont}$ could be in erg cm$^{-2}$ per Angstrom, the equivalent width would be in Angstroms and $F\_{\rm line}$ would be in erg cm$^{-2}$.

If $F\_{\rm cont}$ is not expressed per unit of wavelength, then it needs to be converted to be so before multiplying it by equivalent width.


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