Fraunhofer line width

Question

What sets the width of Fraunhofer lines on the solar spectrum ?

I first thought of Doppler broadening, but numerical applications result in much too high temperatures. For instance, using these data, I find a $Delta lambda =$ 0.01nm line width on the 630.25nm line of iron, corresponding to a temperature of
$$
T = frac{mc^2}{k_B} frac{Delta lambda ^2}{lambda ^2} simeq 100, 000 , {rm K}
$$
which is way above the Sun's photosphere temperature.

Is there something wrong with the above calculation, or is the line width coming from something else ?

Pen · Answer

The only reference I could find is a 1925 (!) paper criticizing the idea that a Doppler broadening could explain Fraunhofer lines width ; but it doesn't suggest a quantitative way to analyze the line profile...

http://adsabs.harvard.edu/full/1925MNRAS..85..732S

Nicolas · Answer

Your calculation sounds legit… Line profile looks similar in other high resolution data. I don't have any complete answer ; my guess would be unresolved Zeeman effect. It could be unresolved due to variation in B field over the field of view, even if the spectrometer itself is of high enough resolution.

Other reasons I could imaging for line broadening :

Collisionnal broadening (limited time in an energy level between collisions $Rightarrow$ uncertainty in energy)
Stark effect (I highly doubt there are such electric fields there).

None of them looks convincing to me.

Peter Z · Answer

To begin with, your reasoning assumes near transparency of the solar atmosphere.  This is generally not true.  The solar atmosphere is “optically thick” (highly absorbing in the vicinity of a spectral line) as opposed to “optically thin” (nearly transparent).  The shape of such a spectral line generally requires radiation transport theory (Foukal “Solar Astrophysics”) to describe adequately.
Also, in addition to thermal broadening, there is a “non thermal” contribution to the (Gaussian) width which arises from unresolved random motion along the line of sight.  This non thermal velocity component is generally referred to as "microturbulence".  I went through the exercise of calculating a solar filament temperature using the H alpha and Ca K lines based on a simple application of transport theory which incorporates the effect of microturbulence .  You can read it here:
https://solarchatforum.com/viewtopic.php?f=8&t=25215
Hope this helps.

Fraunhofer line width

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