Fraunhofer line width 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 ?
 A: I think the lines you have been looking at have a width contributed to by the spectral resolution of the instrument and Zeeman broadening.
You haven't considered the spectral resolution of the spectrograph. The maximum possible for Hinode spectra is about 0.003 nm (Tsuneta et al. 2007) and there is nothing in the source you have used that says what modes of observation were used or how the spectra have been treated during any subsequent analysis.
In addition to this, there are other broadening mechanisms present. The source you quote is all about Zeeman broadening/splitting of the iron lines that are displayed. The series of spectra show the development of this as you move towards the centre of the sunspot. The top spectrum, which I guess you have used to estimate the intrinsic linewidth (looks like a FWHM of about 0.014 nm) is still going to have unresolved Zeeman components at some level, since it is on the edge of a sunspot.
Bulk Doppler motions are unlikely to contribute much. In spatially unresolved spectra these amount to an extra broadening of about 1 km/s, which is only 0.002 nm at this wavelength. It should be less in the spatially resolved Hinode spectra.
A: 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
A: 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.
A: 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.
