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I've slightly modified the title to try to attract some attention. If we call sunlight "white" and limb darkening is a result of seeing deeper at normal incidence and shallower at oblique incidence, then the center end edge of the solar disk viewed from earth should appear to have slightly different effective color temperatures, since the temperature is varying rapidly with depth.

I'd like to have an approximate expression for the wavelength-dependent limb darkening of the sun in the visible spectrum, either a relatively simple analytical expression that I can understand (with the appropriate coefficients for the sun) or just some linear images of the sun in various bands in the visible wavelengths so I can try to make one of my own.

This question received this helpful comment which links to here but honestly I can't make my way through that to a practical expression I can use. The Wikipedia article is not helping me much either, except for the image there. I plotted scans of RGB but by the time an image gets into the internet, things like sRGB and gamma mean it may not be linear.

update: At the Solar Dynamics Observatory (SDO) website, I just found the image sdo.gsfc.nasa.gov/assets/img/latest/latest_1024_HMIIC.jpg. The color gradient of the limb darkening seems very similar to the Wikimedia image below. I've discovered that it is called a "colorized intensitygram" and the color gradient is purely artificial - the data is single channel intensity. The limb darkening is certainly real (compare to the artificially "flattented" display!)

From http://www.solarham.net/latest_imagery/hmi1.htm

enter image description here

I appreciate (the existence of) the complexities and intricacies of photon transport, instrumental effects, and color perception, but I am just starting to do astronomically correct animations, so please for right now, something imperfect, or not absolutely correct is good enough for me.

20 pixel wide averages of horizontal (-) and vertical (--) "scans" across the center of this 600x600 pixel image from here

note: It seems this is a somewhat futile example, as the image is likely to be a monochrome continuum image with false color!

enter image description here

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You might find this paper helpful:

http://www.physics.hmc.edu/faculty/esin/a101/limbdarkening.pdf

Look specifically at Eq. 5 for the wavelength dependence. To get the intensity, use Equation 1. The value of $u$ can be found in the caption to Figure 2.

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  • $\begingroup$ Thanks. In section 2 1st paragraph: "Putting $u$ = 1 in Eq. 1, a single-parameter power law fit is performed..." and since Petro et al. (1984) is only narrow-band continuum at 4451Å Its not clear to me yet if the paper really says $u=0.85$ is a good fit throughout the visible wavelength range. Can you elaborate on this? $\endgroup$
    – uhoh
    Commented Jun 10, 2016 at 1:10
  • $\begingroup$ also found PS (Pierce and Slaughter 1977) and NL (Neckel and Labs 1994). $\endgroup$
    – uhoh
    Commented Jun 10, 2016 at 1:11

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