The Color of Infinite Temperature

 

This is the color of something infinitely hot. Of course you’d instantly be fried by gamma rays of arbitrarily high frequency, but this would be its spectrum in the visible range.

This is also the color of a typical neutron star. They’re so hot they look the same.

It’s also the color of the early Universe!

This was worked out by David Madore.



As a blackbody gets hotter and hotter, its spectrum approaches the classical Rayleigh–Jeans law. That is, its true spectrum as given by the Planck law approaches the classical prediction over a larger and larger range of frequencies.

So, for an extremely hot blackbody, the spectrum of light we can actually see with our eyes is governed by the Rayleigh–Jeans law. This law says the color doesn’t depend on the temperature: only the brightness does!

And this color is shown above.

This involves human perception, not just straight physics. So David Madore needed to work out the response of the human eye to the Rayleigh–Jeans spectrum — “by integrating the spectrum against the CIE XYZ matching functions and using the definition of the sRGB color space.”

The color he got is sRGB(148,177,255). And according to the experts who sip latte all day and make up names for colors, this color is called ‘Perano’.

Here is some background material Madore wrote on colors and visual perception. It doesn’t include the whole calculation that leads to this particular color, so somebody should check it, but it should help you understand how to convert the blackbody spectrum at a particular temperature into an sRGB color:

• David Madore, Colors and colorimetry.

In the comments you can see that Thomas Mansencal redid the calculation and got a slightly different color: sRGB(154,181,255). It looks quite similar to me:

16 Responses to The Color of Infinite Temperature

  1. Tom Carroll says:

    At least I would feel soothed while being fried to a crisp.

  2. amarashiki says:

    It is quite surprising that color mimics the color of our skies during the sunny days in our planet!

    • John Baez says:

      Yeah, that’s cool!

      It’s not exactly a coincidence: Rayleigh scattering of light by particles in the atmosphere is also governed by a power law, with light of higher frequencies scattered more!

      Are Rayleigh scattering and the Rayleigh–Jeans law governed by the same power law? If so, why? Was Rayleigh just trying to get his name on the same law twice? Is it just a coincidence? Or are the two laws related for some reason?

      • kram1032 says:

        Afaik it is, in fact, the same falloff

        As to why, I couldn’t say though. Seems like a different situation to me, since scattering isn’t obviously the same as thermal radiation

        • John Baez says:

          Hi! Right, it’s not obvious why these give the same law; the calculations seem different. I should check out how things change when space has some other dimension! For example, if space were just two-dimensional, Rayleigh scattering would give power per wavelength falling off like wavelength-3 instead of wavelength-4. Rayleigh derived Rayleigh scattering using dimensional analysis in 1871, so one can see using this method how his result depends on the dimension of space.

  3. Hi John,

    I computed the colour and find slightly different value, i.e. [154, 181, 255].

    Here is a Google Colab Notebook that has the colour for 10^200 along with comparisons with a blackbody: https://colab.research.google.com/drive/1Oyn913zkXYB8Uf8k1hiM8_5gifuMVqta?usp=sharing

    Do you have any more information on how David came up with those numbers?

    • John Baez says:

      Coming up with a slightly different answer counts as confirmation, as far as I’m concerned. Alas, I have no more information on how David Madore came up with his numbers. I just asked him.

      • David Madore says:

        It could be due to a number of reasons: the color matching functions used could be different (I seem to remember there are two different versions of the XYZ functions of the CIE), the numerical integration method could be different (I didn’t try to be smart there: I took matching functions defined with 1nm resolution and integrated using the rectangle method — I don’t know if there’s any standard for one one “should” do), the gamma correction could be applied differently (maybe sRGB changed their gamma function slightly while I wasn’t looking: the page https://www.w3.org/Graphics/Color/sRGB which was standard when I wrote my program mentions “during standardization, a small numerical error caused by rounding error was corrected”), and of course the final rounding applied can be different (though that shouldn’t change more than by ±1).

        If someone really wants to track down the reason for the difference, I’ll try to upload the code I used to GitHub, but it’s hard to make sense of because it’s part of a set of custom programs to do all sorts of colorimetric computations.

        However, one crucial intermediate value my program returns is the (x,y) coordinates of the color before it is converted to sRGB, namely: (0.239877, 0.234037, 0.526086).

    • kram1032 says:

      Colorspaces are a tricky thing and not exactly absolute. The exact values will depend on many things up to and including “how is your monitor calibrated” – If you don’t have a properly colormanaged screen, the very premise of an exact RGB value is nonsense anyway.
      There are also multiple standard ways to convert from spectral data to RGB. If you are using the older results, extreme wavelengths, especially on the shorter end, will be considered less than in the newer models.
      If you want to explore the visual impression of the color in question more clearly, it might be possible to look how, for instance, iCAM06 treats this spectrum.

    • John Baez says:

      Here is David’s color sRGB(148,177,255):

      and here is Thomas’ color sRGB(154,181,255):

  4. betelgeeuse says:

    And according to the experts who sip latte all day and make up names for colors …

    I would like to imagine that this was in reference to the name given to the average color of the universe: https://en.wikipedia.org/wiki/Cosmic_latte

  5. Carl Feynman says:

    The color appears as pure white in Safari.

  6. arch1 says:

    It would be amusing if either of those computed color values were super close to a web-safe color😊

  7. […] Jakou barvu má viditelná část spektra záření nekonečně horkého zdroje, jakým byl raný vesmír a jakým víceméně jsou nově vzniklé neutronové hvězdy? Přesný název pro ni neexistuje, její HTML kód je #9AB5FF. (Líbí se vám? Mně ano.) […]

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