"Magenta" brown dwarfs?

[grant hutchison]

In at the deep end with a rather technical first post. Sorry folks!

I've been trying to track down the origin of the fairly widespread contention that cool brown dwarfs are magenta in colour. It seems to come from: Burrows et al. The theory of brown dwarfs and extrasolar giant planets. Reviews of Modern Physics 2001; 73: 719-65. (text is here). In section VII D, they say:

Indeed, the recent measurement of the spectrum of the L5 dwarf 2MASSW J1507 from 0.4 to 1.0 [microns] (Fig. 21 ...) indicates that this L dwarf is magenta in (optical) colour. This is easily shown with a program that generates the RGB equivalent of a given optical spectrum (in this instance, R:G:B::1.0:0.3:0.42, depending on the video "gamma").

They don't give a reference for which program they used or how they used it.

But a look at the relevant Fig. 21 spectrum suggests that something is wrong with their derivation (examine it here).
The optical bit of the spectrum is between 4000 and 7000 Angstrom. Notice the flux on the vertical axis of Fig. 21 is logarithmic.
For the human eye, blue receptor sensitivity is maximum at 4400A; green at 5350A and the red receptor peaks at around 6000A. So we're getting blue stimulation at a normalized log flux of vaguely -2.2 (in the midst of that fuzz of spectral lines); green at about -2; and the red receptor sees very little at its peak sensitivity, but gets the advantage of the flux rising towards -1 at the long wavelengths towards 7000A. Converting the logarithms, red wavelengths are peaking at 10 times the green and blue peak energies.

Tightening up on that arm-waving argument a little, I sampled the flux graph at sixteen points across the visual range, and summed the X,Y,Z chromaticity vectors for those sixteen wavelengths, weighted by their relative flux, to find a final approximate colour coordinate for the spectrum. That final XYZ value converts to RGB at around 1:0.1:0.1, depending on your monitor white point. (The underlying MathCAD sums are tested and true, since they accurately reproduce the well-known colours of black-body spectra.) In agreement with the handwaving argument above, that final colour is very distinctly red.

So: I think there's a flaw in the "magenta" story, but I may be missing something. In particular, it would be nice to know if anyone is aware of the spectrum => colour program Burrows et al. used but failed to reference.

Grant Hutchison

[George]

=D> Welcome. Delighted you've made it. Now....where have you been? [-( :wink:

I needed you back in January. There is another star whose color some are curious about - The Sun. The fun in the "Quest for the Color of the Sun" has progressed to... here . It is a rather different approach to color determination.

I've been trying to track down the origin of the fairly widespread contention that cool brown dwarfs are magenta in colour.

Are any brown?

It seems to come from: Burrows et al. The theory of brown dwarfs and extrasolar giant planets. Reviews of Modern Physics 2001; 73: 719-65. (text is here). In section VII D, they say:

Indeed, the recent measurement of the spectrum of the L5 dwarf 2MASSW J1507 from 0.4 to 1.0 [microns] (Fig. 21 ...) indicates that this L dwarf is magenta in (optical) colour. This is easily shown with a program that generates the RGB equivalent of a given optical spectrum (in this instance, R:G:B::1.0:0.3:0.42, depending on the video "gamma").

They don't give a reference for which program they used or how they used it.

But a look at the relevant Fig. 21 spectrum suggests that something is wrong with their derivation (examine it here). [/url]

It appears the strength is almost all in the red. The blue seems a little too weak to produce magenta. Yet I am not qualified to say.

Is this an AMO (no atmosphere - in space) spectral irradiance or is it from a ground-based scope? If it is ground-based, much more blue would exist in it's true spectrum which could make a difference, maybe. About half the blue is taken out by the atmosphere (less at lower altitudes).

Tightening up on that arm-waving argument a little, I sampled the flux graph at sixteen points across the visual range, and summed the X,Y,Z chromaticity vectors for those sixteen wavelengths, weighted by their relative flux, to find a final approximate colour coordinate for the spectrum. That final XYZ value converts to RGB at around 1:0.1:0.1, depending on your monitor white point.

This makes sense based on normalized eye reception. I have been perplexed why so few blue color cones could be so receptive.

(The underlying MathCAD sums are tested and true, since they accurately reproduce the well-known colours of black-body spectra.)

I would enjoy learning more of this program.

In agreement with the handwaving argument above, that final colour is very distinctly red.

That makes sense.

Try [1:0.2:.15] to, roughly, simulate atmospheric correction (assuming it is a ground-based spectrum). [I'd guess it's still red]

So: I think there's a flaw in the "magenta" story, but I may be missing something. In particular, it would be nice to know if anyone is aware of the spectrum => colour program Burrows et al. used but failed to reference.

Hopefully, this is not a dark rouge ruse. :wink:

There are some here that are accustomed to chromaticity programs and should be able to offer help.

Mainly....Welcome.

[grant hutchison]

I needed you back in January. There is another star whose color some are curious about - The Sun.

Nice idea.

I've been trying to track down the origin of the fairly widespread contention that cool brown dwarfs are magenta in colour.

Are any brown?

Nope. The name was coined in a PhD thesis in 1975, although the author (Jill Tarter) said at the time "Brown is not a color." By which I think she meant that "brown" is really our brain's interpretation of orange/yellow objects with low reflectivity, in the same way grey objects are actually white with low reflectivity.
So it's impossible to have a luminous source that "glows brown" or "glows grey".

Is this an AMO (no atmosphere - in space) spectral irradiance or is it from a ground-based scope?

Good point. I haven't chased the original reference, so I don't know, and I should. Burrows et al. claim to have analysed the colour of the spectrum given, however, so it's a moot point.

(The underlying MathCAD sums are tested and true, since they accurately reproduce the well-known colours of black-body spectra.)

I would enjoy learning more of this program.

MathCAD is just a nice bit of maths software that lets you type in recognizable equations and have them solved for you. The X,Y,Z chromaticity information I plugged in to the equations comes from a splendid book called Light, Colour and Vision by Yves Le Grand. It's long out of print, I think, but I picked up a second-hand copy easily from one of the used book websites.

Try [1:0.2:.15] to, roughly, simulate atmospheric correction (assuming it is a ground-based spectrum). [I'd guess it's still red]

It is.

Grant Hutchison

[George]

I needed you back in January. There is another star whose color some are curious about - The Sun.

Nice idea.

If I finally perfect it, or someone else, I will be happy to make a new mask and see what happens. I am looking for fiber cable which gives details on transmissivity. Do you know of any?

Try [1:0.2:.15] to, roughly, simulate atmospheric correction (assuming it is a ground-based spectrum). [I'd guess it's still red]

It is.

How much blue do you have to add to obtain magenta? That should be convincing of it's unliklyhood.

[dgavin]

Also need to account for how the Receptors in eyes work.

Humas are most sesitive to green, less to blue, and least to red***

In which case thier values make sense.

I pluged in the proportions into paintbrush as Red 100, Green 30, and Blue 42 and got a very intresting shage of Dark Megenta.

*** (and also that there is some variation betweeen people as to what freqencies are percievied at what color. For Example my entire life, i've seen thin 'glow' outlines aroung things. When i was tested some years ago for light sensitivity, it was found that my 'red' detection was sligtly off, and slipped just a bit towards the near IR. Best i could understand as it was explained, was that the brain knows what frequency light is deceted. (if your cells are off, the brain adapts to them) and precevied this close to near IR as backbody variations that show up as an almost imperceptable glow around objects with different temperatures).

[Crimson]

Crimson would like them to be....crimson!

[grant hutchison]

Also need to account for how the Receptors in eyes work.

Humas are most sesitive to green, less to blue, and least to red

Which certainly makes magenta a less likely outcome for any given energy distribution. But the X,Y,Z chromaticity values I used convert directly from energy to colour, so they take that varying sensitivity into account.

I pluged in the proportions into paintbrush as Red 100, Green 30, and Blue 42 and got a very intresting shage of Dark Megenta.

Yeah, I've no argument with that - the RGB values they give are definitely magenta. What I was trying to say is that I believe there is an error in their RGB calculation.

Grant Hutchison

[grant hutchison]

I am looking for fiber cable which gives details on transmissivity. Do you know of any?

Yikes. Sorry, I'm entirely clueless on that topic.

How much blue do you have to add to obtain magenta? That should be convincing of it's unliklyhood.

I'll try bumping the values in my MathCAD calcs and get back to you.

Grant Hutchison

[Jeff Root]

*
If I correctly understand the problem here, I can scarcely
believe how silly it is.

All objects emit electromagnetic radiation due to thermal motion
of the atoms.**A graph of the emission showing intensity versus
wavelength resembles an ideal blackbody curve more or less closely,
depending on the material and conditions.**The hotter the object
is, the more radiation it emits, and the shorter the wavelengths
are where the peak of the curve occurs.**Emissions range from
radio waves at the least-energetic (longest wavelength) end of
the spectrum, through microwaves, infrared, visible, ultraviolet,
X-rays, and gamma rays at the most-energetic (shortest wavelength)
end of the spectrum.

Emissions given off by a lightbulb, a burning candle, the Sun,
your body, and an ice cube all resemble blackbody curves fairly
closely.**The cosmic microwave background radiation, while very
weak, is the most perfect thermal radiation ever measured, with
essentially no detectable difference from an ideal blackbody.

Some EM radiation emissions are nothing like blackbody emission.
Fluorescent lights, neon lights, emission nebulae, LEDs, lasers,
TV screens, and computer monitors all give off light with spectral
curves completely unlike blackbody curves.

The human eye can detect only visible light.**It does so in
three overlapping bands: red, green, and blue.**TVs and computer
monitors are designed to emit red, green, and blue light in such
a way as to simulate the full range of human-visible light as
closely as possible.**An unusual example of this simulation is
the case of the color violet.**Violet light is near the limit
of human vision.**You would expect only the blue receptors in
the eye to respond to this part of the spectrum.**If that were
the case, violet light would simply look blue.**But the red
receptors are also slightly sensitive to this light.**So when
you see violet light, your blue receptors and red receptors are
both being triggered.**The light looks like a slightly reddish
blue.**Computer monitors cannot emit violet light.**But they can
emit blue light and red light.**The combination of the two colors
looks violet to the eye. A combination of roughly equal amounts
of blue and red makes purple or magenta.

A color wheel is a circle of colors that the human eye can see.
A range of colors which resembles a spectrum is wrapped around
and joined together so that short-wavelength violet shades through
purple or magenta into long-wavelength red.**This color wheel
arrangement is very common in computer graphics programs which
try to simulate the entire range of colors the eye can see.

Brown dwarfs glow due to thermal radiation, and must have light
curves which closely resemble blackbody curves.**The peaks of
their emissions will be near the transition from infrared to
visible light.**Their emissions will contain almost no blue light
at all, but will consist mostly of infrared, with significant
amounts of red light.

Any simulation of the light given off by a brown dwarf should
show that most of it is infrared.**If the computer program does
not have the concept of infrared programmed into it, but instead
wraps the spectrum around from red to violet, then a very large
amount of blue will show up, resulting in magenta, and the
simulation will be totally wrong.

I suspect that that's what happened here.

***-- Jeff, in Minneapolis
*

[Jeff Root]

*
After all that I finally looked at the spectral curve linked
in the original post, and have an alternative explanation:

Whoever put the spectral data into the program used the
logarithmic values assuming they were linear.**Result:
Blue and green both get pumped way up over what they
should be.

***-- Jeff, in Minneapolis
*

[Jeff Root]

dgavin wrote:

> Humans are most sensitive to green, less to blue, and least to red

My understanding is that the red receptors are more sensitive
than the blue receptors, and respond to a relatively wide range
of wavelengths.**Stimulation of the blue receptors causes very
little sensation of brightness compared to an equal degree of
stimulation of green or red.

***-- Jeff, in Minneapolis
*

[grant hutchison]

If I correctly understand the problem here, I can scarcely believe how silly it is.

It would certainly be a silly programmer who looped IR wavelengths around into the visual. Starting from a plot of wavelength against flux, you'd pretty much have to write extra code specifically to mess things up this way! :wink:

An unusual example of this simulation is
the case of the color violet.**Violet light is near the limit
of human vision.**You would expect only the blue receptors in
the eye to respond to this part of the spectrum.**If that were
the case, violet light would simply look blue.**But the red
receptors are also slightly sensitive to this light.**So when
you see violet light, your blue receptors and red receptors are
both being triggered.

There's no little spike of red sensitivity at short wavelengths, however - although both red and green receptors are still firing feebly at short wavelengths, the decline in sensitivity is steady as you drop into wavelengths shorter than their peak sensitivities. We see "blue" when our blue receptors are firing against a background of moderate green and red activity, and "violet" when our blue receptors fire against minimal green and red activity.

Computer monitors cannot emit violet light.**But they can emit blue light and red light.**The combination of the two colors
looks violet to the eye.

To quibble, that red/blue mix is technically a purple, but it does indeed generate the same sensation as a slightly desaturated spectral violet.

Brown dwarfs glow due to thermal radiation, and must have light curves which closely resemble blackbody curves.

Their atmospheres are cool enough to support many molecules and atoms, and so the underlying black body curve is extensively dissected by absorption features, so that the thermal background curve is difficult to make out.

Whoever put the spectral data into the program used the logarithmic values assuming they were linear. Result: Blue and green both get pumped way up over what they should be.

The fact that the logarithms are negative would make this a little difficult to do without noticing (negative flux!?). But I did wonder if perhaps a scanned curve had been used (thereby bypassing the hint of the negative values), so I tried entering the data as proportions relative to an imagined zero axis at -3 on the normalized log scale. I just end up with a less saturated red value.

My understanding is that the red receptors are more sensitive than the blue receptors, and respond to a relatively wide range
of wavelengths. Stimulation of the blue receptors causes very
little sensation of brightness compared to an equal degree of
stimulation of green or red.

At blue wavelengths, you're actually getting as much of a sense of luminous intensity from the residual green and red receptor firing as you are from the peak activity of the blue receptors. So there's a bit of summation going on at short wavelengths which bolsters sensitivity. That said, sensitivity certainly falls off more rapidly towards short wavelengths than it does towards long wavelengths.

Grant Hutchison

[grant hutchison]

How much blue do you have to add to obtain magenta? That should be convincing of it's unliklyhood.

I'll try bumping the values in my MathCAD calcs and get back to you.

I should read the labels - Figure 21 is captioned as being a "Keck II spectrum". So it's ground-based. Keck is at ~19.5N, and 2MASSW J1507 is at ~16.5S, giving the brown dwarf a zenith angle of 36 degrees when it passes due south. I don't know if the spectrum already contains a suitable air mass correction, and I've yet to get hold of the original paper in which the spectrum was reported.
But I've plugged in a correction for AM1.5, which doesn't generate magenta - just desaturates the red and makes it a little more orange.

Grant Hutchison

[jnik]

You can play with the (rough) visual perception of various spectra at http://lite.bu.edu/. (Not my project )

[George]

My understanding is that the red receptors are more sensitive than the blue receptors, and respond to a relatively wide range
of wavelengths. Stimulation of the blue receptors causes very
little sensation of brightness compared to an equal degree of
stimulation of green or red.

At blue wavelengths, you're actually getting as much of a sense of luminous intensity from the residual green and red receptor firing as you are from the peak activity of the blue receptors. So there's a bit of summation going on at short wavelengths which bolsters sensitivity. That said, sensitivity certainly falls off more rapidly towards short wavelengths than it does towards long wavelengths.

Ok, just to muddy this a little :P , there appears to be two eye sensitivity charts. Most are adjusted to a unit intenstity level which gives emphasizes to the respective wavelength for each cone. A few others attempt to show actual sensitivity levels along with wavelength.
Tall blue response curve.... here
Adjusted to unity response.... here.
Very low blue response... here

FWIW, there seems to be a debate going on regarding the ability of our eye/brain to see so much blue. Only about 2% of the cones are blue cones, IIRC. Their location also adds to the mystery. I think some say there is a physical/electrical amplification process involved and others may be arguing for powerful brain color processing.

[George]

How much blue do you have to add to obtain magenta? That should be convincing of it's unliklyhood.

I'll try bumping the values in my MathCAD calcs and get back to you.

I should read the labels - Figure 21 is captioned as being a "Keck II spectrum". So it's ground-based. Keck is at ~19.5N, and 2MASSW J1507 is at ~16.5S, giving the brown dwarf a zenith angle of 36 degrees when it passes due south. I don't know if the spectrum already contains a suitable air mass correction, and I've yet to get hold of the original paper in which the spectrum was reported.
But I've plugged in a correction for AM1.5, which doesn't generate magenta - just desaturates the red and makes it a little more orange.

Grant Hutchison

AM1.5 makes sense considering their altitude, otherwise AM2 might be applicable. I would be curious if they do bother with adjustments of this kind for the ground based scopes, or would they choose to adjust the space-based scope result colors to match the traditional understanding. Or, do they bother doing it at all. You would think the B-V or worse, B-R mag. results would be erroneous by close to one magnitude in some cases.

[grant hutchison]

Tall blue response curve.... here
Adjusted to unity response.... here.
Very low blue response... here

The last one is the only one attempting to show what's called the "psychophysical" response to colour - that is, the integration of the simple physiology of isolated cone cells with the whole bunch of nerves and brains to which they're connected.
The first one, despite its claims, has nothing at all to do with cone cells or retinas. This graph gets loosely touted around a lot, and it probably accounts for the common misconception that there is a little kick of red cone sensitivity in the blue wavelengths. It's actually a sketch of a colour matching function, which weights the mixture of standard red, green and blue primaries to achieve a representation of a particular spectral colour. You'll find the various graphs displayed and referenced all together here.

Let me see if I can explain this at all comprehensibly:
Because we have only three colour receptors in our retinas, we ought to be able to represent any colour by mixing together different proportions of three suitably chosen primary colours - red, green and blue, for instance. We can then uniquely describe our chosen colour by giving it three "colour coordinates" in terms of the proportions of our three standard primaries. Such a scheme is desirable, because it lets us describe colours in a precise way, without actually having to mail each other colour swatches.
In practice, no matter what primaries we choose, some very saturated real-world colours are inaccessible to us. You can't get the spectral green of a laser pointer, for instance, by mixing together the less saturated red, green and blue of CRT phosphors. Just how inaccessible the spectral green is is illustrated here - the big coloured blob is all the colours in the world, the central triangle is the colours accessible by mixing typical coloured phosphors.
This doesn't stop you describing the laser in terms of the CRT phosphors, though, if you choose to. What you need to do is desaturate the laser colour until you can get at it with the green phosphor. So you add a lot of red to the laser colour, to bring it into the space accessible to your CRT phosphors, and then you colour-match to that diluted laser colour. Algebraicly, adding colours to the laser is the equivalent of subtracting them from the other side of the equation - so your laser ends up with colour space coordinates that feature a negative red value. No worries - it's still uniquely specified.
However, the Commission Internationale de l'Eclairage were unhappy with the negative coordinates - they felt they could be dropped or misread, and therefore a source of confusion. So they created a set of standard primaries that are mathematically abstract, which only ever generate three positive colour coordinates for real-world colours. These "colours" would lie at coordinates (1,0), (0,1) and (0,0) in the colour diagram I linked to above - off the edges of the real world. And it's that red, green and blue which are being mixed in your "tall blue response" example - in effect, an imaginary "bluer-than-blue" blue being mixed with a touch of red to produce a fully saturated violet.
If the concept of such imaginary primaries messes with your head, you are far from alone. Here's a rather splendid quotation:

The CIE triangle is brilliantly ingenious as an aid to the calculation of chromaticities which can be upheld in a court of law where colour specification is in dispute. But the triangle is monstrous as an indication of what is going on in the mechanism of vision. It displays all colours as a mixture of three primary lights, none of which has an existence that can be easily imagined. One of the three primaries is bright: it is a pure green from which is subtracted a lot of red which it does not contain. The other two primaries are quite dark; they have a strong colour but zero luminance. These do not seem to me ingredients that lead to clarity in our conception of colour mechanisms and I am astonished that some physiologists and many psychologists employ them to instruct the young and bewilder the old. Journal of Physiology 1972; 220: p17P.

Anyway, that's the story of the funny "tall blue response curve" graph. Hope it was of interest. If it wasn't, I hope you stopped reading a while ago ... :wink:

Grant Hutchison

Edited to correct the link to CIE colour chart.

[grant hutchison]

You can play with the (rough) visual perception of various spectra at http://lite.bu.edu/. (Not my project )

Ah, that's nice, thanks very much. I downloaded their Spectrum Explorer, which lets you plot hand-drawn graphs.
Took the brown dwarf spectrum, ruled it off and read it at 10nm intervals into a spreadsheet; converted to linear normalized values between 400-700nm, and hand-plotted them (quite precisely, since a tool is provided to let you position the cursor accurately). The program doesn't provide RGB or other coordinates, but it does produce a calculated colour on screen. And the result is ...
Pink, only slightly more saturated than the colour I came up with.

This is a particularly useful confirmation of my own efforts, since Spectrum Explorer has a rather cooler white point than my own program, so can be expected to make things look a little bluer, if anything.

Curiouser and curiouser ...

Grant Hutchison

[George]

The last one is the only one attempting to show what's called the "psychophysical" response to colour - that is, the integration of the simple physiology of isolated cone cells with the whole bunch of nerves and brains to which they're connected.

I tend to assign the physical processes to physioloical and the brain's activity to physchological. Is this logical and/or customary?

In practice, no matter what primaries we choose, some very saturated real-world colours are inaccessible to us. You can't get the spectral green of a laser pointer, for instance, by mixing together the less saturated red, green and blue of CRT phosphors. Just how inaccessible the spectral green is is illustrated here

(same as prior link). Interesting are these limitations in description.

If the concept of such imaginary primaries messes with your head, you are far from alone. Here's a rather splendid quotation:

The CIE triangle is brilliantly ingenious as an aid to the calculation of chromaticities which can be upheld in a court of law where colour specification is in dispute. But the triangle is monstrous as an indication of what is going on in the mechanism of vision. It displays all colours as a mixture of three primary lights, none of which has an existence that can be easily imagined. One of the three primaries is bright: it is a pure green from which is subtracted a lot of red which it does not contain. The other two primaries are quite dark; they have a strong colour but zero luminance. These do not seem to me ingredients that lead to clarity in our conception of colour mechanisms and I am astonished that some physiologists and many psychologists employ them to instruct the young and bewilder the old. Journal of Physiology 1972; 220: p17P.

=D> Polemic?

Anyway, that's the story of the funny "tall blue response curve" graph. Hope it was of interest. If it wasn't, I hope you stopped reading a while ago ... :wink:

Still reading because it is quite helpful. This is information I need to learn but have put off too long. This, and more, is critical to stellar color determination as it applies to the grand Quest for the Color of the Sun! Related comments probably should go on that thread .

Another related issue is the ability of the brain, apparently, to make things look white. Incandescent lighting will make a sunlight ray appear bluish. I would guess the brain has an auto "white balance" function similar to cameras. Is this the proper way to address this issue?

[grant hutchison]

I tend to assign the physical processes to physioloical and the brain's activity to physchological. Is this logical and/or customary?

That seems right to me, too. A better word might have been "neurophysical" in this instance, I think, because we're summating the physical effect of light on cone pigments with the neural integration that takes place downstream of that. But perhaps the word was deliberately framed to remind us that everything to do with individual colour perception is filtered through the psyche before it gets out into the world where we can assign numbers to it.

(same as prior link)

Sorry, I fixed the link pretty quickly, but you must have been already browsing.

Interesting are these limitations in description.

I don't understand you, here - sorry.

Polemic?

Oh yes. But the rhetoric is a joy to behold, isn't it? :wink:

Another related issue is the ability of the brain, apparently, to make things look white.

"Colour constancy" is the buzz-phrase used to label this phenomenon. Any reasonably continuous spectrum will be interpreted as white light, as you say, and your colour perception is then tuned to accommodate that spectrum. So green looks green, whether it's illuminated by sunlight, incandescent light, or fluorescent light. (Science fiction writers probably need to contemplate the fact that the filament of an incandescent lamp is at the same temperature as a red dwarf star - we can deduce that "red" stars shed white light on their planets.)
But you can see the difference when two illuminants are juxtaposed - the classic experiment (to which I think you're alluding) is to set up some object on a window ledge so that it's illuminated by both sunlight and an incandescent lamp. The shadow cast by the sun (and illuminated by incandescent light) looks pink, whereas the shadow cast by the lamp (and illuminated by sunlight) looks blue.
But your brain's not perfect at the colour constancy trick. As a pale pink Celt, I certainly prefer an incandescent light rather than a fluorescent light above my bathroom mirror - the former lends a healthy glow, but the latter can turn me a little too corpse-like for early-morning equilibrium. And I once owned a turquoise Datsun that I could never find under car-park security lights at night - it was too close to the borderline between blue and green for my brain to get the trick right.

Grant Hutchison

[George]

Another related issue is the ability of the brain, apparently, to make things look white.

"Colour constancy" is the buzz-phrase used to label this phenomenon. Any reasonably continuous spectrum will be interpreted as white light, as you say, and your colour perception is then tuned to accommodate that spectrum. So green looks green, whether it's illuminated by sunlight, incandescent light, or fluorescent light.

You are referring to monochromatic green, I'll bet.

Here is a spectral irradiance comparison. Each are from sunlight.



The post-atmosphere spectrum is surprisingly flat with the exception of the blue end. If I understand your point on color constancy, this should produce a white looking sun, which it does. The sky irradiance plot is dominant in blue enough to produce a blue-looking sky, which is easily verified. The pre-atmosphere spectrum is very near a blackbody at 5850K which contains significant blues and greens (plus a couple of extra peaks in the blue). It stands somewhere between the prior two. This might produce a non-white color near the blue end. For this reason, I have been engaged in the solar color quest. 8) The net color may rest on this color constancy issue. [I would discuss details on this but I'd prefer to not do it on this magenta dwarf thread.]

(Science fiction writers probably need to contemplate the fact that the filament of an incandescent lamp is at the same temperature as a red dwarf star - we can deduce that "red" stars shed white light on their planets.)

Bulb mfgs. offer a surprising range of radiance spectrums (mostly non-incandescent, no doubt). IIRC, one high efficency lamp had three spikes in the spectrum - red, green and blue.

But you can see the difference when two illuminants are juxtaposed - the classic experiment (to which I think you're alluding) is to set up some object on a window ledge so that it's illuminated by both sunlight and an incandescent lamp. The shadow cast by the sun (and illuminated by incandescent light) looks pink, whereas the shadow cast by the lamp (and illuminated by sunlight) looks blue.

Yours is better. The example I had was allowing a beam of sunlight into the room lighted by incandescent lighting. The sunbeam appears blue, according the article.

I have noticed that white paper placed in the shade has a bluish appearance, regardless of any available comparitive sunlight nearby. This makes sense as the specturm, as shown in the above graph, is so intense in blue.

But your brain's not perfect at the colour constancy trick. As a pale pink Celt, I certainly prefer an incandescent light rather than a fluorescent light above my bathroom mirror - the former lends a healthy glow, but the latter can turn me a little too corpse-like for early-morning equilibrium.

In this case, which would be the best color paint to use on your bathroom walls to offset this effect - pinkish-white, pink, bluish-white or blue? In other words, would color constancy help to add some color to your image due to pinkish walls or would blue walls cause pink to stand-out? I suspect a very light bluish white would be best.

[grant hutchison]

Well, I tracked down the original paper referenced for the "magenta" brown dwarf spectrum. Interestingly, the spectrum in this original paper isn't log-transformed, so it's very clear there's really minimal flux in the blue-green section of the spectrum. It's essentially red.

But I now have a theory as to how this spectrum might erroneously yield a magenta shade. There are two common methods of measuring energy flux - in W/mē per wavelength (F-lambda) and in W/mē per frequency (F-nu). To convert F-nu to F-lamda, you divide by wavelength-squared, and jigger in a constant of proportionality.
Now, if you type F-lambda data (which is what we have in the brown dwarf spectrum under discussion) into a program that's expecting F-nu, it will effectively bump the shortest wavelengths three-fold (700nm/400nm)^2, and the boundary of blue and green two-fold (700nm/500nm)^2 relative to the longest red wavelengths.
And if I simulate this error with my own little program, it produces a nice shade of magenta. Ta-da!

I recently contacted Adam Burrows, the lead author on the original paper which made the "magenta" statement about this brown dwarf, and he wrote back saying "I used a program off the web put together by TV people. They calculate CMKY and RGB colors." I've written to ask if he can give me any more detail on the program but, meanwhile, does this ring a bell with anyone? It would be interesting to look at the specific program used.

Meanwhile, again, I've been looking for data on very cool brown dwarfs (which might be less red-dominated in the visible spectrum), and I found another paper by Burrows. This one features a number of theoretical curves for T dwarfs plotted in F-nu, and I suspect once they're transformed to F-lambda they will become good candidates for that elusive magenta shade.

I'll report back.

Grant Hutchison

[publiusr]

That's okay--the Fab Five were just freshing up some of the Dwarfs for makeovers.

[George]

But I now have a theory as to how this spectrum might erroneously yield a magenta shade. There are two common methods of measuring energy flux - in W/mē per wavelength (F-lambda) and in W/mē per frequency (F-nu). To convert F-nu to F-lamda, you divide by wavelength-squared, and jigger in a constant of proportionality.
Now, if you type F-lambda data (which is what we have in the brown dwarf spectrum under discussion) into a program that's expecting F-nu, it will effectively bump the shortest wavelengths three-fold (700nm/400nm)^2, and the boundary of blue and green two-fold (700nm/500nm)^2 relative to the longest red wavelengths.

I presume this is from a radiance equation (not just a simple wavelength to freq. conversion).

And if I simulate this error with my own little program, it produces a nice shade of magenta. Ta-da!

Impressive. =D>

[grant hutchison]

I presume this is from a radiance equation (not just a simple wavelength to freq. conversion).

Yes, you're interested in how much energy is packed into each 1Hz step in frequency, as compared to each 1nm step in wavelength. Since wavelength decreases as frequency increases, you find that the F(nu) and F(lambda) graphs are distinctly different shapes. You get the conversion factor by differentiating frequency with respect to wavelength - that comes out to be c/lambda^2, multiplied by some exponent of ten to allow for your choice of units.

You can find out a heck of a lot about flux units here.

I've just finished looking at some theoretical curves for the cooler T-type dwarfs. After making the conversion from F(nu) to F(lambda), they are all magenta, some with a little red dominance, some with a little blue.
In a hand-waving way, what happens is this - the broad Na I line absorbs a load of yellow light, which would leave a previously flat background spectrum looking blue. But the background slope of the spectrum is actually a little red-dominated, so we see a mix of blue and red.

So it seems that cool T-class brown dwarfs are likely to be magenta, whereas the warmer L-types (like the brown dwarf that started this thread) are actually red. The early report by Burrows of a magenta L5 dwarf seems to be an error.

Grant Hutchison

[George]

I've just finished looking at some theoretical curves for the cooler T-type dwarfs. After making the conversion from F(nu) to F(lambda), they are all magenta, some with a little red dominance, some with a little blue.
In a hand-waving way, what happens is this - the broad Na I line absorbs a load of yellow light, which would leave a previously flat background spectrum looking blue. But the background slope of the spectrum is actually a little red-dominated, so we see a mix of blue and red.

So it seems that cool T-class brown dwarfs are likely to be magenta, whereas the warmer L-types (like the brown dwarf that started this thread) are actually red. The early report by Burrows of a magenta L5 dwarf seems to be an error.

Sounds logical. If you wish, I will make a mask and test your idea using the SPACC. It does appear to be mainly red and blue. Is the actual irradiance data available (400nm to 700nm)?

[grant hutchison]

Is the actual irradiance data available (400nm to 700nm)?

Well, only in so far as I've manually gridded the graphs, read off approximate values of log(F-nu), linearized, and then converted to relative values of F-lambda. At 20nm intervals, 400-700nm. It would make a rather lumpy mask but, then again, it's a rather lumpy colour estimate.
(Fortunately a little experimentation shows that saturated shades are quite insensitive to minor variations in the flux estimates.)

Grant Hutchison

[George]

Is the actual irradiance data available (400nm to 700nm)?

Well, only in so far as I've manually gridded the graphs, read off approximate values of log(F-nu), linearized, and then converted to relative values of F-lambda. At 20nm intervals, 400-700nm.

Yeah, that's it. Could you put a scoop of ice cream on top? :P

It would make a rather lumpy mask but, then again, it's a rather lumpy colour estimate.
(Fortunately a little experimentation shows that saturated shades are quite insensitive to minor variations in the flux estimates.)

Grant Hutchison

The mask shape compensates for the variations inherent in AM2 fluctuations. So, it's shape is odd even with a flat spectrum. I don't mind interpolating to derive 10nm increments, if necessary. I have it all on a spreadsheet which draws the mask and prints precisely (w/m^2-nm). Then I cut it out with an Exact-O knife.

Actually, I am anxious to conduct the test to further develop SPACC-2.

[grant hutchison]

Here you go:

nm  F(lambda)
400   0.109
420   0.099
440   0.090
460   0.082
480   0.085
500   0.098
520   0.091
540   0.060
560   0.010
580   0.000
600   0.001
620   0.040
640   0.151
660   0.356
680   0.669
700   1.000

The approximate 1300K spectrum, flux expressed as a proportion of the 700nm value. I could tweak the calculations to get W/mē/m if you need, but I imagine all that's required for the mask shape is the relative values.

Grant Hutchison

[George]

Here you go:

nm  F(lambda)
400   0.109
420   0.099
440   0.090
460   0.082
480   0.085
500   0.098
520   0.091
540   0.060
560   0.010
580   0.000
600   0.001
620   0.040
640   0.151
660   0.356
680   0.669
700   1.000

The approximate 1300K spectrum, flux expressed as a proportion of the 700nm value. I could tweak the calculations to get W/mē/m if you need, but I imagine all that's required for the mask shape is the relative values.

Grant Hutchison

Thanks. It may be a week or so before I'll have time. However, I look forward to doing it (along with the blue sky mask).