APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by VictorBorun » Fri Dec 09, 2022 1:59 am

I can see 2 quotes here stating that coloured light (of red dwarfs or blue giants) gives way to white (of white dwarfs):

(1)
A 100,000 K star will photograph as white with RGB photography. Because it is white... nearly equal intensity across all visible wavelengths.

(2)
The gamma ray pulsar Geminga must be extremely hot, but I remember reading, after its visible spectrum had been detected, that the visible spectrum was quite flat.

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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by Chris Peterson » Fri Dec 09, 2022 1:57 pm

VictorBorun wrote: Fri Dec 09, 2022 1:59 am I can see 2 quotes here stating that coloured light (of red dwarfs or blue giants) gives way to white (of white dwarfs):

(1)
A 100,000 K star will photograph as white with RGB photography. Because it is white... nearly equal intensity across all visible wavelengths.
Indeed. Nearly flat across the visible spectrum. Which is precisely what we get from the Rayleigh–Jeans law. And a spectrum which varies in intensity by only a few percent from blue to red is essentially white to the eye and to an RGB camera.
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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by VictorBorun » Sat Dec 10, 2022 11:56 am

Chris Peterson wrote: Fri Dec 09, 2022 1:57 pm
VictorBorun wrote: Fri Dec 09, 2022 1:59 am I can see 2 quotes here stating that coloured light (of red dwarfs or blue giants) gives way to white (of white dwarfs):

(1)
A 100,000 K star will photograph as white with RGB photography. Because it is white... nearly equal intensity across all visible wavelengths.
Indeed. Nearly flat across the visible spectrum. Which is precisely what we get from the Rayleigh–Jeans law. And a spectrum which varies in intensity by only a few percent from blue to red is essentially white to the eye and to an RGB camera.
the Rayleigh–Jeans law, B ~ ν²/T, gives a spectrum shape that is dependent not on T, but rather on ν = c/λ. The frequency does rise 2 times from red to violet making Brightness vary 4 times. Well, in fact 3 times, when we crop extreme margins, red and violet, that are poorly seen, but the result is readily seen as bluish. I mean "blue" is the colour that S-cones report as bright as white pixels in the scene, the L-cones report as dark as black pixels in the scene, and M-cones report as middle-bright.
And I mean "bluish" is the colour that the observer interpret as mixing tiny particles of white with tiny particles of blue. A white dwarf must look bluish for a comfortably set observer, because L-cones will register some yellow and red photons and report the thing as half-bright, just like they report a mixture of white and blue powders in equal portions.

the Rayleigh–Jeans law gives as bluish a colour as they come.

To get that colour from a thermal source you must heat it to 100,000°K or more.
If your source is mere 12,000°K, the spectrum will be flatter; you only get a pale bluish, like a mixture of much white powder and little blue powder.

Oh, now I get it! The reason why the myth of the Flat Thermal Spectrum of white dwarfs was born.
The physicists discussed the broad band of a 100,000°K source and plotted Brightness that varied much from light to X-rays.
To fit the plot to window they had to compress the Brightness scale a lot.
Then the plot did show the 1000 times variations, but sadly pictured 3 times variations at red-to-violet band as flat zero.

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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by VictorBorun » Sat Dec 10, 2022 5:38 pm

Chris Peterson wrote: Wed Dec 07, 2022 9:36 pm 100000K.png
Image
A plot with a flat line at the zero height would be unfriendly, so a zero above the horizontal axis is used.

What Rayleigh–Jeans law says, B ~ ν²/T, dictate the Brightness, or Spectral Radiance, to fall (.4/.1)² = 16 times with wavelength 0.1 μm to 0.4 μm and fall another (.7/.4)² = 3 times with wavelength 0.4 μm to 0.7 μm, and here this plot is not correct: this plot makes Spectral Radiance fall ~100 times and stay flat zero, respectivly.

Would the plotter generate the same result for me?
It does:
100000°K 2guest2125416477.png
Is it because Rayleigh–Jeans law fails at such short wavelengths?
No, the peak (according to Planck's law) is at much shorter wavelengths:
100000°K 3guest2125416477.png
So my guess is that thos plotter uses too few a point in the spline to show such nuances correctly
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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by johnnydeep » Sat Dec 10, 2022 8:33 pm

VictorBorun wrote: Sat Dec 10, 2022 5:38 pm
Chris Peterson wrote: Wed Dec 07, 2022 9:36 pm 100000K.png
Image
A plot with a flat line at the zero height would be unfriendly, so a zero above the horizontal axis is used.

What Rayleigh–Jeans law says, B ~ ν²/T, dictate the Brightness, or Spectral Radiance, to fall (.4/.1)² = 16 times with wavelength 0.1 μm to 0.4 μm and fall another (.7/.4)² = 3 times with wavelength 0.4 μm to 0.7 μm, and here this plot is not correct: this plot makes Spectral Radiance fall ~100 times and stay flat zero, respectivly.

Would the plotter generate the same result for me?
It does:
100000°K 2guest2125416477.png

Is it because Rayleigh–Jeans law fails at such short wavelengths?
No, the peak (according to Planck's law) is at much shorter wavelengths:
100000°K 3guest2125416477.png

So my guess is that thos plotter uses too few a point in the spline to show such nuances correctly
Well, we are perhaps missing the small picture due to the scale of the graph, or else that calculator I used is flawed (yeah, it was I who introduced it!). Compare these two graphs:

Screenshot_20221210_025422.png
Screenshot_20221210_025517.png

The average slope of these graphs is clearly different: .it is .2 / 2e10 = 1e-10 from .4 to .6 and .2 / 3e9 = 6.6e-11 from .6 to .8.

That is, the graph is 1.5 times steeper from .4 nm to .6 nm as it is from .6 nm to .8 nm. This makes some sense because the graph flattens out toward longer wavelengths. Yet, it sure seems like the slope isn't even close to flat over 2 to .4 or even .4 to .6.

And still - if the calculator can be believed - the radiance is 10 times greater at .4 nm than at .8 nm.
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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by VictorBorun » Sun Dec 11, 2022 5:07 pm

Sorry, I was not quite correct on numbers and plots.
Blackbody Calculator generates spectra on wavelength λ and I proclaimed bluishness for spectra on frequency ν. Both kinds of spectral functions are called Planck's law and, for a narrow band with photon energies much lower than kT, such as visible light band in a 100,000°K white dwarf's spectrum, the approximation is called the Rayleigh–Jeans law.

But those functions are not quite the same, even bearing the same name.
Rayleigh–Jeans law is in fact 2 things:
B(ν) = 2ν²kT/c²
B(λ) = 2ckT/λ⁴

And that means that
λ-spectrum falls 10 times violet to red when λ rises 1.8 times
ν-spectrum falls 3.2 times violet to red when ν falls 1.8 times

However as to the myth of the Flat Spectrum, it is nothing more than a myth born from unfriendly info-graphic

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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by Chris Peterson » Sun Dec 11, 2022 5:33 pm

VictorBorun wrote: Sun Dec 11, 2022 5:07 pm Sorry, I was not quite correct on numbers and plots.
Blackbody Calculator generates spectra on wavelength λ and I proclaimed bluishness for spectra on frequency ν. Both kinds of spectral functions are called Planck's law and, for a narrow band with photon energies much lower than kT, such as visible light band in a 100,000°K white dwarf's spectrum, the approximation is called the Rayleigh–Jeans law.

But those functions are not quite the same, even bearing the same name.
Rayleigh–Jeans law is in fact 2 things:
B(ν) = 2ν²kT/c²
B(λ) = 2ckT/λ⁴

And that means that
λ-spectrum falls 10 times violet to red when λ rises 1.8 times
ν-spectrum falls 3.2 times violet to red when ν falls 1.8 times

However as to the myth of the Flat Spectrum, it is nothing more than a myth born from unfriendly info-graphic
The right way to do this is to apply Planck's Law, then to convolve the resulting spectrum with the transmission curves of the three filters, then to look at the ratios of the signal from each of those bands, then to convolve it again with the corrected output of the three display channels. I've actually done this and, no surprise, found that a 100000 K source is pretty much what we'd call white. I need to generate a couple of graphs, then I'll post my analysis.
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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by VictorBorun » Sun Dec 11, 2022 6:18 pm

Chris Peterson wrote: Sun Dec 11, 2022 5:33 pm
VictorBorun wrote: Sun Dec 11, 2022 5:07 pm Sorry, I was not quite correct on numbers and plots.
Blackbody Calculator generates spectra on wavelength λ and I proclaimed bluishness for spectra on frequency ν. Both kinds of spectral functions are called Planck's law and, for a narrow band with photon energies much lower than kT, such as visible light band in a 100,000°K white dwarf's spectrum, the approximation is called the Rayleigh–Jeans law.

But those functions are not quite the same, even bearing the same name.
Rayleigh–Jeans law is in fact 2 things:
B(ν) = 2ν²kT/c²
B(λ) = 2ckT/λ⁴

And that means that
λ-spectrum falls 10 times violet to red when λ rises 1.8 times
ν-spectrum falls 3.2 times violet to red when ν falls 1.8 times

However as to the myth of the Flat Spectrum, it is nothing more than a myth born from unfriendly info-graphic
The right way to do this is to apply Planck's Law, then to convolve the resulting spectrum with the transmission curves of the three filters, then to look at the ratios of the signal from each of those bands, then to convolve it again with the corrected output of the three display channels. I've actually done this and, no surprise, found that a 100000 K source is pretty much what we'd call white. I need to generate a couple of graphs, then I'll post my analysis.
That will be a treat.
By the way, what white to place in the scene for comfortably viewing a white dwarf?
If you put a flat spectrum cloud, then stars like Sun will look greenish.
If you put a Sun's spectrum cloud, then a flat spectrum object will look pinkish.
My guess for now is though that those nuances would not change the blueshness of a white dwarf, it will look the same as 1:1 mixture of white powder (LMS = 1 1 1) and blue powder (LMS = 0 ½ 1).

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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by Chris Peterson » Sun Dec 11, 2022 6:42 pm

VictorBorun wrote: Sun Dec 11, 2022 6:18 pm
Chris Peterson wrote: Sun Dec 11, 2022 5:33 pm
VictorBorun wrote: Sun Dec 11, 2022 5:07 pm Sorry, I was not quite correct on numbers and plots.
Blackbody Calculator generates spectra on wavelength λ and I proclaimed bluishness for spectra on frequency ν. Both kinds of spectral functions are called Planck's law and, for a narrow band with photon energies much lower than kT, such as visible light band in a 100,000°K white dwarf's spectrum, the approximation is called the Rayleigh–Jeans law.

But those functions are not quite the same, even bearing the same name.
Rayleigh–Jeans law is in fact 2 things:
B(ν) = 2ν²kT/c²
B(λ) = 2ckT/λ⁴

And that means that
λ-spectrum falls 10 times violet to red when λ rises 1.8 times
ν-spectrum falls 3.2 times violet to red when ν falls 1.8 times

However as to the myth of the Flat Spectrum, it is nothing more than a myth born from unfriendly info-graphic
The right way to do this is to apply Planck's Law, then to convolve the resulting spectrum with the transmission curves of the three filters, then to look at the ratios of the signal from each of those bands, then to convolve it again with the corrected output of the three display channels. I've actually done this and, no surprise, found that a 100000 K source is pretty much what we'd call white. I need to generate a couple of graphs, then I'll post my analysis.
That will be a treat.
By the way, what white to place in the scene for comfortably viewing a white dwarf?
If you put a flat spectrum cloud, then stars like Sun will look greenish.
If you put a Sun's spectrum cloud, then a flat spectrum object will look pinkish.
My guess for now is though that those nuances would not change the blueshness of a white dwarf, it will look the same as 1:1 mixture of white powder (LMS = 1 1 1) and blue powder (LMS = 0 ½ 1).
You can't ignore the display device. A typical monitor puts out twice the intensity of blue light that it does red just to produce white.
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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by VictorBorun » Mon Dec 12, 2022 12:07 am

Chris Peterson wrote: Sun Dec 11, 2022 6:42 pm You can't ignore the display device.
We can only hope for user's displays, printers and projectors to be good enough to tell 50% bluish from 100% white.
The thing to see as 50% bluish must look for the observer like it reflects
.5 .75 1
portion of illumination as reported by
L M S cones after they adapt to what is 0 (as in black) and what is 1 (as in white) in the same scene

I think of a human in an observatory on Moon looking at a white dwarf in a highly zoomed star field. If some stars are too bright, then it will be their spikes that will be comfortable; if the image will be uncomfortably sharp, you can lower the resolution to turn the stars into dots.

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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by alter-ego » Mon Dec 12, 2022 12:26 am

VictorBorun wrote: Sat Dec 10, 2022 5:38 pm
Chris Peterson wrote: Wed Dec 07, 2022 9:36 pm 100000K.png
Image
A plot with a flat line at the zero height would be unfriendly, so a zero above the horizontal axis is used.

What Rayleigh–Jeans law says, B ~ ν²/T, dictate the Brightness, or Spectral Radiance, to fall (.4/.1)² = 16 times with wavelength 0.1 μm to 0.4 μm and fall another (.7/.4)² = 3 times with wavelength 0.4 μm to 0.7 μm, and here this plot is not correct: this plot makes Spectral Radiance fall ~100 times and stay flat zero, respectivly.

Would the plotter generate the same result for me?
It does:
100000°K 2guest2125416477.png

Is it because Rayleigh–Jeans law fails at such short wavelengths?
No, the peak (according to Planck's law) is at much shorter wavelengths:
100000°K 3guest2125416477.png

So my guess is that thos plotter uses too few a point in the spline to show such nuances correctly
A couple things.
First, as you pointed out, the issue is not the calculator. Your calculations using the RJ law in frequency space can't be directly applied to the spectral radiance plotted in wavelength space. The inverse proportionality of frequency to wavelength result in totally different spectral radiance plots. Below, the x-axis ranges are identical, 0.1um to 0.7um (3000 THz to 428 THz) expressed as wavelength and frequency.
 
Black Body Spectral Radiance_Wavelength Space.jpg
Black Body Spectral Radiance_Frequency Space.jpg
 
• At 100,000 K, the RJ law is reasonably accurate in the visible range with a lower wavelength limit = 0.4um (750 THz). In this range the SR drops by 2.85x.
• 1,000,000 K is required to reduce the RJ SR over-estimation error to 2% at 0.1um.

Second, interestingly, the SR (as function of frequency) also peaks. However, considering a solar black body 5800 K, the peak occurs at 339.5 THz = 0.88 microns, which is not even close to the eye's peak sensitivity near 0.5 microns.
 
Solar Black Body Spectral Radiance_Frequency Space.jpg
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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by alter-ego » Mon Dec 12, 2022 1:17 am

VictorBorun wrote: Sun Dec 11, 2022 6:18 pm
Chris Peterson wrote: Sun Dec 11, 2022 5:33 pm
VictorBorun wrote: Sun Dec 11, 2022 5:07 pm Sorry, I was not quite correct on numbers and plots.
Blackbody Calculator generates spectra on wavelength λ and I proclaimed bluishness for spectra on frequency ν. Both kinds of spectral functions are called Planck's law and, for a narrow band with photon energies much lower than kT, such as visible light band in a 100,000°K white dwarf's spectrum, the approximation is called the Rayleigh–Jeans law.

But those functions are not quite the same, even bearing the same name.
Rayleigh–Jeans law is in fact 2 things:
B(ν) = 2ν²kT/c²
B(λ) = 2ckT/λ⁴

And that means that
λ-spectrum falls 10 times violet to red when λ rises 1.8 times
ν-spectrum falls 3.2 times violet to red when ν falls 1.8 times

However as to the myth of the Flat Spectrum, it is nothing more than a myth born from unfriendly info-graphic
The right way to do this is to apply Planck's Law, then to convolve the resulting spectrum with the transmission curves of the three filters, then to look at the ratios of the signal from each of those bands, then to convolve it again with the corrected output of the three display channels. I've actually done this and, no surprise, found that a 100000 K source is pretty much what we'd call white. I need to generate a couple of graphs, then I'll post my analysis.
That will be a treat.
By the way, what white to place in the scene for comfortably viewing a white dwarf?
If you put a flat spectrum cloud, then stars like Sun will look greenish.
If you put a Sun's spectrum cloud, then a flat spectrum object will look pinkish.
My guess for now is though that those nuances would not change the blueshness of a white dwarf, it will look the same as 1:1 mixture of white powder (LMS = 1 1 1) and blue powder (LMS = 0 ½ 1).
A visual chromaticity diagram often shows s locus (arc) of points representing the visual color of black bodies (<1500 K → Infinity). "White" in the diagram nominally occurs at 6000 K (around the suns BB temperature). So as the BB temperature increases beyond 6000 K, the apparent color will trend along this arc toward a bluish color.
Planckian Locus
Chromaticity Diagram with Plankian Locus.jpg
 
The links below discuss converting wavelengths to colors. As Chris said, the display device matters. Each has a different color gamut, and there's matrix calculations involving the CIE color match functions to get to display colors. RGB is just one display color system.
Converting a spectrum to a colour
Colour Rendering of Spectra
RGB Color Rendoring of Black Bodies.jpg
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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by VictorBorun » Mon Dec 12, 2022 1:31 am

alter-ego wrote: Mon Dec 12, 2022 1:17 am As Chris said, the display device matters. Each has a different color gamut
Can't imagine so bad a gadget display that a bluish white dwarf falls out of the gamut. Gamuts are all about rendering monochromatic and colour-saturated things; pale colours like thermal spectrum is no problem to render.
But to calculate the colour is a problem indeed

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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by VictorBorun » Tue Dec 13, 2022 9:19 am

why Antares (3,660±120°K) feels red when it's pale orange (pale amber, peach)?
I think an observer makes some wrong corrections. A star is perceived as seen poorly and treated like a bright saturated colour point drowned in a halo of electrically excited neighbour cones of all three types.

Scholz's Star (3,300±120°K) is a little redder and much darker. I wonder if it was perceived (passing Solar system) less red than Antares. We have no red dwarfs now in our sky to compare.

Had there ever been a guest white dwarf in Earth's sky? Not in the human history

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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by Chris Peterson » Tue Dec 13, 2022 2:42 pm

VictorBorun wrote: Tue Dec 13, 2022 9:19 am why Antares (3,660±120°K) feels red when it's pale orange (pale amber, peach)?
I think an observer makes some wrong corrections. A star is perceived as seen poorly and treated like a bright saturated colour point drowned in a halo of electrically excited neighbour cones of all three types.

Scholz's Star (3,300±120°K) is a little redder and much darker. I wonder if it was perceived (passing Solar system) less red than Antares. We have no red dwarfs now in our sky to compare.

Had there ever been a guest white dwarf in Earth's sky? Not in the human history
The blackbody spectrum results in a peak intensity at one specific wavelength, and a distribution around that which elicits some kind of visual response. Color is a physiological property that follows not only from the wavelength distribution, but from intensity. The same exact hue, displayed at two different intensity levels, is seen by humans as two completely different colors.
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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by Fred the Cat » Tue Dec 13, 2022 5:07 pm

VictorBorun wrote: Tue Dec 13, 2022 9:19 am Had there ever been a guest white dwarf in Earth's sky? Not in the human history
Hi Victor. Your question made me curious. They're not visible to the naked eye but there are a few examples. For white dwarfs, we'd all need some help. :shock:

Now if there were dark stars, good luck on that. :wink:
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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by VictorBorun » Wed Dec 14, 2022 12:53 am

Fred the Cat wrote: Tue Dec 13, 2022 5:07 pm
VictorBorun wrote: Tue Dec 13, 2022 9:19 am Had there ever been a guest white dwarf in Earth's sky? Not in the human history
Hi Victor. Your question made me curious. They're not visible to the naked eye but there are a few examples. For white dwarfs, we'd all need some help. :shock:

Now if there were dark stars, good luck on that. :wink:
well, a telescope may contain an illuminated plate scale; it can even be white (of low brightness), aiming to help recognizing a star's colour.
Now even in a telescope a star is a point-source of light, not comfortable for recognizing a star's colour.
It can be helped: you can dis-focus the image, or use a reflector telescope giving a star a few spikes helpful for recognizing a star's colour.

In short, there should be some reports on white dwarves' colour, should they not?

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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by Fred the Cat » Wed Dec 14, 2022 5:13 pm

:yes:
VictorBorun wrote: Wed Dec 14, 2022 12:53 am
Fred the Cat wrote: Tue Dec 13, 2022 5:07 pm
VictorBorun wrote: Tue Dec 13, 2022 9:19 am Had there ever been a guest white dwarf in Earth's sky? Not in the human history
Hi Victor. Your question made me curious. They're not visible to the naked eye but there are a few examples. For white dwarfs, we'd all need some help. :shock:

Now if there were dark stars, good luck on that.
well, a telescope may contain an illuminated plate scale; it can even be white (of low brightness), aiming to help recognizing a star's colour.
Now even in a telescope a star is a point-source of light, not comfortable for recognizing a star's colour.
It can be helped: you can dis-focus the image, or use a reflector telescope giving a star a few spikes helpful for recognizing a star's colour.

In short, there should be some reports on white dwarves' colour, should they not?
Sometimes, it seems, astronomers have reported on most topics you can imagine; age and color or temperature due to their constituent elements. As a group, they are busier than bees. :yes:
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Re: APOD: NGC 7293: The Helix Nebula (2022 Dec 07)

Post by VictorBorun » Wed Dec 14, 2022 10:48 pm

Fred the Cat wrote: Wed Dec 14, 2022 5:13 pm :yes:
VictorBorun wrote: Wed Dec 14, 2022 12:53 am
Fred the Cat wrote: Tue Dec 13, 2022 5:07 pm
Hi Victor. Your question made me curious. They're not visible to the naked eye but there are a few examples. For white dwarfs, we'd all need some help. :shock:

Now if there were dark stars, good luck on that.
well, a telescope may contain an illuminated plate scale; it can even be white (of low brightness), aiming to help recognizing a star's colour.
Now even in a telescope a star is a point-source of light, not comfortable for recognizing a star's colour.
It can be helped: you can dis-focus the image, or use a reflector telescope giving a star a few spikes helpful for recognizing a star's colour.

In short, there should be some reports on white dwarves' colour, should they not?
Sometimes, it seems, astronomers have reported on most topics you can imagine; age and color or temperature due to their constituent elements. As a group, they are busier than bees. :yes:
But their lingo is dangerous. The abstract for the arcticle you refer to says
they reach the turn–off in their colors and become blue at ages well below 10 Gyr
Sounded like cooling=turning blue (from white?) to my ear, playing in the hands of the myth of Flat Spectrum white dwarves.
So I began to read and saw this:
Fig. 6. (B − V, V − K) color–color diagram.jpg
B—V is comparing Blue to Green, logarithmically and the lower the bluer
V—K is comparing Green to IR, with maximum for Sun-like stars

Turning point is where a white dwarf cools all the way down to Sun's colour and next goes red (after being a small white dwarf for 8 billion years).
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