<p>This comment is too long for a comment.</p>

<p>I could not find a source (yet) stating explicitly that it is a scalar quantity that is plotted, so I thought I would investigate the colors themselves for any sign of additional information.</p>

<p>What I found was inconclusive. </p>

<p>From <a href="https://eventhorizontelescope.org/" rel="nofollow noreferrer">https://eventhorizontelescope.org/</a> I found the smaller size image <code>https://static.projects.iq.harvard.edu/files/styles/os_files_xlarge/public/eht/files/20190410-78m-800x466.png</code> which I've imported below in png format (lossless-compression only) then broken into r, g, b components, flattened, and then plotted in 2D (and 3D) scatter plots.</p>

<p><strong>It certainly looks like some standard colormap was used to plot a image of a single scalar quantity,</strong> but something has fuzzed up the color a bit. It could be the interpolation routings used to make the graphic for public release, or some "internet color adjustment" before publication. The world of publishing color is pretty confusing.</p>

<p>Note, I've slimmed down the data before flattening and plotting:</p>

<pre><code>n = 8
img     = plt.imread(fname)[::n, ::n]
</code></pre>

<p><a href="https://i.sstatic.net/OtCXB.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/OtCXB.png" alt="enter image description here"></a></p>

<p><a href="https://i.sstatic.net/7ySFI.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/7ySFI.png" alt="enter image description here"></a></p>

<p><a href="https://i.sstatic.net/bBbcf.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bBbcf.png" alt="enter image description here"></a></p>

<pre><code>import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

fname = '20190410-78m-800x466.png'
n = 8
img     = plt.imread(fname)[::n, ::n]
rgb     = np.array([x.flatten() for x in np.rollaxis(img, 2, 0)][:3])
r, g, b = rgb
rgbavg  = rgb.sum(axis=0)/3.

if True:
    fig = plt.figure(figsize=[10, 8])  # [12, 10]
    ax  = fig.add_subplot(1, 1, 1, projection='3d')
    ax.plot(r, g, b, '.k')
    ax.set_xlim(0, 1)
    ax.set_ylim(0, 1)
    ax.set_zlim(0, 1)
    plt.show()

titles = ('g vs r', 'b vs g', 'r vs b', 'r vs mean', 'g vs mean', 'b vs mean')
if True:
    plt.figure()
    for i in range(0, 3):
        plt.subplot(2, 3, i+1)
        plt.plot(rgb[i%3], rgb[(i+1)%3], '.k')
        plt.title(titles[i], fontsize=16)
        plt.xlim(0, 1)
        plt.ylim(0, 1)
    for i in range(3, 6):
        plt.subplot(2, 3, i+1)
        plt.plot(rgbavg, rgb[i%3], '.k')
        plt.title(titles[i], fontsize=16)
        plt.xlim(0, 1)
        plt.ylim(0, 1)
    plt.show()
</code></pre>

CC BY-SA 4.0
2019-04-12T08:22:54.857Z
In the paper (IV or V) the library used is mentioned.  About scalar or not it might be over thinking.  The values certainly correlate with a number of photons. I think is always so  with photos or imagery.
Alchimista
CC BY-SA 4.0
2019-04-12T08:35:05.487Z
Uhoh unless you refer to vectir as to form an image, I do not see what else should have been plotted not inherently scalar. The amount of energy impinging a detector pixel is just a number (photons, energy, power, whatever related). Here they choose Tbrightness for a reason mentioned in their paper (that anyway remain somehow obscure but I am not into such details).
Alchimista
CC BY-SA 4.0
2019-04-12T09:07:47.750Z
Ii think you misunderstood the question. Which simply ask " I resume: is the picture a radio waves intensity or brightness map, or conversely a kind of "as it would be" picture in the Vis (modelled from the behaviour of the collected radio waves and theories)?". Which can be obviously answered or not depending on the knowledge of bh behaviour and a lot of things. It is totally obscure what do you mean by "that is scalar quantity that is plotted". I leave comments to discuss and clarify the issue that OP rised. I could have downvoted instead, but why? Probably nothing wrong in the "A"., but?
Alchimista
CC BY-SA 4.0
2019-04-12T09:18:02.307Z
@Alchimista the question also has a title: "Do the actual false colours in the M87 black hole picture convey information?" as well as contain the sentence "Discarding the obvious dark, shall the picture be watch at **merely in term of brightness, or considering yellow and red as well?**" And so I've tried to see if there is any meaningful difference between "yellow and red" beyond "merely in term(s) of brightness". I don't see any, it looks like a simple monotonic progression in all three color channels, so I conclude it's the former, and not the latter.
uhoh
CC BY-SA 4.0
2019-04-12T09:20:06.797Z
Ok, that means yellow red reference in my question refers to possibly different wavelengths  of the signal, but it is not.  It simply a kind of flux brightness to mean intensity. It could have convey a doppler like effect, for instance, or suggest a "how it would look like in Vis". Which is both no. As from the A and further reading.
Alchimista
CC BY-SA 4.0
2019-04-12T09:26:03.643Z
No, it (certainly seems that it) refers to the yellow and red in the image. To the question "Does the transition in color from red in some areas to yellow in other areas represent anything more than an increase in brightness?" I have concluded that the answer is "No."
uhoh
CC BY-SA 4.0
2019-04-12T09:39:13.353Z
Up voted last comment for just the "final" statement. The first seems again just dropped.  Fine.
Alchimista
CC BY-SA 4.0
2019-04-11T08:54:24.557Z
2019-04-11T08:54:24.557Z
uhoh
<p>See <a href="https://doi.org/10.3847%2F2041-8213%2Fab0ec7" rel="nofollow noreferrer">this article</a> recently published by the EHT collaboration describing how they generated the image. Specifically, chapter 5 of that article describes the origin of the image. To quote the article (specifically the caption of figure 3):</p>

<blockquote>
  <p>The image is shown in units of brightness temperature, <span class="math-container">${T}_{{\rm{b}}}=S{\lambda }^{2}/2{k}_{{\rm{B}}}{\rm{\Omega }}$</span>, where S is the flux density, λ is the observing wavelength, <span class="math-container">$k_{B}$</span> is the Boltzmann constant, and Ω is the solid angle of the resolution element.</p>
</blockquote>

<p>The false colors in the image convey the surface T brightness (a sort of measurement of the intensity or flux from that area) of the material surrounding the black hole's event horizon. Brighter color means higher brightness temperature. There is not information about the physical T of the in falling materials as the collected radiation is of synchrotron type and not that of a black body. As you say, the image could have been shown in grayscale or any other color scale. The fact that it is shown in an orange-ish color is merely the convention chosen by the scientists who generated the image.</p>

<p>BUT there's a lot more information in the image than just how bright the material is. For example, the fact that the material is brighter on one side than on the other can tell us about the geometry of the material surrounding the black hole, or about how that material is rotating around it. If you have the time, check out <a href="https://www.nature.com/articles/d41586-019-01155-0" rel="nofollow noreferrer">this article</a> and read up on the actual journal articles published by the <a href="https://eventhorizontelescope.org/" rel="nofollow noreferrer">Event Horizon Telescope collaboration</a> linked at the bottom.</p>

CC BY-SA 4.0
2019-04-11T08:47:26.200Z
Yes I am aware of the motion aspects. Thanks
Alchimista
CC BY-SA 4.0
2019-04-11T09:52:24.217Z
@uhoh Done! Specifically, I quoted the caption of the same image from the paper put out by the EHT collaboration.
Jvinniec
CC BY-SA 4.0
2019-04-11T12:49:46.850Z
I have to look with calm what Tb means/represents.
Alchimista
CC BY-SA 4.0
2019-04-11T08:37:08.643Z
2019-04-12T09:12:30.170Z
2019-04-12T09:12:30.170Z
Jvinniec
<p>As for the title. The picture could have been plotted in grey scale, B&amp;W, whatever couple of colours, or perhaps using a window of wavelength in order to show shift of the Doppler/relativistic Doppler kind.</p>

<p>Discarding the obvious dark, shall the picture be watch at merely in term of brightness, or considering yellow and red as well? </p>

<p>And independently, why those colours have been choose?  Just an aesthetic and suggestive choice, or that should be the apparent image as seen by eyes if we could go there? </p>

<p>I resume: is the picture a radio waves intensity or brightness map, or conversely a kind of "as it would be" picture in the Vis (modelled from the behaviour of the collected radio waves and theories)?</p>

<black-hole><radio-astronomy>
Do the actual false colours in the M87 black hole picture convey information?
Alchimista
# Do the actual false colours in the M87 black hole picture convey information?

(Asked by: username_0 on 2019-04-11)

As for the title. The picture could have been plotted in grey scale, B&W, whatever couple of colours, or perhaps using a window of wavelength in order to show shift of the Doppler/relativistic Doppler kind.

Discarding the obvious dark, shall the picture be watch at merely in term of brightness, or considering yellow and red as well?

And independently, why those colours have been choose? Just an aesthetic and suggestive choice, or that should be the apparent image as seen by eyes if we could go there?

I resume: is the picture a radio waves intensity or brightness map, or conversely a kind of "as it would be" picture in the Vis (modelled from the behaviour of the collected radio waves and theories)?

**Tags:** black-hole, radio-astronomy

---

## 2 answers

### Answer by username_2 on 2019-04-11. Score: 4 | Accepted answer

See [this article](https://doi.org/10.3847%2F2041-8213%2Fab0ec7) recently published by the EHT collaboration describing how they generated the image. Specifically, chapter 5 of that article describes the origin of the image. To quote the article (specifically the caption of figure 3):

> The image is shown in units of brightness temperature, ${T}\_{{\rm{b}}}=S{\lambda }^{2}/2{k}\_{{\rm{B}}}{\rm{\Omega }}$, where S is the flux density, λ is the observing wavelength, $k\_{B}$ is the Boltzmann constant, and Ω is the solid angle of the resolution element.

The false colors in the image convey the surface T brightness (a sort of measurement of the intensity or flux from that area) of the material surrounding the black hole's event horizon. Brighter color means higher brightness temperature. There is not information about the physical T of the in falling materials as the collected radiation is of synchrotron type and not that of a black body. As you say, the image could have been shown in grayscale or any other color scale. The fact that it is shown in an orange-ish color is merely the convention chosen by the scientists who generated the image.

BUT there's a lot more information in the image than just how bright the material is. For example, the fact that the material is brighter on one side than on the other can tell us about the geometry of the material surrounding the black hole, or about how that material is rotating around it. If you have the time, check out [this article](https://www.nature.com/articles/d41586-019-01155-0) and read up on the actual journal articles published by the [Event Horizon Telescope collaboration](https://eventhorizontelescope.org/) linked at the bottom.

> **Comments:**
> **username_0**: Yes I am aware of the motion aspects. Thanks  
> **username_2**: @uhoh Done! Specifically, I quoted the caption of the same image from the paper put out by the EHT collaboration.  
> **username_0**: I have to look with calm what Tb means/represents.  

---

### Answer by username_1 on 2019-04-11. Score: 0

This comment is too long for a comment.
I could not find a source (yet) stating explicitly that it is a scalar quantity that is plotted, so I thought I would investigate the colors themselves for any sign of additional information.
What I found was inconclusive. 
From https://eventhorizontelescope.org/ I found the smaller size image https://static.projects.iq.harvard.edu/files/styles/os_files_xlarge/public/eht/files/20190410-78m-800x466.png which I've imported below in png format (lossless-compression only) then broken into r, g, b components, flattened, and then plotted in 2D (and 3D) scatter plots.
It certainly looks like some standard colormap was used to plot a image of a single scalar quantity, but something has fuzzed up the color a bit. It could be the interpolation routings used to make the graphic for public release, or some "internet color adjustment" before publication. The world of publishing color is pretty confusing.
Note, I've slimmed down the data before flattening and plotting:
n = 8
img     = plt.imread(fname)[::n, ::n]




import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

fname = '20190410-78m-800x466.png'
n = 8
img     = plt.imread(fname)[::n, ::n]
rgb     = np.array([x.flatten() for x in np.rollaxis(img, 2, 0)][:3])
r, g, b = rgb
rgbavg  = rgb.sum(axis=0)/3.

if True:
    fig = plt.figure(figsize=[10, 8])  # [12, 10]
    ax  = fig.add_subplot(1, 1, 1, projection='3d')
    ax.plot(r, g, b, '.k')
    ax.set_xlim(0, 1)
    ax.set_ylim(0, 1)
    ax.set_zlim(0, 1)
    plt.show()

titles = ('g vs r', 'b vs g', 'r vs b', 'r vs mean', 'g vs mean', 'b vs mean')
if True:
    plt.figure()
    for i in range(0, 3):
        plt.subplot(2, 3, i+1)
        plt.plot(rgb[i%3], rgb[(i+1)%3], '.k')
        plt.title(titles[i], fontsize=16)
        plt.xlim(0, 1)
        plt.ylim(0, 1)
    for i in range(3, 6):
        plt.subplot(2, 3, i+1)
        plt.plot(rgbavg, rgb[i%3], '.k')
        plt.title(titles[i], fontsize=16)
        plt.xlim(0, 1)
        plt.ylim(0, 1)
    plt.show()

> **Comments:**
> **username_0**: In the paper (IV or V) the library used is mentioned.  About scalar or not it might be over thinking.  The values certainly correlate with a number of photons. I think is always so  with photos or imagery.  
> **username_0**: Uhoh unless you refer to vectir as to form an image, I do not see what else should have been plotted not inherently scalar. The amount of energy impinging a detector pixel is just a number (photons, energy, power, whatever related). Here they choose Tbrightness for a reason mentioned in their paper (that anyway remain somehow obscure but I am not into such details).  
> **username_0**: Ii think you misunderstood the question. Which simply ask " I resume: is the picture a radio waves intensity or brightness map, or conversely a kind of "as it would be" picture in the Vis (modelled from the behaviour of the collected radio waves and theories)?". Which can be obviously answered or not depending on the knowledge of bh behaviour and a lot of things. It is totally obscure what do you mean by "that is scalar quantity that is plotted". I leave comments to discuss and clarify the issue that OP rised. I could have downvoted instead, but why? Probably nothing wrong in the "A"., but?  
> **username_1**: @Alchimista the question also has a title: "Do the actual false colours in the M87 black hole picture convey information?" as well as contain the sentence "Discarding the obvious dark, shall the picture be watch at **merely in term of brightness, or considering yellow and red as well?**" And so I've tried to see if there is any meaningful difference between "yellow and red" beyond "merely in term(s) of brightness". I don't see any, it looks like a simple monotonic progression in all three color channels, so I conclude it's the former, and not the latter.  
> **username_0**: Ok, that means yellow red reference in my question refers to possibly different wavelengths  of the signal, but it is not.  It simply a kind of flux brightness to mean intensity. It could have convey a doppler like effect, for instance, or suggest a "how it would look like in Vis". Which is both no. As from the A and further reading.  
> **username_1**: No, it (certainly seems that it) refers to the yellow and red in the image. To the question "Does the transition in color from red in some areas to yellow in other areas represent anything more than an increase in brightness?" I have concluded that the answer is "No."  
> **username_0**: Up voted last comment for just the "final" statement. The first seems again just dropped.  Fine.  

---

