APOD: Unwinding M51 (2020 Aug 21)

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APOD: Unwinding M51 (2020 Aug 21)

Post by APOD Robot » Fri Aug 21, 2020 4:06 am

Image Unwinding M51

Explanation: The arms of a grand design spiral galaxy 60,000 light-years across are unwound in this digital transformation of the magnificent 2005 Hubble Space Telescope portrait of M51. In fact, M51 is one of the original spiral nebulae, its winding arms described by a mathematical curve known as a logarithmic spiral, a spiral whose separation grows in a geometric way with increasing distance from the center. Applying logarithms to shift the pixel coordinates in the Hubble image relative to the center of M51 maps the galaxy's spiral arms into diagonal straight lines. The transformed image dramatically shows the arms themselves are traced by star formation, lined with pinkish starforming regions and young blue star clusters. Companion galaxy NGC 5195 (top) seems to alter the track of the arm in front of it though, and itself remains relatively unaffected by this unwinding of M51. Also known as the spira mirabilis, logarthimic spirals can be found in nature on all scales. For example, logarithmic spirals can also describe hurricanes, the tracks of subatomic particles in a bubble chamber and, of course, cauliflower.

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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by RocketRon » Fri Aug 21, 2020 4:25 am

logarthimic (sic) spirals = logarithmic spirals ?

Unwinding a spiral galaxy would be a bit like unscrambling an egg !
Interesting exercise though.

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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by Ann » Fri Aug 21, 2020 5:08 am















Why are parts of the image of "unwinding M51" so blurry (in the lower part of the image)? I don't think that the original Hubble image was so blurry. What do the rest of you think?

I do appreciate that the "unwinding" exercise, however. It is interesting.

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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by Boomer12k » Fri Aug 21, 2020 6:20 am

I am sorry, but I don't understand this... how does duplicating parts of the spiral arms, in a straight pattern... alternating the "brushes" like in a paint program to show 6-7 pointed "arms"... "unwind" a galaxy with only 2 spiral arms....yet is overlayed on a 2nd galaxy that is in reality totally disrupted and blocking the whole side of the other galaxy?

I don't understand the concept of this. Can someone please explain it? I get that it is some logarithmic spiral math function...like Fibonacci numbers...there are others in nature as well...
but this seems to be a total fantasy... and not related...

In reality, I think if you unwind a spiral...you get two straight lines in opposite directions...
-----0------ as such....when you wind that...you get a spiral... like a coiled-up spring.
This image shows the ends of the spiral next to each other and duplicated at least twice.

How is M51 "an original spiral galaxy"??? Do they mean it was one of the first studied???

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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by JohnD » Fri Aug 21, 2020 10:18 am

Agree with Boomer - what was the point of this?
It's well known that plotting an exponential curve on semilog paper - logarithmic scale on one axis - delivers a straight line.
Surely that star-forming regions occur along the denser parts of the arms is clear from an unmolested image?

And NGC5195 is only 2 million light years from M51, so is it really affecting the arm that happens to lie between it and us?

John

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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by orin stepanek » Fri Aug 21, 2020 10:42 am

Why? :shock:
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by neufer » Fri Aug 21, 2020 11:13 am

Ann wrote:
Fri Aug 21, 2020 5:08 am

Why are parts of the image of "unwinding M51" so blurry (in the lower part of the image)? I don't think that the original Hubble image was so blurry.
Think of an equirectangular projection
where (for Antarctica, at least):
  • 1) the x axis is longitude

    2) the y axis is (basically) the
    radial distance from the South Pole
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by BDanielMayfield » Fri Aug 21, 2020 1:58 pm

orin stepanek wrote:
Fri Aug 21, 2020 10:42 am
Why? :shock:
I agree, but will hazard some guesses.

Because they could?

To make the straight parts crooked and the crooked parts straight?

Because flattening curves is the in thing now?

:?:
Just as zero is not equal to infinity, everything coming from nothing is illogical.

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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by Chris Peterson » Fri Aug 21, 2020 2:03 pm

Boomer12k wrote:
Fri Aug 21, 2020 6:20 am
I am sorry, but I don't understand this... how does duplicating parts of the spiral arms, in a straight pattern... alternating the "brushes" like in a paint program to show 6-7 pointed "arms"... "unwind" a galaxy with only 2 spiral arms....yet is overlayed on a 2nd galaxy that is in reality totally disrupted and blocking the whole side of the other galaxy?

I don't understand the concept of this. Can someone please explain it? I get that it is some logarithmic spiral math function...like Fibonacci numbers...there are others in nature as well...
but this seems to be a total fantasy... and not related...
Agreed. I don't really get the point of this. I mean, I'm into image processing, and I love all the cool things that can be done with geometric transforms. As a technical exercise this is fun and interesting. But in terms of value in presenting information? I feel like I've lost understanding of what's going on in comparison with the original image.
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by neufer » Fri Aug 21, 2020 3:04 pm

JohnD wrote:
Fri Aug 21, 2020 10:18 am

NGC5195 is only 2 million light years from M51, so is it really affecting the arm that happens to lie between it and us?
Companion galaxy NGC 5195 is not only affecting the arms but
it is actually making M51 more of an Archimedean spiral, IMO.
https://en.wikipedia.org/wiki/Archimedean_spiral wrote:
The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation: r = a + b θ with real numbers a and b. Changing the parameter a moves the centerpoint of the spiral outward from the origin, while b controls the distance between loops. From the above equation, it can thus be stated: the position of particle from the point of start is proportional to the angle θ as time elapses. Archimedes described such a spiral in his book On Spirals. Conon of Samos was a friend of his and Pappus states that the "Archimedean" spiral was discovered by Conon of Samos.>>
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by orin stepanek » Fri Aug 21, 2020 5:49 pm

BDanielMayfield wrote:
Fri Aug 21, 2020 1:58 pm
orin stepanek wrote:
Fri Aug 21, 2020 10:42 am
Why? :shock:
I agree, but will hazard some guesses.

Because they could?

To make the straight parts crooked and the crooked parts straight?

Because flattening curves is the in thing now?

Thanks; I needed That!
+1 :thumb_up: :yes:
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by Ann » Fri Aug 21, 2020 5:57 pm

orin stepanek wrote:
Fri Aug 21, 2020 5:49 pm
BDanielMayfield wrote:
Fri Aug 21, 2020 1:58 pm
orin stepanek wrote:
Fri Aug 21, 2020 10:42 am
Why? :shock:
I agree, but will hazard some guesses.

Because they could?

To make the straight parts crooked and the crooked parts straight?

Because flattening curves is the in thing now?

Thanks; I needed That!
+1 :thumb_up: :yes:
😁😍🤩

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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by orin stepanek » Fri Aug 21, 2020 6:09 pm

Ann wrote:
Fri Aug 21, 2020 5:57 pm
orin stepanek wrote:
Fri Aug 21, 2020 5:49 pm
BDanielMayfield wrote:
Fri Aug 21, 2020 1:58 pm


I agree, but will hazard some guesses.

Because they could?

To make the straight parts crooked and the crooked parts straight?

Because flattening curves is the in thing now?

Thanks; I needed That!
+1 :thumb_up: :yes:
😁😍🤩

Ann
Oh Ann; you're the best across the sea!🚤 😇
Orin

Smile today; tomorrow's another day!

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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by johnnydeep » Fri Aug 21, 2020 6:10 pm

neufer wrote:
Fri Aug 21, 2020 11:13 am
Ann wrote:
Fri Aug 21, 2020 5:08 am

Why are parts of the image of "unwinding M51" so blurry (in the lower part of the image)? I don't think that the original Hubble image was so blurry.
Think of an equirectangular projection
where (for Antarctica, at least):
  • 1) the x axis is longitude

    2) the y axis is (basically) the
    radial distance from the South Pole
That, and the fact that the bottom of the "unrolled" image maps to the center of the galaxy, which is itself blurry in the original image due to resolving limits. See https://hubblesite.org/contents/media/i ... Image.html.
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by johnnydeep » Fri Aug 21, 2020 6:11 pm

Chris Peterson wrote:
Fri Aug 21, 2020 2:03 pm
Boomer12k wrote:
Fri Aug 21, 2020 6:20 am
I am sorry, but I don't understand this... how does duplicating parts of the spiral arms, in a straight pattern... alternating the "brushes" like in a paint program to show 6-7 pointed "arms"... "unwind" a galaxy with only 2 spiral arms....yet is overlayed on a 2nd galaxy that is in reality totally disrupted and blocking the whole side of the other galaxy?

I don't understand the concept of this. Can someone please explain it? I get that it is some logarithmic spiral math function...like Fibonacci numbers...there are others in nature as well...
but this seems to be a total fantasy... and not related...
Agreed. I don't really get the point of this. I mean, I'm into image processing, and I love all the cool things that can be done with geometric transforms. As a technical exercise this is fun and interesting. But in terms of value in presenting information? I feel like I've lost understanding of what's going on in comparison with the original image.
I'm glad you all are of like mind with me. I also fail to see that the unwinding adds to our understanding. So far, I don't see any benefit at all.
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by BDanielMayfield » Fri Aug 21, 2020 8:11 pm

Consensus speaks. The "whys?" have it.
Just as zero is not equal to infinity, everything coming from nothing is illogical.

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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by johnnydeep » Fri Aug 21, 2020 9:20 pm

BDanielMayfield wrote:
Fri Aug 21, 2020 8:11 pm
Consensus speaks. The "whys?" have it.
FWIW, I emailed Paul Howell <phowell@bowdoin.edu> from the Unwinding attribution on the image and he replied as follows:
I suppose at a certain level your question would be better answered by Robert Nemiroff and Jerry Bonnell. Taking a stab at it, I would say the point is education and engagement. It looks like it worked <g>. Not just this image, but the whole idea behind APOD if I may speak for Robert and Jerry.

Sure, there is nothing in the 'unwound' image that could not be measured. In fact, that has certainly been done. But like a plot that illuminates something more intuitively than a column of numbers, this image reinforces the remarkable property that spiral arms (often) obey a log spiral.

I guess I could go a bit further and say that the image demonstrates that the end of one arm closest to NGC 5195 departs from a log spiral which tends to support the idea that there has been an interaction. This too is not something that you could not deduce through analysis but the image is more accessible to a broader group.

I only glanced quickly at the discussions (semester startup and all . . . ), but here's some feedback.

- The progressive 'fuzziness' of the image as you get closer to the bottom is a consequence of the logarithmic transformation. If you look at a plot of y=ln(x), you will see it is steep at first and then flattens. Consequently, pixels that originate close to the origin (the center of M51 e.g.) get stretched more vertically due to the transformation. Additionally, the x-axis is the phase angle of the transformation. Pixels close to the origin subtend a greater angle than those far away. That stretches those pixels along the phase axis. So pixels at a small radius (near the bottom, e.g.) are quite stretched in each direction.

- NGC 5195 comes through largely unscathed for these reasons: At large r and for relatively small changes in r, y=ln(r) is approximately linear. So the y-axis maps pretty much the same way you see it. Then, the small angle approximation gives us that theta ~ sin(theta) where theta is in radians. This means that angular displacement maps to linear displacement in proportion. So the x-axis maps to what you see as well since NGC 5195 is not close to the origin.

- I think I saw a post wondering why two arms don't end up straight but opposed (?). The reason is that each arm is displaced in phase angle by roughly pi radians.

- Not sure if this was discussed, but there is no beginning or end to the image along the x (phase) axis. It just continuously repeats since you are simply wrapping around as you go. Think of it as a picture on a coffee mug that has no start or end. Hmmmmmmm <g>.
Did this help? I'm still not really appreciating it properly I suppose, other than the log plot linear result "proving" the log nature of the spiral. Also, who are Robert Nemiroff and Jerry Bonnell?

EDIT: BDanielMayfield let me know who they are just below :oops:
Last edited by johnnydeep on Sat Aug 22, 2020 3:41 pm, edited 1 time in total.
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by BDanielMayfield » Fri Aug 21, 2020 10:30 pm

The above post was great johnnydeep, except for, GASP,
Also, who are Robert Nemiroff and Jerry Bonnell?
Look at the third line below each and every day's APOD explanation.
Just as zero is not equal to infinity, everything coming from nothing is illogical.

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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by johnnydeep » Sat Aug 22, 2020 12:04 am

BDanielMayfield wrote:
Fri Aug 21, 2020 10:30 pm
The above post was great johnnydeep, except for, GASP,
Also, who are Robert Nemiroff and Jerry Bonnell?
Look at the third line below each and every day's APOD explanation.
Ah. I never look down there!
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by MoreInput » Sat Aug 22, 2020 7:56 am

Hi all,

I did also some unwinding of different other galaxies. I posted it a year ago here: https://asterisk.apod.com/viewtopic.ph ... 73#p293173

And here is my collection of unwinded spiral galaxies and also some planetary nebulae: https://drive.google.com/drive/folders/ ... eyR4r6f9Ej

This is the galaxy M 101: If also works for planetary nebulae, like the cat's eye nebula:

What information can we get if we look at this transformed galaxy pictures? You can follow the spiral arms more convenient and visually follow them in a straight line.

Or look at this wonderful galaxy from apod 15th May 2019: ,

Unwinded you can see the density waves ploughing through the galaxy I fiddled the images around with GIMP using polar coordinate transformations and some other scale functions. This was done manually, so there are artifact like white lines in my images.

Best regards,
Stefan

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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by Ann » Sat Aug 22, 2020 8:59 am

MoreInput wrote:
Sat Aug 22, 2020 7:56 am
Hi all,

I did also some unwinding of different other galaxies. I posted it a year ago here: https://asterisk.apod.com/viewtopic.ph ... 73#p293173

And here is my collection of unwinded spiral galaxies and also some planetary nebulae: https://drive.google.com/drive/folders/ ... eyR4r6f9Ej

This is the galaxy M 101: If also works for planetary nebulae, like the cat's eye nebula:

What information can we get if we look at this transformed galaxy pictures? You can follow the spiral arms more convenient and visually follow them in a straight line.

Or look at this wonderful galaxy from apod 15th May 2019: ,

Unwinded you can see the density waves ploughing through the galaxy I fiddled the images around with GIMP using polar coordinate transformations and some other scale functions. This was done manually, so there are artifact like white lines in my images.

Best regards,
Stefan
Unwinding NGC 4921.png
Unwinding NGC 4921. NASA, ESA, K. Cook (LLNL), Stefan/MoreInput

I did a printscreen of your unwinding version of NGC 4921, and put it next to the unwinding version of M51.

Interesting comparison!

Ann
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by johnnydeep » Sat Aug 22, 2020 3:45 pm

MoreInput wrote:
Sat Aug 22, 2020 7:56 am
Hi all,

I did also some unwinding of different other galaxies. I posted it a year ago here: https://asterisk.apod.com/viewtopic.ph ... 73#p293173

And here is my collection of unwinded spiral galaxies and also some planetary nebulae: https://drive.google.com/drive/folders/ ... eyR4r6f9Ej

This is the galaxy M 101: If also works for planetary nebulae, like the cat's eye nebula:

What information can we get if we look at this transformed galaxy pictures? You can follow the spiral arms more convenient and visually follow them in a straight line.

Or look at this wonderful galaxy from apod 15th May 2019: ,

Unwinded you can see the density waves ploughing through the galaxy I fiddled the images around with GIMP using polar coordinate transformations and some other scale functions. This was done manually, so there are artifact like white lines in my images.

Best regards,
Stefan
Ok, yes, these are indeed lovely. I think all these various galaxy unwindings look like roiling galactic waves with starry froth on a celestial sea! For that alone, I deem them to be worthwhile :)
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by neufer » Sat Aug 22, 2020 8:03 pm

RocketRon wrote:
Fri Aug 21, 2020 4:25 am

Unwinding a spiral galaxy would be a bit like unscrambling an egg !
https://en.wikipedia.org/wiki/Conformal_map wrote:
<<In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths.
  • [Circles (like companion galaxy NGC 5195) map into circles]
For mappings in two dimensions, the (orientation-preserving) conformal mappings are precisely the locally invertible complex analytic functions.>>
[X + iY] = i ln{r exp(iθ)} = i [(iθ)] + i ln{r}
....................................
X = -θ

Y = ln{r}
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Re: APOD: Unwinding M51 (2020 Aug 21)

Post by MoreInput » Sat Aug 22, 2020 9:51 pm

Hi Ann!

Thanks for uploading the image to apod directly.
I still hope that I can understand the dynamics of the spiral arms sometimes.

Best regards,
Stefan