# Astronomy puzzle (angular-size/redshift)

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this is not a puzzle in the sense of a game or riddle. It is a fact from astronomy that (if it is not already familiar) you might want to think about and get to understand

In ordinary experience with earth-based geometry, the farther away something is the smaller it looks. That is true for short distance geometry done with metal rulers and yardsticks on the earth surface. But it is not true in space for very long distance geometry.

In ordinary shortrange geometry there is even an approximate reciprocal relation between angularsize and distance that works for objects with small angular size. If it is TWICE AS FAR then it looks HALF AS BIG. If you double the distance then you cut the angular size (the angle the thing makes, the angular diameter) in half. But past a certain point that doesnt work for galaxies.

Past a certain point galaxies look bigger the farther away they are.

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Can anyone come up with a clear simple explanation? I expect several people may UNDERSTAND why, but saying it clearly (so another person can get it) is different.

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Here are some articles.

The least technical, and shortest, is what Wikipedia has

http://en.wikipedia.org/wiki/Angular_size_redshift_relation

the Wiki doesnt say very much but at least it is comparatively easy to follow what it does say.

I tried to find something more on the web, but so far I didnt find anything for general audience.

these articles are technical and don't directly explain the puzzling effect.

http://arxiv.org/abs/astro-ph/0309390

Tight Cosmological Constraints from the Angular-Size/Redshift Relation for Ultra-Compact Radio Sources

J. C. Jackson

21 pages, 7 figures, published version

JCAP 0411 (2004) 007

"Some years ago (Jackson and Dodgson 1997) analysis of the angular-size/redshift relationship for ultra-compact radio sources indicted that for spatially flat universes the best choice of cosmological parameters was Omega_m=0.2 and Omega_Lambda=0.8..."

http://arxiv.org/abs/astro-ph/0605065

Legacy data and cosmological constraints from the angular-size/redshift relation for ultra-compact radio sources

J C Jackson, A L Jannetta

24 pages, 9 figures

[my comment: far too technical for our purposes]

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Too bad I can't find some more accessible reading on this. There probably is some SciAm article, I just dont know of it.

Anyway, if you measure distance by REDSHIFT z, there is a certain distance out there at which the angular size is a MINIMUM----if I remember it is somewhere roughly like z = 1.5-----and beyond that things farther out actually look bigger.

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I don't know the answer. I am therefore no use.

Here is something I will try tomorrow though: when an object is around z=1.5 redshift, what will its angular size be, and how does this compare to the frequency of light we would be observing?

I notice that both your articles have to do with radio waves, which will have a much, much larger wavelength than optical ones. Maybe that makes it more pronounced.

There. I made a guess. Tomorrow (or sooner) I will find out if it has any merit.

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Hi Locrian,

the effect is not wavelength dependent, within reason.

visible light versus radio shouldnt make any difference.

I don't think the links I found are any good! I would still like to find a good explanatory source. maybe Swansont or one of the others has something.

I think you may as well just ignore those two technical articles. Trouble is, I dont know anything to recommend.

I have researched this some more in the meantime and the minimum angular size comes around z=1.6

closer to 1.6 than 1.5 anyway.

So the same object if it is FARTHER than 1.6, then it will look BIGGER.

Wikipedia says 1.5 but that is only approximate. Actually Wikipedia is all right on this, but just very very brief----only a couple of sentences.

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the reason for this funhouse optics effect is that it is visual evidence of the universe having EXPANDED

so back in old times it was SMALLER and a galaxy of a given size (say 30 kiloparsecs) occupied MORE OF THE SKY

so when we look back to z=2, and 3, and 4

we are looking back at things in a smaller and smaller ball of universe

and they fill more and more of the sky and have a larger and larger angular size. how else could it be?

I just didnt want to have to say it. would prefer a nice polished online tutorial.

I bet you were planning to try Ned Wright's cosmo calculator on this.

That is a good way to learn about it.

His calculator reads out to you the angular size of things at various z.

It gives the "kiloparsecs per arcsecond"-----that is the kpc/"

" stands for arcsecond of angle

using his calculator one can check that z=1.6 is the place that something of fixed diameter stops looking smaller (as it gets farther) and starts looking bigger

have fun

http://www.astro.ucla.edu/~wright/CosmoCalc.html

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• 5 weeks later...

Stupid stupid layman's question:

If something were far enough away, would it in fact appear to occupy a goodly part of our sky, ( not bright enough, I know) or even would enough of them form some kind of barrier to further observation?

If true, what are the ramifications for standard cosmic models and astronomocal observation?

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If something were far enough away' date=' would it in fact appear to occupy a goodly part of our sky, ( not bright enough, I know) or even would enough of them form some kind of barrier to further observation?

If true, what are the ramifications for standard cosmic models and astronomocal observation?[/quote']

A+

respect.

the CMB does in fact fill the whole sky and it IS a barrier to further observation (by means of light)

and the "object" which radiated the light, which we observe and study when we make maps of the CMB, is called the SURFACE OF LAST SCATTERING

this surface was about 3000 Kelvin, like the surface of a star (a smaller redder star than the sun, which is more like 5000 Kelvin) and basically it was partially ionized hydrogen.

it was opaque for the same reason as the surface of the sun is opaque---gas is opaque when a high enough percentage is ionized because the charged particles are effective at scattering light. more effective than neutral atoms.

the surface of last scattering was a relatively SMALLER object at the time. It has expanded over 1000 fold.

So if you want to think of a distant object which USED TO BE MUCH SMALLER and which now looks big and is an OBSTACLE, then imagine one of those red and blue OVAL MAPS OF THE CMB that you have seen which have BLOBS of, like, red. And think of of one of those blobs as an "object"---a region where the S.o.L.S. (surf. of last. scat.) happened to be a bit hotter---and figure that this blob USED to be only a million or so LY across. like maybe ten times the size of a modern-day galaxy which would only be a pinpoint of light if it were nearer to us, say as near as the Virgo cluster, and we would be squinting thru a telescope to see it. but as you can see by looking at the CMB map, that blob (which is imaged in microwave) is actually FILLING A SIZABLE PORTION OF THE SKY.

so yeah, your intuition---following thru the logic of the thought---was right on

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the OPener post was dated 31 July

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gcol, as you say "if something were far away enough..."

being far away enough also means being at a high redshift-----the universe has expanded in the meantime and the light from the object has been stretched out to longer wavelength

so when you observe one of these odd old objects you may have to observe them in microwave or infrared instead of optical wavelength light

there are galaxies observed in the infrared which look larger than they "ought to" but it is the CMB blobs that correspond best to what you were talking about---that fill a "goodly portion" of the sky

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I don't know much about astronomy, and this is just a guess that might not even make sense. If it doesn't I'd appreciate it if someone could explain why. [/disclaimer]

Ok, so the more distant an object is, the older the light we receive from it, right? Also, the universe, specifically the volume of space in the universe, is and has always been expanding. Third, in normal, Euclidian space (in which we would expect farther away objects to be smaller), the amount of area of a sphere increases without limit with the square of the radius, as, therefore, does the "amount of stuff" at a given distance away. For example, a lot more stuff is roughly 20 light years away than roughly 5 light years away.

Given all of these things together, it seems like we would run into a paradox. The farther away something is, the less of the sky it ought to take up, because it's the same object in a much larger space (that space being the shell of space roughly equidistant from us). However, also, the farther away it is, the older it is, meaning that there is less space, since the universe was smaller in the past. A given object, then, would take up a larger percentage of the sky, as a result of there simply being "less sky." If we could see an object so distant that the light took the entire of the universe to reach us, then we would be seeing something from the very beginning, when pretty much everything was right on top of each other, and it would appear very large (I think). There must be a point, then, somewhere in between, where the second effect becomes greater than the first, and objects stop looking smaller with distance and start looking larger. That point would be a distance of minimal angular size, just like you describe.

...maybe that's it.

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Given all of these things together' date=' it seems like we would run into a paradox. The farther away something is, the less of the sky it ought to take up, because it's the same object in a much larger space (that space being the shell of space roughly equidistant from us). However, [i']also,[/i] the farther away it is, the older it is, meaning that there is less space, since the universe was smaller in the past. A given object, then, would take up a larger percentage of the sky, as a result of there simply being "less sky." If we could see an object so distant that the light took the entire of the universe to reach us, then we would be seeing something from the very beginning, when pretty much everything was right on top of each other, and it would appear very large (I think). There must be a point, then, somewhere in between, where the second effect becomes greater than the first, and objects stop looking smaller with distance and start looking larger. That point would be a distance of minimal angular size, just like you describe.

...maybe that's it.

Sisyphus, so glad you responded! It is a bad time for me I was just going to leave the and do some other stuff. I will get back later.

for now, briefly, you MUST learn to use Ned Wright calculator if you havent already----it shows how to convert redshift to lightyears distance

the turnaround is at z=1.6

galaxies start to look bigger after you get beyond z = 1.6

(use the calculator to convert that to some figure in billion of LY)

this IS a paradox, and it is something that is actually OBSERVED.

and it is easily explainable by the universe having expanded

so those older galaxies were in a sphere that used to be smaller, so they occupied more of it---more of an angular size---filled a bigger angle on that sphere

it is hard to say in words. but when you look back in time you are looking at a universe that was smaller and is going to expand and...sorry it is really hard to say in words.

rats.

nuts.

believe me it's simple:-)

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So, you're saying my explanation is more or less correct?

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...since the universe was smaller in the past. A given object, then, would take up a larger percentage of the sky, as a result of there simply being "less sky." If we could see an object so distant that the light took the entire of the universe to reach us, then we would be seeing something from the very beginning, when pretty much everything was right on top of each other, and it would appear very large (I think)..

YES!

You have figured it out quite right on your own.

Earlier i was in a rush---wife wanted me to drive her somewhere---and had several things to do. Sorry about haste.

this is exactly right.

You also reasoned out that there must be a critical distance.

It is the distance at which something with a given diameter has the MINIMAL ANGULAR SIZE.

this critical distance can be determined using Ned Wright's cosmology calculator. Google Ned Wright. (you may have already but in case someone else looks in:-) )

the critical distance is z= 1.6

I forget what it is in lightyears. the calculator will tell you just put in 1.6.

something with a fixed diameter----like a galaxy diameter 100 thousand LY.

it looks small and small as it is farther away, until it gets to critical, and after that, the farther away it is the larger it will look, the more angle it will make.

you sound pretty savvy already Sisyphus, did you already study this or did you just figure it, or is it easier and more obvious than I thought. Wll it doesnt matter. dont feel you have to answer.

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Another stupid stupid question:

If the early objects although appearing larger, still occupy the original portion of their space, does this mean they and the space between them have as it were maintained the same mark/space ratio? And if so, can I attribute the same properties to what we perceive as matter and the supposed empty spaces between matter?

This is leading me onto dangerous ground now, and flights of fancy: For example if what we perceive as matter and space are essentially the same, and what we perceive as matter is an optical illusion caused by a density boundary between them, then possibly gravity would seem to be a natural property of a continuous medium.

I hesitated a long time before writing that, it seemed daft and far-fetched. But fear not, tell me where I am wrong if you have the patience.

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• 3 weeks later...

what is red shift????????

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what is red shift????????

I don't have a good web link for you.

You can begin by reading Wiki

http://en.wikipedia.org/wiki/Redshift

try it though, for starters

it has a lot of pictures and is written in simple language.

afterwards you can read some more technical stuff about cosmological redshift which can correct the oversimplification in the Wiki article

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Another stupid stupid question:

If the early objects although appearing larger, still occupy the original portion of their space, does this mean they and the space between them have as it were maintained the same mark/space ratio? And if so, can I attribute the same properties to what we perceive as matter and the supposed empty spaces between matter?

.

hi gcol, I did not see your post earlier, and now that I see it I do not understand the question very well.

the expansion of space does not affect stuff at the level of rocks, or planets because they are held together by chemical bonds

even galaxies are virtually unaffected by it because they are BOUND structures-----they are coherent objects held together by gravity

the expansion of space affects the separation between distant galaxies, which are not gravitationally bound to each other----so distances between them can increase

so there is a scale at which you see expansion, and at smaller scale you do not see it-----and a piece of matter, a crystal lattice, just remains the same

so one cannot extrapolate down to small scale very well

hope this helps

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For one who did not completely understand the question, you nevertheless gave a perfectly satisfying answer. Well guessed!.

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If the expansion stretches light to a longer wavelength, which is at a very small scale, I don't see why it has no effect within galaxies or even within molecules.

If I understand this correctly, gravity and atomic forces "work faster" than the expansion of the universe and negates any effect it may have? Maybe I'm getting something wrong here...

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If the expansion stretches light to a longer wavelength, which is at a very small scale, I don't see why it has no effect within galaxies or even within molecules.

If I understand this correctly, gravity and atomic forces "work faster" than the expansion of the universe and negates any effect it may have? Maybe I'm getting something wrong here...

It's not stretching light directly, it's stretching space. So things "move" farther apart, which makes redshift. Except it doesn't move all things, since some (like solar systems, or galaxies, or atoms) are held together by other forces. That's why galaxies can get farther apart, but the galaxy itself doesn't get any bigger. Because one is held together by gravity, and the other isn't. Not that galaxies don't exert gravity on each other, mind you, just that they're more or less evenly distributed, and therefore have more or less equal gravitational pull from all directions, which amounts to zero net gravity.

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Sisyphus:

Assuming you are correct, it expands Martin's answer nicely, thanks.

But for me, it also begs another dumb question:

1. Would a cluster of (smaller) galaxies count as one larger one for this balancing out effect?

2. Also, presumably, black holes would similarly balance out and be part of a self-limiting size mechanism?

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Well, assuming I'm correct, then yes, a cluster of galaxies would, to some extent, be considered to be held together by gravity, though not nearly as coherently as the individual galaxies themselves. The impression I had was that at the largest scales, even beyond galaxy clusters, space is essentially "flat," meaning the net gravitation on a very large region is almost zero.

I don't really understand the second question.

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I don't really understand the second question.

Sorry, not phrased well. Just tidying up by trying to confirm that black holes, either single massive or clustered small, would form part of the null gravitation effect at large scales, and when a black hole was in a null gravitation region, it would thus cease to accrete further mass/matter?

If so, then (1) could I reason that at large scales all masses tend to settle into a nicely balanced gravitical position? And (2), at large scales, beyond a certain "fuzzy" boundary limit, perhaps the minimum angular size, there is no relative movement caused by gravity?

I may be stating the obvious, but I am definitely wet behind the ears in such matters. Trying to get "the big picture".

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I don't see what would be special about black holes. Unless you're right on top of it, its gravitational effects on its surroundings are no different from any other massive object, so I don't think you can consider them as a separate system from other objects, if that is in fact what you're suggesting.

As for (1), I think that's the case, although "nicely balanced" may be misleading. There are velocities unrelated to gravity that may complicate things, I'm not sure. I suppose simply zooming out in scale solves the problem, though.

And for (2), I'm almost certain that's correct.

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