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john hunter
2010-Apr-17, 11:17 PM
Apparently a maximum in the angular size - z graph is predicted, at about z=1.65 (depending on cosmological model)....

e.g. http://en.wikipedia.org/wiki/Angular_diameter_distance

has a maximum been observed yet at any z value? If so, at what value of z?

Thanks everyone,

John Hunter.

Spaceman Spiff
2010-Apr-18, 04:13 AM
The problem is to find a "standard ruler" that is large and bright enough to observe over a range in redshift. This experiment has been tried, but not anything conclusive as far as I know.

john hunter
2010-Apr-18, 03:26 PM
Thanks Spaceman,

while we're on this subject...do you know how it is possible for objects to subtend a larger angle than before, as z increases past 1.65.....Surely if this happened for every object around a cicle, the total angle for all combined would be greater than 360 degrees???which seems impossible.

John H.

StupendousMan
2010-Apr-18, 04:29 PM
Thanks Spaceman,

while we're on this subject...do you know how it is possible for objects to subtend a larger angle than before, as z increases past 1.65.....Surely if this happened for every object around a cicle, the total angle for all combined would be greater than 360 degrees???which seems impossible.

John H.

The phenomenon causes the angular size of objects to be larger than you'd expect: in other words, if you could look at a set of identical galaxies, each really 20 kpc in diameter, placed at regular intervals of distance (1 Mpc, 2 Mpc, 3 Mpc, etc.) away from you, you would see the galaxies grow smaller at first, then remain roughly the same size, then grow slightly larger again.

The arrangement of objects around a circle would not be different.

john hunter
2010-Apr-18, 09:07 PM
Dear StupendousMan,

When you wrote "you would see the galaxies grow smaller at first, then remain roughly the same size, then grow slightly larger again"...is this the angle subtended by the galaxy which "grows smaller..etc..".
If it is, this still doesn't seem possible. Imagine a circle say 2Mpc away from us, with earth at centre....made up of lots of (say 1000) identical rulers which just fill the circumference. If this circle is at the point where any increase in radius increases the angular size of each ruler, then it seems impossible as follows.

More such rulers would be needed to make a circle at 3Mpc, but if the angular size of each one is increased compared to that at 2Mpc, then surely the total angle of all the rulers added, would be more than 360 degrees??? Presumably the images couldn't overlap.... let me know if there is a misunderstanding in the question!

John H.

Nereid
2010-Apr-19, 12:29 AM
Apparently a maximum in the angular size - z graph is predicted, at about z=1.65 (depending on cosmological model)....

e.g. http://en.wikipedia.org/wiki/Angular_diameter_distance

has a maximum been observed yet at any z value? If so, at what value of z?

Thanks everyone,

John Hunter.
The best, most recent work is that of Bonamente et al. (2006) (http://cdsads.u-strasbg.fr/abs/2006ApJ...647...25B); at least AFAIK. It covers the range 0.14 < z < 0.89. Take your pick of opinions on when observations will be up to constraining any z ~ 1.65 maximum.

The most cited paper describing the theory is, AFAIK, Birkinshaw (1999) (http://cdsads.u-strasbg.fr/abs/1999PhR...310...97B).

Bonus: check out Freedman and Madore (2010) (http://fr.arxiv.org/abs/1004.1856) "The Hubble Constant" (will this, too, get >1500 citations, in < 10 years?)

StupendousMan
2010-Apr-19, 12:50 AM
When you wrote "you would see the galaxies grow smaller at first, then remain roughly the same size, then grow slightly larger again"...is this the angle subtended by the galaxy which "grows smaller..etc..".

Yes, that's right.



If it is, this still doesn't seem possible. Imagine a circle say 2Mpc away from us, with earth at centre....made up of lots of (say 1000) identical rulers which just fill the circumference. If this circle is at the point where any increase in radius increases the angular size of each ruler, then it seems impossible as follows.

More such rulers would be needed to make a circle at 3Mpc, but if the angular size of each one is increased compared to that at 2Mpc, then surely the total angle of all the rulers added, would be more than 360 degrees???
John H.

I suspect that your problem understanding this concept is that you are mixing up "the appearance of identical objects at different distances" with "the physical size of an object as it moves to different distances."

I don't think I can help you without each of us drawing lots of pictures.

Jeff Root
2010-Apr-19, 07:03 PM
I suspect that your problem understanding this concept is that you are mixing up
"the appearance of identical objects at different distances" with
"the physical size of an object as it moves to different distances."
I suspect that he is just mixing up
"the appearance of identical objects at different distances" with
"the appearance of an object as it moves to different distances."

-- Jeff, in Minneapolis

speedfreek
2010-Apr-19, 08:07 PM
The reason that the angular-diameter distance increases with redshift and then decreases again above a certain redshift is due to the superluminal expansion of the universe.

Consider the distance where an object (or a coordinate co-moving with the expansion of the universe) is apparently receding at the speed of light. As the rate of expansion (or more accurately, the change in the scale factor of the background metric) was very fast in the early universe, this means that the distance at which a co-moving coordinate was apparently receding at c was close to this point in space. Imagine, if you will, that right after the Big-Bang (or inflation) distances down at the Planck length were increasing at the speed of light, but that the rate of expansion instantly decelerated from that value.

If the expansion rate had remained constant, then so would the distance at which a co-moving coordinate was receding at c would have remained constant. But the rate of expansion decelerated over the first six billion years or so and therefore the distance at which a co-moving coordinate was apparently receding at c became larger.

After inflation the observable universe was the size of a grapefruit, but 380,000 years later it had a radius of around 42 million light years. The edge of the observable universe had, at that point, receded from what would become this point in space at many multiples of the speed of light in order to move 42 million light years in only 380,000 years, so at that time the distance where a co-moving coordinate was receding at c would have been well within that radius.

And yet, we receive photons today that were emitted from the edge of the observable universe all those years ago. We receive photons that were emitted from the "surface of last scattering", which was receding from this point in space at least 50 times of the speed of light at the time those photons were emitted. They were only 42 million light years away when they were emitted, but they took 13.7 billion years to reach us.

The rate of expansion continued to slow, and after something over 100 million years, the earliest galaxies formed. The observable universe was something around 2 billion light years in radius at that time. We have seen dim blobs that might be these galaxies, but the oldest, dimmest, most distant galaxy we have reliable measurements for emitted its light around 800 million years after the Big-Bang, it has a redshift just under z=7 and is estimated to have been 3.5 billion light years away when it emitted its light.

Now lets look at a galaxy at redshift z=3. This (much brighter) light was emitted when the universe was 2.2 billion years old, 11.5 billion years ago when that galaxy is estimated to have been 5.3 billion light years away.

Now we move closer still to redshift z~1.4 and here is where we find the galaxies that are apparently receding at the speed of light – that is, they were receding at the speed of light when they emitted the light we are now seeing, light emitted from the edge of our Hubble sphere as it was then. The light we are seeing was emitted when the universe was around 4.6 billion years old, just over 9 billion years ago. These galaxies are estimated to have been 5.7 billion years away when they emitted the light we see, and what is more, they are the most distant objects we have seen in the universe!

Let me say that again. Objects that are apparently receding at the speed of light are the most distant objects we have actually seen. Let me explain what I mean by this...

We use measurements of a galaxy's angular diameter (how big the object actually looks in the sky) to help confirm how far away they were when they emitted the light we are now seeing. This makes sense, as you always see any object at the distance it was when the light left it, regardless of whatever it does or however it moves afterwards. Anyway, that is one method used by astronomers to help confirm the distance a galaxy was from us when it emitted the light we are now seeing (of course, they also have to determine what the galaxy's actual or absolute size was to do this, and this is a whole other subject unto itself!).

We therefore should find that the most distant galaxies by angular size are the ones that are apparently receding at c, and yet we see light from more distant (in time) galaxies that are dimmer and more redshifted, and those galaxies have increasing angular diameter the further we look in that direction, because they were closer to us when the universe was younger.

Lets look at the figures (The first line is the CMBR or surface of last scattering) I took from Ned Wrights cosmology pages.

Redshift____Distance then____Time since emission
z=1089_____42 million ly_____13.7 billion years ago
z=7________3.5 billion ly_____12.8 billion years ago
z=3________5.3 billion ly_____11.5 billion years ago
z=1.4______5.7 billion ly_______9 billion years ago
z=1________5.4 billion ly______7.7 billion years ago
z=0.8______5.0 billion ly______6.8 billion years ago
z=0.5_______4 billion ly_______5 billion years ago
z=0.3______2.9 billion ly______3.3 billion years ago

So you can see that if our criteria is the object that was furthest away when it emitted the light we are now seeing, then the most distant object we have seen, seen as it was when it was that distant, was a galaxy at redshift z=1.4 at 5.7 billion ly. But we have also seen objects that are a lot older, were a lot closer when they emitted the photons and are now estimated to be a lot more distant as we receive those photons, than the objects that are currently apparently receding at the speed of light were, when they emitted the light we see!

Now if I haven't lost you or bored you to death so far, hopefully you will be getting an inkling into how this all works and what an apparent recession speed of c actually represents.

The key thing to remember is that light never overtakes light. If you look at those figures above and also remember that we received all those photons at pretty much the same time you will find that:

Photons were emitted 3.5 billion light years away, 12.8 billion years ago. 1.3 billion years later, photons were emitted 5.3 billion light years away and if light never overtakes light then those older photons must have “been moved away by the rate of expansion” to that distance. 2.5 billion years later still, photons were emitted 5.7 billion years away and so our older photons must have moved away that far by then. And all those photons reached us at the same time.

So, from our point of view, the light from that redshift=7 galaxy was receding from us (as it made its way towards us from the point of view of its source) from emission at 12.8 billion years ago until it passed the point where objects are apparently receding at lightspeed from us, 9 billion years ago. All light we receive that was emitted before that time was effectively moving away from us whilst it made its way towards us until it passed that point 5.7 billion light years away that was receding at c, 9 billion years ago, and then took another 9 billion years to reach us after that through a universe where the rate of expansion was levelling out and starting to accelerate again.

If those z=7 and z=1.4 galaxies were the same absolute size, the apparent angular size of the z=7 galaxy would be quite a lot larger that of the lower redshift galaxy, as it was quite a lot closer at the time its light was emitted.

Hmmm... looking back over all that, I see what StupendousMan meant about it being easier with drawings!

john hunter
2010-Apr-19, 10:18 PM
Thanks, everone so far....it'll take some time to digest all this!, but at first thoughts it still can't overcome the problem described in post 5??? can it???

John H.

speedfreek
2010-Apr-19, 11:21 PM
If we were once hypothetically surrounded by galaxies that were just touching each other, and we could see the light from them today, they would still look as if they were just touching each other. The angular size of a galaxy and the angular distance between galaxies will be seen to be as it was when the light was originally emitted, relative to our position.

If we could see all the way back to the Big-Bang, we would be seeing what happened right here, 13.7 billion years ago. Then the universe expanded and everything else follows on from that.

Jeff Root
2010-Apr-20, 12:20 PM
John,

If you watched one distant galaxy over the entire history of the Universe,
its angular diameter would always be decreasing as it moves farther away.
The angular diameters of all the galaxies at the same distance as the selected
galaxy would of course also be decreasing as they move farther away. The
angular size of the gaps between those galaxies would always be increasing.

On the other hand, looking at galaxies which appear to be at different distances
from us at one point in our time -- which is what we are actually doing -- the
relationship between apparent distance and angular diameter is more complex,
because we see them as they were when they emitted the light, nomatter how
long it took the light to reach us. Whatever the angular diameter of a galaxy
when it emitted its light is the angular diameter we see now. Likewise for the
gaps between galaxies.

-- Jeff, in Minneapolis

john hunter
2010-Apr-20, 10:54 PM
Thanks Jeff,

That's starting to make sense...(if we accept that the expansion happens to the gaps, but not to the galaxies)...but in the graph in http://en.wikipedia.org/wiki/Angular_diameter_distance what is the maximum angular size for at z=1.65, the gaps or the galaxies?

John H.

Jeff Root
2010-Apr-21, 01:14 AM
in the graph in http://en.wikipedia.org/wiki/Angular_diameter_distance
what is the maximum angular size for at z=1.65, the gaps or the galaxies?
The peak of the curve is the redshift at which a galaxy (or any other object) of
a given proper diameter has the smallest angular diameter.

Galaxies with small redshifts (to the left of the peak) are close to us now, and
emitted their light recently, so they have large angular diameters. Because we
see these galaxies as they were recently, after billions of years of expansion,
the gaps between them are large.

Galaxies with redshifts near the peak of the curve were far away from us a
middling time ago, when they emitted the light we see now, so they have small
angular diameters. Because we see them as they were a middle time ago,
midway in the cosmic expansion, the gaps between them are of middle size.

Galaxies with large redshifts (to the right of the peak) were close to us long ago,
when they emitted the light we see now, so they have large angular diameters.
Because we see them as they were long ago, before much of the expansion, the
gaps between them are small.

-- Jeff, in Minneapolis

speedfreek
2010-Apr-21, 06:04 PM
Great explanation Jeff. :)

John, the graph at the bottom of the page at http://www.atlasoftheuniverse.com/redshift.html shows all the distance measures, which might be an aid to understanding. As Jeff said, the peak of the graph represents the greatest angular diameter distance, where the angular diameter of an object of a given size would be the smallest at the peak and largest near to the horizontal axis.

john hunter
2010-Apr-21, 10:19 PM
OK thanks,

Last question on this...

How confident are astronomers that the angular diamter distance behaves as in the graph on the link on the last post. We've already discussed the maximum, and it seems that this hasn't been observed yet. Has the low z part of the graph been observed and found to match the theory. If so up to what value of z has the graph been checked to?

(the variation of the luminosity distance graph, (from standard theory at the time) was one reason for the concept of dark energy being accepted.)

John H.

Nereid
2010-Apr-21, 11:44 PM
OK thanks,

Last question on this...

How confident are astronomers that the angular diamter distance behaves as in the graph on the link on the last post. We've already discussed the maximum, and it seems that this hasn't been observed yet. Has the low z part of the graph been observed and found to match the theory. If so up to what value of z has the graph been checked to?

(the variation of the luminosity distance graph, (from standard theory at the time) was one reason for the concept of dark energy being accepted.)

John H.
Did you read the papers I provided links to in post #6?

Do you have any questions on them?

john hunter
2010-Apr-22, 09:39 PM
Thanks Nereid, no questions at the moment.

John H.

speedfreek
2010-Apr-22, 10:28 PM
See also Sandage (2009) (http://arxiv.org/abs/0905.3199),

The Tolman Surface Brightness Test for the Reality of the Expansion. V. Provenance of the Test and a New Representation of the Data for Three Remote HST Galaxy Clusters