why the difference: observable vs. farthest galaxy?

[thoth II]

I'm am having difficulty understanding a concept. Please explain in relatively simple terms.

It is known that the observable universe may go out to a radius of 13 Gpc. But the farthest galaxy discovered is about 13 GLY distant. That is a difference in about 4 factor.

[antoniseb]

Anyone who said 13 billion parsecs was making a mistake.
the Observable universe if 13.7 billion lightyears in radius from here.

[astromark]

Yes 13.7 billion light years. To the edge of the observable universe. Any light emitting object further than that is still on its way here... and is not yet known to us.
We do not really think we are in the centre of a universe that is just 13.7 billion LY in radius...

[Jeff Root]

I'm not familiar with any measurement of anything of 13 Gpc, so I suspect
that antoniseb is right that the figure was a mistake. But an object that
appears to be at a distance of 13 billion light-years would actually be much
farther away now, since everything that far away from us was moving away
with the cosmic expansion at the time the light was emitted. I only just
read very briefly about this galaxy which is believed to be so far away.
It must have been among the first, biggest, and brightest galaxies to form.

There must be galaxies much farther away from us, but their light hasn't
had time to reach us since the time they started emitting light. Since the
cosmic expansion is now known to be accelerating, their light will probably
never reach us. The distance between us and the places where the light
headed in our direction from those galaxies is now, is increasing faster than
the light is moving toward us.

-- Jeff, in Minneapolis

[speedfreek]

Perhaps the OP was referring to 14 Gpc or 46 billion light-years, the co-moving distance to the particle horizon, the radius of our observable universe.

So the question then is, of course, how can the observable universe be 46 billion light-years in radius, after only 13.7 billion years?

The answer is that the universe is expanding and was expanding incredibly fast to begin with, so fast that the edges of the part we can see were separating from each other far faster than the speed of light. Today, when the rate of expansion is far slower than it was to begin with, the edge of our observable universe is still receding from us at around 3 times the speed of light.

The expansion of the universe causes distant galaxies to appear to have been receding from us at superluminal speeds, but if that is the case, how can we see them at all?

Well it seems that the rate of expansion was slowing for a very long time, and as the rate of expansion slows, the light from distant galaxies (that were receding faster than light when the light was emitted) can find itself in regions of the universe that are only receding from us at less than the speed of light. That being the case, the light will eventually reach us.

[thoth II]

The answer is that the universe is expanding and was expanding incredibly fast to begin with, so fast that the edges of the part we can see were separating from each other far faster than the speed of light. Today, when the rate of expansion is far slower than it was to begin with, the edge of our observable universe is still receding from us at around 3 times the speed of light.

That makes sense.

When they report that the farthest galaxy discovered was approx. 13 GLY distant, does that mean that if we could somehow measure it's distance with a large meter stick today, it would measure a distance of 13 billion light years?

Also, does this allow the possibility that someday the Hubble Space Telescope will discover a galaxy that will be reported to be 40 billion light years approx.? (because that seems to be the farthest galaxies we will ever be able to see).

[Jeff Root]

As I'm currently arguing in another thread, the distance of 13 Gly means
that the galaxy we see now emitted its light 13 billion years ago, when
it was much closer to us than 13 billion light-years. During that time, we
have been moving away from each other, so that it is now much farther
away than 13 billion light-years. The distance given is the distance the
light travelled from the time it was emitted to the time we see it.

-- Jeff, in Minneapolis

[Spaceman Spiff]

As I'm currently arguing in another thread, the light travel time distance (= c * t_lookback = c * t_{light travel}) of 13 Gly means that the galaxy we see now emitted its light 13 billion years ago, when it was much closer to us than 13 billion light-years. During that time, we have been moving away from each other, so that it is now much farther away than 13 billion light-years. The distance given is the distance the light travelled from the time it was emitted to the time we see it.

-- Jeff, in Minneapolis

Note correction to Jeff Root's post. As a matter of fact, assuming some standard cosmic expansion parameters (Hubble parameter, etc) a lookback time of 13 Gyr corresponds to a measured redshift, z, of about 5.9, an emission distance (distance there and then) of 4 Gly and a co-moving distance (distance here and now) of 28 Gly, as one may determine from cosmologist Ned Wright's cosmocalculator (two others here and here).

I suggest going here, here, here and here(pay close attention to the two embedding diagrams) for details. Cosmologist Ned Wright weighs in on the use of light travel time distances when conversing with non-astronomers. He thinks it a bad idea because of the confusion it causes (as exemplified by how many times this question pops up in this forum).

[thoth II]

ok,

thanks, I'm not an expert in cosmology, I'll have to study those links.

My conclusions so far: the press only reports the "lookback time" like 13 GLY (really the distance light would travel in 13 GY if the universe was static). But actually, the galaxy is "really" (proper distance) of 28 GLY from earth currently.

By this, I would conclude, that theoretically they could get a galaxy found that is a proper distance of 45 GLY from earth, the distance to edge of observable universe.

[Ken G]

As I'm currently arguing in another thread, the distance of 13 Gly means
that the galaxy we see now emitted its light 13 billion years ago, when
it was much closer to us than 13 billion light-years.

As Spaceman Spiff points out, Ned Wright makes excellent points about the limited usefulness of the "lookback time" approach to reporting distances, as it tends to create more misconceptions than it resolves, and generally hinges on a lack of understanding of relativity. Even the concept of a "lookback time" is dependent on a particular way of coordinatizing time, called "comoving frame coordinates", where we imagine that all matter comes with a clock that has been ticking since the Big Bang, and we compare the readings on those clocks on Earth today to what they would read at the place the light was emitted, and call the difference the "lookback time". That is a well-defined coordinate time, though it is not a proper time because we have to compare two different clocks. It is far worse to associate that time with a distance, as it is unresponsive to most of the concepts of relativity to do so.

[antoniseb]

the press only reports the "lookback time" like 13 GLY (really the distance light would travel in 13 GY if the universe was static). But actually, the galaxy is "really" (proper distance) of 28 GLY from earth currently ....

Instead of saying "currently", you might say when the universe seems 13.7 billion years old there. Simultaneity is hard to talk about between here and the edge of the visible universe... but even then you're hoping to measure a huge distance between superluminal bodies at a particular time. Tough to do.

[Ken G]

By this, I would conclude, that theoretically they could get a galaxy found that is a proper distance of 45 GLY from earth, the distance to edge of observable universe.

That's pretty close, but I'll offer two clarifications:
1) you are not actually talking about a "proper distance," because proper distance is an observer-dependent quantity from special relativity that really doesn't exist in general relativity (which is needed for cosmology). Instead, the concept that still works in general relativity is proper time, which is the time elapsed on a clock that moves between two events. However, proper time is not unique, because different clocks may take different paths between the same two events, and register different proper times as a result. What's more, when you are talking about two events connected by emission and absorption of light (across a vacuum), the proper time is always zero.
2) the distance of 45 GLY, or whatever it comes out, requires the choice of comoving-frame coordinates, so it is purely a coordinate distance (that means our own choices play a role in it, it is not unique or absolute), and it also requires the application of a cosmological model to tell us what gravity is doing in the interim. So for both those reasons, it is a conceptual result, not a physically measurable result. Still, it is a meaningful number, if one understands these caveats.

[thoth II]

2) So for both those reasons, it is a conceptual result, not a physically measurable result. Still, it is a meaningful number, if one understands these caveats.

Is the parameter which is actually physically measured the redshift of a galaxy?

[Ken G]

Yes.

[thoth II]

What's more, when you are talking about two events connected by emission and absorption of light (across a vacuum), the proper time is always zero.

Is this the formal way of stating the popular idea that "time stops or freezes if you move on a light beam" ?

[Ken G]

Yes, but the popular way of saying things is often pretty misleading! The only way to imagine "moving on a light beam" is to imagine a sequence of observers moving faster and faster relative to some reference observer, and then in the limit as that sequence gets closer and closer to moving at c, you will see less and less time elapsing on their clock, relative to the time interpreted by the reference observer (I say "intepreted" because the latter would not actually be measuring a proper time, because he/she is not actually at the events timed by the moving observer). So in the limit of moving on a light beam, the time elapsed would be zero (these are thus called "null geodesics"). But it is important to note that time itself would not appear to be stopping for that sequence of observers-- indeed, each of those observers would think time was proceeding perfectly normally, there just wasn't very much of it between the events in question. In other words, they would not say time is stopping, they would say the two events are getting closer and closer to being simultaneous, if you see that distinction-- they would blame the events, not time itself.

[speedfreek]

Note correction to Jeff Root's post. As a matter of fact, assuming some standard cosmic expansion parameters (Hubble parameter, etc) a lookback time of 13 Gyr corresponds to a measured redshift, z, of about 5.9, an emission distance (distance there and then) of 4 Gly and a co-moving distance (distance here and now) of 28 Gly, as one may determine from cosmologist Ned Wright's cosmocalculator (two others here and here).

Oops! For a lookback time of 13 Gyr it should be a redshift of z~7.9, an angular diameter distance of 3.3 Glyr and and comoving distance of 29.7 billion Glyr, using those calculators.

[speedfreek]

Is the parameter which is actually physically measured the redshift of a galaxy?

Yes.

And so, the "best" way to understand these concepts is to use the redshift of the object you are examining, and then compare the various time and distance measures for that redshift.

For instance, the galaxy with the highest confirmed redshift we have seen is one with a redshift of around z=7. That light was emitted around 780 million years after the Big Bang, 12.9 billion years ago (light travel time). That galaxy was only 3.5 billion light-years away at that time (angular diameter distance), and is now estimated to be around 29 billion light-years away (comoving distance).

The angular diameter distance represents how close an object looks to have been when it emitted that light (simply put, how large it looks in the sky tells us how close it was!), and the comoving distance is the estimate of how far away it is "now".

http://www.wolframalpha.com/input/?i=redshift+7

(I prefer Neds calculators myself, but you can't pre-insert the figures with the links!)

[Ken G]

Score one for WolframAlpha, they were quite clear on the coordinates they were using to determine those distances and times. I'll have to knock their grade down a level for not specifying what cosmological model was being used, but it was probably the current leading model, with dark energy and dark matter.

[speedfreek]

You have to click on "also include" / universe model / for that.

(which is what I should have done to begin with!)

[Spaceman Spiff]

Oops! For a lookback time of 13 Gyr it should be a redshift of z~7.9, an angular diameter distance of 3.3 Glyr and and comoving distance of 29.7 billion Glyr, using those calculators.

Yes, for the default parameters of those calculators. However, I had assumed:

H_o = 70 km/s/Mpc
omega_matter = 0.26
flat
(resulting in an age of 14 Gyr, and the other numbers I quoted, above)

but didn't (at the time) think I needed to be so specific for the purposes of this posting.

[Ken G]

You have to click on "also include"

Ah, fair enough.

[speedfreek]

Yes, for the default parameters of those calculators. However, I had assumed:

H_o = 70 km/s/Mpc
omega_matter = 0.26
flat
(resulting in an age of 14 Gyr, and the other numbers I quoted, above)

but didn't (at the time) think I needed to be so specific for the purposes of this posting.

I apologise if it seems as if I was nitpicking, but you did tell us we could determine those figures using those calculators, so we might need to know we have to change the parameters to get those figures!

[Spaceman Spiff]

I apologise if it seems as if I was nitpicking, but you did tell us we could determine those figures using those calculators, so we might need to know we have to change the parameters to get those figures!

Oh, no problem. I concur.

[sirjon]

Hubble Telescope confirmed that the most distant galaxies are moving away from us approaching the speed of light. Maybe, there are more galaxies beyond, speeding away that Hubble could not detect them coz they're are faster than light.But maybe it is also interesting to ask why they are moving away from us? I created blogs that could relate to this subject, it has to do with space-time, a far different kind of space time. Check it out.


Taken out link to ATM blog.
sirjon if you want to promote a different view on gravity etc. please do it in the ATM section of BAUT.
(tusenfem)

[speedfreek]

The most distant galaxies (with the highest redshifts) that we have observed were apparently receding much faster than light when they emitted the light we see.

[Spaceman Spiff]

The most distant galaxies (with the highest redshifts) that we have observed were apparently receding much faster than light when they emitted the light we see.

As a matter of fact, those galaxies with redshifts greater than about ~1.6 have recession speeds greater than light, using a commonly adopted definition of recession speed. But as is always the case general relativity steps in and says that in the real world there is no absolute measure of recession speed (or any speed), except locally (in the limit thereof).

Locally the speed of light c is still the speed limit, but there is no absolute means of measuring either spatial intervals dx or time intervals dt between two non-local (and so greatly deviating) frames of reference. There and then (the event in space-time at which the light we see now was emitted), here and now (the event of our measurement of this light) -- these are two completely different frames of reference, and because of expansion space-time is highly curved between these two coordinates. In the end it comes down to choosing one's coordinates, as long as it is done self-consistently, to define "what you mean" by speed of recession -- and so there is no absolute measure thereof.

[robross]

As a matter of fact, those galaxies with redshifts greater than about ~1.6 have recession speeds greater than light, using a commonly adopted definition of recession speed.

When you say a galaxy has a redshift that indicates it is receding faster than light, are we talking about a purely mathematical calculation? We can't actually *see* such galaxies in any EM frequency, correct?

Rob

[grant hutchison]

When you say a galaxy has a redshift that indicates it is receding faster than light, are we talking about a purely mathematical calculation? We can't actually *see* such galaxies in any EM frequency, correct?

No, we can (and do) see them, by light which has a redshift of 1.6 or greater.
This is the difference between conventional Doppler redshift and the redshift produced by the expansion of the Universe. In the expanding Universe, photons manage to reach us from objects that were receding from us faster than light when they emitted the photons. The photons spend some time being carried farther away from us by the expansion of space, but eventually cross the Hubble horizon and make progress towards us. They arrive with a significant (but not infinite) redshift.

Grant Hutchison

[RAF_Blackace]

The photons spend some time being carried farther away from us by the expansion of space, but eventually cross the Hubble horizon and make progress towards us.

Some questions here, what is the Hubble horizon ?

Why and How, does light cross that horizon ?

It seems that you are saying that light that was once travelling away from us can stop this recession and then begin to travel towards us. I would like to know the explanation for both these phenomena.

Isn't fast expansion just a mathematical fudge, a way of making things fit. And in the grand scale of things not the best way to solve a problem, yes it works, but no one knows why or how. Didn't Ptolomy once try the same thing until someone came up with a much simpler and correct explanation.