# Exploring the Effects of the Universe's Expansion on Faraway Galaxies

• itsthemac
It seems to me that since the light is traveling through more space than there initially was between us and the galaxy, that the light "sphere" emanating from the galaxy would expand to a greater diameter by the time it reached us (than it would have if space weren't expanding), and thus it would be dimmer (than it would have been without expansion) and it would therefor appear farther away than it was at the time of emission.

#### itsthemac

I'm only talking about galaxies far enough away where the only significant motion between us and them is caused by the expansion of space itself. When we look at a faraway galaxy, does it appear to be as far away to us as it was at the time it emitted the light that we're seeing? Or does it appear to be (visually) farther away than it was at that time, since the light has traveled a greater distance than there initially was (at the time of emission) between us and the galaxy (due to the expansion of the universe)?

Also, if it does appear to be farther away than it was at the time that the light we're seeing now was emitted, how much farther away does it appear to be?
And another follow-up: what's the relationship between how far that galaxy appears to be and how far it ACTUALLY is at the current time? Is it's apparent visual distance somewhere in between its distance at the time the light was emitted and its current distance?

It seems to me that since the light is traveling through more space than there initially was between us and the galaxy, that the light "sphere" emanating from the galaxy would expand to a greater diameter by the time it reached us (than it would have if space weren't expanding), and thus it would be dimmer (than it would have been without expansion) and it would therefor appear farther away than it was at the time of emission.

But is this (if that's even true) the only affect? Does it just get dimmer? Or is the galaxy's angular size in the sky smaller than it would have been if space weren't expanding (and it was at the same initial distance when the light was emitted)?

Distant galaxies appear to be exactly as far away as they were when the photons we now observe were emitted. I guess I don't understand the question.

Chronos said:
Distant galaxies appear to be exactly as far away as they were when the photons we now observe were emitted. I guess I don't understand the question.

I don't get how it could be that it would look the same whether the universe were expanding or whether it were static. In an expanding universe, the light has to travel a greater distance (and thus a longer time) to reach us than it would in a static universe (btw, in the static universe the galaxy would have no motion relative to us, just to be clear. its only "motion" is caused by the expansion of spacetime in my question with the expanding universe case). The space it's traveling through to reach us from the galaxy is getting bigger while it's on its journey toward us. So how could this not affect the way the light appears when it arrives (besides it just being redshifted)? I'm definitely no expert in this, so please correct me if I have something wrong.

I think I see what you're asking: if a galaxy (for example) was 1 bly away when it emitted the light we now see but has moved 1bly in that time, do we see it as 1bly or 2bly away? The answer, I think, is somewhere in between. The light hasn't traveled 2 bly but it has traveled more than 1 bly.

russ_watters said:
I think I see what you're asking: if a galaxy (for example) was 1 bly away when it emitted the light we now see but has moved 1bly in that time, do we see it as 1bly or 2bly away? The answer, I think, is somewhere in between. The light hasn't traveled 2 bly but it has traveled more than 1 bly.

Yes, that's exactly what I'm asking. And I was also suspecting that it would appear to be somewhere between those two distances.
But this doesn't mean that if you see a galaxy that looks 1.5 bly away, you're seeing it as it looked less than 1.5 billion years ago, right? You're still seeing it as it was 1.5 billion years ago?

Itsth,
in a static nonexpanding geometry there are two effects of distance:
diminished angular size
dimming from the thinning out of photons (fewer per square meter)

The angular size that a galaxy appears depends on how far it was THEN when the light was emitted.

In Wright's calculator, this is given as the "angular size distance", in the read-out.

If you google "wright calculator" and put in redshifts > 1.7
you will see that the angular size distance actually decreases as you put larger and larger redshift.

The angular size of a fixed diameter object actually gets larger as you go from redshift 2 to redshift 3 to redshift 4.

That is because the sucker was actually closer when it emitted the light we are getting today. So naturally its angular size is bigger, it occupies more of the sky.

Check it out and ask more questions.

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To answer directly, it is NO and YES

No, they do not look farther away (than they were when they emitted the light) in the sense of angular size. Their diameter fills out the same angle as it did THEN when the light started towards us.

Yes, they do look farther away in the sense of looking dimmer.

The photons per square meter of detector surface is thinned out corresponding to the distance* NOW. Wright's calculator gives that as the "comoving radial distance".

If z is the redshift, then the ratio between distance Now and Then should be z+1

If redshift z=3 then the ratio should be 4. That is, the distance now should be 4 time the angular size distance, aka the distance back then.

So your question "do they look farther away" is complicated because we learn to judge "how far it looks" by a combination of visual cues.

Also notice that brightness or luminosity is not just determined by photons hitting the square meter, it also depends on the energy of the photons. Redshift drags down the energy, lengthens the wavelength. So that makes the galaxy look way more dimmer than it would look merely due to the spreading out of the photons over a larger larger sphere.

*squared of course

marcus said:
To answer directly, it is NO and YES

No, they do not look farther away (than they were when they emitted the light) in the sense of angular size. Their diameter fills out the same angle as it did THEN when the light started towards us.

Yes, they do look farther away in the sense of looking dimmer.

The photons per square meter of detector surface is thinned out corresponding to the distance* NOW. Wright's calculator gives that as the "comoving radial distance".

If z is the redshift, then the ratio between distance Now and Then should be z+1

If redshift z=3 then the ratio should be 4. That is, the distance now should be 4 time the angular size distance, aka the distance back then.

So your question "do they look farther away" is complicated because we learn to judge "how far it looks" by a combination of visual cues.

Also notice that brightness or luminosity is not just determined by photons hitting the square meter, it also depends on the energy of the photons. Redshift drags down the energy, lengthens the wavelength. So that makes the galaxy look way more dimmer than it would look merely due to the spreading out of the photons over a larger larger sphere.

*squared of course

Thank you very much for the replies. I don't quite understand why its angular size would not diminish, yet its brightness would. I'm just visualizing that sphere of a single light pulse centered around a distant galaxy (I'm imagining it as a completely spherical source of light for this thought) whose radius is increasing with time. And at the same time, the distance between the center of that sphere and us (on Earth) is getting larger and larger, so the sphere has a bigger radius when it reaches us than it would in a non-expanding universe. This completely makes sense for why it would be dimmer, but I would also (I guess intuitively) assume that its angular size would be smaller as well. I just can't think of how else it would work in, for instance, a regular, non-expanding situation where you have one flashlight that's 10 feet away and another one that's 50 feet away. The one that's 50 feet away has a smaller angular size, but the only difference is the distance that the light had to travel to reach our eyes. So what else would determine how big it looks to us, if not this distance? And clearly the light from the galaxy in the expanding universe traveled a greater distance then the light from the same galaxy in a non-expanding one. So why wouldn't it have a smaller angular size?

Please understand, I'm only trying to gain a better understanding of this, not trying to be combative or anything.

Also, don't we normally use the apparent brightness to determine the distance of standard candles? So when we get this distance, is it a greater distance than the thing actually was when it was emitting the light we're receiving? Or has it been calibrated so that we get the (proper) distance that it actually was when the light was emitted? And if it's not calibrated this way, wouldn't this distance we got using apparent brightness not match up with the distance we would get if we were to use angular size instead, assuming we knew the actual size of the object (I know we normally don't do this for objects very far away, but I'm just asking)?

I have a lot of questions, sorry.

Uniform expansion of distances preserves angles.
So think of the galaxy when it sent the light, and was nearer. think of a photon coming from the righthand edge to us, and another photon coming from the lefthand edge, to us. they make an angle at our eye.

Now expand the whole picture. the galaxy gets farther away but the angle where the rays meet stays the same.

Have to go out. Talk some more later.

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You think carefully and ask good questions so I want to suggest that you get familiar with two common calculators people use. One is the "wright calculator", also called "cosmo calculator".

The other one is "cosmos calculator" (remember the s on cosmos). To use it you have to first prime it with 3 numbers: .27, .73, 71 over on the left where it says matter density, cosmological constant, and Hubble constant. With those parameter values entered, it will give the same standard results as Wright's calculator.

Wright just has the standard parameters already entered for you, to save trouble.

So google "cosmos calculator" and see what you get.

Try different redshifts like z = 2, or z=3, or 4, 5, 6, and see distances what you get.

The redshift of the ancient light background is around 1100. You can try putting that in as well.

Redshift is the main scale in cosmology. You play with these calculators in order to get familiar with the z scale. It gives us a handle both on time and on distances.

If you start using these calculators to convert redshift to distances and times, like distance from us THEN and distance from us NOW and age back THEN and light travel time, you will most likely have questions. Feel free to ask. Let me know if the calculators don;'t work as expected for you.

Ultimately the main result of all the stuff with cepheid variables and standard candles and Type IA supernovae---a principal end result of all that is to calibrate the redshift scale (especially to get those those three numbers right that go into the model) so that you end up with something like Wright's calculator----an embodiment of the standard cosmology model. Good to get some handson experience with it. It tells you what is happening out at various distances and that really means at various redshifts. Redshift is what you measure, the other dimensions are secondary stuff you calculate from redshift using the model.

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