Question about the surface of last scattering

[Jens]

In a thread last year the issue of the surface of last scattering came up, and there's something I've been interested in but can't seem to find a good answer. The question is, what would happen to the surface in a non-expanding universe? How far away would it be? In some article it says that it would be receding from us at the speed of light. What would happen if the universe were infinitely old and non-expanding? I assume there would still be a last scattering surface, but how far away would it be?

[DrRocket]

In a thread last year the issue of the surface of last scattering came up, and there's something I've been interested in but can't seem to find a good answer. The question is, what would happen to the surface in a non-expanding universe? How far away would it be? In some article it says that it would be receding from us at the speed of light. What would happen if the universe were infinitely old and non-expanding? I assume there would still be a last scattering surface, but how far away would it be?

So you start with a universe that is very dense, so that photons can't travel very far without being absorbed and re-emitted. Then as things expand and cool, photons can travel long distances unimpeded. The point at which the fog clears is "last scattering".

What does it mean to you to talk about last scattering in an infinitely old non-expanding universe ?

[WayneFrancis]

In a thread last year the issue of the surface of last scattering came up, and there's something I've been interested in but can't seem to find a good answer. The question is, what would happen to the surface in a non-expanding universe? How far away would it be? In some article it says that it would be receding from us at the speed of light. What would happen if the universe were infinitely old and non-expanding? I assume there would still be a last scattering surface, but how far away would it be?

Well in an infinitely old universe that is not expanding there would be no CMBR.
in an infinitely old universe that is expanding...well that implies that it has been expanding for a finite period of time and we'd see much like we see now.

Without expansion the universe would still be opaque and thus no SoLS would have taken place.

[Jens]

What does it mean to you to talk about last scattering in an infinitely old non-expanding universe ?

I suppose that is the question I should be asking: would there be a surface in such a universe? I don't know if the analogy is appropriate, but somewhere I heard a description of the surface being compared to people talking faraway, where you can't make out the individual voices because they become mixed together. So I was imagining that the same could happen with light. But I suppose I'm wrong in that guess. If the universe were infinitely old and expansive, then the only limitation to how far we could see would be the sensitivity of the telescope?

[WayneFrancis]

I suppose that is the question I should be asking: would there be a surface in such a universe? I don't know if the analogy is appropriate, but somewhere I heard a description of the surface being compared to people talking faraway, where you can't make out the individual voices because they become mixed together. So I was imagining that the same could happen with light. But I suppose I'm wrong in that guess. If the universe were infinitely old and expansive, then the only limitation to how far we could see would be the sensitivity of the telescope?

Basically, the further away an object is the longer we'd have to collect light to get any reasonable image of it. I think that a blurring effect would overwhelm the object based on the luminosity and distance of the object from us at some point.

[Jens]

I think that a blurring effect would overwhelm the object based on the luminosity and distance of the object from us at some point.

I guess that's what I'm asking. I used to think so, but now I'm not so sure. Would it? If so, what distance would that be?

[Cougar]

What would happen if the universe were infinitely old and non-expanding? I assume there would still be a last scattering surface, but how far away would it be?

Your assumption would be incorrect. There is a surface of last scatter only because the universe was once very hot, but expanding and hence cooling. When it cooled below x^{[citation needed]} degrees, the bare hydrogen and helium nuclei could finally hold onto passing electrons they captured without the heat radiation knocking them apart again. Thus all the charged particles, which interfered with the propagation of light, joined and became neutral atoms, which didn't interfere. No more scattering!

[trinitree88]

Your assumption would be incorrect. There is a surface of last scatter only because the universe was once very hot, but expanding and hence cooling. When it cooled below x^{[citation needed]} degrees, the bare hydrogen and helium nuclei could finally hold onto passing electrons they captured without the heat radiation knocking them apart again. Thus all the charged particles, which interfered with the propagation of light, joined and became neutral atoms, which didn't interfere. No more scattering!

Cougar. That would be ~3000K at an age of ~ 379,000 years....SEE:http://en.wikipedia.org/wiki/Cosmic_...ound_radiation

[Cougar]

3000 K. Got it. Still pretty hot, but cool enough for atoms. AND lab testable.

[DrRocket]

3000 K. Got it. Still pretty hot, but cool enough for atoms. AND lab testable.

3000K is about the flame temperature of solid rocket propellant. Plenty cool enough for atoms. Well below temperatures in an electric arc. Seems a bit cool to me. I wonder if that figure is correct.

[BioSci]

3000K is about the flame temperature of solid rocket propellant. Plenty cool enough for atoms. Well below temperatures in an electric arc. Seems a bit cool to me. I wonder if that figure is correct.

It does sound low, but is explained here:
http://nedwww.ipac.caltech.edu/level...weaver7_4.html

"Recombination occurs when the CMB temperature has dropped low enough such that there are no longer enough high energy photons to keep hydrogen ionized; gamma + H <-> e- + p+. Although the ionization potential of hydrogen is 13.6 eV (T ~ 105 K), recombination occurs at T approx 3000 K. This low temperature can be explained by the fact that there are a billion photons for every proton in the Universe. This allows the high energy tail of the Planck distribution of the photons to keep the comparatively small number of hydrogen atoms ionized until temperatures and energies much lower than 13.6 eV. The Saha equation (e.g. Lang 1980) describes this balance between the ionizing photons and the ionized and neutral hydrogen. "

[DrRocket]

It does sound low, but is explained here:
http://nedwww.ipac.caltech.edu/level...weaver7_4.html

"Recombination occurs when the CMB temperature has dropped low enough such that there are no longer enough high energy photons to keep hydrogen ionized; gamma + H <-> e- + p+. Although the ionization potential of hydrogen is 13.6 eV (T ~ 105 K), recombination occurs at T approx 3000 K. This low temperature can be explained by the fact that there are a billion photons for every proton in the Universe. This allows the high energy tail of the Planck distribution of the photons to keep the comparatively small number of hydrogen atoms ionized until temperatures and energies much lower than 13.6 eV. The Saha equation (e.g. Lang 1980) describes this balance between the ionizing photons and the ionized and neutral hydrogen. "

Ok that makes sense. Photon density, and not just temperature, is a driver.

[Ken G]

There would be a surface of last scattering in a static, infinitely old universe, and it would not be expanding at the speed of light. That is because every such universe would have some kind of opacity for scattering light. Given that opacity, there is some distance a photon can travel before it has a roughly 50/50 chance of scattering (more correctly, 1-1/e), and that would be the distance to the "surface of last scattering." Never mind all the other paradoxes such a universe gives us, like Olbers' paradox. (Note one resolution of that is called the "steady-state" but expanding universe, which reaches a finite temperature because it is always expanding, and always has new matter coming into being. That model would also have a SOLS, with no paradoxes, and was taken seriously for a long time.)

[Ken G]

Ok that makes sense. Photon density, and not just temperature, is a driver.

More important than photon density is actually the particle density. Indeed, by the magic of thermodynamic equilibrium, it is not actually necessary to specify a photon density at all to find that recombination happens at about 3000 K-- all you need is temperature and particle density. You just assert that the collisional ionization rate equals the collisional recombination rate, and since you know it's happening in equilibrium with the radiation field, you don't even need to include a radiation field at all to get it (in thermodynamic equilibrium, all processes balance their inverse process, including collisional ionization and 3-body recombination).

[trinitree88]

More important than photon density is actually the particle density. Indeed, by the magic of thermodynamic equilibrium, it is not actually necessary to specify a photon density at all to find that recombination happens at about 3000 K-- all you need is temperature and particle density. You just assert that the collisional ionization rate equals the collisional recombination rate, and since you know it's happening in equilibrium with the radiation field, you don't even need to include a radiation field at all to get it (in thermodynamic equilibrium, all processes balance their inverse process, including collisional ionization and 3-body recombination).

Ken G Thanks that's new to me. Pete

[DrRocket]

There would be a surface of last scattering in a static, infinitely old universe, and it would not be expanding at the speed of light. That is because every such universe would have some kind of opacity for scattering light. Given that opacity, there is some distance a photon can travel before it has a roughly 50/50 chance of scattering (more correctly, 1-1/e), and that would be the distance to the "surface of last scattering." Never mind all the other paradoxes such a universe gives us, like Olbers' paradox. (Note one resolution of that is called the "steady-state" but expanding universe, which reaches a finite temperature because it is always expanding, and always has new matter coming into being. That model would also have a SOLS, with no paradoxes, and was taken seriously for a long time.)

That would be rather thick "surface" and hence not well-defined (meaning not having a sharp boundary) unless the density of this university were rather high. Qualitatively different from what is now called the surface of last scattering. In the usual big bang model the surface forms under conditions in which the mean distance between photon scatterings is small, and in this case it would be enormous.

You can find a serious discussion of the steady-state cosmology model in Bondi's (dated) book Cosmology.

One other aside, which I mentioned in another thread but might be of interest here. For some reason copies, in extremely good shape, of Principles of Physical Cosmology by P.J.E. Peebles are now available at ridiculously low prices. See alibris.com. I bought a second copy, ex libris, but apparently never opened, for $0.99 plus $3.99 shipping -- and got a discount that reduced the delivered price to just the shippiing charge. For anyone interested in the subject who does not already own a copy, this is just too good to pass up.

[Ken G]

That would be rather thick "surface" and hence not well-defined (meaning not having a sharp boundary) unless the density of this university were rather high. Qualitatively different from what is now called the surface of last scattering.

Yes, it would be a very diffuse kind of "surface", kind of like the "surfaces" of giant stars.

In the usual big bang model the surface forms under conditions in which the mean distance between photon scatterings is small, and in this case it would be enormous.

You are right that in the usual model, the term "surface" is much more appropriate, because the mean-free-path there is much smaller than the distance to us.

[Jeff Root]

The temperature of the hydrogen which emitted the CMBR we see
was not measured, it is assumed, based on laboratory observations,
which show that hydrogen becomes transparent at 3000 K. It is
assumed that the CMBR came from hot hydrogen. If that assumption
is correct, then the temperature of the hydrogen had to have been
3000 K. If the CMBR came from something other than hydrogen,
then the temperature would probably have been something else.
But hydrogen is far and away the most plausible source of the CMBR.

Fifteen years ago or so I asked astronomer Larry Rudnick how thick
was the shell of gas which emitted the CMBR we see now. He said
it was about 100 parsecs thick. Big compared to a planet; tiny
compared to a galaxy.

-- Jeff, in Minneapolis

[Jens]

That would be rather thick "surface" and hence not well-defined (meaning not having a sharp boundary) unless the density of this university were rather high. Qualitatively different from what is now called the surface of last scattering.

Thanks, that is what I'm trying to get at. So from the posts by Ken G (#13) and yours, I guess there would be some kind of a surface, but it would be very different from what we see. I'm guessing it would be much further away, and would not be well-defined. So in other words, the existence of the CMBR itself is evidence of a finite universe, or at least that some kind of expansion is going on even if the universe itself is infinite, right? My fundamental interest is whether the CMBR is compatible with the big bang, or if it actually rules other things out. I gather that the latter is true.

[Ken G]

I'm guessing it would be much further away, and would not be well-defined. So in other words, the existence of the CMBR itself is evidence of a finite universe, or at least that some kind of expansion is going on even if the universe itself is infinite, right?

Yes, it was considered a "smoking gun", though one can always try very hard to salvage other models.

My fundamental interest is whether the CMBR is compatible with the big bang, or if it actually rules other things out. I gather that the latter is true.

It was certainly very convincing, the consensus crystallized in a big way.

[DrRocket]

Thanks, that is what I'm trying to get at. So from the posts by Ken G (#13) and yours, I guess there would be some kind of a surface, but it would be very different from what we see. I'm guessing it would be much further away, and would not be well-defined. So in other words, the existence of the CMBR itself is evidence of a finite universe, or at least that some kind of expansion is going on even if the universe itself is infinite, right? My fundamental interest is whether the CMBR is compatible with the big bang, or if it actually rules other things out. I gather that the latter is true.

The CMBR is not only compatible with the big bang, it is one of the major pieces of evidence used to support the big bang theory.

It does not tell you anything with regard to whether the universe is infinite or finite. That is a different kettle of fish entirely, and nobody knows the answer. I think most bets are that it is infinite.

You might want to see if you can find a copy of General Relativity, An Einstein Centenary Survey edited by Hawking and Israel. There is an interesting article by Geroch on the potential topologies of the universe. You might also be interested in this paper by Marsden and Tipler and this paper by Hawking and Penrose. This issue of the spacial structure of the universe and the nature of he singularity of the big bang is quite subtle. If you read at the least the intnroduction to Marsden and Tipler you will see that there are apparently several mistakes in the literature.