"Depth" of the CMB

1. Nov 17, 2015

Gerinski

The Wiki article on the CMB says that recombination lasted for around 115,000 years, from 372,000 years after the BB (when all baryonic matter was in the form of ions) until around 487,000 years after the BB when all electrons had bonded to nuclei. So Thomson scattering gradually decreased from 100% to 0% during this period, or in other words the mean free path of electrons increased gradually during this period.

Does this mean that the CMB is not really a surface but it has a depth of around 115,000 light years, including a mix of photons emitted along this 115,000 years period?

If that is the case, does this have any significant effect in the structure or analysis of the CMB?

https://en.wikipedia.org/wiki/Cosmic_microwave_background

2. Nov 18, 2015

sunrah

Remember the plasma was in thermal equilibrium (homogeneous CMB), so when it cooled enough for recombination, it cooled enough everywhere for recombination. That means it happened instantaneously for all regions.

3. Nov 18, 2015

Buzz Bloom

Hi sunrah:

As I understand the process, you are mostly right, but there are some subtle corrections needed.

1. The cooling, that is the temperature, was almost the same everywhere at "a given time", although there is a subtle relativity issue about simultaneity. The small differences in different places were due to small random variations.
2. The recombination, of electrons to nuclei, was not instantaneous, but took 115,000 years to complete, as mentioned in post #1.

I believe that in post #2 Gerinski was asking about whether the observed variations in the CMB might reflect what was happening during this 115,000 year period.

Regards,
Buzz

4. Nov 18, 2015

Gerinski

Indeed, thanks Buzz B.

If recombination lasted for 115,000 years, the chance for photons to escape the "ions fog" went from 0% at 372,000 years (all ionized plasma) to 100% at 487,000 after the BB (all neutral atoms). The precision of these age figures is not the important point though, only the principle.

So what we observe as the CMBR would consist of a mix of photons of different ages, a very few oldest ones dating to 372,000 years after BB which would be relatively more red-shifted than all the others, up to the vast majority dating to 487,000 years after BB which would be relatively less red-shifted, and everything in between gradually decreasing in proportion as we go further back in time from the 487,000 to the 372,000 years. The observed CMBR would not be simply a "surface of last scattering" as it is often characterized, but it would have a thickness of around 115,000 light years, even if the closer photons would be much more prominent than the older, farther ones.

In this sense it may sound weird when we so often read that the CMBR is 380,000 years old when only a small fraction of its photons would be that age, and most of them would be closer to the upper limit of 487,000 years old?

I wonder if this mix of ages (and therefore of redshift) in the CMB photons has any significant effects, or consequences at the time of analyzing the CMB.

TX folks!

5. Nov 18, 2015

Buzz Bloom

Hi Gerinski:

I wonder if this mix of ages (and therefore of redshift) in the CMB photons has any significant effects​
I will take a crack at it, although I am not a physicist.

Except for a very small possible difference which I will describe later, the average redshift of the photons now detected in the CMB created when the universe age t1 = 380,000 years and from age t2 = 487,000 years should be exactly the same. The temperature profile of photons from t1 will later at t2 have redshifted to look like the temperature profile of photons from t2.

The small possible difference is: the t2 photons may have a slightly higher temperature profile than the t1 photons have when they arrive at t2. This is because the t2 photons may have been heated a very tiny amount from the energy released by the electrons binding to the protons during the time between t1 and t2. I very much doubt that this tiny difference could be detected.

Regards,
Buzz

Last edited: Nov 18, 2015
6. Nov 18, 2015

Chronos

We see a mix of different redshifts in CMB photons, not a single, uniform value like popular presentation might lead you to believe. The figure of z~1090 [ t~375,000] is near the peak for a gaussian distribution. Recombination actually began around z~1587 when the universe was about 200,000 years old and continued until about z~820, or 600,000 years old. The figure given in the popular press of z~1090 [t~375,000 years] represents the point at which recombination was about 70% complete [based on the Peebles model]. For further discussion see http://www.tapir.caltech.edu/~chirata/ph217/lec06.pdf

7. Nov 18, 2015

Buzz Bloom

Hi @Chronos:

I do understand that the generally quoted single value redshift is for the peak of a Planck black-body distribution. That is why I said
.​
The peak and the average of the distribution redshift by exactly the same amount between t1 and t2, although the peak and average wavelengths will be different.

Let me try to be a bit clearer. The entire distribution of photons from t1 will have a Planck black-body distribution corresponding to the temperature at t1, and when these photons arrive at t2 they will still have a Planck black-body distribution, but due to their red-shifting between t1 and t2, the temperature of this distribution will now be (except for the possible tiny difference I discussed in my previous post) exactly the same distribution temperature as the t2 photons.

Regard,
Buzz

8. Nov 18, 2015

Chalnoth

Yes. It has a very large effect on small angular scales. Essentially, it makes our image of the CMB blurry. This makes it so that there is less variation on small angular scales than if the CMB was emitted instantaneously.

9. Nov 20, 2015

Buzz Bloom

Hi Chalnoth:

This is an intersting concept. I think I am understanding the logic of the effect you are describing, but I'm not sure. The total volume of CMB photon production occupies a volume of space in the form of a spherical shell with us at its center. At the time of CMB photon generation, the thickness of the shell is about 100,000 ly, and the inner radius of the shell, corresponding to the end of recombination, was about 10,000,000 ly. (This number is derived from rounding the current radius of 13 Gy to 10 Gy and multiplying that by the value of the scale factor a rounded to 0.001. )

Statistical variablilty should occur over a volume of space, not just over the area at the nearest end of a volume. A CMB feature occupying a roughly cubic volume, say A, of 100,000 ly on each edge of the "cube", would not be much effected by the 100,000 ly depth of the "image". On the other hand, the "image" of a CMB feature occupying a smaller cube, say B, of 1/1000 the volume of A, and 1/100 of A's area at the nearesst end of the cube, would be distorted by about ten times of much CMB producing volume behind the B cube sending photons through B.

Is this a reasonable explanation for the "blurry" images you mention in the quote?

Regards,
Buzz

10. Nov 20, 2015

Chalnoth

Yes.

11. Dec 14, 2015

Dr. Strange

How does that happen if the regions are not causally connected?

12. Dec 14, 2015

Chalnoth

They were at approximately the same temperature (to one part in 100,000), and the temperature changed in the same way everywhere due to the expansion.

13. Dec 14, 2015

Dr. Strange

Getting back to the original question, is the 'Optical Depth', the tau, τ, of the ΛCDM parameters, the depth of the CMB 'surface'? If t1 = 380,000 years and t2 = 487,000, is the optical depth then 107,000 years (or the equivalent in z)?

14. Dec 15, 2015

Chalnoth

No. That parameter is the optical depth between Earth and the CMB. The optical depth of $\tau \approx 0.1$ indicates that approximately 90% of the photons emitted from the surface of last scattering were able to reach us (not including the obstruction from localized sources such as other galaxy clusters or our own galaxy).