# Early CMB temperature?

1. Jan 1, 2014

### martix

I had this question pop up while watching something:
Was early CMBR still CMBR or was the M something else, possibly even visible light?

Scouring wiki yielded the following:
Since decoupling, the temperature of the background radiation has dropped by a factor of roughly 1,100 due to the expansion of the universe.

But I have no idea if that would that be enough to push M to IR or beyond for example.
I'm sort of sceptical it would be as simple as x*1100.

2. Jan 1, 2014

### TumblingDice

Original CMBR was still all about temperature, at about 3,000 degrees Kelvin. That's how cool we needed to get to for the universe to become transparent and allow photons and electromagnetic radiation to travel freely for the first time.

That original 3K temperature threshold is what inflation has reduced by a factor of about 1100 to today's 3 degree CMBR. Bandersnatch posted a really cool chart of star temperature and color in another post yesterday. I don't know if it applies directly to this topic, but it indicates that a temp of 3000 Kelvin is below the range of visible light:

3. Jan 1, 2014

### martix

Well, this chart is the basic definition of Black Body Radiation.

Upon further research the numbers actually also sort of match up, and it appears to be exactly that simple.
This would put early background in the near-IR, very close to visible light.

So slightly reddish and very toasty. :)

4. Jan 2, 2014

### Staff: Mentor

At 3,000 k the light output would have peaked at around 965 nm's, which is in the near infrared range. However, an object at this temperature would still emit visible light. At 500 nm's, which is approximately green light, the output has dropped off to 20% of what it is at 965 nm's, with the output at shorter wavelengths dropping to near zero very quickly.

Use the following calculator if you want to see it for yourself.
http://www.spectralcalc.com/blackbody_calculator/blackbody.php

5. Apr 6, 2015

### Buzz Bloom

I am having a bit of trouble in putting a quote in this post, so I will do it the hard way. [Moderators Note: Quote merged with post.]

"Original CMBR was still all about temperature, at about 3,000 degrees Kelvin."
Quote from post by TumblingDice.

I have been trying to calculate the temperature at which the plasma state of the universe cooled to an atomic fluid, that is, to a fluid of mostly (about 80% by weight) H atoms (and 20% He atoms) rather than the common hydrogen ( and Helium) moleecular H2 (and He gas). For this purpose I found the following Hydrogen phase diagram from http://militzer.berkeley.edu/diss/node5.html .

Can someone explain (or cite a refeence for) how the 3000 K temperature was calculated?

Thabove phase diagram show a temperature boundary roughly between 20,000 K and 40,000 K corresponding repectively to a desnsity of 10^-6 g/cm^3 (=10^-3 kg/m^3) and 10^-1 g/cm^3 (=10^2 kg/m^3). The 3000 K temperature would more-or-less correspond to the later phasae transition of atomic H fluid to ordinary H2 gas.

While the temperature of an cosomoloically explanding fluid is inversely proprtional to the scale function a(t), its density is inversely proportional to a^3. If we arbitrrarily set a=1 correspong the the current time, then a(t) for the time of the phase transition would about 10^-3. Therefore the corresponding density at this time would be rho = rho0 * 10^9. Since the current density given for baryobic matter (atoms) is
rho0 = 4.6 x 10^-26 kg/m3, then the density at the phase transition would be
pho = 4.6 x 10^-17 kg/m = 4.6 x 10-20 g/cm^3. Note that this value would be very far to the left of the diagram.

I have no idea the proper way to extrapolate the phase boundary to left to be in the desired range of the rho value. So I did a linear extraoplation on a log:log chart, I found that the extrapolated phase boundary intersected a T(a) vs rho(a) line for varying the value of a. The point of intesection is:
T= 568 K and rho = 4.16 x 10-19 kg/m^3.

I do not have much confidence that my calculation gives a correct result. I would much appreciate seeing how the calculation should be properly done.

Last edited by a moderator: Apr 6, 2015
6. Apr 6, 2015

### Staff: Mentor

AFAIK it is based on the redshift of the CMB, which is about 1000; therefore the temperature of the CMB when it was generated is about 1000 times its current temperature, or about 3000 K.

7. Apr 6, 2015

8. Apr 7, 2015

### Buzz Bloom

Thank you PeterDonis and Chronos for your responses.
Your AFAIK may be right, Peter, about the redshift, but I am somewhat doubtful. All the redhifts I have ever seen have been given with several decimal places. This 3000 redshift is apparently reported only with an order of magnitude precision. My guess would be that the techology used for measuring Fraunhofer lines in microwaves is somewhat immature.

I just found the following article about this methodology: Measurement of the microwave background temperature at a redshift of 1.776.
http://www.nature.com/nature/journal/v371/n6492/abs/371043a0.html

Here is a quote from the abstract: Here we report the detection of absorption from the first fine-structure level of neutral carbon atoms in a cloud at a redshift of 1.776, towards the quasar Q1331 + 170. The population ratio yields a temperature of 7.4 ± 0.8 K, assuming that no other significant sources of excitation are present. This agrees with the theoretical prediction of 7.58 K.

Note that this "agreement" with theory is that the difference between theory and measurement is 0.18 K which is more than twice the given measurement range of error of ± 0.8 K. Would it be fair to say that this descrepancy suggests something is a bit wrong with the theory or with the measaurement? The quote acknowledges the possibility: no other significant sources of excitation are present. If there were such other sources involved, then the actual CMB temperature at resshift 1.776 could be significantly lower, and that would imply the temperature at phase shift might be significant lower than 3000 K. Am I understanding this correctly?

The readshift of 1000 corresponds to the 3rd small square from the left on the red line in my chart. If that reshift value is correct for the CMB, then the phase boundary shown in the chart from Berkeley would have to curve upward somewhat when extraoplated to the left. Can anyone help me find out more about the phase transitions for Hydrogen at these much lower densities?

BTW: I would like to have corrected my misremembering of the realtive abunances of H and He, but I was unable to edit my earlier post.
From http://www.webelements.com/periodicity/abundance_universe/ I find that by weight the universe is 75% H, 23% He, and 2% everything else.

9. Apr 7, 2015

### Chronos

In http://arxiv.org/abs/0804.0116 they derive a temperature of 9.13K +/- 0.72 at z=2.418 which is consistent with the expected value of 9.315K+/- .007 from the hot big bang theory. The cited measurement at z = 1.776 was 7.4K +/- 0.8 [6.6 to 8.2K] which appears entirely consistent with the expected value of 7.58.

Last edited: Apr 7, 2015
10. Apr 8, 2015

### Buzz Bloom

Thank you Chronos. I feel quite foolish for consistently reading "0.8" as ".08". I still intend to find out more (if I can) about the phase transition between atomic gas and plasma for temperatures near 3000 K. I have found the names of several physicists who work with phase diagrams for hydrogen, and I will see if I can get any email responses from them.

I try hard to not let my tendency toward skepticism regarding recent work in cosmology to become overly extreme. I have been much influenced by a personal anecdote about my wife's experiences when she has an undergraduate at MIT. She tells about a physics lab experiment to determine the speed of light. The effort involved investigating many "errors" in the results by making changes to the protocol and equipment settings until a result was obtained that was close enough to 300,000 km/sec. Then the effort to find and correct more "errors" stopped.

Another anecdote: In 1929 Eddington believed for theoretical reasons the fine structure constant, alpha, was exactly 1/137, and many of his contemporaries accepted this. Experiments continued for quite a while to find results within experimental error of 1/137 until eventually much more precise measurements found it was different from 1/137 by an amount exceeding the upper bounds of experimental error.
The current value of 1/alpha is 137.035999173(35). Also it was found in 1999 that alpha changes over time.
https://en.wikipedia.org/wiki/Fine-..._fine-structure_constant_actually_constant.3F

11. Apr 8, 2015

### Chronos

You are probably the only person in history to misplace a decimal point. Besides, accuracy within an order of magnitude would be considered quite the success in any number of studies. The variation in the fine structure constant claimed by Chand in 1999 has since been dismissed. To the best of my knowledge there is no credible evidence of evolution over time in any fundamental constants of the universe, although the search continues. .

12. Apr 14, 2015

### Buzz Bloom

I am continuing my search for an explanation for the often quoted value for a (about 1000) at the time of universe transparancy. Currently I am studying the Saha Ionization Equation. (See https://en.wikipedia.org/wiki/Saha_ionization_equation .) The particular form of the equation

is relevant for any ion with a single electron fully removed. For H, since there is only one electron, this form applies.

In an arbitrary volume, n is the total number of atoms, and n[e] is the number of ionized atoms.
g[1] is t he degeneracy of states for the ionozed atom, and g[0] is the degeneracy of states for the base state un-ionized atom. According to my limited understanding of the physics, for H: g[1] =g[0] = 1.
epsilon is the energy needed to fully ionzise one atom of H.
k is the Boltzmann constant.

Lambda, the thermal de Broglie wavelength of an electron, is defined by:

m[e]
is the mass of an electron.
T is the temperature.

Since n = n[0]/a^3, and T = T[0]/a, the equation can be put into the form n/n[e] = f(a) = the fraction of ionization for a value of a that corresponds to the boindary between gas and plasma, as might be shown in a state transition diagram. If anyone can tell me what fraction of ionization is appropriate for transparency, it will save me a lot of work making my own estimate from the boundary line given in the state transition diagram I inculded in a previous post. The value of a that gives f(a) this fraction value would then be reasonable justified as a good estimate for the value of a at transparancy.

I would much appreciate any comments and corrections.

13. Apr 15, 2015

### Chronos

The electron density is just one factor to consider. The Saha equation is only valid so long as the universe is in thermodynamic equilibrium. Thereafter you should use the Peebles equation. You then need to determine the optical depth and visibility function. It's rather messy. For further discussion see http://folk.uio.no/hke/AST5220/v10/AST5220_recombination_2010.pdf

14. Apr 15, 2015

### Buzz Bloom

Thanks Chronos. The PDF you cited looks very interesting.

Regarding equilibrium, I recently read about equilibrium somewhere that as I remember seemed to be authoritative. The article said that .the last time thermodynamic interaftions were operating to maintain thermal equilibrium among the constituents of the primordial plasma was when the universe was only a few minutes old, soon after thermonuclear fusion created He and a a very small trace of other atoms and isotopes. However the article went on to explain that the temperature, pressure, and density during the expansion maintained all the same relative values as if equilibrium reactions had continued until the present time. One charactestic of a body of gas out of equilibrium is that the raidation distribution by wavelength is no longer the blackbody Planck function. THe most significant evidence of the utility of the equilibrium assumption is the Planck distibution shape for the CBR. Another recent piece of evidence is a recent study that measured the radiation from a large body of gas still likely to be primordial at about z=2. The profile for this was also a Planck distibution with a temperature T = T[0] / (z+1). I can't give you references now, but I will try to find them tomorrow and post them then.

Last edited: Apr 15, 2015
15. Apr 15, 2015

### rootone

Well Buzz, if you can present something that is able to explain the universe better than the so far accepted, but questionable standard model, I am sure a lot of people who visit his forum would be interested.

16. Apr 15, 2015

### Chronos

To expand on what I was saying about the Saha vs Peebles equations, the ionization fraction computes as follows: re: http://www.tapir.caltech.edu/~chirata/ph217/lec06.pdf
% hydrogen recombination, z - Saha, z - Peebles
50, 1370, 1210
90, 1250, 980
99, 1140, 820
The agreed upon value for the CMB redshift is, z=1091 which corresponds to a recombination percentage of slightly less than 71% under Peebles, and virtually 100% under Saha.

17. Apr 16, 2015

### Buzz Bloom

Hi Chronos:

You have certainly convinced me that I definitely need to study the Peebles equations as well as the Eriksen recombination paper. Thank you very much for the links.

What has motivated me to investigate this topic is that I have not yet been able to find any detailed explanation justifying the accuracy of the z = 1091 value for transparency . The sugestion that the redshift was determined the usual way by measuring the shift for particular Fraunhoffer lines seemed very unlikely. From the 71% Peebles value for % H atoms and 29% H ions, it now seems likelty that the justification I am looking for could well be in the explanation for why one should expect that transparency should correspond to a % atoms = 71%. I am now hopeful that the Eriksen paper will provide a way to explain that.

I tried this morning to track down where I read the ideas about equilibrium I posted previously, but unfortunately I have not yet been able to find the source. I will keep looking as time permits.

18. Apr 16, 2015

### George Jones

Staff Emeritus
Another place to look is "2.3 Recombination and last scattering" from Weinberg's 2008 book "Cosmology".

19. Apr 16, 2015

### Chronos

The CMB redshift is not a firmly measured value based on spectral line shifts, it is calculated based on CMB temperature measurements relative to the transition temperature for neutral hydrogen. Measurement of emission line shifts in the CMB spectrum is difficult in part because it is so faint. An excellent discussion is offered by this paper http://arxiv.org/abs/astro-ph/0607373, Lines in the Cosmic Microwave Background Spectrum from the Epoch of Cosmological Hydrogen Recombination.

20. Apr 16, 2015

### Buzz Bloom

Hi Chronos and George Jones:

Thank you both for your recomendations. I was able to download the CMB spectrum lines paper and it looks interesting. I have requested the Weinberg book through my town research librarian and I am hopeful she will be able to find a copy for me.