Question about Recombination Redshift values

AI Thread Summary
The discussion centers on the differences between the recombination redshift values of z = 1500 and z = 1090, with z = 1500 derived from the Saha equation assuming thermal equilibrium, while z = 1210 is based on the Peebles equation without that assumption. The value of z = 1090 is linked to the optical depth, representing the point where the universe became transparent to radiation. Participants seek clarification on the redshift at which electrons traveled freely and the physical meaning of optical depth, τ, which is crucial in cosmological models like ΛCDM. The conversation also touches on the relationship between the BAO spectrum's first peak and these redshift values, indicating a need for deeper expertise. Overall, the thread highlights the complexities of understanding cosmic recombination and its implications in cosmology.
Dr. Strange
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Wikipedia gives the redshift of recombination at z = 1500 (roughly 4,000 K). The Plank report list a 'redshift for which the optical length equals unity' and gives a value of 1090. What is the difference between the two?
 
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z=1500 is approximated based on achieving a 50% ionization fraction under the Saha equation. This calculation, however, assumes the universe was in a state of thermal equilibrium, which it was not. Under the Peebles equation, which does not assume equilibrium, the 50% ionization fraction is achieved around z=1210. The value of z=1090 merely represents the ratio between the reionization temperature of hydrogen and the current measured temperature of the CMB.
 
Sorry, I didn't follow all of that. In layman's terms, which value represents the red-shift where the electrons traveled freely through the universe. Also, if it isn't asking too much, could you also give a layman's description of optical depth, τ. I see it's a parameter to ΛCDM and if you Google it, you get tons of information about various attempts to measure and constrain it, but I can't find a conceptual guide to tell me what this parameter is physically.
 
Dr. Strange said:
Is there any relation between the first peak of the BAO spectrum and one of these z values
Hi Dr. Strange:

You question requires expertise way over my head. The two people who have been particularly helpful in answering my questions about recombination are
@Chronos and @Chalnoth. Perhaps they can answer your question,

Regards,
Buzz
 
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