Question about Recombination Redshift values

[Dr. Strange]

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?

 

[Chronos]

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.

 

[Dr. Strange]

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.

 

[Buzz Bloom]

could you also give a layman's description of optical depth,

Hi @Dr. Strange:

I think my post #9 in another thread might help.
https://www.physicsforums.com/threads/depth-of-the-cmb.843673/#post-5295553

Regards,
Buzz

 

[Dr. Strange]

I think my post #9 in another thread might help.
https://www.physicsforums.com/threads/depth-of-the-cmb.843673/#post-5295553

Yes, that was very helpful. Is there any relation between the first peak of the BAO spectrum and one of these z values (for example, the 1090 value quoted in the Plank final results).

 

[Buzz Bloom]

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