Hydrogen thermal equilibrium decoupling

[Mordred]

Interesting in the following article it describes the reaction rate of Hydrogen as it drops out of thermal equilibrium. Using the temperature to redshift relation

 

T=T0(1+z)

or alternateIy the inverse of the scale factor a. I calculated the temperature of 4000 kelvin to z= 1492.  The article evidently rounded this to z=5000, this corresponds to universe age 218,000 years old for the universe. The table also shows the reaction rate for higher and lower temperature values.

https://iopscience.iop.org/article/10.3847/1538-4357/ab2d2f/pdf.

This additionally tested the mathematics I was examining using a method by Juan Garcıa-Bellido. Details are in the following thread.

 

 For the Nucleosynthesis calculation to get an accurate method to correlate redshift to temperature relations so as I examine when different particle species drop out of thermal equilibrium I can calculate the age of the universe, volume, and subsequently the number density of each particle species.  You  often see in literature the value of 3000 kelvin given. Results are in the above article, using the method of said article. This corresponds to Z=1100 roughly 350,000 Years age for the Observable universe. 

 

The conjecture I am going to examine next is that at Higher temperature in the chart of said article the photon interactions with hydrogen atoms will cause higher scatterings of the atoms.  Hence the 3000 Kelvin value is the more stable decoupling temperature but does not represent the beginning stages of hydrogen decoupling.

 this may also help explain some of the earlier universe star formations. Though certainly not solve the entirety of issue of early star formation in terms of how rapidly they formed in the early universe.

I will also likely examine the methodology of equation 25 of the above article and compare it to the classical Bose_Einstein, Fermi-Dirac statistics method mainly to get a feel for the deviations that may occur between the two methods. 

 

 Thoughts ?

pS @Sensei I seem to recall a few years back you had an examination regarding star formation. If you still have that work handy and if you feel it would relate to this I wouldn't mind looking over it again.

 

Edited December 15, 2022 by Mordred

[Sensei]

2 hours ago, Mordred said:

pS @Sensei I seem to recall a few years back you had an examination regarding star formation. If you still have that work handy and if you feel it would relate to this I wouldn't mind looking over it again.

You are probably referring to this thread:

https://www.scienceforums.net/topic/85656-solar-fusion-neutrinos-and-age-of-solar-system/

 

[Mordred]

lol that's the one accidently replied in the other thread. The T=1490 with T=4000 is 50% decoupling. Hence the recombination Epoch where the mean free path of photons becomes near infinite is set at the T=3000 K  Z-1100. age 366,000

T=6000 can be representative of the early stages of decoupling at Z=2189 giving age at 112,000 years 

calculation based on 2018 dataset

Edited December 16, 2022 by Mordred