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Redshift at recombination

  • Thread starter utopiaNow
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1. Homework Statement

We are to assume the recombination happens at redshift [tex]z_{rec}[/tex] when the number density of photons [tex] n_{\gamma}(z_{rec}) [/tex] capable of ionizing hydrogen is exactly equal to the number density of baryons [tex] n_{b}(z_{rec}) [/tex]. Use the measured number density of baryons, the temperature of the CMB and the blackbody radiation to find out at what redshift [tex]z_{rec}[/tex] we have [tex] n_{\gamma}(z_{rec}) = n_{b}(z_{rec}). [/tex]


2. The attempt at a solution
Sorry I don't have time to write in detail what I have so far. But basically I come down to [tex] \Omega_{\gamma}E_{bary} \over hf_{mean}\Omega_{bary} [/tex] [tex]= 1 [/tex]

However this doesnt make use of blackbody radation, or the temperature of the CMB, if I'm supposed to equate [tex] \Omega_{\gamma} [/tex] to Temperature of the CMB, then I'm not sure how to do that step.

Thanks
 

George Jones

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Forget cosmology for a while.

If [itex]E_I[/itex] is the ionization energy of hydrogen, any photon with energy greater than [itex]E_I[/itex] can ionize hydrogen. Now consider a blackbody at temperature [itex]T[/itex]. What is the number density for photons with energies greater than [itex]E_I[/itex]?
 
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