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To my understanding, the Cosmic Microwave Background Radiation (CMBR) is light released during the recombination epoch where the formation of neutral hydrogen atoms allowed for a sudden drop in the universe's free electron density, hence allowing for light to travel long distances undisturbed by Compton scattering for the first time. This light has been travelling throughout the transparent universe since recombination, and after redshifting, is exactly the CMBR we observe.

The source of the photons in the first place, as far as I know, is thermal radiation of the particles in the universe during the time of recombination. This is caused by the microscopic oscillations of matter particles, and should produce a continuous blackbody spectrum consistent with Planck's Law. Indeed, this is what we observe the CMBR to be like.

However, during recombination of hydrogen atoms (and I guess the heavier elements too), photons were emitted as atoms which formed in excited state quickly transitioned to the more energetically favourable ground state. I would have expected that this would contribute emission lines corresponding especially to the spectral lines of hydrogen. This is not what we observe and the CMBR almost perfectly follows an ideal blackbody curve.

Q. What happened to these photons reemitted by hydrogen during recombination?

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  • $\begingroup$ Just for clarification: the recombination as such results in a (quasi)-continuous spectrum (assuming the free electrons are distributed randomly in energy). It is only the subsequent cascading between bound atomic states that produces spectral lines. $\endgroup$
    – Thomas
    Feb 24 at 8:24
  • $\begingroup$ @Thomas Yes, that's what I meant. Thanks for the clarification. $\endgroup$
    – YiFan
    Feb 24 at 8:30

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There should indeed be emission lines at the appropriately redshifted frequencies. However, they are going to be incredibly faint and diluted because the ratio of photons to baryons at the epoch of recombination was more than $10^9$. i.e. There were more than a billion photons (distributed in a blackbody spectrum) already present for every proton $+$ electron recombination event.

Further, because recombination did not occur at exactly one redshift, but over a range of redshift, from perhaps $900<z<1300$, the recombination lines are smeared out in the frequency spectrum.

A calculation of the size and shape of the recombination lines is given by Sathyanarayana et al. (2015) (which is a paper actually putting forward a proposal to try and detect these lines). I've labelled some of the main recombination lines, which are an additive contribution to the main CMB spectrum. The y-axis is in units of Jy/sr. For comparison the CMB spectrum peaks is about $300\times 10^6$ Jy/sr at $\sim 100$ GHz. So these lines are fluctuations of order 1 part in $10^9$ in accordance with the arguments above. Current instrumentation is capable of detecting spectral intensity deviations of something like 1 part in $10^5$ so these features are many orders of magnitude below current detection thresholds.

Recombination spectrum. Recombination spectrum predicted from the CMB. This is to be added to the main CMB continuum, which is about 9 orders of magnitude brighter [adapted from Sathyanarayana et al. (2015)].

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    $\begingroup$ I see. Thanks for the detailed answer! $\endgroup$
    – YiFan
    Feb 24 at 8:58

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