What Lies Between the CMB and the First Stars?

[bapowell]

Imagine being in an infinitely large room filled uniformly with photographers. Suppose they've got the old flash bulb type cameras. Imagine they all snap your picture at the same time: what would you see? You'd see an outwardly expanding ring of light as the flashes from ever further, equidistant cameras reach you.

The photographers snapping the picture is the "last scattering" of CMB photons as the universe becomes transparent. (Yes, it's true the real CMB was not generated instantaneously like this, but it's a fine assumption for what we're talking about). The ring of light seen moment to moment is the last scattering sphere of the CMB, likewise seen moment to moment.

The key is recognizing that the CMB photons were spread uniformly throughout the cosmos prior to their release from the baryon photon plasma.

 

[Chronos]

CMB photons did not decouple all at once. The oft quoted figure of 380,00 years as the age of the universe when CMB photons were last scattered represents the most likely age at which any given CMB photon was emitted. CMB photons continued to be released for another 115,000 years thereafter, and over a correspondingly similar time period prior to age 380,000 years, according to this excerpt:

'The thickness of the LSS refers to the fact that the decoupling of the photons and baryons does not happen instantaneously, but instead requires an appreciable fraction of the age of the Universe up to that era. One method to quantify exactly how long this process took uses the photon visibility function (PVF). This function is defined so that, denoting the PVF by P(t), the probability that a CMB photon last scattered between time t and t+dt is given by P(t)dt.

The maximum of the PVF (the time where it is most likely that a given CMB photon last scattered) is known quite precisely. The first-year WMAP results put the time at which P(t) is maximum as 372 +/- 14 kyr . This is often taken as the "time" at which the CMB formed. However, to figure out how long it took the photons and baryons to decouple, we need a measure of the width of the PVF. The WMAP team finds that the PVF is greater than half of its maximum value (the "full width at half maximum", of FWHM) over an interval of 115 +/- 5 kyr. By this measure, decoupling took place over roughly 115,000 years, and when it was complete, the universe was roughly 487,000 years old."

ref: http://cs.mcgill.ca/~rwest/wikispeedia/wpcd/wp/c/Cosmic_microwave_background_radiation.htm

 

[Chalnoth]

The maximum of the PVF (the time where it is most likely that a given CMB photon last scattered) is known quite precisely. The first-year WMAP results put the time at which P(t) is maximum as 372 +/- 14 kyr . This is often taken as the "time" at which the CMB formed. However, to figure out how long it took the photons and baryons to decouple, we need a measure of the width of the PVF. The WMAP team finds that the PVF is greater than half of its maximum value (the "full width at half maximum", of FWHM) over an interval of 115 +/- 5 kyr. By this measure, decoupling took place over roughly 115,000 years, and when it was complete, the universe was roughly 487,000 years old."

ref: http://cs.mcgill.ca/~rwest/wikispeedia/wpcd/wp/c/Cosmic_microwave_background_radiation.htm

This looks like there's a factor of two error in the estimate. I believe that 115,000 years would be the full duration during which photons were emitted (well, at least the full duration where the emission rate was greater than half the peak: photons would have been emitted before and after at lower rates). So the approximate time where the photon emission dropped below half the peak emission rate would be somewhere near 57,500 years after the peak emission time, not 115,000 years.