Rick's Cosmology Tutorial: Chapter 9B Abstract

In Chapter 9 we saw that atomic hydrogen forms in the period 185,000 years (1%) to 363,000 years (99%). How small must the density of free electrons become before recombination stops? In this Chapter we show that, once again, cosmic expansion causes freeze-out of this reaction. Recombination effectively ceases at 460,000 years when the temperature is 2574 K. A fraction 0.00007 of the electrons and protons remain free thereafter. These will be important in providing a cooling mechanism for the formation of the first stars.

In Chapter 9B we saw that the universe becomes transparent during the period of recombination, at about 300,000 years. Consequently, the universe is already transparent before recombination freezes out. This is fortunate. If transparency had required a lower density of free electrons than the lower bound which occurs at freeze-out (0.00007), the universe might never have become transparent and astronomy would not be possible.

Varying the photon:baryon ratio, we find that the remnant fraction of free electrons at freeze-out varies in proportion. This means that the absolute remnant free electron density is essentially the same for any photon:baryon ratio. This implies that the universe will become transparent before freeze-out for any photon:baryon ratio. The results of calculations assuming a range of different photon:baryon ratios are illustrated in the graphs of Chapter 9b.

The definition of transparency employed is that the mean free path of a photon is greater than, or comparable with, the size of the universe. It is virtually obvious, therefore, that radiation pressure cannot prevent structure formation once the universe is transparent. The only doubt is that the vast numerical preponderance of photons means that only one in ~10^9 photons would need to interact to imply that most baryons would be affected. The doubt is allayed by Peebles (1993), Equ.(6.142), which implies that, after freeze-out, the characteristic time for deceleration of streaming gas particles by radiation drag is longer than the prevailing age of the universe for red-shifts less than ~8,000 (i.e. for times later than ~20,000 years). Consequently, radiation pressure is no barrier to structure formation after recombination freeze-out.

The Sombrero Galaxy (M104 or NGC4594): an unbarred spiral galaxy in Virgo. Its bright nucleus is due to a central supermassive black hole