7.4 Nuclear abundances as evidence for the big bang
What we have seen is that a theoretical model based on the assumption that there was a big bang, and incorporating an assumption about the present-day value of the baryonic density, ρb,now, leads to definite predictions as to what the nuclear abundances must have been when the elements froze-out. This, therefore, provides us with a third way of checking out the big bang hypothesis: Do the present-day cosmic nuclear abundances agree with these predictions for any plausible value of the present-day baryonic density?
Obtaining an answer to this question is not as easy as one might think. The trouble is that since the freeze-out abundances were established, about 20 minutes after the big bang, further modifications to the nuclear abundances have been going on. The story of most matter is that it exists for a few hundred million years as a rarefied gas, and then is slowly drawn into a star, where its nuclear composition is altered because it is heated up to temperatures at which further nuclear reactions take place. Because the temperature and density conditions in a star are very different from those encountered during the big bang epoch of nuclear synthesis, the thermonuclear reactions in stars are different, and they lead to a different mix of end products. Therefore, the freeze-out concentrations of the various elements are not reflected directly in the abundances found in stars, or indeed on the Earth which itself condensed out of stellar matter thrown out of stars during supernova explosions.
Figure 33 shows in a schematic way the conditions of temperature and density under which cosmological nuclear reactions are important (region on the left), and the conditions for stellar nuclear reactions (region on the right).
(a) Why is the area between A and B inclined to the axes rather than being vertical?
(b) Why does the area for the nucleosynthesis in the big bang not continue above A?
(c) Why does it not continue to the left of B?
(d) Why does the area for stars not continue below C?
(a) While the Universe was expanding and the density decreasing during the big bang, the temperature dropped. (A universe that was perfectly uniform at all stages would be shown as a line between A and B. We have chosen to show a narrow area instead, corresponding to some non-uniformities of density and temperature.)
(b) Above A, collision energies were too high for nuclei to hold together.
(c) Because of the reduced density to the left of B, collisions occur too infrequently to have much importance.
(d) Below C, because the nuclei are moving slowly they have difficulty in overcoming the electrostatic repulsion between their charges, and thus getting close enough for fusion to take place. For this reason, fusion reactions proceed only slowly and the energy release is not sufficient to make the body glow (and by definition, stars give off light). This region would correspond to planets, rather than stars. Jupiter, for instance, our largest planet, misses being a star by a factor of about 50.
These additional conditions have been included in Figure 34.
The ways in which present-day observations of abundances can be compared with the predicted abundances at freeze-out are best considered by treating each of the relevant nuclei in turn.
First, we can note that there is good evidence from a wide range of astronomical bodies that the 1H nuclide is the most common. This fits well with the freeze-out predictions, but is hardly conclusive. For more detailed insight we need to look at how the abundances of other nuclei (as expressed by their mass fractions) compare with that of 1H.
Turning to the second most abundant nuclide, 4He, we must confront the problem that much of the helium in the present-day Universe has been produced in stars. Fortunately, stars also produce other, heavier elements, and we can use these to determine how much of the helium in any region is the result of stellar processing rather than the big bang. Most stars are not hot enough to show helium lines in their spectra, and those that do are unsuitable for primordial abundance measurements. Instead, helium is best measured in the clouds of diffuse glowing gas that astronomers call HII regions, and even these clouds are best studied in smaller galaxies where there has been less stellar processing than in our own Galaxy.
One way of proceeding is to use spectral techniques to measure both the helium mass fraction and the relative abundance of oxygen nuclei for a number of extragalactic HII regions. Once the measurements have been made (and the uncertainties in those observations estimated) a plot such as that shown in Figure 35 can be compiled. By extrapolating the data back to zero relative abundance of oxygen, a ‘primordial’ value for the helium mass fraction can be deduced. Figure 35 implies a value of about 0.23 for this primordial helium mass fraction, in line with several other attempts to determine this quantity.
Comparing this ‘observed’ primordial helium mass fraction (0.23) with the predicted values in Figure 32, there is a reasonable level of agreement for a range of present-day baryonic densities.
The abundance of 3He is less useful. A number of observational difficulties make it very hard to deduce anything reliable about the primordial abundance. The comparison of prediction and measurement has little to offer in this case.
The present-day abundance of 7Li can be deduced from spectral studies of metal-poor dwarf stars. The outer layers of these stars are believed to be relatively unchanged since they were formed. Most share the same lithium abundance despite having different amounts of other elements and different masses. This makes it probable that the lithium in these outer stellar layers has not been processed, and thus gives a direct indication of the primordial mass fraction of lithium. The observations favour a 7Li mass fraction close to 8 × 10−10. According to Figure 32, this corresponds to a present-day mass density of baryonic matter of around (1 to 5) × 10−28 kg m−3.
Finally consider the case of deuterium, 2H. Deuterium is destroyed in stars so its currently observed mass fraction provides a lower limit on its primordial mass fraction. This lower limit is about 3 × 10−5 to 7 × 10−5, consistent (according to Figure 32) with present-day baryonic mass densities of about 5 × 10−28kg m−3 or less.
Bringing all of the observed abundances together, it does seem that they are consistent with the predicted primordial abundances (Figure 32), provided the present-day baryonic mass density is around 10−28 kg m−3.
Pleasingly, at least to those who like consistency, a present-day baryonic mass density of a few times 10−28 kg m−3 is in excellent agreement with the rather precise value of ρb,now/c2 deduced by those who attempt to deduce cosmological parameters from the observed anisotropies in the cosmic microwave background radiation (as described in Section 6.3). The fact that there is a narrow range of values for the present-day baryonic densities in which the predicted and ‘observed’ light nuclear abundances agree, is a significant success for big bang cosmology. The fact that this narrow range of baryonic densities includes the value deduced by a quite different technique is a truly remarkable achievement.