15.2 Extant actinides

The age of the universe has estimated at between 12 and 15 Byr based on application of the Hubble constant to quasar red-shifts, and on the ages of the oldest stars calculated from nucleosynthetic models (e.g. Lineweaver, 1999). More recently, evidence from the anisotropy of the cosmic microwave background has been used to determine a much more precise age of 13.7 " 0.2 Byr (Bennett, 2003). Therefore, the age of the galaxy at the time of solar-system condensation was ca. 9 Byr, which is of the same order as the lifetime of a typical star like the Sun. However, large stars have much shorter lifetimes, which may even be less than 1 Myr in duration. Since the solar-system coalesced from the debris of ‘dead’ stars, it is theoretically possible that any given atom in the solar-system could have been processed through only one previous star, or through numerous previous stars.

This indeterminacy leads to uncertainty in the production rate of solar-system nuclides over the life of the galaxy. This uncertainty is particularly severe for r-process nuclides, which are only generated in the supernova explosions which terminate the life-histories of large stars (section 1.2.1). Uncertainties in the production rate of extinct nuclides are a major source of uncertainty in the determination of ). However, the best constraints on long-term r-process production rates are provided by long-lived ‘extant’ nuclides. Therefore the extant actinides, ²³⁵U, ²³⁸U and ²³²Th will be examined before discussion of individual extinct nuclides.

The gulf of unstable nuclides between the end of the s-process nucleosynthetic ladder and the actinide elements (section 1.2.2) means that these nuclides can only be generated by the r-process. The seed nuclei for this process are clearly the nuclei at the top of the s-process ladder, but these nuclides, especially Pb, have small neutron capture cross-sections, creating a nucleosynthetic barrier. As a result, the production ratios of the actinides are constrained to be close to unity. This factor is critical in using them to model r-process production rates over the life-time of the galaxy.

We begin with the abundances of these nuclides in chondritic meteorites. Normalising to ²³⁵U = 1, ²³⁸U and ²³²Th have present-day abundances of ca. 138 and 520 respectively in carbonaceous chondrites. Correcting for decay to initial abundances at 4.55 Byr and re-normalising to ²³⁵U = 1, we obtain lower relative abundances of 3.45 and 8.18 for ²³⁸U and ²³²Th respectively, but these are still higher than estimated production ratios (relative to ²³⁵U) of 0.66 and 1.27 respectively (e.g. Broecker, 1986). Therefore, we can use these differences, along with the different half-lives of the three nuclides, to test alternative production models. Two of the extreme models are shown in Fig. 15.2 (a and b), and will be examined.

Fig. 15.2. Schematic illustration of the relationship between production models and ) calculation. a) Single supernova event yielding maximum value of ); b) constant ‘continuous’ production followed by a short ) period; c) complex variation in production rate (‘granular model’). After Wasserburg and Papanastassiou (1982).

If all uranium formation was attributed to a single supernova event (Fig. 15.2a), then we could calculate the apparent timing of this event by the subsequent decay of short-lived ²³⁵U (half-life ca. 700 Myr) relative to longer-lived ²³⁸U (half-life ca. 4500 Myr). The calculation based on uranium isotopes alone may be somewhat more reliable than that involving thorium because no chemical fractionation can have occurred during solar-system coalescence. This model leads to a calculated ) value for the nucleosynthetic event of 2.1 Byr before solar-system coalescence. However, evidence for the presence of the short-lived actinide ²⁴⁴Pu in the early solar-system rules out a model with such a large ) value.

The other extreme model involves ‘continuous’ supernova production (Fig. 15.2b). Taken to its limit this is an impossibility, since each supernova event terminates the evolution of a star, and the scattered debris must be incorporated in a new star before nucleosynthesis can continue. However, for nuclides with half-lives of hundreds of Myr, a supernova frequency as low as one per 100 Myr in the production history of an element will be a close approximation to continuous production. Under this model, the abundance of an unstable nuclide builds up until it reaches a level where the rate of synthesis is equalled by the rate of decay. This point of saturation is reached sooner in short-lived than long-lived nuclides (Fig. 15.3).

Fig. 15.3. Contrasting rates of approach of U and Th isotopes to the steady-state abundance in a model of ‘continuous’ supernova actinide production. After Broecker (1986).

The growth curves in Fig. 15.3 can be presented in the form of isotope ratios (Fig. 15.4) of ²³⁸U and ²³²Th against ²³⁵U. The time at which the curves intersect the primordial solar-system composition (calculated above) yields a crude estimate for the age of the galaxy at solar-system coalescence. Adding 4.55 Byr, we obtain estimates for the age of the galaxy of 16.5 and 13.5 Byr from Figs. 15.4a and 15.4b respectively. Given the many assumptions made, these estimates for the age of the galaxy agree surprisingly well with the estimated 13 – 14 Byr age of the universe, and therefore provide strong support for the ‘continuous supernova’ model. Under this model, the extant actinides provide a very poor constraint on the value of ). However, that is the role of the extinct nuclides.

Fig. 15.4. Growth curves for ²³⁸U/²³⁵U and ²³²Th/²³⁵U in a ‘continuous’ supernova production model, relative to the primordial solar-system value. After Broecker (1986).

In between the two extreme models described above, there is an infinite number of intermediate models where discrete production events of variable size occur at variable intervals (e.g. Fig. 15.2c). These are termed ‘granular’ models. Ideally, we would like to use the actinide data to put an upper limit on the ‘granularity’ of these models. However, the indeterminancy of the system prevents the application of precise limits. Many workers have used rather arbitrary models involving a combination of ‘continuous’ production and late ‘discrete’ events. However, Trivedi (1977) suggested that it was more reasonable to assume supernova events at regular intervals. He proposed a simple model in which 50 supernova spikes of equal size were equally spaced with an interval of 140 Myr (assuming a galactic age at solar-system formation of 7 Byr). Relative to a theoretical ‘stable’ actinide, this means that the most recent supernova products would undergo 50-fold dilution by isotopically ‘cold’ material generated in previous events. This model represents a useful yardstick for comparison with the dilution factors proposed for extinct nuclides.

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