The uranium isotopes age and evolution of stellar nucleosynthesis

In the more common, higher-metallicity, case, where the observed abundances of radioactive isotopes are considered to result from continuous evolution, evolutionary models can be constructed. Such an approach can make use of the terrestrial 235U/238U and 232Th/238U ratios, which are very well known (Table 28.1). The principal unknown in these models, and an important parameter of galactic chemical evolution (GCE), is the rate of the preterrestrial contribution of r-process isotopes to the interstellar medium, GCE(t), which should be added to Eqn (1.1):

The isotopes 235 U, 238U and 232Th are produced simultaneously, with model initial ratios (235U/238U)0 - 1.45 and (232Th/238U)0 - 1.7 (or slightly higher, - 2.2, according to another r-process model; see Schatz et al., 2002). These ratios should be compared with the solar system (SOS) present-day ratios recalculated to the time of solar system formation, 4.570 Gyr ago (Table 28.1); these SOS initial ratios are the principal constraints for modelling (Fig. 7.1).

For the simplest case, in which all these r-nuclides were produced in a single hypothetical nucleosynthetic event, GCE(t) = 0 and the rearrangement of Eqn (7.1) for the U-isotope ratio gives and analogously for the 232Th/238U ratio. When the above ratio values are substituted into Eqn (7.2), the age of the event, T, is found to be 6.4 and 8 Gyr for the U/U and Th/U systematics respectively (Model I, Fig. 7.1). These values are much less than the Hubble time and the Th-Eu and Th-U estimates discussed above and are also significantly different from each other. As expected, the one-short-event model appears to be a gross oversimplification for high-metallicity systems.

A slightly more complicated model envisages the production of nuclides at a constant rate before they were isolated from the nucleosynthesis environment 4.57 Gyr ago: GCE(t) = constant. The solution gives T(U/U) = 14.5 and T(Th/U) = 12.5 Gyr (Model II, Fig. 7.1). This opposite order of "nucleosynthesis ages" obtained for U/U and Th/U from the two above models implies that an intermediate scenario with a decreasing rate of nucleosynthesis would fit the data best. Indeed, an exponentially decreasing rate, by a factor ~ 2 per 10 Gyr (similar to the rate of supernovae nucleosynthesis, see the inset in Fig. 7.1), gives the same age, ~ 12 Gyr, for the beginning of nucleosynthesis of the heavy elements for both ratios. This value is in overall agreement with the Th-U chronology of metal-poor stars.

Time, Gyr

Time, Gyr

Fig. 7.1 Radiometric chronology of nucleosynthesis: the 238U-235U-232Th sys-tematics. Among three models of the rate of nucleosynthesis (see the inset: early short synthesis, Model I; continuous synthesis at a constant rate, Model II; exponentially decaying synthesis, Model III) only Model III gives a self-consistent solution (broken-line arrow), i.e. similar ages for the 235U-238U and 232Th-238U systematics at ~ 12 Gyr. For comparison, the rate of birth of supernovae, the major generators of these elements in the Galaxy, is also shown in the inset (grey line); the production rate in the early Galaxy (~ 13 Gyr ago) is estimated at ~ 30 stars per century. From Timmes et al. (1995). Reproduced by permission of the American Astronomical Society.

Age, Gyr

Fig. 7.1 Radiometric chronology of nucleosynthesis: the 238U-235U-232Th sys-tematics. Among three models of the rate of nucleosynthesis (see the inset: early short synthesis, Model I; continuous synthesis at a constant rate, Model II; exponentially decaying synthesis, Model III) only Model III gives a self-consistent solution (broken-line arrow), i.e. similar ages for the 235U-238U and 232Th-238U systematics at ~ 12 Gyr. For comparison, the rate of birth of supernovae, the major generators of these elements in the Galaxy, is also shown in the inset (grey line); the production rate in the early Galaxy (~ 13 Gyr ago) is estimated at ~ 30 stars per century. From Timmes et al. (1995). Reproduced by permission of the American Astronomical Society.

0 0

Post a comment