Annu. Rev. Astron. Astrophys. 1994. 32: 153-90
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4.3. Constraints on s-Process Sites

What constraints can help to evaluate the proposed sites discussed in the previous section? s-process branchings are the first important constraints. The likelihood that a beta-unstable nucleus in the s-process beta decays depends on the rate of beta decay compared to the rate of neutron capture. Evidence for branching provides information about these rates. In particular, with knowledge of the beta-decay rate from laboratory experiments, the degree of branching constrains the neutron capture rate nn<sigma v>. Then knowledge of <sigma v> from the laboratory constrains nn, the neutron number density during the s-process. On the other hand, if the beta-decay rate is temperature sensitive (e.g. Takahashi & Yokoi 1987), branching data yield constraints on the temperature during the s-process. Branching data may also yield constraints on the mass density during the s-process through electron capture rates. Finally, branching data can constrain the duration of the neutron pulses (Ward & Newman 1978). If the pulse period were much shorter than the lifetime of the branching point isotope, there would be no branching. Pulses that were too long in duration would allow too much neutron capture.

What do we find for the s-process in nature? For the main component of the s-process, the isotopes 134Cs, 148Pm, 151Sm, 154Eu, 170Yb, and 185W are branch-point isotopes with potential as diagnostics of the temperatures and neutron densities prevailing during the s-process. Beer et al (1984) used 151Sm, 170Yb, and 185W to find limits on the neutron number density and temperature. Uncertainty in the population of the 137 keV isomeric state in 148Pm during the s-process makes conclusions from this isotope difficult. Uncertainties in cross sections and abundances limit the usefulness of 134Cs and 154Eu.

As for the mass density, Yokoi & Takahashi (1983) noticed that 163Dy could beta decay in stars, even though it is stable on Earth. In stars, the 163Dy atom is ionized so that in fact the daughter atom 163Ho would be at slightly lower mass. 163Ho then could either capture a neutron or electron capture back to 163Dy. The electron capture rate depends on the density of electrons, which in turn depends on the mass density. Beer et al (1985) were able to constrain the mass density in the s-process in this way.

Finally, Beer & Macklin (1988) studied 151Sm in order to determine a lower limit to the duration of the neutron pulse in the s-process. Studies of 86Kr may give an upper limit to the pulse duration (Beer & Macklin 1989). Unfortunately the weak component in this region introduces ambiguities into such an analysis.

The net results of branching studies in the context of the classical model give a temperature for the main component of 2.8 - 3.9 × 108 K, a neutron density of 2.3 - 4.5 × 108 cm-3, a mass density of 2.6 - 13 × 103 g cm-3, and a pulse duration of greater than 3 years (Kappeler et al 1989). These numbers agree reasonably well with those expected from stellar models. A similar analysis for the weak component yields a temperature of 1.8 - 3.0 × 108 K and a neutron density of 0.8 - 1.9 × 108 cm-3 (Kappeler et al 1989).

The relatively high temperatures found in this analysis for the main component suggest that 22Ne(alpha, n)25Mg is the neutron source for the s-process. Howard et al (1986) studied the s-process nucleosynthesis with this neutron source. They obtained poor fits to the solar sigmaN curve when they used parameters derived from stellar models. In particular, the average neutron density during the pulses was too high to reproduce the correct branchings. Busso et al (1988) have confirmed these results. On the other hand, the high temperature 22Ne source may simply be the last hot part of the neutron burst that was primarily from 13C at lower temperature (see below).

Let us consider now the evidence from observations of stars. It was the observation of technetium in certain red giant stars (Merrill 1952) that showed that stars do indeed synthesize elements and led Cameron (1955) to work out many of the details of the s-process. Since all isotopes of Tc are unstable, any Tc present in the surface of a star must have been synthesized in the interior of the star by the s-process and then dredged up to the surface. Recent observations show that red giant stars in the solar neighborhood that do have s-process abundance enhancements in their atmospheres do not show the accompanying enhancements of 25Mg and 26Mg that one would expect from alpha capture on 22Ne (e.g Smith & Lambert 1986, McWilliam & Lambert 1988). In addition, observations of Rb and 96Zr constrain s-process branching at 85Kr and 95Zr. Astronomers find that the s-process occurring in the interiors of the stars observed must be happening at low neutron densities (nn ltapprox 109 cm-3), not the high neutron densities characteristic of the 22Ne(alpha, n)25Mg reaction (e.g. Lambert 1993).

From this evidence, it appears that 13C is more promising as the source of s-process neutrons, indicating that low-mass AGB stars are probably the site of the s-process. Such stars give a low temperature s-process (~ 1.5 × 108 K) which would seem to contradict the higher temperatures found from the analysis of the s-process branchings in the classical model (T = 2.8 - 3 - 9 × 108 K) discussed above. In the low-mass AGB star s-process calculations that do show good agreement with solar abundances (e.g. Gallino et al 1988, Kappeler et al 1990), there are two bursts of neutrons per pulse: a strong burst due to the 13C(alpha, n)16C reaction at T ~ 1.5 × 108 K, and a second, weaker one, due to the 22Ne(alpha, n)25Mg reaction. This weaker burst occurs when the helium shell contracts following the first burst and heats to a temperature of T ~ 3 × 108 K. It resets the branch-point thermometers to this higher temperature, in agreement with the analysis from the classical model.

More evidence for 13C as the dominant source for neutrons in the s-process comes from studies of galactic abundance evolution. Mathews et al (1992, 1993) studied the evolution of the Ba/Fe ratio in our Galaxy. Ba is predominantly an s-process element and hence must be secondary (ie. made from initial Fe). Mathews et al found that only an s-process behaving as a primary process fit well the observations of Ba abundances in the atmospheres of old stars. 13C is a primary neutron source, as discussed in Section 3.3. 22Ne is secondary because it must be built up from pre-existing CNO nuclei. The Fe seeds are of course secondary. Clayton (1988a) described how the secondary s-process with the 13C neutron source is able to mimic primary nucleosynthesis. The idea here is that while the galactic abundance of Fe seed for the s-process grows with time, so does the abundance of s-process neutron poisons.

A final point of increasing relevance is the new information from pre-solar SiC grains found in the Murray and Murchison meteorites. These grains are carriers of isotopic anomalies in s-process isotopes (Srinivasan & Anders 1978, Tang & Anders 1988). In addition, these grains are anomalous in their Si and C (Zinner et al 1987, Anders & Zinner 1993). It appears that these grains have condensed in carbon-star atmospheres, which are s-process enriched and have variable 13C-rich compositions (Lambert et al 1986). As surviving stardust, the grains are almost pure end members in the "cosmic chemical memory" theory for interpreting isotopic anomalies in solar system samples (Clayton 1978, 1982). From studies of trace s-isotopes in these grains (Ott & Begemann 1990a, b; Zinner et al 1991; Richter et al 1992; see Anders & Zinner 1993 for a review) the abundance ratios only fit if the grains come from low-mass AGB stars (Gallino et al 1990). A vexing problem with this idea, however, is that such stars cannot explain the anomalous Si isotopes (a major constituent of the grains). One suggested answer is higher mass AGB stars, in which burning of Mg isotopes in late pulses resets the ratio of 29Si / 30Si (Brown & Clayton 1992). Galactic abundance evolution of Si isotopes may also hold the key (Clayton 1988b, Gallino et al 1994). Alternatively, some other site may be responsible for these grains (e.g. Arnould & Howard 1993). These tiny, sturdy grains have traveled from afar carrying important messages about the s-process which have yet to be deciphered.

In summary, low-mass AGB stars are at present the most promising site for the main component of the s-process. Confirmation of this site will require continued interplay of nuclear physics, meteoritics, stellar evolution and structure theory, nucleosynthesis theory, galactic abundance evolution theory, and stellar astronomy. Many people will be busy for quite some time to come!

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