Fig. 3. Calculated ²³⁸U/²³²Th production ratio as a function of the age of the Milky Way based on the U/Th ratio measured in low-metallicity halo stars (curve LMHS, equation (17)) and the U/Th ratio measured in solar system material (curve GCE, equation (16)). By combining these two approaches, it is possible to estimate both the age T_G and the production ratio P^U/Th (Dauphas, 2005a).

ISM can be estimated in a deterministic way [τ > 5 m.y. (Meyer and Clayton, 2000)] . This comprises the nuclides ⁵³Mn (mean-life 5.4 m.y.), ⁹²Nb (50.1 m.y.), ¹⁰⁷Pd (9.4 m.y.), ¹²⁹I (22.6 m.y.), ¹⁴⁶Sm (148.6 m.y.), ¹⁸²Hf (13.0 m.y.), and ²⁴⁴Pu (115.4 m.y.). The abundances of all these nuclides in the ESS are well known. For calculating the remainder ratio, the abundances of these nuclides must be normalized to the abundances of neighbor nuclides produced in the same stellar environment. Hence, the normalizing nuclides used in the present contribution are not always identical to those used in the initial publications reporting extinct nuclide abundances. For evaluating the remainder ratio in the ESS, the basic ingredients are the normalized abundances of the short-lived nuclides in the ESS at the time of calcium-aluminum-rich inclusion (CAI) formation and the associated production ratios.

Manganese-53 is synthesized together with ⁵⁵Mn in massive stars. As discussed by Meyer and Clayton (2000), because solar system ⁵³Cr must have been primarily synthesized as ⁵³Mn, the production ratio ⁵³Mn/⁵⁵Mn can be approximated by the solar system ⁵³Cr/⁵⁵Mn ratio of 0.13 (Anders and Grevesse, 1989). The SN II models of Rauscher et al. (2002) predict a comparable production ratio, ⁵³Mn/ ⁵⁵Mn = 0.15, when individual yields from SN II of different masses are weighted by a typical initial mass function. Note that Sne II underproduce Fe-peak nuclides relative to ¹⁶O by a factor of 2–3 (Rauscher et al., 2002); the rest must be produced in SN Ia. This underproduction feature is reflected in the abundance patterns of low-metallicity halo stars (Wheeler et al., 1989; McWilliam, 1997). The initial ⁵³Mn/⁵⁵Mn ratio in CAIs is estimated to be 2.81 ± 0.31 × 10^–5 (Birck and Allègre, 1985; Nyquist et al., 2001). However, a lower initial value may be required in order to bring the chronologies based on the various extinct and extant radionuclides into agreement (Lugmair and Shukolyukov, 1998; Dauphas et al., 2005). We shall adopt here an initial ratio of 1.0 ± 0.2 × 10^–5. The remainder ratio is therefore ℜ_ess⁵³ = 7.7 ± 1.5 × 10^–5.

Niobium-92 was most likely synthesized by the p-process in SN. This radionuclide cannot be normalized to another isotope of the same element because the only stable isotope of Nb, ⁹³Nb, was synthesized by the s-process. It can instead be normalized to ⁹²Mo, which is also a pure p-process nuclide. The ⁹²Nb/⁹²Mo production ratio during photodisintegration of seed nuclei in SN II is 1.5 ± 0.6 × 10^–3 (Rauscher et al., 2002; Dauphas et al., 2003). The initial ratio in meteorites is 2.8 ± 0.5 × 10^–5 (Harper, 1996; Schönbächler et al., 2002). The remainder ratio is therefore ℜ⁹²_ess = 1.9 ± 0.8 × 10^–2 (Dauphas et al., 2003). Note that Münker et al. (2000) and Yin et al. (2000) found higher initial ratios, but the CAI measurements of Münker et al. (2000) might have been affected by nucleosynthetic effects, and the zircon measurement of Yin et al. (2000) was not replicated by Hirata (2001).

The initial ¹⁰⁷Pd/¹¹⁰Pd in the ESS was 5.6 ± 1.1 × 10^–5 (Kelley and Wasserburg, 1978; Chen and Wasserburg, 1996). This corresponds to ¹⁰⁷Pd/¹¹⁰Pd^r = 5.8 ± 1.2  × 10^–5, where ¹¹⁰Pd^r is the r-process contribution to the solar abundance of ¹¹⁰Pd (Arlandini et al., 1999). Palladium-107 is primarily a r-process nuclide that could also have received a contribution from the s-process. For most r-process radionuclides, their production ratios can be reliably estimated by decomposing the abundances of their daughter nuclides into s- and r-process contributions. For instance, the entire r-process abundance of ¹⁰⁷Ag must have been channeled through ¹⁰⁷Pd. The sites of r-nucleosynthesis are not well established but they very likely correspond to the late stages of rapidly evolving stars. The ¹⁰⁷Pd/¹¹⁰Pd production ratio can therefore be approximated to the solar system ¹⁰⁷Ag^r/¹¹⁰Pd^r, where ¹⁰⁷Ag^r and ¹¹⁰Pd^r are obtained by subtracting the s-process contribution to solar abundances (Arlandini et al., 1999). The ¹⁰⁷Pd/110Pd r-process production ratio is therefore 1.36 and the remainder ratio is ℜ¹⁰⁷_ess = 4.3 ± 0.9 × 10^–5.

Iodine-129 is also primarily an r-process nuclide. It was historically the first short-lived nuclide to have been found to have been alive in the ESS (Reynolds, 1960). When the Pb/Pb age of Efremovka CAIs [4567.2 ± 0.6 Ma (Amelin et al., 2002)] is combined with the observed ¹²⁹I/¹²⁷I-Pb/ Pb age correlation in ordinary chondrite phosphates (Brazzle et al., 1999), the early solar system ¹²⁹I/¹²⁷I is estimated to be 1.19 ± 0.20 × 10^–4. This corresponds to a ¹²⁹I/¹²⁷I^r initial ratio of 1.25 ± 0.21 × 10^–4. As discussed in the case of ¹⁰⁷Pd, the ¹²⁹I/¹²⁷I r-process production ratio can be estimated from decomposition of ¹²⁹Xe into r- and s-processes (Arlandini et al., 1999). Because ¹²⁹Xe is predominantly synthesized by the r-process, little uncertainty affects the production ratio, ¹²⁹I/¹²⁷I = 1.45. The remainder ratio for ¹²⁹I is ℜ¹²⁹_ess = 8.6 ± 1.5 × 10^–5.

Samarium-146 is a pure p- process isotope. The ESS ¹⁴⁶Sm/¹⁴⁴Sm ratio is 7.6 ± 1.3 × 10^–3 (Lugmair et al., 1983 ; Prinzhofer et al., 1992) . Its production ratio as obtained in the most recent models of the p- or γ- process in Sne II is 1.8 ± 0.6 × 10^–1 (Rauscher et al., 2002; Dauphas et al., 2003). The remainder ratio is therefore ℜ¹⁴⁶_ess = 4.2 ± 1.6 × 10^–2 (Dauphas et al., 2003).

Hafnium-182 is presumably an r- process isotope. From the decomposition of the abundance of its daughter isotope ¹⁸²W into r- and s-processes (Arlandini et al., 1999), the ¹⁸²Hf/¹⁷⁷Hf production ratio is estimated to be 0.81. The initial ¹⁸²Hf/¹⁷⁷Hf ratio in the ESS is 1.89 ± 0.15 × 10^–4 (Yin et al., 2002). Note that Quitté and Birck (2004) have derived a higher initial ratio from W-isotopic measurements of the Tlacotepec iron meteorite, but this may be affected by cosmogenic effects. The initial ratio of Yin et al. (2002) corresponds to ¹⁸²Hf/¹⁷⁷Hf^r = 2.31 ± 0.18 × 10^–4. The remainder ratio is therefore ℜ¹⁸² = 2.86 ± 0.23 × 10^–4.

Plutonium-244 is an rprocess isotope. As with other actinides, its production ratio is uncertain because the closest stable r-process nuclide that can anchor the models is ²⁰⁹Bi, 35 amu away. Goriely and Arnould (2001) evaluated nuclear model uncertainties on the production of actinides. Among the various models, only those that give a ²³⁸U/²³²Th production ratio consistent with meteoritic abundances are retained. The ²⁴⁴Pu/²³⁸U production ratio is thus estimated to be 0.53 ± 0.36. The initial ²⁴⁴Pu/²³⁸U in the solar system is estimated to be 0.0068 ± 0.0010 (Rowe and Kuroda, 1965; Hudson et al., 1989) . The ratio of the remainder ratios

ℜ²⁴⁴_ess /ℜ²³⁸_ess is therefore 1.28 ± 0.89 × 10^–2. The remainder ratio of ²³⁸U can be estimated in the framework of the open nonlinear GCE model (Dauphas et al., 2003) to be 0.71 for a galactic age of 13.7 G.y. (0.53 in the closed-box model). The remainder ratio of ²⁴⁴Pu is thus ℜ²⁴⁴_ess = 9.1 ± 6.3 × 10^–3 (Dauphas, 2005b). All these ratios are compiled in Table 1.

The remainder ratios in the ESS can be compared with those in the ISM as predicted by GCE models. In order to account for the possible isolation of the solar system parent molecular cloud core from fresh nucleosynthetic inputs, a free-decay interval (∆) is often introduced [see Clayton (1983)  for a more complicated treatment]. This corresponds to a time when radioactive species decay without being replenished by stellar sources. The remainder ratio in the

ESS is related to that in the ISM through

ℜ_ess = ℜ_ismexp −     (18)

The remainder ratio in the ISM is itself a function of the mean-life of the considered nuclide (equation (14)). For radionuclides whose mean-lives are long enough that their abundances in the ESS can be explained by their steadystate abundance in the ISM, combining equations (14) and

(18) gives a relationship between the remainder ratios in the

ISM and the ESS (Dauphas et al., 2003; Dauphas, 2005b)

ℜ_ess = ℜ_ismexp− κ∆(19)

Tℜism

The remainder ratios of several short-lived radionuclides determined in the ESS are plotted vs. the ISM ratios derived from GCE models in Fig. 4. Also shown are curves corre-

Fig. 4.  Remainder ratios of several extinct nuclides in the ESS (ℜ _ess = R/P) are plotted against the corresponding remainder ratios in the ISM (see text). Theoretical expectations corresponding to different free-decay intervals ( ∆) are represented as dashed-curves (equation (19)) (Dauphas et al., 2003; Dauphas, 2005b). Extinct radionuclides are grouped according to nucleosynthetic processes. The forbidden region is the place where ℜ_ess is higher than ℜ_ism (the extinct radionuclides cannot be inherited from GCE). Error bars are 2σ.

sponding to equation (19) calculated with different values of the free-decay interval ∆. Some implications of the presence of extinct radionuclides in meteorites on stellar nucleosynthesis and solar system formation are discussed in detail in the following sections.

4.3.1. Niobium-92 and the nucleosynthesis of molybdenum-ruthenium p-isotopes. The radionuclides ⁵³Mn and ¹⁴⁶Sm define the same free-decay interval within uncertainties (∆ = 10 m.y.). They were probably synthesized in supernovae and were inherited in the ESS from GCE. Niobium-92 is a special case because it lies in a mass region of the nuclide chart where SN models underproduce p- process isotopes (⁹²Mo, ⁹⁴Mo, ⁹⁶Ru, and ⁹⁸Ru) by a factor of 10 (Rauscher et al., 2002) . This nuclide can therefore be used to test the various hypotheses that have been advanced to remedy the underproduction feature of supernovae in the Mo-Ru mass region (Yin et al., 2000; Dauphas et al., 2003). 4.3.2. The puzzling origins of extinct r-radioactivities. The r-process radionuclides ¹²⁹I and ²⁴⁴Pu were inherited from GCE with a free-decay interval of approximately 100 m.y. (Fig. 4). If the other r-process nuclides ¹⁰⁷Pd and ¹⁸²Hf had been inherited from GCE with the same freedecay interval (100 m.y.), then their abundances in the ESS would have been much lower than what is observed in meteorites (they require a shorter free-decay interval, 30 m.y.). The extinct radionuclides ¹⁰⁷Pd and ¹⁸²Hf must therefore have a different origin. Two distinct scenarios have been advocated for explaining the origin of these two short-lived nuclides.

Wasserburg et al. (1996) and Qian et al. (1998) questioned the universality of the so-called rprocess. They suggested that two kinds of r- process events are responsible for the nucleosynthesis of neutron-rich nuclei. One of these events would synthesize heavy r-nuclei and actinides (¹⁸²Hf and ²⁴⁴Pu, H events) while the other would synthesize light r-nuclei (¹²⁹I, L events). The H events would occur 10 times more frequently than the L events, which would explain why the free-decay interval inferred from ¹⁸²Hf is lower than that inferred from ¹²⁹I. Observations of elemental abundances in low-metallicity stars support the view that all r-nuclides are not produced at the same site (Sneden et al., 2000; Hill et al., 2002). Such stars formed early enough in the galactic history that contributions of a limited number of stars can be seen in their spectra. Sneden et al. (2000) analyzed the ultra-low-metallicity ([Fe/H] = –3.1) halo star CS 22892052 and found that low-mass r-process elements such as Y and Ag were deficient compared to expectations based on heavier r-process elements. More recently, Hill et al. (2002) determined the abundance of U, Th, and Eu in another metal-poor ([Fe/H] = –2.9) halo star (CS 31082-001). The age of this star based on the U/Th ratio is 14.5^+2.8_–2.2 G.y. (section 4.2), which agrees with independent estimates of galactic ages. In contrast, the Th/Eu ratio corresponds to an age that is younger than the age of the solar system, which is impossible (Hill et al., 2002). This suggests that actinides were produced independently of lighter r-process nuclides. Observations of low-metallicity stars therefore point to a multiplicity of r-process events, possibly as many as three. Wasserburg et al. (1996) and Qian et al. (1998) grouped ¹⁸²Hf with actinides, including ²⁴⁴Pu. However, Dauphas (2005b) showed that ²⁴⁴Pu requires a longer free-decay interval (∆ = 100 m.y.) compared to ¹⁸²Hf (∆ = 30 m.y.). This discrepancy may indicate that, in addition to the L and H events, another event must be added to explain actinides (A events). Note that this would be consistent with observations of low-metallicity stars, which require three distinct production sites. According to the multiple r-processes model, ¹⁰⁷Pd was synthesized by the s-process in a lowmetallicity, high-mass AGB star that polluted the ESS with a stellar wind (Wasserburg et al., 1994; Gallino et al., 2004). Alternatively, it could have been injected by the explosion of a nearby SN, where it would have been synthesized by the weak s-process (Meyer and Clayton, 2000).

Another possible scenario is that the nuclides that are overabundant in the ESS compared to GCE expectations (¹⁰⁷Pd and ¹⁸²Hf, as well as ²⁶Al, ³⁶Cl, ⁴¹Ca, and ⁶⁰Fe) were injected in the presolar molecular cloud core by the explosion of a nearby SN that might have triggered the protosolar cloud into collapse (Cameron and Truran, 1977; Meyer and Clayton, 2000; Meyer et al., 2004). The dynamical feasibility of injecting fresh nucleosynthetic products in the ESS has been studied carefully by Vanhala and Boss (2002). In the most recent version of the pollution model, it is assumed that only a fraction of the stellar ejecta is efficiently injected in the nascent solar system [the injection mass cut is the radius in mass coordinates above which the envelope of the SN is injected (Cameron et al., 1995; Meyer et al., 2004)]. For a 25 M star, an injection mass cut of 5 M, and a time interval of 1 m.y. between the SN explosion and incorporation in the ESS, the abundances of ²⁶Al, ⁴¹Ca, ⁶⁰Fe, and ¹⁸²Hf are successfully reproduced (Meyer et al., 2004). Chlorine36 and ¹⁰⁷Pd are slightly overproduced but this may reflect uncertainties in ESS abundances and input physics. Because the injection scenario requires only one source for explaining all extinct radionuclides that cannot be produced by GCE or irradiation in the ESS while the multiple r- processes scenario requires many, the principle of Ockham’s Razor favors the SN pollution model.

4.3.3. Predicted abundance of curium-247 in the early solar system. Among the short-lived nuclides that have mean-lives higher than 5 m.y., only one has eluded detection, ²⁴⁷Cm [τ = 22.5 m.y., decays to ²³⁵U (Chen and Wasserburg, 1981; Friedrich et al., 2004)] . Modeling of stellar nucleosynthesis and GCE allows the prediction of its abundance in the ESS. Curium-247 is expected to be produced at the same site that synthesized ¹²⁹I and ²⁴⁴Pu. The same free-decay interval can therefore be applied (∆ = 100 ± 25 m.y.). Goriely and Arnould (2001) estimated uncertainties on actinide production ratios. As already discussed in the case of ²⁴⁴Pu, we only consider the models that give a ²³⁸U/²³²Th production ratio consistent with the meteoritic measurement. The inferred ²⁴⁷Cm/²³⁸U production ratio is 0.138 ± 0.054. The remainder ratio in the ISM of ²⁴⁷Cm can be calculated using the open nonlinear GCE model of Dauphas et al. (2003), ℜ²⁴⁷_ism = 7.0 ± 1.6 × 10^–3. Using the estimated remainder ratio of ²³⁸U (0.71, see discussion on ²⁴⁴Pu), we get the ratio of the remainder ratios of ²⁴⁷Cm and ²³⁸_U, ℜ²⁴⁷_ism/ℜ²³⁸_ism = 9.8 ± 2.2 × 10^–3. Allowing for free decay ∆ = 100 ± 25 m.y., the ratio in the ESS is ℜ²⁴⁷_ess/ℜ_ess²³⁸ = 1.2 ± 0.4 × 10^–4. This value must be multiplied by the production ratio to get the expected ratio in meteorites. The ratio in the ESS is thus estimated to be ²⁴⁷Cm/²³⁸U = 1.6 ± 0.8 × 10^–5 (²⁴⁷Cm/²³⁵U = 5.0 ± 2.6 × 10^–5 at solar system formation). The present upper limit for the ²⁴⁷Cm/²³⁵U ratio obtained from U-isotopic measurements of meteoritic materials is 4 × 10^–3 (Chen and Wasserburg, 1981), which is entirely consistent with the predicted abundance based on modeling of GCE and nucleosynthesis.

5.       GALACTIC CHEMICAL EVOLUTION OF STABLE-ISOTOPE RATIOS

As discussed above in section 2, elemental abundance ratios measured in stars are a powerful tool for constraining models of GCE, because different elements are made by different processes in different types of stars with different evolutionary timescales. This statement is of course not limited to elements, but applies equally well to stable-isotope ratios. Many elements are comprised of both primary and secondary isotopes, as defined in section 2, so GCE theory anticipates that many isotopic ratios should evolve in the galaxy. As discussed above, the simple closed-box GCE model predicts that the ratio of a secondary to a primary isotope increases linearly with metallicity in the galaxy. As an example, let us consider the stable isotopes of silicon. Numerical supernova nucleosynthetic calculations (Woosley and Weaver, 1995; Timmes and Clayton, 1996)  indicate that ²⁸Si is a primary isotope, whereas ²⁹Si and ³⁰Si are secondary. Thus, it is not surprising that the numerical GCE model of Timmes and Clayton (1996) predicts that the ²⁹Si/²⁸Si and ³⁰Si/²⁸Si ratios increase monotonically with metallicity. The

Fig. 5. Silicon-isotopic evolution predicted in the solar neighborhood by Timmes and Clayton (1996) and by the “simple” closedbox GCE model (R stands for isotopic ratio). Silicon-isotope ratios increase with metallicity, due to secondary nature of the heavy isotopes ²⁹Si and ³⁰Si. (a) Unnormalized calculation: the predicted ratios miss the solar composition due to errors in nucleosynthesis models. (b) Isotopic ratios “renormalized” to reproduce the solar values at solar metallicity. The calculated isotope trends are shallower near solar metallicity than is predicted by the simple model of GCE.

Si-isotopic ratios as a function of metallicity predicted by this model are shown in Fig. 5a. The secondary nature of the rare Si isotopes is clear. However, it is also immediately apparent that the model does not exactly reproduce the solar isotopic ratios at solar metallicity; the ³⁰Si/²⁸Si ratio is high by ~50% and the ²⁹Si/²⁸Si ratio is slightly subsolar. The discrepancy is almost certainly due to errors in the supernova nucleosynthesis calculations that went into the GCE model, and agreement within a factor of 2 is usually considered a success in GCE modeling. However, this is not sufficient for comparison with presolar grain data measured with 1% precision (see next section). As discussed at length by Timmes and Clayton (1996), to compare high-precision isotope data with the GCE models in a self-consistent way requires that the models be “renormalized” so that they reproduce the solar abundances. The simplest approach is to rescale the GCE trends so that they pass through the solar composition at solar metallicity. The renormalized Si-isotope trends, scaled in this fashion, are shown in Fig. 5b. With this renormalization, it is clear that the GCE model predicts that the ratios vary in lockstep with one another during galactic evolution. This reflects that ²⁹Si and ³⁰Si are made in similar processes in supernovae. The dotted line indicates the prediction of the simple model for a pure secondary/primary ratio. The renormalized numerical trends clearly show a shallower metallicity dependence near solar metallicity than is predicted by the simple model.

An early application of the idea that isotope ratios evolve in the galaxy was proposed by Clayton (1988b) to explain the well-known ¹⁶O excess measured in CAIs in meteorites (Clayton et al., 1973; Clayton, 1993). In this model, the meteoritic data represents a “chemical memory” of interstellar dust. The interstellar dust is postulated to consist of refractory cores of Al₂O₃ mantled by more volatile O-bearing materials. Because the cores are more robust to destructive processes, they are on average older than the dust mantles. Analogous to Si, ¹⁷O/¹⁶O and ¹⁸O/¹⁶O ratios are expected to increase in the galaxy with time, since ¹⁶O is a primary isotope and the others are secondary. Thus, the older refractory dust cores are expected to be rich in ¹⁶O, relative to the bulk ISM, which is dominated by more recent stellar ejecta. If the CAIs formed from materials preferentially enriched in the refractory interstellar dust cores, their ¹⁶O-richness, compared to typical solar system materials, could be naturally explained. Current belief favors chemical processes in the early solar system to explain the CAI O-isotope data (e.g., Thiemens and Heidenreich, 1983; Clayton, 2002), but the GCE suggestion of Clayton (1988b) has never been disproved.

6.       PRESOLAR GRAINS IN METEORITES

AND GALACTIC CHEMICAL EVOLUTION

Presolar grains are micrometer-sized and smaller solid samples of stars that can be studied in the laboratory (Bernatowicz et al., 1987; Lewis et al., 1987; Zinner, 1998; Nittler, 2003; Clayton and Nittler, 2004; Meyer and Zinner, 2006) . They formed in stellar outflows more than 4.6 G.y. ago, became part of the Sun’s parent molecular cloud, survived formation of the solar system, and became trapped in asteroids and comets, samples of which now intersect Earth as meteorites and interplanetary dust. They are recognized as presolar grains by their extremely unusual isotopic compositions. These compositions reflect those of the gas from which they condensed and thus provide a great deal of information about the nuclear history of their parent stars. Two types of presolar grains are believed to provide information about GCE (in addition to information about the evolutionary processes of the individual parent stars):

SiC and oxides, mostly Al2O3 and MgAl2O4.

As discussed in the previous section, many isotopic ratios are expected to evolve in the galaxy. Because the isotopic ratios of individual presolar grains can in many cases be measured with much higher precision than element ratios can be measured in stars, these grains have the potential to provide additional constraints on GCE. Note, however, that the grains formed in disk stars, probably between ~5 and 10 G.y. ago, and thus span a narrower range of time than can be probed by astronomical observations. Moreover, their parent stars have been dead for eons and thus their properties (stellar type, mass, etc.) have to be inferred from the grain properties, primarily isotopic compositions, themselves.

values are indicated in (a).

6.1.         Galactic Chemical Evolution and

Presolar Silicon Carbide

The best-studied presolar phase in meteorites is silicon carbide (SiC). The vast majority of these grains (the “mainstream” population) is now believed to have originated in C-rich red giant stars during the AGB phase of evolution. This conclusion is supported both by the close similarity of the measured distributions of ¹²C/¹³C ratios (mainly between 20 and 100) in the grains and the stars, and by stunning agreement with models of AGB stars of the isotopic compositions of heavy elements such as Ba, Zr, and Mo, measured in individual grains by resonance ionization mass spectrometry (e.g., Lugaro et al., 2003). However, the good agreement between the grain compositions and those observed or expected for AGB stars does not extend to the 50% of the grains’ atoms that are Si! The Si-isotopic ratios, expressed as δ values, for the mainstream SiC grains are shown in Fig. 6. The grains form a linear array of slope 1.3 on this plot, with isotopic ratios ranging from ~0.95 to 1.2× solar. In AGB stars, heavy element isotopic compositions can be modified by n-capture reactions in the He-burning shell followed by convective mixing with the stellar envelope. As shown in Fig. 6a, this mixing results in Si-isotopic compositions distinct from the observed grain trend. The slope of the grain data is much steeper than predicted Si-isotopic evolution for single AGB stars [~0.3–0.8 (Lugaro et al., 1999)]. Moreover, the range of ratios is larger than that predicted for low-mass, ~solar-metallicity AGB stars (<4% shifts in ratios, compared to the observed 25% range). It is now believed that the mainstream Si array reflects a spread in the initial compositions of a large number of individual stellar sources (Alexander, 1993; Gallino et al., 1994 ; Timmes and Clayton, 1996; Alexander and Nittler, 1999).

In many presolar SiC grains, Ti is in high enough abundance to determine its isotopic composition. Titanium-isotopic measurements of mainstream SiC grains have indicated a similar behavior to that of Si. Namely, the ^46,47,49,50Ti/⁴⁸Ti ratios are correlated with the Si-isotopic ratios, forming arrays on three-isotope plots with slopes distinct from those predicted for the mixing of He-shell material with the envelopes of individual AGB stars (Ireland et al., 1991; Hoppe et al., 1994; Alexander and Nittler, 1999; Lugaro et al., 1999) . This is illustrated in Fig. 6b, showing the observed correlation between ²⁹Si/²⁸Si and ⁴⁶Ti/⁴⁸Ti [see Fig. 4 of Lugaro et al. (1999) for all Ti ratios]. Note that ⁴⁹Ti and ⁵⁰Ti are in fact more strongly affected by n-capture in AGB stars than are the Si and other Ti isotopes, so that the ⁴⁹Ti/ ⁴⁸Ti and ⁵⁰Ti/⁴⁸Ti ratios are somewhat less strongly correlated with Si-isotopic ratios in the mainstream grains.

The most obvious explanation for a spread in initial isotopic compositions of individual stars is that it reflects some sort of GCE process. As discussed in the previous section, GCE theory predicts that ²⁹Si/²⁸Si and ³⁰Si/²⁸Si ratios increase as the metallicity of the ISM does (Fig. 5). Galactic chemical evolution predictions of Ti isotopes are much less secure than those of Si due to lingering uncertainties in the nucleosynthesis processes responsible for some of them (Timmes et al., 1995). Nonetheless, ⁴⁸Ti is believed to be a primary isotope while the rarer ⁴⁶Ti, ⁴⁷Ti, ⁴⁹Ti, and ⁵⁰Ti are secondary ones, and the ⁱTi/⁴⁸Ti ratios probably increase with metallicity.

The renormalized Si- and Ti-isotope GCE predictions of Timmes et al. (1995) and Timmes and Clayton (1996) are plotted with the SiC data in Fig. 6. Clearly, GCE predicts a better fit to the grain data than does He-shell mixing in single AGB stars. A GCE interpretation of the Si and Ti data is further supported by the rare SiC subgroups known as Y and Z grains (Meyer and Zinner, 2006). Y grains (~2%) have ¹²C/¹³C ratios higher than mainstream grains and Si-isotopic compositions that plot to the right of the mainstream grains in Fig. 6a. These grains are believed to have originated in AGB stars of ~0.5 Z (Amari et al., 2001). When a component due to dredge-up of He-shell material is subtracted from their Si-isotopic compositions, they are inferred to have lower initial ²⁹Si/²⁸Si and ³⁰Si/²⁸Si ratios than mainstream grains, as expected for lower metallicity stars. Z grains have similar C isotopes to mainstream grains, but have ²⁹Si depletions and ³⁰Si enrichments, relative to mainstream grains (Hoppe et al., 1997). These grains most likely formed in AGB stars of even lower metallicity than did the Y grains, perhaps as low as 1/₃ Z (Hoppe et al., 1997; Nittler and Alexander, 2003), and their inferred initial Si-isotopic ratios are even lower than the Y grains, consistent with GCE expectations. Moreover, Ti-isotopic measurements of several Z grains indicate depletions of ⁴⁶Ti, ⁴⁷Ti, and ⁴⁹Ti, relative to solar (Amari et al., 2003; Zinner et al., 2005a), as expected if Ti-isotopic ratios decrease with decreasing metallicity.

There are significant problems with a simple homogeneous GCE interpretation of the SiC data, however, as illustrated in Fig. 6. First, the slope of the mainstream line is 1.3, steeper than the slope-1 line predicted by GCE theory. Second, most of the grains are enriched in the secondary, neutron-rich isotopes relative to the Sun, but formed in stars born earlier than the Sun. In a homogeneous GCE model that produces the Sun, older stars should have ^29,30Si/²⁸Si ratios lower than the Sun. Finally, taking the Timmes and Clayton (1996) GCE calculation at face value, the mainstream SiC data require a difference of about 5 G.y. to explain the range of Si isotopes from the bottom to the top of the mainstream. From stellar evolutionary considerations, it seems most likely that the SiC grains originated in stars at least as massive as ~1.5–2 M (Lugaro et al., 1999). Such stars have evolutionary timescales much shorter than 5 G.y., so the time difference indicated by the GCE model would indicate an exceedingly large range in interstellar residence ages of the grains themselves. This hardly seems credible, since there are many ISM processes destructive to dust grains (Jones et al., 1997), making a simple temporal interpretation of the Si data implausible. Even if a temporal interpretation is discarded, the grains still appear to have originated in donor AGB stars with higher initial metallicities than the Sun and the problem of the 1.3 slope remains. A number of attempts have been made to resolve these problems, while maintaining a GCE interpretation of the data.

Clayton and Timmes (1997) postulated that the Sun’s Siisotopic composition is strongly peculiar, compared to the mean GCE of the ISM. If so, then the slope-1 line on a Si three-isotope plot predicted by GCE theory could be rotated into a slope-1.3 line as observed for the grains, when normalized to the unusual solar isotope ratios. For this to work quantitatively requires that the Sun must lie far to the right (³⁰Si-rich) side of the initial GCE line in Fig. 6a. However, in this case dredge-up of He-shell material in the parent AGB stars would have to increase the surface ³⁰Si/²⁸Si ratio so much that the final (observed mainstream) line falls, as if by a miracle, very near the Sun’s abnormal composition. Moreover, such a large increase of ³⁰Si/²⁸Si in AGB stars is not regarded as possible, based both on the grains’ C-isotopic ratios (Alexander and Nittler, 1999) and on AGB nucleosynthesis calculations (Lugaro et al., 1999).

A second approach, proposed by Clayton (1997), invokes outward diffusion of stars from the metal-rich inner regions of the galaxy. He suggested that the SiC parent stars formed on circular orbits at smaller galactocentric radii than did the Sun and subsequently scattered from massive molecular clouds into more elongated orbits, eventually ending their lives (during their AGB phases) near the radius of solar birth. Because metallicity gradients exist in the galactic disk, these stars could have higher metallicities than the Sun, despite forming earlier. Stellar orbital diffusion models like this have been advanced to explain the large scatter in metallicity for local disk stars of the same age (Edvardsson et al., 1993; François and Matteucci, 1993; Wielen et al., 1996). A semianalytic model by Nittler and Alexander (1999), using astronomically derived parameters, indicates that such outward orbital diffusion of stars probably would not result in the observed Si-isotopic distribution of the SiC grains. Moreover, unpublished Monte Carlo calculations (D. D. Clayton, personal communication, 2004) do not indicate large-scale outward scattering of presolar AGB stars.

Alexander and Nittler (1999) took a different approach, attempting to use the grain data themselves to directly infer the relative GCE trends of the isotopic ratios. They took advantage of the fact that the different isotope ratios of Si and Ti are affected to differing degrees by n-capture in the AGB He-shell and performed a χ² fit to the mainstream SiC Si- and Ti-isotopic data. The composition of each grain was assumed to be a linear mixture of an initial composition and a He-shell composition, predicted by an AGB nucleosynthesis model (Gallino et al., 1994) . Contrary to what was claimed in their paper, this fit cannot uniquely determine the relationship between isotopic ratios and metallicity. However, it can infer the relative isotopic ratio GCE trends, i.e., the slopes of mean GCE trends on three-isotope plots. Based on their fit, Alexander and Nittler concluded that the true slope of the Si-isotope GCE trend on the Si δ- value plot is closer to 1.5 than to 1. One possibility to obtain such a slope would be that the initial mass function changes with time in the galaxy, since high-mass supernovae models produce Si with ²⁹Si/³⁰Si > solar and low-mass ones produce ²⁹Si/³⁰Si < solar (Woosley and Weaver, 1995). Alternatively, a faster evolution of ²⁹Si than ³⁰Si near solar metallicity would imply a faster evolution of ³⁰Si at low metallicities.

Thus, if there were a large source of ³⁰Si relative to ²⁹Si at low metallicity, the required steep slope on the Si three-isotope plot might be obtained. There is no hint of an “extra” source of ³⁰Si in low-metallicity supernova calculations, but other possibilities include ONe novae and low-metallicity AGB stars. Recent calculations of each of these stellar types indicate relatively large production factors of ³⁰Si and smaller or no production of ²⁹Si (Amari et al., 2001; José and Hernanz, 1998). Galactic chemical evolution calculations taking these sources into account to test this idea are still lacking.

An alternative approach was anticipated by Timmes and Clayton (1996), who showed that when the nucleosynthetic yields from supernovae are normalized to the solar-metallicity ISM composition calculated by their GCE model, heterogeneous mixing of individual supernova ejecta into an initially ~solar composition could possibly reproduce a slope 1.3 line on the Si three-isotope plot. Lugaro et al. (1999) followed up on this suggestion and explicitly modeled, using a Monte Carlo technique, the effect of inhomogeneous mixing of SN ejecta into localized regions of the ISM. They showed that with a range of model parameters, the model could easily explain the range and scatter of mainstream SiC Si-isotope ratios. They further argued that the observed distribution of SiC Si isotopes probably reflects an interplay of homogeneous GCE gradually increasing the average ISM ^29,30Si/²⁸Si ratios and heterogeneous GCE leading to local variations about the mean, although the balance between heterogeneous and homogeneous GCE in shaping the mainstream distribution would depend on the range of ages of the parent stars. An attractive feature of this model is that it can naturally account for the isotopic heaviness of the grains with respect to the Sun. However, Nittler (2005) extended this model to Ti and O isotopes and showed that it could explain neither the high degree of correlation between Si and Ti isotopes in the grains nor the range of O-isotopic compositions observed in presolar oxide grains (see next section). The observed correlation between ²⁹Si/²⁸Si and ⁴⁶Ti/⁴⁸Ti ratios in the grains allows at most ~40% of the total spread in Si-isotopic composition to be explained by this specific heterogeneous GCE model. It is also highly unlikely that any model of this sort could account for the SiTi correlations because the isotopes of these elements are made in different types and/or masses of supernovae and the isotope ratios in the ejecta of supernovae of different masses and types are hence uncorrelated. In fact, the observed Si-Ti isotope correlations indicate that the disk ISM in the vicinity of solar birth 4.6 G.y. ago was remarkably well-mixed with regard to the ejecta of individual supernovae.

Recently, Clayton (2003) suggested a radically different explanation for the mainstream SiC Si- (and Ti-) isotopic ratio distribution. In his model, the isotopic correlation lines are two-component mixing lines due to a merger of a lowmetallicity dwarf galaxy with the Milky Way disk some 6– 7 G.y. ago. At that time, Clayton postulates that the ²⁹Si/ ²⁸Si and ³⁰Si/²⁸Si ratios of the local Milky Way ISM were higher than the solar ratios and the merging galaxy had lower-than-solar ratios. The merger induced a period of star formation during which the SiC parent stars were born with a range of initial isotopic compositions due to variable mixing of the interstellar gas from the two components. Since the Sun formed in the same region of the disk, it incorporated its own mix of the two galaxies as well as the local ejecta of stars that occurred between the time of merger and that of solar birth. This model has many attractions, including explanations for the tight correlation between the mainstream SiC Si- and Ti-isotope ratios, the placement of the Sun at the bottom of the SiC mainstream, and the unusual ¹⁸O/¹⁷O ratio of the Sun, compared with the local ISM (Penzias, 1981). Moreover, mergers like that postulated are now commonly believed to be how much of the mass of the galaxy was acquired (e.g., Shetrone et al., 2003; Wyse, 2003) . However, it clearly needs much critical scrutiny by assorted scientific disciplines before it can be accepted. For example, it might be possible to find a fossil record of such a merger in the chemical compositions of nearby stars formed at that time.

We note that the rare SiC Y grains might provide some support for the galactic merger model outlined above (Clayton, 2003). The initial Si-isotopic compositions of most Y grains are inferred to lie near the lower end of the mainstream line. Moreover, there is a smooth and rapid increase in the fraction of SiC grains with high ¹²C/¹³C (a rough proxy for AGB mass) with decreasing ²⁹Si/²⁸Si ratios (Nittler and Alexander, 2003). Because more-massive stars evolve faster than less-massive ones, these results imply a more recent formation for the parent stars of grains near the bottom of the mainstream compared with those with higher ^29,30Si/²⁸Si ratios. This runs counter to the expectations for the temporal galactic evolution interpretation of the mainstream line, but is compatible with the physical mixing model, assuming that the mixing fraction of the accreting dwarf galaxy material increases with time during the merger event.

6.2.         Galactic Chemical Evolution and

Presolar Oxide Grains

Galactic chemical evolution has also been implicated in interpretations of isotope data for presolar oxide grains in meteorites, primarily corundum, Al₂O₃, and spinel, MgAl₂O₄ (e.g., Nittler et al., 1997; Choi et al., 1998; Meyer and Zinner, 2006). The O-isotopic ratios for several hundred identified presolar oxide grains are plotted in Fig. 7; most of the grains have been assigned to four groups by Nittler et al. (1997). We focus here on the Group 1 and 3 grains, since, as discussed below, these provide information about GCE. The initial O-isotopic compositions of the parent stars of the highly ¹⁸O-depleted Group 2 grains are believed to have been completely erased by nucleosynthetic processes and the origin of the ¹⁸O-rich Group 4 grains is enigmatic (Meyer and Zinner, 2006).

The majority of the presolar oxide grains are believed to have formed in low-mass red giant and AGB stars. In par-

Fig. 7. Oxygen-isotopic ratios measured in presolar oxide minerals (mostly Al₂O₃ and MgAl₂O₄) from meteorites. Ellipses indicate group definitions of Nittler et al. (1997). Arrows indicate the expected GCE of O isotopes in the ISM (solid line: ¹⁸O/¹⁷O = 5.2; dash-dot arrow: ¹⁸O/¹⁷O = 3.5). Open diamonds indicate predicted average O-isotopic compositions of presolar red giant stars of different masses, taking into account GCE, the first dredge-up, and stellar lifetimes (Nittler et al., 1997); stellar masses are indicated for some points. The good agreement between the GCE model and the Group 1 and 3 oxide grains indicates that these grains formed in red giant stars and that the ¹⁸O/¹⁷O ratio of the Sun is not atypical for its age and location in the galaxy. Data from Nittler (1997, and references therein), Choi et al. (1998), and Zinner et al. (2003).

ticular, the O-isotopic ratios of the dominant Group 1 grains are consistent both with spectroscopic observations of Orich red giants and AGB stars (Harris and Lambert, 1984) and with model calculations of nucleosynthesis and mixing processes in these stars (Boothroyd and Sackmann, 1999; Dearborn, 1992; El Eid, 1994). The ¹⁷O/¹⁶O ratios of these grains are explained by a range of masses of the parent stars, but the range of ¹⁸O/¹⁶O ratios is larger than can be explained by mixing processes in the stars themselves. Analogous to the Si isotopes in SiC grains, a range of initial ¹⁸O/ ¹⁶O ratios in the parent stars is required. As discussed in section 5, this ratio is expected to increase with time in the galaxy, so GCE is an obvious explanation for the data.

Models of O-isotopic GCE have been reported over the last decade (Timmes et al., 1995; Prantzos et al., 1996; Romano and Matteucci, 2003). Unfortunately, although the more recent models can well explain the ¹⁷O/¹⁶O ratio of both the Sun and of molecular clouds throughout the galaxy, a quantitative understanding of the GCE of the ¹⁸O/¹⁶O ratio is still lacking. For example, there are gradients with galactocentric radius in the molecular cloud ¹⁷O/¹⁶O and ¹⁸O/¹⁶O ratios, but no such gradient in the ¹⁸O/¹⁷O ratio (Penzias, 1981; Wilson and Rood, 1994). This is consistent with the expected primary(secondary) behavior of ¹⁶O(^17,18O), but the molecular cloud ¹⁸O/¹⁷O ratio is ~3.5, much lower than the solar value of 5.2. There is still no good explanation for this discrepancy, although both systematic errors in the molecular cloud observations and a local enrichment by massive supernova ejecta of the solar system’s progenitor molecular cloud have been suggested (e.g., Prantzos et al., 1996).

The secondary nature of ¹⁸O implies that presolar oxide grains with lower ¹⁸O/¹⁶O ratios originated in stars with lower metallicity than the parent stars of grains with higher ratios. However, the precise relationship between ¹⁸O/¹⁶O and metallicity is unknown. Nittler et al. (1997) presented a simple model to explain the distribution of O-isotopic ratios of Group 1 and 3 presolar oxide grains. This model predicted the average ¹⁷O/¹⁶O and ¹⁸O/¹⁶O ratios of red giant stars as a function of mass (from ~1.2 to 3 M) , such that the stars ended their life 4.6 G.y. ago. Lower-mass stars formed earlier in galactic history (since they have longer lifetimes) than higher-mass stars and hence would be expected to have lower metallicity and lower initial ¹⁸O/¹⁶O ratios. Highermass stars also are predicted to have higher ¹⁷O/¹⁶O ratios following mixing of interior material to the stellar surface during the red giant phase of evolution (“first dredge-up”). For lack of a good O-isotopic GCE trend, this model assumed that the ¹⁷O/¹⁶O and ¹⁸O/¹⁶O ratios in the ISM increase linearly with metallicity (Boothroyd and Sackmann, 1999) and that at solar metallicity the solar ¹⁸O/¹⁷O (rather than the molecular cloud one) is reproduced. Predictions of the resulting model are shown on Fig. 7; the model curve passes through the center of the distribution of both Group 1 and 3 oxide grains. This result strongly suggests that the Group 3 grains also formed in red giants and AGB stars, albeit ones with initial O-isotopic ratios lower than solar. Moreover, note that the first dredge-up in red giants can only decrease the surface ¹⁸O/¹⁷O ratio. Thus, if the typical presolar ISM had an ¹⁸O/¹⁷O ratio similar to that observed today in molecular clouds, one would expect all Group 1 and 3 presolar oxide grains to have ¹⁸O/¹⁷O < 3.5. But in fact, some 30% of the grains have ratios higher than this value. Thus the grain data imply that typical ISM ¹⁸O/¹⁷O ratios were greater in presolar times than is observed today in molecular clouds throughout the galactic disk, perhaps indicating a problem with the molecular cloud observations themselves. Alternatively, the galactic merger model proposed by Clayton (2003) to explain mainstream SiC grains (previous section) might also explain the discrepancy between ¹⁸O/¹⁷O in the present-day ISM and in the Sun.

Because low-mass stars have long evolutionary timescales and the parent stars of the presolar grains must have ended their lives prior to the formation of the Sun 4.6 G.y. ago, the grain data also can be used to constrain the age of our galaxy (Nittler and Cowsik, 1997). The age of the galaxy must be larger than the longest lifetime of a grain parent star added to that of the Sun. Nittler and Cowsik (1997) calculated a lower bound on the age of the disk as 10.5 G.y. and an actual age of 14.4 G.y. The systematic uncertainties affecting this estimate are potentially large (several gigayears), but the age agrees well with those estimated by other means and was determined in a fundamentally new way.

Since the distribution of ¹⁸O/¹⁶O ratios observed in the Group 1 and 3 presolar oxide grains is in good agreement with expectations for GCE, the metallicities of the parent stars can be estimated from grain O-isotope ratios and theoretical models. The grains can then be used to trace evolutionary histories of other isotope systems, if the relevant isotope measurements can be made on the grains. For example, Mg is another element that has both primary (²⁴Mg) and secondary (²⁵Mg, ²⁶Mg) isotopes. Both theoretical models (e.g., Timmes et al., 1995) and spectroscopic observations of main-sequence stars (e.g., Gay and Lambert, 2000) indicate that the ^25,26Mg/²⁴Mg ratios decrease with decreasing metallicity, but the stellar data have large error bars. Presolar grains often have large ²⁶Mg excesses due to in situ decay of radioactive ²⁶Al (Meyer and Zinner, 2006). Measurements of ²⁵Mg/²⁴Mg ratios in mainstream SiC grains (Huss et al., 1997) revealed no variations due to GCE or otherwise, but because Mg contents are very low in the grains, terrestrial contamination cannot be ruled out. Recently, Mg-isotopic data have been reported for a number of presolar MgAl₂O₄ grains (Nittler et al., 2003; Zinner et al., 2005b). Although the isotopic systematics of the grains are complex, the ²⁵Mg/²⁴Mg ratios suggest that the evolution of this ratio as a function of metallicity is relatively shallow near solar metallicity. This is consistent both with recent observational data (Gay and Lambert, 2000) and GCE models taking AGB star nucleosynthesis into account (Fenner et al., 2003).

Titanium-isotopic ratios have been measured in a few presolar Al₂O₃ grains as well (Choi et al., 1998; Hoppe et al., 2003). Because of low Ti concentrations, error bars for most reported measurements are large. However, a few grains have large anomalies and/or small error bars and allow a comparison with SiC Ti data. In general, the observations are consistent with the GCE interpretation of Ti isotopes in SiC (section 6.1) (Alexander and Nittler, 1999). For example, there is a general correlation between ⁴⁶Ti/⁴⁸Ti and ¹⁸O/¹⁶O as expected since both are secondary/primary isotope ratios.

7.       CONCLUDING REMARKS

It might seem audacious to attempt to use microscopic constituents of rare and unusual rocks to draw broad inferences about the vast reaches of space in time encompassed by the chemical history of the Milky Way. However, it is clear at this point that galactic evolution has left an isotopic record within meteorites, both in the fossil remnants of radioactive nuclei and in presolar grains of stardust. Our attempts to decode this record are, of course, far from complete. For example, although a signature of GCE is clearly imprinted on some isotopic ratios measured in presolar grains, the exact process or processes involved (e.g., homogeneous GCE, heterogeneous GCE, a galactic merger) have not been unambiguously identified. Full exploitation of the potential of the grains for GCE science will require both additional theoretical and observational work. For example, a presolar galactic merger in the solar neighborhood should have left some record in the chemical compositions of the stars formed at the time. Moreover, GCE models including the relevant isotopic ratios and current nucleosynthetic yields from all types of stars (including, for instance, novae and low-Z AGB stars) are sparse or lacking. There will no doubt be considerable progress in the coming decades as the sophistication of computer models increases as well as new astronomical and meteoritical data are obtained by advances in technology.

As mentioned in section 1, the solar chemical composition was long considered the “cosmic” composition, and a key question in cosmochemistry remains: Just how typical is the solar composition in the context of the galactic evolution? Based on spectroscopic determination of many elements in the atmospheres of dwarf stars in the solar neighborhood, Edvardsson et al. (1993) concluded that the Sun’s composition is quite typical for its age and location in the galaxy. Moreover, the metallicity distribution for G dwarfs in the solar neighborhood (Nordström et al., 2004) has a peak very close to the solar value ([Me/H] = 0; Fig. 2). A very important observation to be gleaned from section 6 is that the solar composition is also apparently isotopically quite typical. Most presolar SiC grains formed in stars with initial Si-isotopic compositions within ~25% of the solar value and the distribution of O isotopes in presolar oxide grains indicate that their parent stars had ¹⁸O/¹⁷O ratios closer to the solar value than to that measured today in molecular clouds. Furthermore, trace heavy elements in individual presolar grains from AGB stars (Nicolussi et al., 1997; Lugaro et al., 2003) have isotopic compositions consistent with mixing of He-shell material with envelope material of essentially solar isotopic composition. Thus, if nothing else, the meteorite data discussed in this chapter help confirm the utility of using the solar composition, about which we know so much, as a standard with which to compare the chemical makeup of the rest of the remote universe, about which we know much less.

Acknowledgments. This work benefited from many fruitful discussions with C. Alexander, D. D. Clayton, A. M. Davis, R. Gallino, T. Rauscher, B. Marty, L. Reisberg, F. Timmes, J. W. Truran, M. Wadhwa, and R. Yokochi. This chapter was improved by constructive reviews by B. Meyer and E. Zinner.

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