New Insights into the Galactic Chemical Evolution of Magnesium and Silicon Isotopes from Studies of Silicate Stardust

The Mg isotope data presented here are much more precise than those reported previously for presolar silicates (Figure 5). Ten of the 11 Group 1 grains plot on or to the right (i.e., toward a ²⁶Mg-rich composition) of the slope-1 line in an Mg-three-isotope representation (Figure 5). All but two Group 1 grains have δ²⁵Mg and δ²⁶Mg values between −20‰ and +50‰. For δ²⁵Mg, this is compatible with observations for presolar spinel grains (Zinner et al. 2005); the latter, however, have δ²⁶Mg values that extend to much higher values due to contributions from ²⁶Al decay. Five (out of 11) of the Group 1 silicate grains show enrichments in ²⁵Mg and/or ²⁶Mg of more than 2σ, which is qualitatively consistent with the averages of previously studied Group 1 silicates (δ²⁵Mg = 49 ± 12‰, δ²⁶Mg = 77 ± 16‰; Kodolányi et al. 2014) and of astronomical observations of Galactic thin disk stars with −0.2 ≤ [Fe/H] ≤ +0.2 (δ²⁵Mg = 108 ± 45‰, δ²⁶Mg = 60 ± 55‰, taken from a compilation of data in Kodolányi et al. 2014). The Mg isotope composition of presolar grains is determined by the starting composition of their parent stars, i.e., GCE, nucleosynthesis and mixing in their parent stars, and processing in the ISM and solar system. As Group 1 presolar silicates and oxides exhibit similar O-isotopic signatures, they must have been derived from stars of about the same mass (i.e., 1.2–2.2 M_⊙; Nittler 2009) and metallicity ranges. During the main-sequence phase of stellar evolution, temperatures are not high enough to change the Mg-isotopic composition of matter brought to the stellar surface during the first dredge-up. During the AGB phase of low-mass stars, however, the Mg-isotopic composition can be altered by p-capture reactions in the H-burning shell and by α-capture on ²²Ne and n-capture reactions in the He-burning shell (see discussion in Zinner et al. 2005; Kodolányi et al. 2014). Effects on Mg-isotopic compositions remain small as long as C/O < 1, i.e., when O-rich dust can form. For example, the 2 M_⊙ solar metallicity AGB star model of Zinner et al. (2005) predicts enhancements in ²⁵Mg/²⁴Mg and ²⁶Mg/²⁴Mg of less than 20‰ when C/O < 1 and if ²⁶Al decay is ignored. The latter is justified for the presolar silicates from this study as long as ²⁶Al/²⁷Al is <0.01 (see above), which is largely true for presolar oxides; even lower anomalies in ²⁵Mg/²⁴Mg of <9‰ and in ²⁶Mg/²⁴Mg of <12‰ are predicted by the 2 M_⊙ solar metallicity AGB star model of Cristallo et al. (2015). This suggests that the linear trend seen in the Mg-three-isotope plot (Figure 5) represents mostly GCE.

It has been recognized for more than 20 years that the ¹⁸O/¹⁶O ratios of presolar oxides span a wider range than can be explained by nucleosynthesis and dredge-up processes in red giant and AGB stars (Nittler et al. 1997, 2008). In fact, it was shown that a simple GCE model can explain the distribution of O-isotopic compositions of Group 1 and 3 oxides reasonably well (Nittler 2009). This model assumes an average metallicity of [Fe/H] = +0.05 for the local Galactic disk at the time of solar birth, i.e., about 12% higher than solar; an age–metallicity relationship with slope −0.02 dex Gyr^–1; and a metallicity spread of approximately 0.06–0.09 dex (1σ) for stars of a given formation time. This spread is lower than the metallicity spread of 0.2 dex inferred from astronomical observations (Holmberg et al. 2007). Oxygen-isotopic ratios are expected to increase with time, and initial ¹⁸O/¹⁶O ratios can be considered proxies for the metallicity of the parent stars. Also, according to GCE models, both ²⁵Mg/²⁴Mg and ²⁶Mg/²⁴Mg increase with metallicity in the Galaxy (Timmes et al. 1995; Kobayashi et al. 2011; Fenner et al. 2013). One would therefore expect a positive correlation between Mg-isotopic compositions and ¹⁸O/¹⁶O ratios of Group 1 silicates if the GCE interpretation is correct. It should be noted, however, that the correlation between Mg-isotopic compositions and ¹⁸O/¹⁶O does not necessarily need to be perfect due to local heterogeneities in the ISM. Such heterogeneities are responsible for, e.g., the scatter of data in the correlation between δ⁴⁶Ti and δ²⁹Si in SiC mainstream grains, which is interpreted to largely reflect GCE (see below). The existence of a possible relationship between δ²⁵Mg and ¹⁸O/¹⁶O was explored by Nittler et al. (2008) for Group 1 hibonite grains and for Group 1 spinel grains reported by Zinner et al. (2005). Nittler et al. (2008) calculated initial ¹⁸O/¹⁶O ratios of the parent stars by backtracking the evolution of O-isotopic compositions during the first dredge-up using the models of Boothroyd & Sackmann (1999). While the initial ¹⁸O/¹⁶O ratios of the spinel grains discussed by Nittler et al. (2008) span a rather large range (from 0.7 to 1.2 times solar), their δ²⁵Mg values are mostly normal; i.e., there is no correlation between these two quantities. This has been interpreted to be the result of isotope exchange for Mg, either in space or in the meteorite parent body, without erasing the O-isotope anomaly. The existence of Mg isotope anomalies in some of the spinel grains, however, shows that Mg isotope anomalies can survive interstellar or solar system processing. Of particular interest in this respect is a Group 1 spinel grain with high ²⁵Mg/²⁴Mg and low initial ¹⁸O/¹⁶O (grain M20 from Zinner et al. 2005) that most likely reflects an unusual initial composition, perhaps through a binary mass transfer process (Nittler et al. 2008). The hibonite grains discussed by Nittler et al. (2008) reveal a different picture, as there is a moderate positive correlation between δ²⁵Mg and the initial ¹⁸O/¹⁶O ratios, indicative of GCE. One outlier, grain KH14, has a low δ²⁵Mg of ∼−200‰ together with a high initial ¹⁸O/¹⁶O, which was interpreted by Nittler et al. (2008) to reflect local heterogeneities in the ISM due to incomplete mixing of supernova (SN) ejecta. Other Group 1 presolar spinel grains with similarly low ²⁵Mg/²⁴Mg ratios were later reported by Gyngard et al. (2010), suggesting that there might be a distinct population of O-rich presolar grains with δ²⁵Mg of ∼−200‰.

In Figure 7, we show δ²⁵Mg versus initial ¹⁸O/¹⁶O for the Group 1 silicate grains from this study. Initial ¹⁸O/¹⁶O ratios were calculated following the approach by Nittler et al. (2008). At first glance, there is no correlation between δ²⁵Mg and initial ¹⁸O/¹⁶O if the whole data set is considered. In Figure 7, we also show the prediction from the GCE model of Timmes et al. (1995) extended to supersolar metallicities, which was shown to give a good match for Group 1 oxide grains with high δ²⁵Mg (Nittler et al. 2008). The GCE line based on Timmes et al. (1995) in Figure 7 was inferred from predicted ¹⁸O/¹⁶O ratios at [Fe/H] = −0.3 (¹⁸O/¹⁶O = 0.56 × solar) and [Fe/H] = 0 (¹⁸O/¹⁶O = 1.26 × solar); corresponding δ²⁵Mg values are −150‰ ([Fe/H] = −0.3) and +70‰ ([Fe/H] = 0), respectively. The five Group 1 silicate grains with Mg isotope anomalies of >2σ form a linear array slightly to the left of the Timmes et al. (1995) GCE line. We will consider these grains as candidates to best represent the GCE of Mg and O and call them category A grains. The remaining six Group 1 grains are called category B grains. Two of the category B grains overlap with the trend of category A grains defined in Figure 7 and may be "hidden" category A grains. Four of the category B grains are clearly off the trend defined by category A grains and may have experienced Mg isotope exchange, either in interstellar space or in the meteorite parent bodies, as similarly proposed for the majority of presolar spinel grains (see above). High Fe concentrations in presolar silicates have been taken as evidence for secondary processing in the meteorite parent body (Floss & Haenecour 2016). It is remarkable in this respect that grain EET_10_5, the only category B grain for which Fe/Mg ratios are available, has the highest Fe/Mg ratio among the silicates of this study (Table 1). We also note that the four category B grains that are clearly off the trend of category A grains in Figure 7 tend to have higher Si/Mg ratios (0.98 ± 0.12), close to pyroxene composition, compared to category A grains (0.70 ± 0.14), whose Si/Mg ratios are closer to olivine composition. Misidentification of category B grains with true δ²⁵Mg values along the trend of category A grains in ion images acquired during Mg isotope measurements, which would have led erroneously to normal Mg-isotopic ratios, although unlikely (see Section 2), cannot be completely ruled out. For grains Kry_I_42 and MET_01B_61, however, we can definitely rule out this possibility, as expected δ²⁵Mg anomalies would have been approximately −100‰ and +200‰ (see Figure 7), which could not have been overlooked upon visual inspection of Mg isotope ratio images. Krymka is an ordinary chondrite of petrologic type 3.1; i.e., it has seen some thermal metamorphism that could have erased Mg isotope anomalies (see also the discussion on presolar spinel in Krymka in Nittler et al. 2008). Furthermore, the parent star of Kry_I_42 could have experienced CBP, which would mean that the ¹⁸O/¹⁶O ratio cannot be taken as a measure for metallicity. This view is supported by its low ¹⁸O/¹⁶O ratio of ∼0.001, which comes close to those of Group 2 grains (Figure 4). It is, however, unclear how large the effect of CBP on the Mg-isotopic composition of this grain would be. The interpretation of the inferred initial ¹⁸O/¹⁶O ratio of grain MET_01b_61 is complicated by its large error (Figure 7), and it may not be as much off the trend defined by the category A grains as it appears (the actual difference is <3σ).

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In an Mg-three-isotope representation, four of our category A grains plot along a line with slope ∼0.5 and a nonzero, slightly positive intercept (Figure 8). If we include the fifth category A grain, EET_07_25, which is off the trend defined by the other grains, then an error-weighted linear regression (least-squares fit; Bevington & Robinson 1992) gives δ²⁵Mg = (0.61 ± 0.15) × δ²⁶Mg-(4 ± 17) (Figure 8). We call this the Mg mainstream line. The 2σ upper limit on the slope is slightly lower than the slope of ∼1 predicted by GCE models at around solar metallicity (Timmes et al. 1995; Kobayashi et al. 2011; Fenner et al. 2013) but compatible with the slope of 0.85 ± 0.54 inferred by Kodolányi et al. (2014) from a compilation of Mg isotope data for Galactic thin disk stars (Tomkin & Lambert 1980; Barbuy 1985; McWilliam & Lambert 1988; Gay & Lambert 2000; Yong et al. 2003), albeit the slope of the latter has a large uncertainty. The inferred slope of ∼0.6 is largely determined by grain EET_10_29 and should therefore still be taken with care. Grain EET_10_29 has a comparatively large ¹⁸O/¹⁶O ratio, and we can safely rule out the possibility that it is an unrecognized Group 2 grain that may have larger ²⁶Mg than ²⁵Mg excesses (see discussion below for the Group 2 grain Acf_G1@1_15). Even if we would have underestimated the effect of dilution, e.g., because of choosing nonperfect grain boundaries when calculating Mg-isotopic ratios, the slope of the Mg mainstream line would change only marginally. This is because the Mg mainstream line goes, within errors, through the origin, which means that dilution shifts measured Mg-isotopic compositions largely along the Mg mainstream line to less extreme compositions. Similarly, partial Mg isotope equilibration in interstellar space or meteorite parent bodies would lead to Mg compositions along the Mg mainstream line, too. We also note that the average Mg-isotopic composition of the presolar silicates studied by Kodolányi et al. (2014), for which surrounding solar system material was sputtered away by FIB prior to the Mg isotope analyses, falls almost exactly on the Mg mainstream line inferred here (Figure 8).

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Decay of ²⁶Al could have shifted the grains' original Mg isotope composition after their formation away from the predicted slope-1 line to more ²⁶Mg-enriched compositions. However, because of low Al/Mg ratios (Table 1), ²⁶Al/²⁷Al ratios must have been exceptionally large for grains EET_07_25, EET_10_29, and NWA_3_25, which show the largest deviations from the slope-1 line, namely, 0.35 for grain EET_07_25, 0.3 for grain EET_10_29, and 0.7 for grain NWA_3_25, to bring initial Mg-isotopic compositions onto the slope-1 line. These ²⁶Al/²⁷Al ratios are about an order of magnitude higher than the highest values of previously studied Group 1 oxide grains (Zinner 2014). Other potential ways to shift Mg-isotopic ratios toward ²⁶Mg-enriched compositions include much stronger imprints of nucleosynthetic and mixing processes on Mg-isotopic compositions than predicted for low-mass AGB stars when C/O < 1 and/or Mg isotope fractionation in the ISM or solar system. An Mg isotope fractionation at a level of 10–15‰ amu^–1 (enrichment of the heavy Mg isotopes) has been observed in laboratory experiments for sputtering and vaporization of pure Mg and olivine, respectively (Arai et al. 1979; Wang et al. 1999). Evaporation and recondensation were also found to have caused mass-dependent isotopic shifts in calcium–aluminum-rich inclusions up to tens of ‰ in δ²⁶Mg (e.g., Wasserburg et al. 1977). However, none of the above fractionations seems sufficient to account for the deviation of grains EET_07_25, NWA_3_25, and especially EET_10_29 from the slope-1 line. For example, EET_10_29 would require about a −100 ‰ offset in its δ²⁵Mg and about a −200‰ offset in its δ²⁶Mg to lie on a slope-1 line in Figure 8. An argument against significant evaporation-related kinetic fractionation of our category A grains' Mg isotopes is the lack of such isotopic effects in their O and Si isotope systems (Figures 4 and 6). Thus, local heterogeneities in Mg-isotopic compositions in the ISM due to incomplete mixing of SN ejecta may be the best explanation to account for most of the observed scatter in Mg-isotopic compositions around the Mg mainstream line. We point out that the observed scatter of category A grains around the Mg mainstream line is smaller than the scatter around the δ⁴⁶Ti versus δ²⁹Si trend in SiC mainstream grains, believed to largely represent GCE (e.g., Nittler 2005; see also Section 4.2).

As can be seen from the Si-three-isotope representation in Figure 6, most of the Si isotope data reported here are more precise than those obtained previously. The Group 1 presolar silicate grains from this study plot close to the SiC Si mainstream line, with δ²⁹Si values between −10‰ and +200‰ and δ³⁰Si values from −20‰ to +160‰. The five category B grains for which Si isotope data exist have solar Si-isotopic compositions within 2σ uncertainties (Table 2, Figure 9), which for some of them, as concluded for Mg, may be the result of isotope exchange, either in interstellar space or in the meteorite parent bodies. For the five category A grains, a best-fit line gives δ²⁹Si = (1.14 ± 0.12) × δ³⁰Si + (13 ± 12) (Figure 9); i.e., it is shallower than the SiC Si mainstream line but with a significance of only ∼2σ. The significance would be larger if the two category B grains, which might be "hidden" category A grains (see Section 4.1), would be considered. It should be noted that the slope of the SiC Si mainstream line was inferred from the Si isotope data of thousands of SiC grains, with many individual grains lying off the line. Consequently, when sampling only a few grains, as for the population of category A silicate grains presented here, the inferred slopes would be affected by individual outliers much more than for much larger data sets. Similarly, this also holds for the Mg mainstream line inferred here (see Section 4.1).

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The interpretation that the SiC Si mainstream line is dominated by GCE is undisputed (Zinner 2014). The close similarity of the SiC Si mainstream line with our best-fit line for Group 1 silicates from category A gives already strong arguments for the GCE interpretation of the latter. The small analytical errors of Si-isotopic compositions of Group 1 silicates from this study offer in principle the possibility to resolve small differences between Si correlation lines inferred for SiC mainstream grains and Group 1 silicates, e.g., due to higher contributions of s-processed matter in SiC grains (see below).

As for Mg, one would expect to find a positive correlation between δ²⁹Si and initial ¹⁸O/¹⁶O ratios for the parent stars of category A grains if these quantities represent GCE. Indeed, there is a correlation between δ²⁹Si and initial ¹⁸O/¹⁶O, as can be seen from Figure 10. The observed trend is a bit shallower than predicted by the GCE model of Timmes & Clayton (1996), which was inferred and extended to higher metallicities from predicted ¹⁸O/¹⁶O ratios at [Fe/H] = −0.3 (¹⁸O/¹⁶O = 0.56 × solar) and [Fe/H] = 0 (¹⁸O/¹⁶O = 1.26 × solar); corresponding δ²⁹Si values are −500‰ ([Fe/H] = −0.3) and +260‰ ([Fe/H] = 0), respectively. It is interesting to note that astronomical observations of a variety of sources have not detected a variation in Si isotope ratios with galactocentric radius, which stands in contrast to the monotonically decreasing trend for the ¹⁸O/¹⁶O ratio (Monson et al. 2017) and our observations for category A grains. Following the approach of Nguyen et al. (2010), we have inferred a GCE relationship between δ²⁹Si and initial ¹⁸O/¹⁶O, which is based on a tight correlation between ²⁹Si/²⁸Si and ⁴⁶Ti/⁴⁸Ti ratios in SiC mainstream grains (Figure 11, left; data from Hoppe et al. 1994; Alexander & Nittler 1999; Huss & Smith 2007) and a correlation between ⁴⁶Ti/⁴⁸Ti and initial ¹⁸O/¹⁶O ratios in presolar oxide grains (Figure 11, right; data from Choi et al. 1998; Hoppe et al. 2003), interpreted to represent largely GCE. Error-weighted linear regressions yield δ⁴⁶Ti = (0.98 ± 0.08) × δ²⁹Si-(11 ± 7) for SiC mainstream grains and ${\delta }^{46}\mathrm{Ti}=(570\pm 80)\times {}^{18}{\rm{O}}{/}^{16}{{\rm{O}}}_{\mathrm{ini}}/\mathrm{solar}-(530\pm 80)$ for Group 1 oxides. Combining the two equations gives ${\delta }^{29}\mathrm{Si}=(580\pm 90)\times {}^{18}{\rm{O}}{/}^{16}{{\rm{O}}}_{\mathrm{ini}}/\mathrm{solar}-(530\pm 90)$, which is labeled as "SiC-Oxides GCE" in Figure 10. Note that this equation is different from the one presented by Nguyen et al. (2010), which was recognized to be in error (L. Nittler 2018, private communication). Gyngard et al. (2018) recently reported a slightly shallower slope for the δ⁴⁶Ti versus δ²⁹Si of SiC mainstream grains than inferred here, which would make the δ⁴⁶Ti versus ${}^{18}{\rm{O}}{/}^{16}{{\rm{O}}}_{\mathrm{ini}}/\mathrm{solar}$ relationship a bit steeper. Our data for category A grains fall to the right of the SiC-Oxides GCE line but are fully compatible with this line if errors for the SiC-Oxides GCE line are taken into account (Figure 10). Finally, the good correlation between δ²⁵Mg and δ²⁹Si (Figure 12) rounds out the picture emerging from presolar silicate category A grains, suggesting that a subset of presolar Group 1 silicates carries resolvable signatures of the GCE of O, Mg, and Si isotopes.

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Three of the category A grains plot directly onto the SiC Si mainstream line. One category A grain plots to the left of the Si mainstream line but with Si-isotopic compositions compatible with this line when analytical uncertainties are considered, while grain EET_07_25 is significantly off to the ³⁰Si-poor (or ²⁹Si-rich) side (Figure 9). Silicon carbide can form around low- and intermediate-mass AGB stars when C/O > 1 (Lodders & Fegley 1995). In this phase of stellar evolution, material that experienced the s-process (slow neutron-capture reactions) is brought in large amounts to the stellar surface in the third dredge-up. This affects not only the isotopic compositions of typical s-process elements (e.g., Sr, Mo, and Ba) but also of Si-isotopic compositions to some extent. Models of 2 M_⊙ AGB stars of solar metallicity predict enrichments in ²⁹Si of up to 16‰ and in ³⁰Si of up to 37‰ when C/O > 1 compared to the Si composition at stellar birth (Zinner et al. 2006; Cristallo et al. 2015). In contrast, Group 1 silicates must have formed around their parent stars when C/O < 1. In this phase of stellar evolution, fingerprints of the s-process from the third dredge-up are less pronounced, and the models referenced above predict enrichments in ²⁹Si of <4‰ and ³⁰Si of <9‰, i.e., smaller than the analytical errors of our Si isotope data (Table 2). The Si-isotopic composition of silicates can thus be expected to be more representative than that of SiC for the starting composition of Si in the grains' parent stars and a better proxy for the GCE of the Si isotopes. In this context, the shift of grain EET_07_25 relative to the SiC Si mainstream line to a ³⁰Si-poorer composition by ∼40‰ is qualitatively consistent with expectations for the third dredge-up in AGB stars. The fact that grain EET_10_29, which has the highest δ²⁹Si and inferred parent star metallicity among our category A grains, plots directly onto the SiC Si mainstream line (Figure 9) suggests that SiC mainstream grains with high δ^29,30Si formed around AGB stars that had less s-process enrichment in their surface regions than the parent stars of SiC mainstream grains with low δ^29,30Si (and, consequently, lower metallicity). This is in agreement with AGB star models that predict higher temperatures in the He shell (which enhance the efficiency of heavy Si isotope production by the s-process) and more extensive dredge-up of s-process matter (where ³⁰Si is enriched relative to ²⁹Si) in AGB stars of lower metallicities and/or higher masses (Zinner et al. 2006). This led to the proposed origin of the rare SiC Y and Z grains, which have low δ²⁹Si values and ³⁰Si-enriched compositions, in low-metallicity AGB stars (Hoppe et al. 1997; Amari et al. 2001; Nittler & Alexander 2003). From a study of C- and Si-isotopic compositions of more than 3000 presolar SiC mainstream, Y, and Z grains, Nittler & Alexander (2003) argued that the maximum mass of AGB parent stars must increase sharply with decreasing metallicity, also consistent with our inferences from the silicate data presented here.

The Group 2 grain from this study (grain Acf_G1@1_15) has dilution-corrected O-isotopic ratios of ¹⁷O/¹⁶O = 9.5 × 10⁻⁴ and ¹⁸O/¹⁶O = 4.9 × 10⁻⁴ (Figure 4). It exhibits strong enrichments in ²⁵Mg and ²⁶Mg of about 180‰ and 220‰, respectively, and plots slightly above the Mg mainstream line (Figure 8). In the context of the proposed origin of Group 2 grains from intermediate-mass AGB stars that experienced HBB (Lugaro et al. 2017), the O-isotope data of grain Acf_G1@1_15 are compatible with the predictions for a 6 M_⊙ AGB star and 35% dilution with matter of solar composition. The HBB is expected to lead to large ²⁵Mg and ²⁶Mg enrichments by factors of a few (Karakas & Lattanzio 2003), much larger than observed here, even with consideration of dilution. As discussed by Lugaro et al. (2017) for presolar oxide grains, this can be explained either by partial equilibration of Mg isotopes in the grains or by model deficiencies. Enrichments in ²⁶Mg are predicted to be equal to or larger than those of ²⁵Mg. For example, for a 6 M_⊙ AGB star of solar metallicity that experienced HBB, δ²⁵Mg/δ²⁶Mg will be 0.96 (Karakas & Lattanzio 2003); i.e., mixing this composition with matter of solar composition would produce a mixing line in an Mg-three-isotope representation that passes slightly above the Mg-isotopic composition of grain Acf_G1@1_15 (Figure 8).