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Can Galactic chemical evolution explain the oxygen isotopic variations in the Solar System?

A number of objects in primitive meteorites have oxygen isotopic compositions that place them on a distinct, mass-independent fractionation line with a slope of one on a three-isotope plot. The most popular model for describing how this fractionation arose assumes that CO self-shielding produced 16O-rich CO and 16O-poor H2O, where the H2O subsequently combined with interstellar dust to form relatively 16O-poor solids within the Solar Nebula. Another model for creating the different reservoirs of 16O-rich gas and 16O-poor solids suggests that these reservoirs were produced by Galactic chemical evolution (GCE) if the Solar System dust component was somewhat younger than the gas component and both components were lying on the line of slope one in the O three-isotope plot. We argue that GCE is not the cause of mass-independent fractionation of the oxygen isotopes in the Solar System. The GCE scenario is in contradiction with observations of the 18O/17O ratios in nearby molecular clouds and young stellar objects. It is very unlikely for GCE to produce a line of slope one when considering the effect of incomplete mixing of stellar ejecta in the interstellar medium. Furthermore, the assumption that the Solar System dust was younger than the gas requires unusual timescales or the existence of an important stardust component that is not theoretically expected to occur nor has been identified to date.

observations of the 18 O/ 17 O ratios in nearby molecular clouds and young stellar objects. It is very unlikely for GCE to produce a line of slope one when considering the effect of incomplete mixing of stellar ejecta in the interstellar medium. Furthermore, the assumption that the Solar System dust was younger than the gas requires unusual timescales or the existence of an important stardust component that is not theoretically expected to occur nor has been identified to date.

Introduction
Oxygen is produced by stellar nucleosynthesis and is the third most abundant element in the Solar System after hydrogen and helium, which were produced during the Big Bang.
The chemical abundance of O in the precursor molecular cloud (MC) of the Sun was built up by the generations of stars that predated the birth of the Sun. This contribution can be calculated using Galactic chemical evolution (GCE) models, which can also be tested against spectroscopic observations of O in interstellar clouds and stars of different metallicities. The solar O abundance agrees with that observed in the solar neighborhood (see Sec. 4.2 of Asplund et al. 2009 and references therein), particularly so when allowing the Sun to have migrated from an original birth location 2-3 kpc closer to the Galactic centre (Nieva & Przybilla 2012). Most of the O in the Universe is in the form of 16 O (99.8% in the Solar System), an extremely stable isotope with double magic number of both protons and neutrons (Z=N=8). This nucleus is produced by α captures during He and Ne burning in massive ( >10 M ʘ ) stars. These stars end their lives as core-collapse supernovae (SNII) and are responsible for the production of the "α elements", i.e., intermediate-mass elements comprised mostly by nuclei with an integer number of α particles, e.g., 16 O,20 Ne,24 Mg,and 28 Si. These nuclei are produced directly from the initial H and He present in the star and are independent on the initial stellar metallicity, i.e., they are a result of "primary" nucleosynthesis.
The minor isotopes of O, 17 O and 18 O, have much lower abundances than 16 O, representing 0.04% and 0.2% of Solar System O, respectively. As outlined in detail by Meyer et al. (2008), 18 O is predominantly a product of He burning in massive stars via the 14 N(α,γ) 18 F(β + ) 18 O reaction chain, while 17 O is a product of H burning via the 16 O(p,γ) 17 F(β + ) 17 O reaction chain in low-and intermediate-mass stars (<10 M ʘ ) as well as nova outbursts due to the accretion of material onto a white dwarf from a stellar companion in a binary system. These nuclei cannot be produced directly from the initial H and He present in the star and their production depends on the stellar metallicity, i.e., they are a result of "secondary" nucleosynthesis. The 17 O/ 16 O and 18 O/ 16 O ratios can be observed around cool red giant stars and in MCs and young stellar objects (YSOs) using vibration-rotation bands of the different isotopologues of the CO molecules. Oxygen is also a major constituent of dust, where a large number of meteoritic stardust grains are oxides and silicates (e.g., Nittler et al. 1997, Mostefaoui & Hoppe 2004, Nguyen et al 2010. These are analyzed for their O isotopic compositions via mass spectrometry to high precision and show large isotopic anomalies up to orders of magnitude with respect to the bulk of the Solar System. These data can be used to study stellar nucleosynthesis and GCE (e.g., Nittler 2009).
In the Solar System, the relative abundances of the stable oxygen isotopes have been measured to high precision in a large number of different materials (see Fig. 1, Fig. 4 (Young et al. 2002). In contrast, the major components of primitive chondrites -such as calcium-aluminum rich inclusions (CAIs), chondrules, amoeboid olivine aggregates (AOAs), and fine-grained matrices -plot along the slope-1 line (S1L) that connects the Earth and the Sun compositions ( Fig. 1; Clayton et al. 1973;Young & Russell 1998). CAIs and AOAs are more 16 O-rich than fine-grained matrices and chondrules (Yurimoto et al. 2008 System. We will call stardust the meteoritic dust mentioned above that shows large isotopic anomalies up to orders of magnitude with respect to the bulk of the Solar System material. Stardust is believed to have formed in stellar envelopes and ejecta and to have preserved its original composition until today. As such, it carries the signature of nucleosynthesis, mixing, and condensation in stars (Clayton & Nittler 2004). Stardust of size from 20 µm down to ~ 100 nm has been discovered in the matrix of primitive meteorites. Stardust has low abundances, of the order of several to several hundred ppm.
It is not yet known if stardust of smaller size is more abundant. Based on detailed models of the evolution of dust in the Galaxy, Zhukovska et al. (2008)  involving interaction with gas and other dust -in the case of fragmentation, exchange, etc.

Hypotheses for the S1L
The first interpretation following the discovery of 16 O-rich minerals in meteorites was that these materials contained the direct signature of nucleosynthetic events that rendered them "exotic", i.e., different from the bulk of the Solar Nebula (Clayton et al. 1973).
Such an explanation could hold if the compositions of the Sun and Earth were close, instead, the Genesis mission revealed that the Sun is ~6% more 16 O-rich than the Earth.
While the meteoritic materials discovered by Clayton et al. (1973) lie on a line of slope ~0.95, which indicate an anomaly to be present also in the 17 O/ 18 O ratio requiring a nuclear effect, Young & Russell (1998) (2) the GCE evolution of the 18 O/ 17 O ratio is constant, matching the slope of the S1L. The aim of this paper is to analyze in detail these two requirements in relation to current GCE models and observations to determine if the S1L can be explained using GCE. We note that some of the points considered below are also discussed by Nittler & Gaidos (2012).

Models and observation of the 18 O/ 17 O ratio
The simple GCE considerations outlined above for the O isotopes indicate that, in principle, the assumption that the GCE evolution of the 18 O/ 17 O ratio is constant may be correct. In fact, early GCE models (e.g., Timmes et al. 1995 As an example, Figure 2 shows the most recent calculations of the GCE evolution of the O isotopic ratios .  Romano & Matteucci 2003). GCE models have many uncertainties, e.g., stellar yields, the star formation rate, the initial mass function, etc. Traditionally, a GCE model is considered successful when it matches the solar isotopic abundances within a factor of two (e.g., Fig. 3 of Timmes et al. 1995). In our context, this means that the GCE line shown in Figure 2 should not be considered as a final accurate solution, but rather as an illustrative example that we should not expect GCE models to produce the S1L in the O three-isotope plot. If we follow the common approach of renormalizing the GCE model so that the ratios predicted at solar metallicity are scaled to the terrestrial values, we find that the slope of the predicted GCE line is still different from unity, specifically, it is equal to 1.065 if we consider all the points along the GCE curve in Fig. 2 (Young et al. 2010). This is in contradiction with the GCE interpretation of the S1L, which assumes that GCE passes through the solar composition. but is due to SNII pollution, is also in contradiction with the GCE interpretation of the S1L, as in this case GCE does not even pass through the solar O composition.

The effect of incomplete mixing of stellar ejecta in the ISM
When discussing small isotopic variations due to GCE the effect of incomplete mixing of stellar ejecta on the composition of the ISM needs to be considered. Lugaro et al. (1999) and Nittler (2005)  of the ejecta to a = 5.5 x 10 -6 M ʘ -1 , i.e., the ejecta from each star are diluted with an IMS mass of ~ 1.8 x 10 5 M ʘ . The resulting variations in the Si and Ti isotopic compositions are ~ 5-10%. This is insignificant when compared to the overall GCE effect, but of great impact when considering the same-order spread in the Si and Ti isotopic compositions resulting from high-precision measurements of stardust grains (Lugaro et al. 1999, Nittler 2005) and, in our context, the 6% variations of O isotopic ratios in the Solar System.
We have used the same model of Lugaro et al. (1999), with the values of the free parameters reported above that match the stardust data, to analyze the impact of incomplete mixing of stellar ejecta on the GCE evolution of the O isotopes. We used SNII yields for stars in the mass range 11 < M/ M ʘ < 40 from  and supernovae of Type Ia yields (SNIa, resulting from the thermonuclear explosion of C-O white dwarves) from Thielemann et al. (1986). We scaled 17 O from SNII by 0.12 as suggested by Nittler (2005)  We note that more sophisticated GCE models are currently being developed, which also include hydrodynamics and feedback effects (e.g., Kobayashi & Nakasato 2011, Pilkington et al. 2012. These more detailed models perform better at matching the large intrinsic spread in the age-metallicity relation observed in the solar neighbourhood (e.g., Holmberg et al. 2007). Future chemodynamical models of the O isotopic evolution in the Galaxy may predict an even larger spread of values at any given time than that obtained only considering incomplete mixing of stellar ejecta.

The GCE timescale of the O isotopic evolution
The main other requirement for the GCE scenario to explain the S1L is that the dust component of the Solar System is somewhat younger than the gas component. The timescale at which GCE progresses is relatively long, of the order of the age of the Galaxy. One would expect that to modify the O isotopic composition by only 6% at around the time of the formation of the Sun requires a considerable amount of GCE time.
The order of magnitude of this timescale can be obtained by translating the required change in [Fe/H] to the elapsed time using, e.g., Fig. 12 and Fig. 7 of Timmes et al (1995) or Fig. 17 and Fig. 11b of . We derive a timescale of the order of 1 Gyr, which means that in order to explain the solar system systematics the dust component in the Solar System should have formed from stellar ejecta roughly 1 Gyr after the ejecta that contributed to the gas component. We note that this assumes that the Since the GCE timescale is longer than both the timescale required for the ISM to be well mixed (~10 8 yr, de Avillez & Mac Low 2002) and the timescale for dust formation in the ISM (~10 6 -10 7 yr, Zhukovska et al. 2008) the expectation is that MC dust should have the same composition as the MC gas. It follows that for the GCE scenario to work it is required that the signature of more recent stellar ejecta is kept somehow separated from the ~ 1 Gyr older gas in MCs. The segregation has to hold until the Solar System forms when dust and gas can mix together to produce the S1L. It is not clear how this segregation could occur for MC dust.
A possible solution is that the dust component of the Sun was dominated by stardust delivered to the ISM by younger stellar ejecta (Meyer 2009). The composition of this stardust will have to carry the signature of GCE and average to δ 17 O ~ δ 18 O >> 0.
However, O is strongly affected by stellar nucleosynthesis and it follows that the average composition of stardust is expected to (1) carry a much stronger signature of stellar nucleosynthesis than of GCE and (2) be determined by the rate of dust production -also in terms of different sizes -in different stellar objects. Within the collection of stardust currently available, probably sampling the most common and largest size stardust, the vast majority of it shows the signature of an origin in AGB stars, which are also well known to be the predominant contributors to stardust in the Galaxy (Gehrz 1989).
Accordingly  Nittler et al. 1997Nittler et al. , 2008 show large 17 O and 18 O enrichments, and these are explained as the signature of an origin in core-collapse supernovae rather than the imprint of GCE. Finally, the GCE ~1 Gyr timescale is of the same order as the survival time of dust in the ISM (Jones et al. 1996, Gyngard et al. 2009 and one would expect stardust and MC dust present at the time of the formation of the Sun to have ages ~ 1 Gyr older than the gas.

Discussion and conclusions
We have analyzed in detail the basic assumptions of the GCE interpretation of the S1L against current GCE models and observations. The requirement that the 18 O/ 17 O ratio should evolve as a constant is found to be unlikely on the basis of the most recent GCE models and when considering the effect of incomplete mixing of stellar ejecta. A strict correlation has been observed in carbonaceous chondrites (CC) between variations in ε 54 Cr, i.e., the 54 Cr/ 52 Cr ratio with respect to the solar value per ten thousand, and in Δ 17 O = δ 17 O -0.52 δ 18 O, i.e., the distance from the TFL, unaffected by massdependent fractionation (Shukolyukov & Lugmair 2006, Trinquier et al. 2007, Yin et al. 2009 Enrichments in the CC matrix fractions both of Mo isotopes due to the slow neutron capture (s) process in AGB stars (Dauphas et al. 2002) and of 54 Cr, which can also be produced by the s process in AGB stars ( 54 Cr/ 52 Cr ratios up to +20% higher than solar, Lugaro et al. 2004) argue for such common source for these isotopes. As discussed above, AGB stardust carries the signature of 17 O enhancements. Another option is that these correlations may simply reflect the amount of CAI material in the bulk meteorites, with CAIs carrying the anomalies in O and Cr.
In conclusion, for the GCE model to be viable one would need to (1)  Both possibilities seem unlikely at the present. Even assuming one of them is correct, there would still be the issue that incomplete mixing of stellar ejecta results mostly in compositions that do not lie on the S1L. Due to all these problems, we rule out GCE as a likely explanation for the S1L. More effort should be put into providing a working model based on PSS.