EVIDENCE FOR MAGNESIUM ISOTOPE HETEROGENEITY IN THE SOLAR PROTOPLANETARY DISK

The presence and initial abundances of short-lived radionuclides (e.g., ²⁶Al, ⁴¹Ca, ⁵³Mn, ⁶⁰Fe, ¹⁸²Hf) in the solar system are widely used to understand the timescales of processes in the early solar system and to deduce the astrophysical environment where our Sun formed (McKeegan & Davis 2003; Goswami 2004). These radionuclides are believed to have a nucleosynthetic, stellar origin and have been either inherited from the interstellar medium or injected into the protosolar molecular cloud prior to or contemporaneously with its collapse (Sahijpal & Goswami 1998). If ²⁶Al that decays to ²⁶Mg with a half-life of 0.73 Myr was uniformly distributed in the solar system, it potentially provides a precise relative chronometer for early solar system processes (e.g., Lee et al. 1977; Russell et al. 1996; Galy et al. 2000; Bizzarro et al. 2004).

Uniform distribution of ²⁶Al in the solar system with the so-called canonical initial ²⁶Al/²⁷Al ratio of (5.23 ± 0.13) × 10⁻⁵ (Jacobsen et al. 2008) has been inferred from Mg-isotope measurements of primitive meteorites and their components (Thrane et al. 2006; Villeneuve et al. 2009), and from the concordancy between ²⁶Al–²⁶Mg and ²⁰⁷Pb–²⁰⁶Pb ages obtained on the same chondritic components, namely calcium–aluminium-rich inclusions (CAIs) and chondrules (Amelin et al. 2002; Connelly et al. 2008a). However, the resolution required to unequivocally rule out ²⁶Al heterogeneity has been unattainable by state-of-the-art Mg-isotope measurements. For example, accepting the initial ²⁶Al/²⁷Al ratio [(²⁶Al/²⁷Al)₀] of 5.23 × 10⁻⁵ (Jacobsen et al. 2008), the amount of radiogenic ²⁶Mg resulting from the in situ decay of ²⁶Al [μ²⁶Mg* = ((²⁶Mg/²⁴Mg)_sample/(²⁶Mg/²⁴Mg)_standard − 1) × 10⁶] in a reservoir with solar ²⁷Al/²⁴Mg ratio of 0.101 is only 38 ppm (Figure 1(a)). As a result, an uncertainty of ±10 ppm in measurements of the μ²⁶Mg* value in samples of meteorites with an approximately solar ²⁷Al/²⁴Mg ratio could conceal a heterogeneity of up to 50% in (²⁶Al/²⁷Al)₀ (Figure 1(a)). Moreover, the recent discovery of variable U-isotope compositions of early solar system solids (Brennecka et al. 2010) clouds the accuracy of ²⁰⁷Pb–²⁰⁶Pb ages used to infer consistency with the ²⁶Al–²⁶Mg chronometer.

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To understand the degree of ²⁶Al homogeneity in the solar protoplanetary disk, we have developed analytical protocols allowing the measurements of the μ²⁶Mg* value and ²⁷Al/²⁴Mg ratios in meteorites by high-resolution multi-collector inductively coupled plasma source mass spectrometry (HR-MC-ICPMS) with an external reproducibility of 2.5 ppm and 0.5%, respectively (Bizzarro et al. 2011; Paton et al. 2011). Using these techniques, we report bulk Mg-isotope and ²⁷Al/²⁴Mg ratio measurements of a representative suite of inner solar system objects, including CAIs and amoeboid olivine aggregates (AOAs) from the reduced CV (Vigarano type) chondrite Efremovka as well as a number of primitive and differentiated meteorites.

The mineralogy, petrology, and oxygen isotopic compositions of CAIs and AOAs from primitive chondrites suggest a close genetic relationship between these objects. CAIs are formed by evaporation, condensation, and, in some cases, subsequent melting of refractory dust (MacPherson 2003). The CAI-forming processes occurred in an ¹⁶O-rich ($\Delta ^{17}{\rm O} \sim -25\permil$) region with high ambient temperature, at or above the condensation temperature of forsterite (∼1300 K; Krot et al. 2009). AOAs are aggregational objects composed of ¹⁶O-rich ($\Delta ^{17}{\rm O} \sim -25\permil$) forsterite condensates and CAIs; they have avoided significant melting (MacPherson et al. 2005). The temperatures inferred for the formation region of CAIs and AOAs are expected to have been reached in the innermost part of the protoplanetary disk during the initial stages of the solar system formation (Tscharnuter et al. 2009; Ciesla 2010). Thus, CAIs and AOAs can be used collectively to define the initial ²⁶Al/²⁷Al ratio and initial Mg-isotope composition (μ²⁶Mg₀) in this region of the protoplanetary disk.

Bulk analyses of four AOAs (E1s, E2s, E3s, E4s) and four CAIs of different types (one fine-grained spinel-rich (22E), one Type B (E48), and two Type As (E104, 31E)) from the Efremovka CV chondrite define a line with a slope of (5.252 ± 0.019) × 10⁻⁵ and initial μ²⁶Mg₀ value of −15.9 ± 1.4 ppm (Figures 1(b) and (c)). We also analyzed AOA material mantling the E48 and E104 inclusions (i.e., forsterite-rich accretionary rims; Krot et al. 2002). The physical relationship between forsterite-rich accretionary rims and CAIs and their identical ¹⁶O-rich compositions indicate that both types of objects are formed in the same reservoir. The E48 and E104 forsterite-rich accretionary rims plot on the bulk CAI–AOA isochron (Figure 1(c)) thereby confirming the contemporaneous formation of these AOAs and CAIs and, therefore, the validity of collectively using these objects to define the initial ²⁶Al/²⁷Al ratio and μ²⁶Mg₀ value of the CAI- and AOA-forming region. We interpret the bulk CAI–AOA line as an ²⁶Al–²⁶Mg isochron corresponding to the timing of Al/Mg fractionation prior to and/or during formation of the Efremovka CAIs and AOAs by evaporation, condensation, and evaporative melting. The error on the slope of this isochron corresponds to an age uncertainty of ∼4000 years, suggesting a very short duration of these fractionation events. We interpret the intercept of this isochron (μ²⁶Mg₀) as representing the initial Mg-isotope composition of the solar system. The slope of the ²⁶Al–²⁶Mg isochron is in agreement with the canonical ²⁶Al/²⁷Al ratio of (5.23 ± 0.13) × 10⁻⁵ inferred from bulk measurements of CAIs from the oxidized CV chondrite Allende (Jacobsen et al. 2008). The initial μ²⁶Mg₀ value of −15.9 ± 1.4 ppm inferred from the Efremovka CAI–AOA isochron is significantly different from the value of −38 ppm predicted for a uniform distribution of ²⁶Al in the solar system (Figure 1).

The μ²⁶Mg* value of the Efremovka CAI–AOA isochron at a solar ²⁷Al/²⁴Mg ratio of 0.101 is 22.2 ± 1.4 ppm. If the μ²⁶Mg₀ and (²⁶Al/²⁷Al)₀ inferred from the CV CAIs and AOAs are representative of the entire solar system, then solar system materials preserving the solar ²⁷Al/²⁴Mg ratio are predicted to have an identical μ²⁶Mg* value of ∼22 ppm. To test this prediction, we measured the bulk Mg-isotope compositions of three CI (Ivuna type) carbonaceous chondrites (Alais, Ivuna, and Orgueil), which are considered to be the most chemically pristine solar system materials: they have solar abundances of most elements as well as solar ²⁷Al/²⁴Mg ratio (Asplund et al. 2009). The bulk Mg-isotope compositions of CI chondrites have an average μ²⁶Mg* value of 4.5 ± 1.0 ppm, which is significantly lower than the μ²⁶Mg* value of 22.2 ± 1.4 ppm defined by the Efremovka CAI–AOA isochron at a solar ²⁷Al/²⁴Mg ratio (Figure 1(c)).

We also measured bulk Mg-isotope compositions and ²⁷Al/²⁴Mg ratios of one enstatite chondrite, four ordinary chondrites, one R-chondrite, one acapulcoite, two angrites, two ureilites, and one Martian shergottite. The meteorite samples from differentiated asteroids analyzed here are believed to have formed >5 Myr after solar system formation (Amelin 2005, 2007; Goodrich et al. 2010). Thus, the bulk Mg-isotope compositions of these meteorites are not significantly affected by Al/Mg fractionation event(s) associated with their formation. None of the whole-rock Mg-isotope analyses of these meteorites approach the μ²⁶Mg* value of 22 ppm predicted by the CV CAI–AOA isochron and uniform distribution of ²⁶Al and μ²⁶Mg₀. Instead, these record μ²⁶Mg* values that are lower by 4–12 ppm compared to CI chondrites (Figure 2(a)).

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It is possible that the elevated μ²⁶Mg* value of 22.2 ± 1.4 ppm at the solar ²⁷Al/²⁴Mg ratio defined by the CAI–AOA regression reflects a pre-history of elevated ²⁷Al/²⁴Mg ratio for the CAI- and AOA-forming reservoir as a whole. Although evaporation and condensation processes can fractionate Al from Mg, the mineralogy and bulk chemistry of CAIs and AOAs are consistent with formation in a region with approximately solar composition (Grossman et al. 2000). Even allowing for a 15% increase in the ²⁷Al/²⁴Mg ratio of the CAI-forming region relative to the solar value requires timescales in the order of 1.5 Myr to produce the offset of 22.2 ± 1.4 ppm in CAIs and AOAs. Such an extended pre-history of the CAI- and AOA-forming reservoir is absent from the meteorite record and is inconsistent with the brief interval of ∼4000 years for the formation of these objects. Likewise, the observed variations in μ²⁶Mg* values of chondritic meteorites cannot be uniquely explained by Al/Mg fractionation events. For example, R and CI chondrites have nearly identical ²⁷Al/²⁴Mg ratios (Table 1), yet their μ²⁶Mg* values are different by 5.9 ± 2.6 ppm. Similarly, only 2.6 ppm of the observed 8.6 ± 1.4 ppm difference between the average μ²⁶Mg* values of the CI and ordinary chondrites could be attributed to Al/Mg fractionation given the difference in their ²⁷Al/²⁴Mg ratios. Thus, we rule out a pre-history of elevated ²⁷Al/²⁴Mg in the CAI–AOA-forming reservoir and Al/Mg fractionation events to account for the μ²⁶Mg* heterogeneity.

Table 1. Mg and ⁵⁴Cr Isotope Composition of Inner Solar System Materials

Sample	Type of Material	27Al/24Mg	μ26Mg*	μ25Mg	μ26Mg	N	54Cr
31E	Bulk CAI	3.133 ± 0.016	1164.3 ± 2.7	5952 ± 18	12870 ± 41	10	6.80 ± 1.20
22E	Bulk CAI	3.336 ± 0.017	1244.8 ± 1.7	−2405 ± 7	−3454 ± 19	10
E104	Bulk CAI	2.880 ± 0.058	1063.8 ± 4.0	−1031 ± 6	−950 ± 19	4
E48 (1)	Bulk CAI	2.856 ± 0.057	1059.7 ± 3.5	12055 ± 14	24823 ± 29	5
E48 (2)	Bulk CAI	2.674 ± 0.013	991.6 ± 4.1	10140 ± 9	20960 ± 22	6
AR-E48	Fo-rich AR	0.03075 ± 0.0005	−5.6 ± 8.0	−1148 ± 18	−2239 ± 38	4
AR-E104 (1)	Fo-rich AR	0.08501 ± 0.0013	21.6 ± 8.0	−1904 ± 9	−3696 ± 25	5
AR-E104 (2)	Fo-rich AR	0.09237 ± 0.0014	23.8 ± 8.0	−2436 ± 31	−4735 ± 58	5
E1s (1)	Bulk AOA	0.1100 ± 0.0006	26.2 ± 2.1	−1476 ± 8	−2855 ± 21	10	5.40 ± 0.40
E1s (2)	Bulk AOA	0.1330 ± 0.0007	33.2 ± 1.9	−1570 ± 11	−3029 ± 27	10
E2s	Bulk AOA	0.3075 ± 0.0024	100.1 ± 3.6	−2465 ± 9	−4709 ± 21	7
E3s	Bulk AOA	0.3686 ± 0.0018	120.4 ± 3.0	−1270 ± 9	−2355 ± 19	10
E4s	Bulk AOA	0.0756 ± 0.0004	16.1 ± 3.2	−29 ± 14	−32 ± 29	6
Ivuna (1)	CI	0.0977 ± 0.0004	4.6 ± 1.8	−147 ± 8	−276 ± 21	10	1.69 ± 0.25
Ivuna (2)	CI		3.8 ± 1.0	−136 ± 9	−258 ± 21	10
Ivuna (3)	CI		4.5 ± 2.3	−109 ± 10	−200 ± 22	10
Orgueil	CI	0.1030 ± 0.0005	4.3 ± 2.2	−143 ± 6	−277 ± 12	10
Alais	CI	0.0988 ± 0.0005	5.1 ± 2.4	−143 ± 5	−276 ± 10	10
SAH 97159	EC	0.0852 ± 0.0004	0.3 ± 1.9	−130 ± 17	−250 ± 37	50
NWA 753	RC	0.0977 ± 0.0005	−1.3 ± 2.3	−159 ± 15	−298 ± 31	9	−0.11 ± 0.25
NWA 856	Mars	0.596 ± 0.003	−2.3 ± 1.8	−134 ± 6	−258 ± 18	10
Kramer Creek	OC	0.0856 ± 0.0004	−3.4 ± 1.7	−183 ± 8	−355 ± 20	10
Tennasilm	OC	0.0811 ± 0.0004	−4.0 ± 1.2	−157 ± 13	−308 ± 23	10
Barratta	OC	0.0869 ± 0.0004	−4.3 ± 1.7	−172 ± 6	−333 ± 18	10
Heredia	OC	0.0819 ± 0.0004	−4.5 ± 2.1	−162 ± 8	−314 ± 21	10
NWA2999	Angrite	0.505 ± 0.003	−4.1 ± 1.7	−4 ± 12	−5 ± 27	10	−0.53 ± 0.25
NWA4590	Angrite	2.72 ± 0.01	−4.4 ± 2.0	−147 ± 11	−285 ± 24	10
DHO1222	Acapulcoite	0.0878 ± 0.0004	−6.0 ± 1.3	−129 ± 8	−251 ± 21	10	−0.34 ± 0.25
Kenna	Ureilite	0.0059 ± 0.0001	−8.5 ± 1.1	−92 ± 8	−180 ± 22	10	−1.08 ± 0.25
SAH98505	Ureilite	0.0113 ± 0.0002	−7.7 ± 1.6	−101 ± 10	−199 ± 25	10

Notes. Analytical uncertainties for the μ²⁶Mg*, μ²⁵Mg, and μ²⁶Mg values are quoted at the 2se level. For the ⁵⁴Cr measurements, acquired following techniques outlined in Trinquier et al. (2008), the uncertainty reported is the external reproducibility of 25 ppm or internal error, whichever is larger. For the enstatite and ordinary chondrites as well as for the Martian shergottite, we used the values of Trinquier et al. (2007) obtained for the same meteorite groups. AR: accretionary rim; Fo: forsterite; EC: enstatite chondrite; OC: ordinary chondrite; RC: R-chondrite; N: number of acquisitions.

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Large-scale nucleosynthetic isotopic heterogeneity exists among inner solar system solids, planets, and asteroids, most noticeably for neutron-rich isotopes of the iron-group elements such as ⁴⁸Ca, ⁵⁰Ti, ⁵⁴Cr, and ⁶⁴Ni (Birck 2004), and are interpreted as reflecting heterogeneous distribution of presolar components in the solar protoplanetary disk (Rotaru et al. 1992; Trinquier et al. 2007). Two views are considered for the origin of the solar system's ⁵⁴Cr heterogeneity: an ancient galactic component dominated by input from rare type Ia supernovae (Clayton 2003; Meyer et al. 1996) or, alternatively, heterogeneous seeding of the nascent solar system from a recent event, possibly a nearby massive star (Dauphas et al. 2010; Qin et al. 2011). The excesses and deficits in μ²⁶Mg* we find for primitive and differentiated meteorites as well as for the bulk CAI–AOA reservoir correlate with the ⁵⁴Cr abundance for the same samples or meteorite groups (Figure 2(b)). The preservation of a correlation between μ²⁶Mg* and ⁵⁴Cr suggests that the majority of the μ²⁶Mg* variability can be ascribed to a single cause: either ²⁶Al heterogeneity in the precursor material of the various solar system reservoirs or nucleosynthetic Mg-isotope heterogeneity unrelated to the decay of ²⁶Al. Although Mg-isotope anomalies of nucleosynthetic origin were reported in rare ²⁶Al-poor inclusions (Sahijpal & Goswami 1998), mass balance calculations indicate that the potential presence of these anomalous components in chondritic meteorites will not affect their bulk Mg-isotope composition beyond the resolution of our analyses. Contrary to ⁵⁴Cr, which has multiple nucleosynthetic origins (Clayton 2003; The et al. 2007), all three Mg isotopes are coproduced during hydrostatic nucleosynthesis in massive stars (Arnett & Thilelemann 1985; Thilelemann & Arnett 1985), with the production of ²⁵Mg and ²⁶Mg increasing with stellar metallicity (Woosley & Weaver 1995). Therefore, if the solar system's ⁵⁴Cr heterogeneity represents an old, galactically inherited component, then preservation of a simple binary mixing relationship between μ²⁶Mg* and ⁵⁴Cr is difficult to reconcile with widespread Mg-isotope heterogeneity as the main source of variability in μ²⁶Mg*.

In contrast to the solar system's bulk Mg-isotope composition, the initial ²⁶Al/²⁷Al recorded by the Efremovka CAIs and AOAs cannot be explained by the expected contribution from the background abundances of ²⁶Al in the galaxy (Huss et al. 2009). This requires an input of freshly synthesized stellar material prior to or during the collapse of the protosolar molecular cloud to account for the totality of the solar system's inventory of ²⁶Al. Given that the massive stars that synthesize ²⁶Al also produce copious amounts of ⁵⁴Cr compared to the remaining Cr isotopes (The et al. 2007), the correlation we report in Figure 2(b) is most easily understood if it reflects variable incorporation of debris from a nearby stellar event that produced and delivered ²⁶Al and ⁵⁴Cr to the nascent solar system or, alternatively, contamination of the protosolar molecular cloud by a previous generation(s) of massive stars. This is consistent with the discovery of ⁵⁴Cr-rich grains of supernova origin in primitive meteorites (Dauphas et al. 2010; Qin et al. 2011). Because the Mg-isotope composition of supernova ejecta can be highly variable (Gyngard et al. 2010), it is possible that the μ²⁶Mg* heterogeneity reported here represents the cumulative effect of both Mg-isotope and ²⁶Al heterogeneity. However, it is unclear how a late addition of freshly synthesized stellar material to the nascent solar system would result in a homogeneous distribution of ²⁶Al, but a heterogeneous distribution of Mg isotopes. As such, the discovery of widespread μ²⁶Mg* heterogeneity in solar system objects is a highly significant finding, as it requires that some—if not all—of the μ²⁶Mg* variability can be attributed to ²⁶Al heterogeneity. Although quantifying the extent of ²⁶Al heterogeneity solely based on our Mg-isotope measurements is difficult, we note that the magnitude of the μ²⁶Mg* heterogeneity observed across solar system reservoirs (30.3 ± 1.8 ppm) is within the range of expected variations resulting from ²⁶Al heterogeneity (up to 38 ppm).

If the totality of the μ²⁶Mg* variability is related to ²⁶Al heterogeneity, it is possible to estimate the initial ²⁶Al abundance in the accretion regions of asteroids and planets by comparing their present-day μ²⁶Mg* with the initial μ²⁶Mg₀ defined by the CAI–AOA isochron and its intercept at the solar ²⁷Al/²⁴Mg ratio. In Table 2, we show that if this assumption is valid, then large-scale heterogeneity—up to 80% reduction of the canonical ²⁶Al/²⁷Al ratio—may have existed throughout the inner solar system. The CI chondrites record an initial ²⁶Al/²⁷Al ratio of ∼2.8 × 10⁻⁵, that is, approximately 54% of the value defined by Efremovka CAIs and AOAs. Thus, the CV CAI- and AOA-forming reservoir was characterized by an enhanced initial abundance of ²⁶Al compared to the average value of solar system material defined by CI chondrites, whereas the accretion regions of the terrestrial planets, ordinary chondrites, angrites, acapulcoites, and ureilites record variable depletions in ²⁶Al.

Rigorously testing whether the μ²⁶Mg* variability primarily reflects ²⁶Al heterogeneity can be achieved by comparing high-precision U–Pb and ²⁶Al–²⁶Mg ages of pristine solar system materials, given that the U–Pb chronometer provides absolute ages that are free from assumptions of parent nuclide homogeneity. The validity of this approach, however, requires that both the U–Pb and ²⁶Al–²⁶Mg chronometers date the same event. We focus our discussion on the age difference between the CAI SJ101 (Amelin et al. 2011) and the SAH99555 angrite (Connelly et al. 2008b). SJ101 is the only CAI dated by the Pb–Pb method for which the U-isotope composition has been measured and currently defines the absolute age of CAIs. The SAH99555 angrite is one of the most pristine basaltic meteorites and has been dated via both the Pb–Pb and ²⁶Al–²⁶Mg methods by a number of groups (Connelly et al. 2008b; Amelin 2008; Schiller et al. 2010). Given the lack of U data for this meteorite, we measured the U-isotope composition of SAH99555 by HR-MC-ICPMS (Table 3). Based on the U–Pb system, we calculate an age difference of 3.57 ± 0.54 Myr between the formation of SJ101 and crystallization of SAH99555, which is not compatible with the age difference of 5.02^+0.15_{− 0.13} Myr inferred from the ²⁶Al–²⁶Mg system for these two objects. Given the short duration of the CAI-forming process inferred from our study and the consistency in the Pb–Pb age of the SAH99555 meteorite obtained by different studies (Connelly et al. 2008b; Amelin 2008), it is unlikely that this age difference reflects selective disturbance of the isotopic chronometers. Rather, it is consistent with our proposal that the CAI-forming reservoir was characterized by an enhanced abundance of ²⁶Al compared to the accretion region of the angrite parent body. To reconcile the mismatch between the U–Pb and ²⁶Al–²⁶Mg ages of SJ101 and SAH99555, the initial abundance of ²⁶Al in the accretion region of the angrite parent body is required to be reduced by 57%–85% of the ²⁶Al/²⁷Al value present in the CAI-forming reservoir, considering the uncertainties of the U–Pb ages. This is consistent with our independent estimate of 69% based on the Mg isotopes, which corresponds to an initial ²⁶Al/²⁷Al of ∼1.6 × 10⁻⁵ for the angrite parent body and relative ²⁶Al–²⁶Mg age of 3.78 ± 0.23 Myr for SAH99555, and is in excellent agreement with its U–Pb age. We conclude that the bulk of the μ²⁶Mg* variability documented here reflects heterogeneity in the abundance of ²⁶Al across the solar protoplanetary disk at the time of CAI formation.

Covariations in ⁵⁴Cr and ⁵⁰Ti among inner solar system objects have been ascribed to thermal processing of molecular cloud material, which resulted in preferential loss by sublimation of thermally unstable and isotopically anomalous presolar carriers, producing residual isotopic heterogeneity (Trinquier et al. 2009). The initial abundances of ²⁶Al in solar system reservoirs determined here resonate with their ⁵⁴Cr composition, suggesting that the ²⁶Al heterogeneity may have been established in a comparable way. This is consistent with a late-stage pollution of the nascent solar system from supernova debris as suggested by the μ²⁶Mg*–⁵⁴Cr correlation, but only if this occurred prior to the collapse of the protosolar molecular cloud. Thus, we propose that the ²⁶Al heterogeneity in solar system objects reflects variable degrees of thermal processing of their precursor material, probably associated with volatile-element depletions in the inner solar system. In this view, CAIs and AOAs represent samples of the complementary gaseous reservoir enriched in ²⁶Al by thermal processing, which resulted in the widespread ²⁶Al depletions observed among the inner solar system bodies. This implies the existence of a presolar carrier enriched in ²⁶Al among solar system materials, perhaps a presolar silicate, inherited from the protosolar molecular cloud.

The observation of ²⁶Al heterogeneity in the solar protoplanetary disk suggests that the ²⁶Al–²⁶Mg system cannot be readily used to deduce accurate chronologies of solar system events. Thus, current models for the formation and earliest evolution of our solar system based on the ²⁶Al–²⁶Mg chronometer require important revision. For example, the so-called canonical ²⁶Al/²⁷Al ratio of ∼5.2 × 10⁻⁵ is typically used to infer the nature of the stellar source that delivered ²⁶Al to the nascent solar system (Meyer 2005). However, our results suggest that the solar system's initial ²⁶Al inventory is best approximated by the ²⁶Al/²⁷Al ratio of ∼2.8 × 10⁻⁵ defined by CI chondrites (Table 1). A reduced initial abundance of ²⁶Al among some solar system reservoirs may impact the role of this radionuclide as a heat source for asteroid differentiation. However, we note that, assuming no heat loss and accretion contemporaneous with CAI formation, the amount of energy resulting from the decay of ²⁶Al in a body with a (²⁶Al/²⁷Al)₀ ratio of 1 × 10⁻⁵ is ∼1.2 kJ g⁻¹, which is 75% of the energy required to completely melt a chondritic body (Hevey & Sanders 2006); this would lead to the formation of an asteroid-wide magma ocean.

The existing ²⁶Al–²⁶Mg data for chondrules from unequilibrated ordinary chondrites (UOCs) require an age gap of ∼1.5 Myr between the formation of CAIs and chondrules (Kurahashi et al. 2008), assuming a uniform distribution of ²⁶Al in the solar system at the value of ∼5.2 × 10⁻⁵. Recalculating the ²⁶Al–²⁶Mg ages of the UOCs' chondrules using the initial ²⁶Al/²⁷Al ratio of ∼1.6 × 10⁻⁵ inferred for the accretion region of ordinary chondrites (Table 1) reduces the gap and suggests that ordinary chondrite chondrule formation started almost contemporaneously with the CV CAIs and AOAs. Thus, chondrule formation may have been a punctuated, recurrent process active during the entire life span of the solar protoplanetary disk.