Aluminum-26 chronology of dust coagulation and early solar system evolution

Time scales of dust condensation and coagulation are inferred from the refractory inclusions in the Allan Hills A77307 meteorite.

Abstract

Dust condensation and coagulation in the early solar system are the first steps toward forming the terrestrial planets, but the time scales of these processes remain poorly constrained. Through isotopic analysis of small Ca-Al–rich inclusions (CAIs) (30 to 100 μm in size) found in one of the most pristine chondrites, Allan Hills A77307 (CO3.0), for the short-lived ²⁶Al-²⁶Mg [t_1/2 = 0.72 million years (Ma)] system, we have identified two main populations of samples characterized by well-defined ²⁶Al/²⁷Al = 5.40 (±0.13) × 10⁻⁵ and 4.89 (±0.10) × 10⁻⁵. The result of the first population suggests a 50,000-year time scale between the condensation of micrometer-sized dust and formation of inclusions tens of micrometers in size. The 100,000-year time gap calculated from the above two ²⁶Al/²⁷Al ratios could also represent the duration for the Sun being a class I source.

INTRODUCTION

The formation time scale of first solids in the Sun’s protoplanetary disk has been of major interest because it is the first step toward the formation of terrestrial planets. Some of our knowledge about planet formation in the solar system is drawn from theories (1) and astronomical observations of protoplanetary disks around young stellar objects (YSOs) (2). However, the spatial resolution of observations of YSOs is insufficient to reveal details inside the disks. In the past few years, our understanding of planet formation in young stellar systems has been revolutionized by the high–spatial resolution observations of HL Tau, a class I/II object, by ALMA (Atacama Large Millimeter/submillimeter Array) (3). The disk around this <1–million year (Ma)–old young star was found to be characterized by a structure composed of several axisymmetric bright and dark rings, indicating ongoing formation of planets or large planetary precursors at this stage of stellar evolution (3, 4), which is a few million years earlier than would be expected from theories (1). One implication of these new findings, which is consistent with that inferred from the tungsten isotopic compositions of iron meteorites (5), is that our solar system could have also started forming rocky planets (or their precursors) as early as hundreds of thousands of years after its formation. It should, however, be noted that terrestrial planet formation began by the condensation of small refractory dust particles, but observations with telescopes have not provided temporal resolution necessary to probe the timing of this stage. Our current understanding of the chronology of the first formation of solids in the solar protoplanetary disk is largely based on the short-lived ²⁶Al-²⁶Mg systematics (t_1/2 = 0.72 Ma) in refractory Ca-Al–rich inclusions (CAIs), the oldest datable solar system solids with an absolute U-corrected ²⁰⁷Pb-²⁰⁶Pb age of 4.567 billion years (6, 7), found in chondritic meteorites. The use of ²⁶Al as a chronometer requires that this radionuclide be homogeneously distributed in the CAI-forming region(s). Since the discovery of ²⁶Al in 1976 (8), it has been established by numerous studies, especially high-precision in situ and bulk-inclusion analyses in the past 15 years, that large (>5 mm) CAIs in CV3 chondrites are characterized by well-constrained ²⁶Al-²⁶Mg isochrons with slopes corresponding to ²⁶Al/²⁷Al of 5.2 (±0.1) × 10⁻⁵, and intercepts suggesting that the initial (pre-²⁶Al decay) ²⁶Mg/²⁴Mg ratio (≡∆²⁶Mg₀*; see the Supplementary Materials) of CAIs varies from −0.13 to −0.014‰ relative to a terrestrial standard value (9–15). It is noteworthy that in situ measurements are, in general, more sensitive to subsequent thermal reprocessing that disturbed the original magnesium isotopes than are bulk-inclusion analyses and, therefore, provide more information about the timing of the last melting/disturbance event and isotope reequilibration [interested readers are referred to (16) for more detailed discussions]. The fact that bulk-sample and some in situ work yielded ²⁶Al/²⁷Al of 5.2 (±0.1) × 10⁻⁵ but variable ∆²⁶Mg₀* implies a <30,000-year time scale (inferred from the analytical error of ²⁶Al/²⁷Al) for the formation of large CAIs in a reservoir with uniformly distributed ²⁶Al at this abundance level but slightly heterogeneous initial ²⁶Mg/²⁴Mg. However, these centimeter-sized CAIs in CV3 chondrites, despite their primitiveness and early formation inferred from short- and long-lived radionuclides, are thought to have formed by melting and agglomeration of smaller particles (<10 μm) that condensed directly from the nebular gas. This fact calls into question how representative the value of ²⁶Al/²⁷Al = 5.2 (±0.1) × 10⁻⁵ recorded by these large CAIs is of the true initial ²⁶Al abundance and distribution in the protoplanetary disk. Here, we focus on the magnesium isotopic compositions of small refractory inclusions (mostly 30 to 50 μm in size), which are best understood as products of initial coagulation of high-temperature dust condensates (17). The aims of this study were to evaluate the ²⁶Al abundance and distribution during this time period and then to infer the chronologies of these small inclusions relative to those of the large CAIs in CV3 chondrites that have been the focus of many studies.

Previous efforts to understand the ²⁶Al/²⁷Al ratios in small refractory inclusions were mostly focused on SIMS (secondary ion mass spectrometry) analyses of individual 20- to 80-μm hibonite-rich (CaMg_xTi_xAl_12-2xO₁₉) grains, corundum-bearing (Al₂O₃) inclusions, and grossite-bearing (CaAl₄O₇) inclusions primarily separated from the carbonaceous chondritic meteorites and of <10 μm corundum-rich grains extracted from carbonaceous and ordinary chondrites (18–28). According to equilibrium thermodynamics, these phases are predicted to be the first minerals directly condensing from a cooling gas of solar composition at ~1650 K at 10⁻³ bar (28). The inferred ²⁶Al/²⁷Al ratios in CM hibonite-rich samples are strongly correlated with mineralogy and morphology. Spinel-hibonite spherules (SHIBs) are characterized by an apparent scatter in ²⁶Al/²⁷Al from ~6 × 10⁻⁶ to 6 × 10⁻⁵ (18–22, 29). A statistical treatment of the data has revealed a major peak at 4.9 × 10⁻⁵, two secondary peaks at 3.5 × 10⁻⁵ and 6.5 × 10⁻⁶, and two marginally resolved peaks at 6 × 10⁻⁵ and 2.5 × 10⁻⁵ (gray curve in Fig. 1) (21, 22). In contrast, monomineralic platy-hibonite crystals (PLACs) lack resolvable ²⁶Mg excesses that can be attributed to ²⁶Al decay, but instead show small variations of ∆²⁶Mg* (deviation from a mass-dependent fractionation line; see Materials and Methods) between −4 and +5‰, which do not appear to be correlated with Al/Mg of the crystals. The ²⁶Al abundances deduced from corundum- and grossite-rich inclusions are broadly bimodal and do not correlate with mineral chemistry or textures. The two main peaks, composed of >50 and ~40% of measured corundum grains, respectively, are found at ²⁶Al/²⁷Al < 2 × 10⁻⁶ and ²⁶Al/²⁷Al = (4 to 5) × 10⁻⁵ (23–26, 28); an intermediate ratio [²⁶Al/²⁷Al = (1.0 ± 0.1) × 10⁻⁵] has recently been reported (28) and was included in the gray probability density curve in Fig. 1.

Fig. 1. Distribution of ²⁶Al/²⁷Al in 18 ALHA77307 CAIs.

(Top) Inferred ²⁶Al/²⁷Al ratios are plotted against the associated ∆²⁶Mg₀* (errors 2σ) obtained from the isochron plots. Each symbol indicates one inclusion. The solid red square represents ²⁶Al/²⁷Al = (5.2 ± 0.1) × 10⁻⁵ and ∆²⁶Mg₀* = (−0.13 to −0.014‰) inferred from large CV3 CAIs (using both bulk-sample and internal isochron methods). (Bottom) Black solid curve stands for the probability density plot calculated on the basis of the ²⁶Al/²⁷Al ratios acquired in this study. The probability curve based on the data of bulk and internal isochron-derived ²⁶Al/²⁷Al from CM SHIBs and one hibonite-grossite–rich inclusion (gray curve) is shown for comparison. The band formed by two gray dashed lines represents ²⁶Al/²⁷Al = (5.2 ± 0.1) × 10⁻⁵.

The meaning of the ²⁶Al/²⁷Al spread seen in hibonite-, corundum-, and grossite-rich inclusions still remains enigmatic. While isotopic resetting or late formation would be the most straightforward explanation for inclusions with ²⁶Al/²⁷Al < 5.2 × 10⁻⁵, the possibility that these objects formed prior to homogenization of ²⁶Al/²⁷Al to the value of 5.2 × 10⁻⁵ in the solar nebula has also been considered (21, 24, 25). If the latter is true, no constraints on formation time scales could be quantitatively derived for such grains. However, it should be noted that the SIMS primary ion beam used in previous studies was too large (~30 to 40 μm) to permit multiple-spot analyses on single hibonite (in most cases) and corundum grains. Therefore, each measurement was analogous to “bulk” analysis, and the ²⁶Al/²⁷Al ratios were inferred via “model isochrons,” that is, connecting a data point to the assumed origin defined as ²⁷Al/²⁴Mg = 0 and ²⁶Mg/²⁴Mg = 0.13932 (the assumed terrestrial value) (30). This method, however, is only valid if two requirements were met. First, all corundum and hibonite must condense with the terrestrial ²⁶Mg/²⁴Mg ratio. However, the PLAC data, which suggested large ²⁶Mg/²⁴Mg heterogeneity (~10‰) relative to the chondritic abundance in the early solar nebula (21, 31), have rendered this assumption questionable, especially if low ²⁶Al/²⁷Al was attributed to early formation. Second, these inclusions must have escaped any open-system magnesium isotope exchange with an external reservoir (e.g., solar nebula) after their formation, but this assumption has never been proven with certainty. Internal mineral isochrons in the earliest-formed solids are needed to infer assumption-free ²⁶Al/²⁷Al for a better understanding of the meaning of the ²⁶Al/²⁷Al ratio distribution.

As of now, only a handful of internal ²⁶Al isochrons have been obtained for hibonite-rich inclusions (including SHIBs, corundum-bearing hibonite, and grossite-hibonite–bearing CAIs) larger than 70 μm (22, 25, 26, 28). Overall the results corroborated those seen in the model isochron data. Most of the inferred ²⁶Al/²⁷Al ratios cluster at 4.8 × 10⁻⁵, falling right on the major distribution peak at 4.9 × 10⁻⁵ (21). The intercepts of these internal isochrons were chondritic (∆²⁶Mg₀* = 0‰) within analytical errors, indicating no resolvable initial ²⁶Mg/²⁴Mg heterogeneity. Lower ²⁶Al/²⁷Al ratios, broadly consistent with 3.5 × 10⁻⁵ and 2.5 × 10⁻⁵, were also revealed, but no constraints on the associated intercept were obtained, except for one spinel-hibonite–rich sample in a recent study [∆²⁶Mg₀* = 0.8 ± 0.2‰, derived through weighted regression (22)], as the isochrons were forced through the assumed origin (see above). Therefore, how the ²⁶Al/²⁷Al variability seen in those potentially early formed solids relates to ²⁶Al/²⁷Al = 5.2 × 10⁻⁵ recorded in large CAIs (early formation versus late formation) cannot be properly evaluated. To minimize the potential effects of any parent-body alteration, we chose small refractory inclusions, most of which are hibonite rich and have similar mineralogy to those in CM2 chondrites, found in a thin section of the CO3.0 chondrite Allan Hills (ALH) A77307, one of the most pristine meteorites known (32). We have analyzed 22 CAIs (~30 to 100 μm in size) using the University of California, Los Angeles (UCLA) CAMECA ims-1290 ion microprobe to infer ²⁶Al abundances through high-precision internal isochrons in the hope of better understanding the implications of ²⁶Al/²⁷Al variations in the context of early solar system chronology.

RESULTS

A positive correlation between the excesses of radiogenic ²⁶Mg (≡²⁶Mg*) and ²⁷Al/²⁴Mg ratios was found within 18 individual inclusions, indicating in situ decay of ²⁶Al (fig. S1). The inferred ²⁶Al/²⁷Al ratios, calculated from bivariate error–weighted least squares regression by using the algorithm of (33), span a range from 8 (±16.5) × 10⁻⁶ to 5.73 (±1.20) × 10⁻⁵ (2σ errors), and the probability density distribution is in excellent agreement with that calculated with the SHIB ²⁶Al abundances calculated by using model and internal isochrons [Fig. 1 and Table 1; model isochron data from (21) and internal isochron data from (22) and (28)]. The most prominent peak, which falls on ²⁶Al/²⁷Al = 4.9 × 10⁻⁵, is identical to the major 4.9 × 10⁻⁵ peak in SHIBs. Multiple grains form a well-resolved peak at ²⁶Al/²⁷Al = 5.4 × 10⁻⁵. This group and the SHIBs that constitute the marginally revealed 6.0 × 10⁻⁵ peak very likely belong to the same population, but the new data acquired here offer better resolution. The appearance of a small hump at ²⁶Al/²⁷Al = 4.5 × 10⁻⁵ mainly arises from the small error on the inferred ²⁶Al/²⁷Al ratio for CAI 230, but the associated ∆²⁶Mg₀* = 0.33 ± 0.31‰ suggests late isotopic closure, a result of either late formation or isotopic disturbance (see below). The same argument can be applied to two other minor peaks seen at lower ²⁶Al/²⁷Al ratios (~3.5 × 10⁻⁵ and ~2.5 × 10⁻⁵), albeit very limited numbers of samples under each peak, because of the positive ∆²⁶Mg₀* values associated with the samples.

Table 1. Inferred ²⁶Al/²⁷Al ratios, initial Δ²⁶Mg₀*, and goodness of fit for 18 ²⁶Al-bearing ALHA77307 CAIs.

Uncertainties are 2σ. hib, hibonite; pv, perovskite; sp, spinel; mel, melilite; di, diopside rim; and fo, forsteritic olivine.

Sample	Minerals	26Al/27Al (±2σ)	∆26Mg0* (‰, ±2σ)	Reduced χ2
019	hib	(4.86 ± 0.42) × 10−5	0.05 ± 0.26	0.3
021	hib-pv-sp	(0.80 ± 1.65) × 10−5	0.87 ± 0.44	2.0
070	sp-pv-di-ol	(5.12 ± 0.67) × 10−5	−0.13 ± 0.09	0.7
073	hib-pv-sp	(4.85 ± 0.32) × 10−5	0.12 ± 0.10	10
074	hib-pv-sp	(5.37 ± 0.29) × 10−5	−0.21 ± 0.50	1.9
095	hib-sp	(4.94 ± 0.21) × 10−5	−0.06 ± 0.27	1.0
117	hib-pv-sp-di	(3.76 ± 0.37) × 10−5	0.86 ± 0.27	6.7
119	hib-pv-sp-di	(5.46 ± 0.35) × 10−5	−0.16 ± 0.14	0.4
147	hib-sp-di	(5.73 ± 1.20) × 10−5	−0.05 ± 0.43	1.2
148	hib-sp-di	(3.34 ± 0.37) × 10−5	0.46 ± 0.33	9.4
155	hib-sp	(1.72 ± 0.81) × 10−5	1.57 ± 0.46	22.3
164	hib-sp-di	(4.68 ± 0.39) × 10−5	−0.04 ± 0.24	1.8
165	sp-di-fo	(4.32 ± 0.62) × 10−5	−0.01 ± 0.04	0.9
212	sp-pv-di	(4.53 ± 0.80) × 10−5	−0.11 ± 0.11	0.4
222	hib-sp	(2.44 ± 0.44) × 10−5	0.26 ± 0.32	0.2
229	sp-pv-mel-di-ol	(5.59 ± 0.91) × 10−5	−0.15 ± 0.13	1.4
230	hib-pv-sp-mel	(4.48 ± 0.19) × 10−5	0.33 ± 0.31	3.8
230SW	hib-pv-sp-mel	(3.01 ± 0.79) × 10−5	1.77 ± 0.81	0.7

Five CAIs (070, 074, 119, 147, and 229), which can be characterized by ²⁶Al/²⁷Al = 5.2 × 10⁻⁵ within errors, all have a well-defined isochron (reduced χ² < 2; fig. S1). A weighted least squares fit through the data points from the five inclusions together yields a slope corresponding to ²⁶Al/²⁷Al = 5.40 (±0.13) × 10⁻⁵ and an intercept of (−0.14 ± 0.03‰) as the initial ∆²⁶Mg₀* (reduced χ² = 1.1; Fig. 2A). This inferred ²⁶Al abundance, which agrees perfectly with the 5.40 × 10⁻⁵ peak in the probability density distribution, is only marginally resolved from 5.2 (±0.1) × 10⁻⁵. Although the initial ∆²⁶Mg₀* = (−0.14 ± 0.03‰) is resolved from that inferred for pristine bulk CAIs (∆²⁶Mg₀* = −0.04‰) (10), it is identical to the values (∆²⁶Mg₀* = −0.13‰) derived for a couple of large CAIs by using mineral isochrons (14, 15). Inclusions (019, 073, 095, 164, 165, and 212) that contribute to forming the peak at 4.9 × 10⁻⁵ also define an isochron, albeit with some scatter at low ²⁷Al/²⁴Mg (reduced χ² = 4.3), from which ²⁶Al/²⁷Al = 4.89(±0.10) × 10⁻⁵ and ∆²⁶Mg₀* = (−0.04 ± 0.03‰) can be inferred (Fig. 2B). CAIs 117, 148, 155, 222, 230, and 230SW are found to have much lower, yet nonzero, ²⁶Al/²⁷Al ratios and more positive ∆²⁶Mg₀* compared with those in the two main populations, and the first three show apparent scatter along the best fit line (indicated by the reduced χ² values). CAI 021 is characterized by an isochron slope corresponding to ²⁶Al/²⁷Al = (8 ± 16.5) × 10⁻⁶ associated with ∆²⁶Mg₀* = (0.87 ± 0.44‰), suggesting that isotopic resetting took place after ²⁶Al had substantially decayed.

Fig. 2. Multi-CAI isochrons.

(A) Five CAIs that make up the 5.4 × 10⁻⁵ peak in the probability density plot (Fig. 1) form a well-defined isochron (χ² = 1.1), the slope of which corresponds to ²⁶Al/²⁷Al = (5.40 ± 0.13) × 10⁻⁵. (B) Six CAIs under the 4.9 × 10⁻⁵ peak are characterized by tightly constrained ²⁶Al/²⁷Al = (4.89 ± 0.10) × 10⁻⁵, albeit with some scatter (χ² = 4.3). The intercept is broadly consistent with the chondritic value within errors. All errors are 2σ.

Four samples (030, 086, 176, and 181), either monomineralic hibonite or hibonite-corundum inclusions, lack resolvable excesses in radiogenic ²⁶Mg. Rather, their ∆²⁶Mg* values range from −3 to +1‰ and are not correlated with ²⁷Al/²⁴Mg (Fig. 3), similar to what has been found in CM-chondrite PLACs (21, 31) and a couple of hibonite-bearing microspherules from in other CO3 chondrites (34).

Fig. 3. CAIs devoid of resolved excesses in ²⁶Mg that could be attributed to the decay of ²⁶Al.

Instead, ∆²⁶Mg* appears to be slightly heterogeneous even within a single grain. A line corresponding to ²⁶Al/²⁷Al = 5.2 × 10⁻⁵ is shown for reference. All errors are 2σ.

DISCUSSION

The ²⁶Al/²⁷Al variation in small CO3.0 CAIs

Our new “assumption-free” ²⁶Al data from small CAIs in ALHA77307 (CO3.0) show two main populations of inclusions with regard to the inferred ²⁶Al/²⁷Al ratios and ∆²⁶Mg₀*. One group appears to have formed with ²⁶Al/²⁷Al = 5.40 (±0.13) × 10⁻⁵ and initial ∆²⁶Mg₀* = (−0.14 ± 0.03‰), whereas the other group is characterized by ²⁶Al/²⁷Al = 4.89 (±0.10) × 10⁻⁵ and the chondritic ∆²⁶Mg₀* value of (−0.04 ± 0.03‰). This level of ²⁶Al abundance has been found, albeit with poor analytical precision, in three relatively larger CAIs (300 to 400 μm) in ALHA77307 from a previous study (34). Inclusions having ²⁶Al/²⁷Al lower than 4 × 10⁻⁵ are associated with more positive ∆²⁶Mg₀* (up to 1.8‰) and make up two small peaks at 3.5 × 10⁻⁵ and 2.5 × 10⁻⁵. Such an ²⁶Al/²⁷Al−∆²⁶Mg₀* relationship can be best understood in the context of postformation thermal processing, similar to that suggested to account for the ²⁶Al/²⁷Al differences between pristine (unmelted) and thermally reprocessed (igneous) CV3 CAIs [e.g., (35, 13, 36, 16)]. Therefore, inclusions having ²⁶Al/²⁷Al = 5.4 × 10⁻⁵ and ∆²⁶Mg₀* = −0.14‰ could be considered the most pristine among those analyzed here and should most faithfully record the isotopic signatures of the formation region. These two values are in good agreement with the estimates for “true” solar system ²⁶Al/²⁷Al = (5.62 ± 0.42) × 10⁻⁵ and ∆²⁶Mg_0,i* = −(0.052 ± 0.013‰) based on CV CAI data (16). The peaks at lower ²⁶Al/²⁷Al (along with more positive ∆²⁶Mg₀*) would have been a consequence of late thermal processing of these early formed inclusions that had led to (partial) isotopic reequilibration. The major thermal event appears to have occurred to reset the majority of the inclusions when ²⁶Al/²⁷Al = 4.9 × 10⁻⁵, i.e., ~10⁵ years after initial formation. Support for reprocessing of small CAIs at this time can be derived from the fact that average ²⁷Al/²⁴Mg = 2.8, a ratio that would have only existed in a reservoir composed primarily of refractory solids [a gas reservoir would have average solar ²⁷Al/²⁴Mg ~0.101 (37)], would be required to change ∆²⁶Mg₀* from −0.14‰ to −0.04‰ by the decay of ²⁶Al from ²⁶Al/²⁷Al = 5.4 × 10⁻⁵ to 4.9 × 10⁻⁵. It is noteworthy that this ²⁶Al/²⁷Al value of 4.9 × 10⁻⁵ has been registered not only by the CO3 inclusions but also by many CM2 SHIBs, CV3 CAIs, and corundum grains [e.g., (13, 15, 21, 22, 24)], implying that such thermal processing was widespread in the regions where refractory inclusions resided or formed.

There could have been additional thermal events that reset existing solids hundreds of thousands of years after the major one at ²⁶Al/²⁷Al = 4.9 × 10⁻⁵, as indicated by the low ²⁶Al/²⁷Al, but positive ∆²⁶Mg₀*, values of CAIs 021, 117, 148, 155, 222, 230, and 230SW. The following discussion about these CAIs is based on the approach used in previous work (13, 16); more details can be found in these references. All inclusions except 155 are characterized by slightly negative mass-dependent isotope fractionation (δ²⁵Mg = −1 to −4‰; table S1), indicating that they have a condensation origin and most likely have not experienced any evaporation processes. Therefore, we argue that these CAIs obtained their current chemical compositions during initial condensation, and thermal reprocessing did not further fractionate Al/Mg of the inclusions. Consequently, the present-day ²⁷Al/²⁴Mg and inferred ²⁶Al/²⁷Al of CAIs could be used to back-calculate the true initial ²⁶Mg/²⁴Mg (denoted ∆²⁶Mg_0,i* to avoid confusion with isochron-derived ∆²⁶Mg₀*) they formed with. As can be seen in Fig. 4, the ∆²⁶Mg_0,i* values for CAIs 021, 117, 148, 222, 230, and 230SW appear to show a range when ²⁶Al/²⁷Al = 5.4 × 10⁻⁵, but most of them cluster at ~−0.4‰ with a full width at half maximum (~2.3σ) of ±0.3‰, broadly consistent with −0.14‰ within errors. This means that these inclusions could still have formed together with those constituting the ²⁶Al/²⁷Al = 5.4 × 10⁻⁵ peak. It should be noted that given the limited number of data points used in this exercise and analytical errors associated with the measured ∆²⁶Mg₀* and ²⁷Al/²⁴Mg for these inclusions, the individual back-calculated ∆²⁶Mg_0,i* values would also have nonnegligible uncertainties, and thus, the true range of magnesium heterogeneity at this time cannot be precisely constrained. More work is needed.

Fig. 4. The true initial ²⁶Mg/²⁴Mg (≡∆²⁶Mg_0,i*) of individual CAI, calculated from isochron-derived ²⁶Al/²⁷Al and ∆²⁶Mg₀*, and bulk ²⁷Al/²⁴Mg estimated by using scanning electron microscopy–energy-dispersive x-ray spectroscopy.

A gray arrow is drawn from each CAI data point to the ²⁶Al/²⁷Al ratio of 5.4 × 10⁻⁵ (defined as “t_0,” the vertical solid line), with the slope determined from the CAI’s present-day bulk ²⁷Al/²⁴Mg, which is the number shown in a black square. The small orange rectangle stands for ²⁶Al/²⁷Al = (5.40 ± 0.13) × 10⁻⁵ and ∆²⁶Mg₀* = (−0.14 ± 0.03‰). (Inset) A blow-up of the area where arrows intersect the vertical solid line, showing the distribution of back-calculated ∆²⁶Mg_0,i* in the form of a probability density plot. The horizontal orange bar represents ∆²⁶Mg_0,i* = (−0.14 ± 0.03). Most of the values cluster at ∆²⁶Mg_0,i* = −0.4‰ with a full width at half maximum (FWHM) (~2.3σ) of ±0.3‰.

CAI 155 appears to have a different evolution history from the others due to its slightly positive δ²⁵Mg (~3‰; table S1). This level of isotope fractionation suggests that ~20% of the initial magnesium was lost from this CAI by evaporation before the final formation (38). Therefore, the present-day ²⁷Al/²⁴Mg of CAI 155 did not originate from the initial condensation and thus cannot be used to infer ∆²⁶Mg_0,i*. Although it could be possible to constrain the evolution history by calculating the possible bulk ²⁷Al/²⁴Mg for the preevaporation CAI, the highly disturbed magnesium isotopic composition would make this a possible overinterpretation of data.

The above discussion of the ²⁶Al/²⁷Al−∆²⁶Mg₀* relationship is based on reprocessing of inclusions that have formed early at ²⁶Al/²⁷Al = 5.4 × 10⁻⁵. While the samples characterized by ²⁶Al/²⁷Al < 4 × 10⁻⁵ are still best explained in this context (except CAI 155), those making up the peak at ²⁶Al/²⁷Al = 4.9 × 10⁻⁵ (along with ∆²⁶Mg₀* = −0.04‰) may be understood in a different scenario. It is known from the literature data that ∆²⁶Mg₀* in the CAI formation reservoir(s) appeared to be heterogeneous between −0.13 and −0.014‰ when ²⁶Al/²⁷Al was homogeneous at 5.2 × 10⁻⁵, and could have varied even more at an earlier time (at ²⁶Al/²⁷Al = 5.4 × 10⁻⁵; see above). To make ∆²⁶Mg₀* = −0.04‰ at ²⁶Al/²⁷Al = 4.9 × 10⁻⁵ in a gas reservoir of solar composition (²⁷Al/²⁴Mg = 0.101), ∆²⁶Mg_0,i* at ²⁶Al/²⁷Al = 5.4 × 10⁻⁵ would have to be −0.044‰, which is well within the range of variation. Therefore, it is conceivable a reservoir of such ∆²⁶Mg_0,i*, from which one generation of inclusions formed during the nebula-wide thermal event at ²⁶Al/²⁷Al = 4.9 × 10⁻⁵, existed. With our current dataset, it is difficult to prove or disprove this explanation. One testable prediction is that there should exist other populations of inclusions characterized by ²⁶Al/²⁷Al = 4.9 × 10⁻⁵ but with ∆²⁶Mg₀* closer to −0.14‰. More high-precision measurements of small CAIs should be able to shed more light on this issue.

There are still two more alternatives for the observed ²⁶Al/²⁷Al distribution, but we argue that neither of them can account for the ²⁶Al/²⁷Al−∆²⁶Mg₀* relationship. The first possibility is that these inclusions had formed prior to homogenization of ²⁶Al and registered the heterogeneities of ²⁶Al and Mg isotopes in the (inner) solar nebula (21). However, if this was true, one would expect a more random relationship between ²⁶Al/²⁷Al and ∆²⁶Mg₀*. Instead, we observe that lower inferred ²⁶Al abundances are always accompanied by more positive ∆²⁶Mg₀*. Therefore, the ²⁶Al/²⁷Al variation is unlikely to have originated from the ²⁶Al (and magnesium isotope) heterogeneities in the formation region(s) and implies that the early formation hypothesis for SHIBs in a heterogeneous solar nebula based on the model isochron data [e.g., (21)] would be incorrect. The second possible scenario is that samples having lower ²⁶Al/²⁷Al would have formed with elevated ∆²⁶Mg₀* from a reservoir in which ²⁶Al has partially decayed. One serious problem with this explanation is that multiple formation reservoirs in the solar nebula, characterized by different Al/Mg ratios, would be required to result in different ∆²⁶Mg₀*. For example, CAI 222 and CAI 230SW would have formed in a region where Al/Mg = ~1.5 and ~10, respectively, ~800,000 and ~600,000 years after the inclusions with ²⁶Al/²⁷Al = 5.4 × 10⁻⁵. Forming such reservoirs and keeping the required Al/Mg ratios in individual reservoirs for hundreds of thousands of years without being homogenized would be astrophysically difficult, if not impossible [e.g., (39)].

Timing and duration of dust formation and agglomeration

The well-defined distribution peak and multi-CAI isochron revealing ²⁶Al/²⁷Al = 5.40 (±0.13) × 10⁻⁵ (Figs. 1 and 2A), albeit only marginally resolved from the ratio of 5.2 (±0.1) × 10⁻⁵ characterizing pristine large CV3 CAIs, shed light on the timing and time scales of the first stage of dust formation in the solar nebula. These CO3 CAIs have irregular shapes and nodular structures (see the Supplementary Materials), which imply that they have never been melted since their formation, and their small sizes, varying from ~30 μm (CAI 147) to ~100 μm (CAI 229), suggest they represent products from early stages of coagulation of primitive high-temperature condensates directly from a nebular gas. Along with ²⁶Al/²⁷Al = 5.40 (±0.13) × 10⁻⁵, one could infer a time scale of less than 50,000 years (deduced from the error of ²⁶Al/²⁷Al, which corresponds to ±25,000 years) for the formation of refractory inclusions several tens of micrometers in size by accretion of micrometer-sized dust. Centimeter-sized CAIs would have started to emerge during the late period of this coagulation stage and formed in abundance ~40,000 years after the majority of the 30- to 100-μm–sized inclusions have appeared in the nebula. This time scale is consistent with that predicted by a recent astrophysical model, which couples CAI formation to the physics of material infall and disk building (40). ∆²⁶Mg₀* = −0.14‰ inferred for small CO3 CAIs, on the other hand, may not have too much chronological significance when compared with that of CV3 CAIs (−0.04‰), because, as mentioned before, CV3 CAI data suggest that the solar nebula was characterized by slightly heterogeneous ∆²⁶Mg₀*, varying from −0.13 to −0.014‰ while ²⁶Al/²⁷Al = 5.2 × 10⁻⁵ (12, 14, 15). It is therefore conceivable that condensation of micrometer-sized dust particles followed by rapid agglomeration first into 30- to 100-μm–sized CAIs (such as those studied here) and eventually into centimeter-sized ones all took place in a reservoir characterized by ∆²⁶Mg₀* = −0.14‰ within tens of thousands of years of solar system formation.

The short time scale inferred above for dust condensation and agglomeration also allows a more quantitative understanding of the chronology of refractory inclusions devoid of live ²⁶Al. Just as the PLACs from CM2 chondrites, ²⁶Al-free refractory inclusions also exist in CO3 chondrites (CAIs 030, 086, 176, and 181). CM PLACs have been interpreted, albeit very qualitatively, to have formed in an isotopically heterogeneous solar nebula, possibly before CAIs with ²⁶Al/²⁷Al = 5.2 × 10⁻⁵, because they preserve large (up to 300‰) nucleosynthetic anomalies in neutron-rich isotopes ⁴⁸Ca and ⁵⁰Ti (21). Although these four inclusions were not measured for calcium and titanium isotopes here, previous related studies have revealed enrichments or deficits in δ⁴⁸Ca or δ⁵⁰Ti by up to 30‰ in other CO3 chondrite CAIs that show no evidence for incorporation of live ²⁶Al (34, 41). Therefore, based on the similarities in the range of ∆²⁶Mg₀* variation and preservation of nucleosynthetic anomalies, the ²⁶Al-free CO3 CAIs may have formed close in time, if not contemporaneously, with CM PLACs. This would allow for the possibility that reservoirs that were ²⁶Al poor, yet highly heterogeneous in ∆²⁶Mg₀*-δ⁴⁸Ca-δ⁵⁰Ti, may have existed before well-homogenized reservoirs with ²⁶Al/²⁷Al = 5.4 × 10⁻⁵. However, these reservoirs disappeared in less than 50,000 years, a limit set by the dust condensation and coagulation time scale (see above). This broadly agrees with the homogenization time (<10⁴ years) by hydrodynamic mixing in a marginally gravitationally unstable disk (39). Finer temporal resolution could potentially be achieved if more small samples having ²⁶Al/²⁷Al = 5.4 × 10⁻⁵ were found in the future.

Implications for evolution time scales of early solar system

The above interpretations that ²⁶Al/²⁷Al ratios of 5.4 × 10⁻⁵ and 4.9 × 10⁻⁵ have marked, respectively, the onset of dust formation in the protosolar nebula and the major thermal event affecting most already-formed CAIs also have important implications for the evolution time scales of the protosun. Theoretical modeling has shown that the temperature at the disk midplane would increase as material falls into it from the circumstellar envelope and reach the maximum at the cessation of infall. The timing of the latter coincides approximately with the transition from class I to class II stage of YSOs [e.g., (42)]. Therefore, isotopic resetting of most CAIs could have taken place when the inner-disk temperature was at its peak. This implies that ²⁶Al/²⁷Al = 4.9 × 10⁻⁵ would have corresponded to the end of class I or the beginning of class II of the protosun. The 100,000-year time difference calculated from the above two ²⁶Al/²⁷Al ratios is comparable to the mean life (~125,000 years) of the class I stage of YSOs derived from observations of protostars in each evolutionary class (43) and could therefore represent the duration for the Sun being a class I source.

MATERIALS AND METHODS

Sample description

The CAIs in this study were found in situ on a polished thin section of ALHA77307 by using a FEI Quanta three-dimensional field emission gun scanning electron microscope/focused ion beam instrument fitted with an EDAX Apollo 40 SDD Energy Dispersive Spectroscopy system at the University of New Mexico. Of 22 samples analyzed, 18 were hibonite rich, and the rest were hibonite free, spinel rich, with sizes ranging from 10 to ~100 μm (fig. S1). Most hibonite-rich inclusions consist of randomly oriented hibonite laths intergrown with or surrounded by spinel, often rimmed by diopside. However, three inclusions (019, 176, and 181) were spinel-free hibonite crystals. Corundum occurred with hibonite in two inclusions (030 and 086). Four hibonite-free inclusions (070, 165, 212, and 229) have nodular structures consisting of a spinel core surrounded by a diopside rim, often with thin layers of olivine on the exterior of the diopside rim. Fine-grained perovskite is a common accessory mineral in many inclusions, whereas melilite is a rare mineral occurring only in two inclusions (229 and 230). The shape and morphology of the samples suggest that they have not been melted since their initial formation by direct high-temperature condensation (17). More detailed descriptions about individual inclusions can be found in the Supplementary Materials.

Secondary ion mass spectrometry

In situ isotope analyses of ²⁶Al-²⁶Mg were performed in three separate sessions on the CAMECA ims-1290 ion microprobe at UCLA by following a method described previously (44). The target inclusions on the polished meteorite thin section were bombarded with a 1- to 8-nA ¹⁶O⁻ primary ion beam (ϕ ~1.5 to 4 μm) generated by a Hyperion-II oxygen plasma source, yielding Mg and Al secondary ion signals intense enough to be simultaneously measured with multiple Faraday cups without switching the magnetic field setting. Each spot analysis consisted of 45 s of “presputtering” and 300 s (10 s per cycle for 30 cycles) of data acquisition. Mass resolution (M/∆M) was set at 2500 (corresponding to exit slit #1 on the multicollection trolleys) to separate doubly charged interferences (⁴⁸Ca²⁺ and ⁴⁸Ti²⁺) from ²⁴Mg⁺. ²⁴MgH⁺ cannot be fully resolved from ²⁵Mg⁺ under such mass resolution, but the vacuum condition in the analysis chamber (pressure ≤1 × 10⁻⁹ torr) made the hydride contribution negligible (<0.05‰). A suite of terrestrial standards [Burma spinel, San Carlos (SC) olivine, San Carlos pyroxene, Madagascar hibonite, and isotopically normal synthetic glass of fassaite composition known as “P0”] were used to characterize instrumental mass fractionation (IMF) of magnesium isotopes during ion probe analyses. IMF is defined as

$${\mathrm{\alpha }}_i=\frac{{({}^i\text{Mg}/{}^{24}\text{Mg})}_{\mathrm{m}}}{{({}^i\text{Mg}/{}^{24}\text{Mg})}_{\text{true}}}$$

where i = 25 or 26, and m stands for “measured.” All these terrestrial standards were assumed to have the true magnesium isotopic compositions of ²⁵Mg/²⁴Mg = 0.12663 and ²⁶Mg/²⁴Mg = 0.13932 (30). α₂₅ and α₂₆ would have the following relationship when using an exponential mass fractionation law

$${\mathrm{\alpha }}_{25}={({\mathrm{\alpha }}_{26})}^{\mathrm{\beta }}$$

β is the IMF factor. To derive this quantity, we first expressed the deviations of measured isotopic ratios from the assumed true values in modified delta notation as

$${\mathrm{\delta }}^i\text{Mg}\prime (‰)=\text{ln} {\mathrm{\alpha }}_i \times 1000$$

and then obtained the slope of linear regression through data points on Mg-rich standards (spinel, SC olivine, and SC pyroxene) in δ²⁵Mg′-δ²⁶Mg′ space (fig. S2). The β value slightly varied between 0.510 and 0.516 from one session to another, but this range is comparable to those obtained on other ims-1200 series ion microprobe [e.g., (16, 21)]. The horizontal deviation from a mass fractionation line as a result of the decay of ²⁶Al (≡∆²⁶Mg*) was calculated with the formula recommended in (45)

$${\mathrm{∆}}^{26}{\text{Mg}}^{*}={\mathrm{\delta }}^{26}\text{Mg}-[{(1+{\mathrm{\delta }}^{25}\text{Mg}/1000)}^{1/\mathrm{\beta }}-1] \times 1000$$

where δ^25,26Mg = (α_25,26 – 1) × 1000. In this study, δⁱMg and δⁱMg′ are almost identical within errors. A synthetic in-house glass of fassaite composition doped with a 10.3‰ excess in ²⁶Mg, referred to as P10, was measured to check the accuracy of the analysis (fig. S2). It should be pointed out that the calculated ∆²⁶Mg* values depended very little on β. If the recommended β = 0.5128 was used (45), the difference in the resulting ∆²⁶Mg* could not be resolved outside of reported uncertainties. The internal error (σ_internal) of ∆²⁶Mg* for a spot analysis was the standard error of the mean (SEM) on a cycle-by-cycle basis, and the final reported error was calculated as

$${\mathrm{\sigma }}_{\text{final}}=\sqrt{{\mathrm{\sigma }}_{\text{internal}}^2+{\mathrm{\sigma }}_{\text{external}}^2}$$

where σ_external is the SEM of repeated measurements on the corresponding standard.

Aluminum and magnesium ions have slightly different yields during ion probe analysis. Therefore, the relative sensitivity factor (RSF) of Al to Mg, defined as (²⁷Al/²⁴Mg)_true/(²⁷Al/²⁴Mg)_m, needs to be characterized for different mineral phases by using the corresponding standards with known ²⁷Al/²⁴Mg ratios. The true ²⁷Al/²⁴Mg ratios of measured CAI minerals, including Al-rich diopside, spinel, and hibonite were derived by applying the RSFs determined on P0 glass, Burma spinel, and Madagascar hibonite, respectively, in each session. Al/Mg ratios of CAI olivine were not corrected for RSF because (i) they were too low (~0.0086) to have any observable effects on the determination of isochron slope and (ii) the low aluminum concentration in San Carlos olivine did not allow for an accurate estimate of RSF. The RSF values and corresponding errors obtained in each session on each standard are listed in table S2.

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/9/eaaw3350/DC1

Supplementary Materials and Methods

Fig. S1. Individual internal ²⁶Al isochrons obtained in 18 ²⁶Al-bearing inclusions.

Fig. S2. Example of IMF characterized in one analysis session.

Table S1. Magnesium isotopic compositions of 22 inclusions analyzed in this study.

Table S2. Relative sensitivity factors determined on standards with known ²⁷Al/²⁴Mg in three analysis sessions.