Short time interval for condensation of high-temperature silicates in the solar accretion disk

Significance

Combining bulk and in situ Mg isotope measurements allows dating the formation of chondrule precursors relative to that of chondrules themselves. This has never been achieved before and has profound implications for the origin of chondrules, the origin of their precursors, and the evolution of the solar protoplanetary disk. There is a minimum bulk chondrule isochron, analogous in some ways to the bulk calcium−aluminum-rich inclusion isochron, which dates either the cessation of condensation of chondrule precursors or the cessation of their transport to the regions where chondrules formed.

Abstract

Chondritic meteorites are made of primitive components that record the first steps of formation of solids in our Solar System. Chondrules are the major component of chondrites, yet little is known about their formation mechanisms and history within the solar protoplanetary disk (SPD). We use the reconstructed concentrations of short-lived ²⁶Al in chondrules to constrain the timing of formation of their precursors in the SPD. High-precision bulk magnesium isotopic measurements of 14 chondrules from the Allende chondrite define a ²⁶Al isochron with ²⁶Al/²⁷Al = 1.2(±0.2) × 10⁻⁵ for this subset of Allende chondrules. This can be considered to be the minimum bulk chondrule ²⁶Al isochron because all chondrules analyzed so far with high precision (∼50 chondrules from CV and ordinary chondrites) have an inferred minimum bulk initial (²⁶Al/²⁷Al) ≥ 1.2 × 10⁻⁵. In addition, mineral ²⁶Al isochrons determined on the same chondrules show that their formation (i.e., fusion of their precursors by energetic events) took place from 0 Myr to ∼2 Myr after the formation of their precursors, thus showing in some cases a clear decoupling in time between the two events. The finding of a minimum bulk chondrule ²⁶Al isochron is used to constrain the astrophysical settings for chondrule formation. Either the temperature of the condensation zone dropped below the condensation temperature of chondrule precursors at ∼1.5 My after the start of the Solar System or the transport of precursors from the condensation zone to potential storage sites stopped after 1.5 My, possibly due to a drop in the disk accretion rate.

Primitive meteorites (i.e., chondrites) are rocks that escaped melting and differentiation on their parent bodies. As a result, their components preserved a record of the mineralogy, chemistry, and isotopic compositions of the solids formed in the solar protoplanetary disk (SPD) before planetesimal formation. Viscous heating in the inner regions of the SPD (1) brought presolar dust and gas to temperatures higher than the sublimation point of most minerals, producing a gas that upon cooling produced the first Solar System solids by condensation. The relative uniformity of isotope ratios among many early Solar System materials (2) is testament to this phase of homogenization. The calcium−aluminum-rich inclusions (CAIs) that are found in primitive meteorites are considered to be formed from refractory precursors condensed at temperatures in the range from ∼1,400 K to ∼1,800 K (3). Chondrules are millimeter-size once-molten silicate spherules that comprise most of the mass (70–80%) of chondrites. They have compositions indicating that their formation took place from solid precursors condensed below 1,500 K (4, 5). The exact timing (duration, chronology) of (i) the condensation processes that produced the precursors of CAIs and of chondrules, and (ii) the processes that resulted in the formation of CAIs and chondrules, is still poorly known, although it is key to a better understanding of the complex origin and evolution of solids in the solar accretion disk.

The radionuclide ²⁶Al decays to ²⁶Mg with a half-life of 0.72 Myr and correlations between excess ²⁶Mg and Al/Mg in meteoritical materials are tell-tale signatures of ²⁶Al decay. These correlations define ²⁶Al−²⁶Mg isochrons. Major recent advances have been obtained from the development of high-precision measurements of the Mg isotopic compositions of CAIs and chondrules (6–10), increasing the resolution of ²⁶Al−²⁶Mg chronology. The existence of a bulk CV CAI ²⁶Al−²⁶Mg isochron, defined by a very tightly constrained slope and intercept in excess ²⁶Mg vs. Al/Mg space, shows that CV CAIs and their precursors formed in a very short time interval, within less than ∼40,000 years (7, 8) or even less than ∼4,000 years (11). We note, however, that some CAIs and ultrarefractory grains show evidence of heterogeneity in both δ²⁶Mg* (initial excess ²⁶Mg/²⁴Mg in per mil) and initial ²⁶Al/²⁷Al (12–15). The existence of a well-defined bulk CAI isochron demonstrates that agglomeration, melting, and crystallization to form CAIs from their precursor materials might be considered as a single astrophysical event. This CAI formation event, or short period, is generally taken as the “time zero” of the Solar System (referred to as CAIs' age). It can be dated using the absolute U-corrected Pb-Pb chronometer to 4567.30(±0.16) My (16), with older ages up to 4,568.2 being also proposed (17). ²⁶Al studies of CAIs show that some of them were reheated and remelted later in the disk, mostly within the first few hundred thousand years and up to ∼1.8 My later in one case, but the formation of their precursors by recondensation of sublimated presolar solids can be demonstrated to have occurred at time 0, within a few tens of thousands of years (18).

The majority of the solids in the accretion disk formed at lower temperatures than did CAIs, suggesting that they also formed later or at the same time but at different heliocentric distances. The chronology of formation of the ferromagnesian material comprising the major proportion of primitive meteoritical materials (e.g., chondrules) has proven elusive. Most chondrule age dating comes from evidence for the concentrations of short-lived ²⁶Al and to a lesser extent ⁵³Mn in the objects. A time gap of a few million years between CAIs and chondrules (with peaks of chondrule formation between ∼1.5 My and 3 My) is a general conclusion of ²⁶Al studies based on mineral isochrons (e.g., refs. 9, 19, and 20). However, this conclusion relies on the assumption of homogeneity of the ²⁶Al distribution at time 0 in the inner region of the disk [see discussions on ²⁶Al distribution in Villeneuve et al. (9), Larsen et al. (11), and Mishra and Chaussidon (21)]. In addition, mineral ²⁶Al isochrons in chondrules date the last melting event, thus giving no clue on the age of formation of chondrule precursors. In one case, the age of chondrule precursors could be determined using ²⁶Al systematics by calculating a model age from the Mg isotopic composition. This approach gives a precursor age of 0.87(±0.20) My after CAIs for a chondrule which was last melted ∼4 My post-CAI (9), bringing the formation of chondrule precursors closer to that of CAIs. Uranium-isotope-corrected Pb−Pb dating of chondrules are very scarce but recent data do show a ∼3-Myr age range, with several chondrules as old as CAIs, at 4,567.32 ± 0.42 My and 4,566.67 ± 0.43 My (16), as also suggested by ⁵³Mn data (22, 23). The temporal relationships between chondrule precursors and the chondrule formation events are therefore not well understood, especially because of a lack of comprehensive measurements in the same set of objects.

Here we report the Mg isotope study of 14 Mg-rich (type I) and Al-rich chondrules from the Allende carbonaceous chondrite (CV3). Our approach is, for the first time to our knowledge, to look both for mineral ²⁶Al isochrons and bulk ²⁶Al isochrons in the same chondrules. This is done by combining the use of multicollector secondary ion mass spectrometry (MC-SIMS) on eight chondrules for in situ analyses (at CRPG-CNRS Nancy, France) and high-resolution multicollector inductively coupled plasma source mass spectrometry (HR-MC-ICPMS) on 14 chondrules (the same as the ones measured by MC-SIMS, plus six others) for bulk analyses (at IPG Paris and CRPG-CNRS Nancy, France and at University of California, Los Angeles). Note that for Ch#B, three fragments of this chondrule (named Ch#B1, Ch#B2, and Ch#B3) were measured for their bulk Mg isotopic composition. This approach allows us to determine the age of chondrule precursors and the age of their last melting event using multiple lines of evidence. Results constrain the timing of condensation, transport, melting, and accretion of solids in the accretion disk.

Results

The chondrules studied from the Allende CV3 chondrite (see SI Appendix, SI Materials and Methods, SI 2A, and SI 2B) have bulk ²⁷Al/²⁴Mg ratios varying from 0.051 to 1.815 (Table 1), i.e., in the typical range for ferromagnesian to Al-rich chondrules [the latter having >10 wt% bulk Al₂O₃ (24)]. All bulk measurements (Table 1 and Fig. 1) together define a ²⁶Al isochron with a slope corresponding to an initial (²⁶Al/²⁷Al), (²⁶Al/²⁷Al)_{bulk initial}, of 1.23(±0.21) × 10⁻⁵ and an intercept, (δ²⁶Mg*)_{bulk initial}, of −0.009(±0.012)‰ [mean square weighted deviation (MSWD) = 0.62], clearly distinct from those of the bulk CAI isochron [with (²⁶Al/²⁷Al)₀ = 5.25(±0.12) × 10⁻⁵ and (δ²⁶Mg*)₀ = −0.034(±0.032)‰, where the zero subscript refers to the CAI initial values, as calculated from data by Jacobsen et al. (7) and Larsen et al. (11)]. Assuming ²⁶Al homogeneity in the inner Solar System, this chondrule whole-rock slope of 1.23(±0.21) × 10⁻⁵ would correspond to an age of 1.53(±0.18) My after CAI formation. One chondrule (Ch#1) has a bulk radiogenic ²⁶Mg excesses, which could also be consistent with the bulk CAI isochron. Excluding Ch#1 does not change significantly the bulk chondrule isochron [(²⁶Al/²⁷Al)_{bulk initial} = 1.25(±0.21) × 10⁻⁵ and (δ²⁶Mg*)_{bulk initial} = −0.012(±0.013)‰, MSWD = 0.18]. Although Mg evaporative loss does not always result in Mg isotopic fractionation (25, 26), there is no apparent correlation between the bulk ²⁷Al/²⁴Mg ratios and δ²⁵Mg values that would be indicative of such a process during chondrule melting. This suggests that chondrule precursors were never molten in a free vacuum and points to a high mass density of chondrules and their precursors (26). Investigations in more details of three Al-rich chondrules, which are key for the bulk chondrule isochron, showed no detectable effect of metamorphism and/or alteration on the Mg isotopic systematics (see SI Appendix, SI 2B).

Table 1.

Chemistry, Mg isotope bulk data, and ²⁶Al mineral isochrons

		(27Al/24Mg)bulk		(δ25Mg)bulk (‰)		(δ26Mg*)bulk (‰)			(26Al/27Al)i		(δ26Mg*)i (‰)
Chondrule	Type	Value	2σ	Value	2σ	Value	2σ	n	Value	2σ	Value	2σ	n
Ch#1	PP	0.347	0.035	−0.151	0.044	0.075	0.047	8	2.59 × 10−5	1.53 × 10−5	0.063	0.029	10
Ch#2	IO	0.135	0.008	−0.132	0.047	0.013	0.042	7
Ch#5	PO	0.128	0.006	−0.111	0.052	0.008	0.051	7	3.48 × 10−6	5.71 × 10−6	0.018	0.026	9
Ch#6	PO	0.118	0.014	−0.143	0.042	0.003	0.043	7
Ch#10	PO	0.099	0.002	−0.094	0.050	−0.007	0.046	7	8.78 × 10−6	6.27 × 10−6	0.008	0.019	10
Ch#12	PO	0.062	0.005	−0.174	0.043	−0.009	0.046	8	2.29 × 10−5	1.09 × 10− 5	−0.015	0.027	15
Ch#15	PO	0.078	0.003	−0.156	0.051	−0.008	0.042	7
Ch#18	BO	0.121	0.001	−0.387	0.046	−0.006	0.046	7
Ch#20		0.051	0.002	−0.168	0.046	−0.002	0.047	7
Ch#21	BO	0.076	0.005	−0.106	0.044	−0.005	0.044	7	1.17 × 10−5	3.76 × 10−6	−0.047	0.024	15
Ch#A	PO	0.086	0.060			0.002	0.027		2.38 × 10−5	6.97 × 10−6	−0.006	0.026	26
Ch#B1	Al-rich	1.375	0.072			0.127	0.014
Ch#B2		1.710	0.068			0.152	0.034
Ch#B3		2.359	0.057			0.184	0.020
Ch#B		1.815	0.066			0.154	0.023		1.06 × 10−5	1.39 × 10−6	0.030	0.015	35
Ch#C	Al-rich	0.663	0.060			0.038	0.028		1.56 × 10−5	1.95 × 10−6	0.029	0.018	36
Ch#D	Al-rich	0.527	0.060			0.024	0.031

BO, barred olivine; IO, isolated olivine; PO, olivine-rich porphyritic; PP, pyroxene-rich porphyritic. Ch#B1, Ch#B2, and Ch#B3 represent three fragments of the same chondrule. The average of these three fragments (named Ch#B) is used as the bulk value and is represented on Fig. 1 (the three fragments are represented by orange diamonds while the average is in blue). Data for chondrules Ch#A, Ch#B, Ch#C, and Ch#D were previously reported in Ingalls et al. (46), where they were named Allende CH1, CH2, CH3, and CH4, respectively.

Fig. 1.

Comparison between bulk and mineral ²⁶Al isochrons for the 14 Allende chondrules from this study. The best-fit line yields a bulk isochron (blue dashed line defined by the blue diamonds) with a (²⁶Al/²⁷Al)_{bulk initial} slope of 1.23(±0.21) × 10⁻⁵ and an intercept (δ²⁶Mg*)_{bulk initial} of −0.009(±0.012)‰. The mineral ²⁶Al isochrons are represented for each object by the colored segments passing through the bulk compositions. By definition, the slope of the mineral isochron cannot be higher than that of the bulk isochron since the formation of the chondrule itself cannot predate the formation of its precursors. This is verified by nearly all chondrules except a few that might have in fact a bulk ²⁶Al/²⁷Al ratio higher than that of the bulk chondrule isochron (see text).

At the mineral scale within a single chondrule, the ²⁷Al/²⁴Mg ratios are much more variable: A range of a factor of 10 is present in Ch#1 and up to a factor of ∼335 in Ch#B. This range in composition allowed for determination of mineral ²⁶Al isochrons for each chondrule, although not all of the isochrons are well defined. These ²⁶Al mineral isochrons (see individual diagrams in SI Appendix, SI 2C) show slopes corresponding to (²⁶Al/²⁷Al)_i from 3.48(±5.71) × 10⁻⁶ to 2.59(±1.53) × 10⁻⁵, and (δ²⁶Mg*)_i intercepts from −0.047(±0.024)‰ to 0.063(±0.029)‰ (Table 1). This is consistent with previous mineral isochrons [3 × 10⁻⁶ < (²⁶Al/²⁷Al)_i < 1 × 10⁻⁵ for chondrules in LL3.0 chondrites (9, 20, 27–29), CO3.0 chondrites (20, 30, 31), and Acfer 094 (Ungrouped C 3.0; 20, 32, 33)]. The (²⁶Al/²⁷Al)_i ratios are higher than, equal to, or lower than (²⁶Al/²⁷Al)_{bulk initial} depending on the chondrules (Fig. 1). There is no clear relationship between the (²⁶Al/²⁷Al)_i ratios and (δ²⁶Mg*)_i values, or between the (²⁶Al/²⁷Al)_i ratios and the bulk ²⁷Al/²⁴Mg ratios. Assuming ²⁶Al homogeneity in the inner Solar System, the (²⁶Al/²⁷Al)_i ratios of the chondrule mineral isochrons correspond to an average age of 1.2 My after CAI formation [total range from 0.73(+0.93/−0.48) to 1.86(+1.30/−0.56) My after CAIs]. Ch#5 is the only chondrule which has a significantly lower (²⁶Al/²⁷Al)_i corresponding to a younger age of 2.81(±1.00) My after CAIs.

Constraints from the Bulk ²⁶Al Isochron on the Age of Chondrule Precursors

The simplest interpretation of a bulk composition of a chondrule is to consider that it reflects the average composition of its solid precursors. Assuming that ²⁶Al and Mg isotopes were homogenized to ∼±10% at time 0 in the regions of the SPD where the precursors of CAIs and chondrules formed (9, 21), the present bulk chondrule ²⁶Al isochron with (²⁶Al/²⁷Al)_{bulk initial} = 1.23(±0.21) × 10⁻⁵ would measure the average age of the precursors of the 14 Allende chondrules studied relative to CAIs under the assumption that chondrules and CAIs are averages of the same materials sampled at different times. In this case, chondrule precursors formed 1.53(±0.18) My after CAIs. Using the same reasoning as that used to constrain CAI precursors formation times from the bulk CAI ²⁶Al isochron (8, 11), the scatter of data around the bulk chondrule isochron would indicate that the precursors of the present chondrules formed over a short period (< 180 kyr).

However, this conclusion does not seem to be valid for chondrules in general when considering all existing high-precision Mg isotopic data for bulk chondrules [Galy et al. (34) and Bizzarro et al. (35) for the Allende CV3 carbonaceous chondrite, and bulk compositions recalculated from data by Villeneuve et al. (9) for the Semarkona LL3 ordinary chondrite]. A significant number of chondrules plot on the bulk CAI isochron and five chondrules plot in between the bulk CAI isochron and the bulk chondrule isochron from this study (Fig. 2). In addition, because “normal” ferromagnesian chondrules have low ²⁷Al/²⁴Mg ratios (<0.2), they cannot develop high enough ²⁶Mg* excesses (relative to the analytical uncertainties) to distinguish between the two isochrons (Fig. 2). Seven chondrules with high ²⁷Al/²⁴Mg ratios [three from this study, one from Galy et al. (34), two from Bizzarro et al. (35), and one from Villeneuve et al. (9)], plot unambiguously on the bulk chondrule isochron defined herein (Fig. 2). The regression line calculated from these seven chondrules corresponds to (²⁶Al/²⁷Al)_{bulk initial} = 1.30(±0.20) × 10⁻⁵ and (δ²⁶Mg*)_{bulk initial} = −0.013(±0.005)‰, with an MSWD = 1.1, and is identical within errors to that calculated from all of the chondrules from this study, thus confirming the robustness of this isochron.

Fig. 2.

²⁶Al−²⁶Mg isochron diagram for bulk chondrules, with all available data. All chondrules plot between the bulk CAI isochron (or on it) and the minimum bulk chondrule isochron determined in this study (or on it). The minimum bulk chondrule isochron might date the end of the formation of chondrule precursors in the disk, 1.5(±0.2) My after time 0. The 2-sigma error bars are shown when larger than the data points.

It is tempting to ascribe the distribution of chondrules between the bulk CAI isochron and the present bulk chondrule isochron (Fig. 2) to the formation of chondrule precursors starting contemporaneously with the formation of CAI precursors and ending ∼1.5 Myr later. However, we note that the bulk Mg isotopic data do not exclude the possibility that all chondrule precursors formed at the same time as CAI precursors (or very close to CAI precursors). This is because Mg isotopic compositions of chondrules could have been reset during chondrule forming events by high-temperature Mg isotopic exchange with the nebular gas, producing an ²⁶Al isochron with a ²⁶Al/²⁷Al slope and initial δ²⁶Mg* intercept corresponding to the isotopic composition of the gas at the time. When ²⁶Al/²⁷Al decreased to 1.3 × 10⁻⁵ (i.e., 1.5 My after CAI) in a nebular gas with initial Al and Mg isotopic compositions identical to that defined by the bulk CAI isochron, the Mg isotopic composition calculated for the gas gives a new radiogenic Mg isotopic composition of δ²⁶Mg* = −0.007‰. This would be consistent with the present bulk chondrule isochron. However, had this resetting happened for chondrules, it should have occurred for CAIs, too. The absence of CAIs plotting on the chondrule isochron argues in favor of a genuine difference between chondrules and CAIs. Thus, we propose that the present bulk chondrule ²⁶Al isochron (defined from a subset of Allende chondrules) can be considered as the minimum bulk chondrule ²⁶Al isochron. If this interpretation is correct, this would imply that there is in chondrites no chondrule existing with precursors formed in the SPD by nebular processes later than ∼1.5 My after the start of the Solar System [chondrules formed by impact between planetesimals can be made later (36)].

Time Difference Between the Formation of Chondrules and That of Their Precursors as Indicated by the Mineral and Bulk ²⁶Al Isochrons

Further insights into the timing of formation of the Allende chondrules from this study and of their precursors can be obtained by comparing the mineral ²⁶Al isochron of each chondrule to the bulk chondrule ²⁶Al isochron. This can also be done for chondrules from Villeneuve et al. (9) for which the bulk δ²⁶Mg* values can be recalculated from the mineral isochrons and the bulk ²⁷Al/²⁴Mg ratios. The bulk chondrule ²⁶Al isochron dates the time when the bulk ²⁷Al/²⁴Mg ratio of the precursors was established (e.g., during their formation by condensation from the gas), while the mineral isochron dates the time when the ²⁷Al/²⁴Mg ratios were fractionated between the different components of a chondrule by crystallization during the last chondrule melting event. Because final crystallization must postdate establishment of the precursor chemistry, it is expected that all chondrules should exhibit mineral isochrons with slopes [(²⁶Al/²⁷Al)_i] lower than, or equal to, the slope of the bulk chondrule isochron [(²⁶Al/²⁷Al)_{bulk initial}]. For internal consistency, we also expect that the initial δ²⁶Mg* (δ²⁶Mg*_i, intercepts) of the mineral isochrons should be greater than, or equal to, that of the bulk isochron and that the differences in initial δ²⁶Mg* should be consistent with the differences in slopes (i.e., initial ²⁶Al/²⁷Al) between the mineral and bulk isochrons.

This check on internal consistency is verified for Ch#5, Ch#10, Ch#21, Ch#B, Ch#C, and all chondrules from Villeneuve et al. (9). Ch#10, Ch#21, Ch#B, and Ch#C have (²⁶Al/²⁷Al)_i ratios identical within errors with the (²⁶Al/²⁷Al)_{bulk initial} ratio (Fig. 1), in agreement either with formation of their precursors contemporaneously with chondrule melting or Mg isotopic reequilibration with the nebular gas during chondrule melting. As discussed in Constraints from the Bulk ²⁶Al Isochron, the present data do not provide the basis for favoring one hypothesis or the other definitively. Ch#5 and all chondrules from Villeneuve et al. (9) have (²⁶Al/²⁷Al)_i ratios that are significantly lower [e.g., 4.2(±5.3) × 10⁻⁶] than the (²⁶Al/²⁷Al)_{bulk initial} ratio of 1.3(±0.2) × 10⁻⁵. This implies that the last melting event that affected these chondrules took place later than the formation of their precursors. For example, for Ch#5, the youngest possible age for the formation of chondrule precursors constrained by the minimum bulk chondrule isochron being ∼1.5 My after CAIs is 2.8(±1.0) My after CAIs; chondrules were being reset for at least ∼1 Myr, if not longer.

Two chondrules exhibit (²⁶Al/²⁷Al)_i ratios defined by their constituent minerals higher than the (²⁶Al/²⁷Al)_{bulk initial} ratio defined in this study: This is the case for Ch#A [(²⁶Al/²⁷Al)_i = 2.0(±0.4) × 10⁻⁵] and marginally for Ch#12 [(²⁶Al/²⁷Al)_i = 2.0(±0.9) × 10⁻⁵]. Because these two chondrules have low ²⁷Al/²⁴Mg bulk ratios (0.062 and 0.086 for Ch#12 and Ch#A, respectively), their bulk δ²⁶Mg* values plot between the bulk chondrule isochron of this study and the bulk CAI isochron (Fig. 2). The mineral isochrons imply that the precursors of Ch#A (and possibly of Ch#12) formed when ²⁶Al/²⁷Al was ≥ 2.0 × 10⁻⁵ in the SPD and perhaps when it was as high as 5.2 × 10⁻⁵.

²⁶Al Model Ages of Chondrule Precursors

When chondrules have ²⁷Al/²⁴Mg ratios significantly higher than chondritic (the case of Al-rich chondrules), a ²⁶Al model age of their precursors can be calculated relative to the Solar System growth curve of δ²⁶Mg*, as explained in Villeneuve et al. (9). These model ages record the time of separation of the material from the bulk, or average, solar reservoir (in this case, the enrichment in Al). In a diagram showing (δ²⁶Mg*)_i versus (²⁶Al/²⁷Al)_i (i.e., time), any excess in ²⁶Mg relative to the growth curve of the Solar System (anchored by the composition defined by the bulk CAI isochron and calculated for a Solar System ²⁷Al/²⁴Mg ratio of 0.101) can be explained by ²⁶Al decay in a closed system comprising the chondrule's Al-rich precursors. This evolution is defined by the following:

$${\left(\delta {}^{26}\text{M}{\text{g}}^{\ast }\right)}_i={\left(\delta {}^{26}\text{M}{\text{g}}^{\ast }\right)}_0+\frac{\mathrm{1,000}}{0.13932}\times \left[\left({\left(\frac{{}^{26}\text{A}\text{l}}{{}^{27}\text{A}\text{l}}\right)}_0-{\left(\frac{{}^{26}\text{A}\text{l}}{{}^{27}\text{A}\text{l}}\right)}_{\mathit{precursors}}\right)\times {\left(\frac{{}^{27}\text{A}\text{l}}{{}^{24}\text{M}g}\right)}_{\mathit{Solar}}+\left({\left(\frac{{}^{26}\text{A}\text{l}}{{}^{27}\text{A}\text{l}}\right)}_{\mathit{precursors}}-{\left(\frac{{}^{26}\text{A}\text{l}}{{}^{27}\text{A}\text{l}}\right)}_i\right)\times {\left(\frac{{}^{27}\text{A}\text{l}}{{}^{24}\text{M}\text{g}}\right)}_{\mathit{precursors}}\right]$$ [1]

where (²⁶Al/²⁷Al)_precursors is the ²⁶Al/²⁷Al ratio at the time of formation of Al-rich precursors, (²⁷Al/²⁴Mg)_precursors is the ²⁷Al/²⁴Mg of the precursors assumed to be the bulk ratio of the chondrule, and 0.13932 is the reference ²⁶Mg/²⁴Mg ratio. In this two-stage model, it is assumed that between (²⁶Al/²⁷Al)₀ and (²⁶Al/²⁷Al)_precursors (i.e., between the solar initial ²⁶Al/²⁷Al defined by CAIs and the initial ²⁶Al/²⁷Al of the chondrule precursors), the evolution of Mg isotopes takes place in the SPD gas with the solar ²⁷Al/²⁴Mg ratio, and that at the time given by the intersection between the chondrules growth curve and the Solar System growth curve, chondrule precursors formed with (²⁷Al/²⁴Mg)_precursors. Precursors model ages can be calculated for one chondrule from Villeneuve et al. (9) and three chondrules from the present study (Fig. 3). This gives 0 ± 0.12 My for Ch#1, 0.87 ± 0.20 My for Sem-ch4 from ref. 9, 1.12 ± 0.52 My for Ch#C, and 1.51 ± 0.17 My for Ch#B (Fig. 3; see SI Appendix, SI Materials and Methods for details of error propagation). These ages represent the formation time of the material from which the chondrules formed. Ch#B and Ch#C plot on the bulk chondrule isochron, indicating that their precursors formed at 1.5 ± 0.2 My. Conversely, Ch#1 and Sem-ch4 are evidently composed of precursors formed much earlier, dating all of the way back to CAI formation in the case of Ch#1 (see, in SI Appendix, Possible Fraction of CAI Material in Al-Rich Chondrules, an alternative explanation of Ch#1 composition).

Fig. 3.

²⁶Al model ages of the precursors of 4 FeO-poor type I chondrules [Ch#1, Ch#B, and Ch#C from this study, Sem-ch4 from Villeneuve et al. (9)] calculated from the intersection between the Solar System (SS) ²⁶Mg growth curve (black line) and the chondrules ²⁶Mg growth curves (colored lines). The SS growth curve is anchored by the (²⁶Al/²⁷Al)₀ and (δ²⁶Mg*)₀ of bulk CAIs, and is calculated for a solar ²⁷Al/²⁴Mg ratio of 0.101 (47). The chondrule growth curves are anchored by the (²⁶Al/²⁷Al)_i and (δ²⁶Mg*)_i of bulk chondrules, and calculated using the bulk ²⁷Al/²⁴Mg ratios of each chondrule assuming that this is bulk composition of their precursors and that they evolved in closed system between their accretion and chondrule melting (see ²⁶Al Model Ages of Chondrule Precursors for details). This gives precursor ²⁶Al model ages of 0(±0.12) My for Ch#1, 1.51(±0.17) My for Ch#B, 1.12(±0.52) My for Ch#C, and 0.87(±0.20) My for Sem-ch4.

Arguments For and Against ²⁶Al Homogeneity in the CAIs- and Chondrules-Forming Region of the Disk

All of the present Mg isotopic data can be understood in the context of homogeneous, or nearly homogeneous, ²⁶Al/²⁷Al and Mg isotope ratios in the regions of the accretion disk where CAIs, chondrules, and their precursors formed. In this case, variable initial ²⁶Al/²⁷Al and δ²⁶Mg* values have a chronological significance. Similar observations were made previously for chondrules (9) and CAIs (21). However, other observations exist that are used to suggest significant heterogeneity in these isotope ratios from ultra-high-precision (a few parts per million level) Mg isotopic composition of CAIs and AOAs (11) or from apparent age discrepancies between the Pb−Pb and ²⁶Al chondrule age dates (16). We explore in the following if the chondrule Mg isotopic data presented here can be understood in the context of ²⁶Al/²⁷Al heterogeneity and what the consequences would be for our understanding of the formation of chondrules and their precursors.

Because all chondrules show ²⁶Al mineral isochrons having similar initial δ²⁶Mg* values, the only scenario for heterogeneous distribution that would be consistent with the chondrule data is one in which most of the heterogeneity is due to variations in the ²⁶Al/²⁷Al ratio of the nebular gas and not to large variations in its δ²⁶Mg* value. To explain the minimum bulk chondrule ²⁶Al isochron by heterogeneity in ²⁶Al/²⁷Al, two gaseous reservoirs should have coexisted at time 0 (given by the bulk CAI isochron and corresponding to an absolute age of ∼4,568 My; see the Introduction), one with ²⁶Al/²⁷Al = 5.2 × 10⁻⁵ and one with ²⁶Al/²⁷Al = 1.2 × 10⁻⁵, both having similar δ²⁶Mg* values in the range from −0.034‰ to ∼−0.006‰ (see Constraints from the Bulk ²⁶Al Isochron), and possibly similar ²⁷Al/²⁴Mg ratios. This conclusion results from the fact that it is highly unlikely that the minimum bulk chondrule ²⁶Al isochron is a mixing line between two types of components having different Mg isotopic compositions (one Mg-rich with ²⁷Al/²⁴Mg ≈ 0 and δ²⁶Mg* = −0.006‰ and the other Mg-poor with ²⁷Al/²⁴Mg ≈ 2.5 and δ²⁶Mg* ≈ +0.2‰) because the mineral isochrons demonstrate that live ²⁶Al was present in several of these chondrules at a level of (²⁶Al/²⁷Al)_i ≈ 1.2 × 10⁻⁵. The initial ²⁶Al/²⁷Al ratios in these objects are not readily explained as spurious products of mixing unless an extraordinary coincidence is invoked.

While unlikely on the basis of the data, the scenario of heterogeneous isotopic distribution in the disk cannot be ruled out unequivocally. However, significant heterogeneity sufficient to invalidate chronological interpretations seems unlikely for two additional reasons. First, it is difficult to understand why precursors of chondrules would be formed from the two contemporaneous gas reservoirs while precursors of CAIs formed only from the one reservoir with ²⁶Al/²⁷Al ≈ 5.25 × 10⁻⁵. Second, in the scenario of isotopic homogeneity, the variations in initial ²⁶Al/²⁷Al ratios and variations in initial δ²⁶Mg* values observed in chondrules are both well explained by decay of ²⁶Al from a reservoir homogenized at time 0 (with a precision of ∼10% for ²⁶Al/²⁷Al and a few parts per million for δ²⁶Mg*). This would appear to be an extraordinary coincidence in the case of isotopic heterogeneity. This later argument was previously developed in Villeneuve et al. (9) and Mishra and Chaussidon (21).

In conclusion, heterogeneity at some level must have existed in the SPD, and perhaps early or locally it was pronounced (12–14), but on a global scale for the majority of chondrules (and all chondrules in the present study), it does not seem to be a requirement from the data. This does not explain the apparent age discrepancy observed for chondrules between ²⁶Al ages and Pb−Pb ages (16) but we note that the bulk δ²⁶Mg* of chondrules (in the hypothesis of ²⁶Al homogeneity) implies that many chondrules had their precursors formed at the same time as CAIs.

Astrophysical Implications

While chondrules do not contain precursors (i.e., high-temperature condensation from a gas of solar composition) formed later than 1.5 My after “time zero,” the formation of chondrules (i.e., fusion of their precursors by energetic events) took place from 0 My to ∼2 My after the formation of their precursors (as shown by the present data and also, most presumably, for many chondrules from several previous studies for which the bulk δ²⁶Mg* is not available). This observation is quite interesting in the framework of most recent models of protoplanetary disks (37). The condensation of mineral precursors of chondrules occurred within the hot zone of the SPD, bound by the sublimation and condensation fronts (∼isotherms) for silicates. This region, probably maintained hot by viscous heating that is the natural consequence of accretion, extended from a few tenths of an astronomical unit (AU) (38) to 1 AU or so (39). Since chondrule formation evidently occurred a few astronomical units from the star (40), it implies that chondrule precursors were transported from the inner hot disk region to the (now) region of the present-day asteroid belt. However, a transport mechanism based on the viscous expansion of the disk (41, 42) is applicable only in the case of early (within a few 10⁵ years of CAI formation) condensation of chondrule precursors.

Because, in some (rare) cases, chondrule formation appears to be delayed relative to the condensation of their precursors, it implies that the precursors can be stored for times possibly as long as ∼2 Myr before the energetic chondrule-forming events. The so-called dead zone, where the disk gas is immune to cosmic ray ionization and the gas flow is laminar rather than turbulent, is a region of choice to store solids, especially since the accumulation of dust does not alter its properties (43). In a majority of cases, however, it appears that the melting to form chondrules occurred contemporaneously (within errors) with the condensation of the precursors. This implies that the source of energy that caused the formation of chondrules occurred where condensation was occurring. This in turn implies that the chondrule-forming process was in the inner part of the dead zone, perhaps related to planet formation (44).

Some of the present observations could also be understood in the framework of alternative models for chondrule formation. For example, in the case of chondrule formation by solidification of melts generated by impacts between planetesimals, the age of the precursors can be viewed as the age of the planetesimals, and the age of the chondrules as the age of the collision. The storage of the precursors at the surface of planetesimals could be an alternative to their storage in a dead zone of the SPD. However, planetesimals accreted earlier than 1.5 Myr post-CAIs are likely to have experienced rock−metal differentiation (45) as a result of heating by ²⁶Al decay (assuming an initial solar ²⁶Al/²⁷Al near 5.2 × 10⁻⁵), and this does not appear to be consistent with the isotopic and chemical characteristics of ferromagnesian chondrules. On the other hand, the basaltic crusts of differentiated objects should have been characterized by high ²⁷Al/²⁴Mg ratios and high δ²⁶Mg* values, making them a potential source of precursors to Al-rich chondrules.

In conclusion, although we are still far from a detailed understanding of the evolution of the solar protoplanetary disk, the present ²⁶Al chondrule data help bridge the gap between the timing of processes in the SPD recorded in meteorites and modeling of physical processes such as condensation, transport, and energetic events anticipatory to, or resulting from, planet formation.