A LOWER INITIAL ABUNDANCE OF SHORT-LIVED ⁴¹Ca IN THE EARLY SOLAR SYSTEM AND ITS IMPLICATIONS FOR SOLAR SYSTEM FORMATION

The samples studied here are the E44 and E65 CAIs from the CV chondrite Efremovka. They are of particular importance in potassium isotopic analyses because the prior existence of ⁴¹Ca/⁴⁰Ca = 1.4 × 10⁻⁸ in the solar system was primarily inferred in them (Srinivasan et al. 1996). Other earlier studies on their petrology, mineral chemistry, and magnesium and boron isotopic compositions can be found in Goswami et al. (1994), Young et al. (2005), McKeegan et al. (2001), and Srinivasan & Chaussidon (2012). Recent high precision analyses of Mg isotopes revealed that E44 and E65 are characterized by ²⁶Al/²⁷Al ratios of (4.8 ± 0.3) × 10⁻⁵ and (4.46 ± 0.25) × 10⁻⁵ (Young et al. 2005; Srinivasan & Chaussidon 2012), respectively. The two inclusions have also been shown to preserve fossil records of ¹⁰Be (t_1/2 = 1.3 Myr; Korschinek et al. 2010), with ¹⁰Be/⁹Be = (8.4 ± 1.9) × 10⁻⁴ and (7.0 ± 1.7) × 10⁻⁴ consistent with one another within analytical uncertainties (McKeegan et al. 2001; Srinivasan & Chaussidon 2012).

Measurements of potassium isotopes were made on the CAMECA 1280 HR2 ion microprobe at CRPG, Nancy. The major challenge in obtaining the true radiogenic component of ⁴¹K is to accurately quantify the magnitudes of all interferences at m/e = 41, including (⁴⁰Ca⁴²Ca)⁺⁺ and scattered ions from ⁴⁰Ca⁺ and ⁴⁰CaH⁺ tails, and correct for them. Given that the initial ⁴¹Ca/⁴⁰Ca ratio in the early solar system appears to be ≈10⁻⁸, only phases with ⁴⁰Ca/³⁹K exceeding 5 × 10⁵ (K concentrations <200 ng g⁻¹) could potentially provide large enough ⁴¹K excesses compared to the analytical errors. However, two problems come with such high ⁴⁰Ca/³⁹K ratios. First, low K count rates, especially at mass 41, limit the analytical precision. Second, intensities of Ca-related interferences at m/e = 41 become significant relative to that of ⁴¹K⁺, making accurate determinations of ⁴¹K/³⁹K ratios very difficult. These challenges, in theory, could be eased by using a large-geometry SIMS, whose high throughput and high mass resolution (compared to those of smaller ones, e.g., CAMECA 3-7f) help improve analytical precision as well as separation between interferences and the peaks of interest.

The 1280HR2 was operated with a mass resolution (M/ΔM) of 8000, sufficient to separate ⁴⁰CaH⁺ from ⁴¹K⁺, and other minor interferences from the peaks of interests (Figure 1). Since the major interference at mass 41, (⁴⁰Ca⁴²Ca)⁺⁺, was not resolvable under any available mass resolution (M/ΔM = 34,000 is needed), we estimated its contribution indirectly by assuming that the following equality holds (see Hutcheon et al. 1984; Srinivasan et al. 1996):

$${\rm \frac{(^{40}Ca^{42}Ca)^{++}}{^{42}Ca^{+}} = \frac{(^{40}Ca^{43}Ca)^{++}}{^{43}Ca^{+}}},$$

(⁴⁰Ca⁴³Ca)⁺⁺ can be found at m/e = 41.5. Due to its extremely low intensity (<1 counts s⁻¹), the location of (⁴⁰Ca⁴³Ca)⁺⁺ (41.4607 amu) was set by anchoring the magnetic field to the reference peak (⁴⁰Ca²⁷Al¹⁶O)⁺⁺ (41.4695 amu). The high transmission of the instrument enabled the measurement of (⁴⁰Ca⁴³Ca)⁺⁺ to determine (⁴⁰Ca⁴³Ca)⁺⁺/⁴³Ca⁺ for every spot analysis, as opposed to stand-alone characterizations of this ratio independent of K isotope analyses (see Srinivasan et al. 1996). We confirmed that (⁴⁰Ca⁴³Ca)⁺⁺/⁴³Ca⁺ is matrix dependent (Hutcheon et al. 1984; Srinivasan et al. 1996), and the values obtained here are identical within errors to those in Srinivasan et al. (1996). We used the measured (⁴⁰Ca⁴³Ca)⁺⁺/⁴³Ca⁺ ratio in each run to estimate the level of (⁴⁰Ca⁴²Ca)⁺⁺ in that given spot and correct for it.

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In addition to (⁴⁰Ca⁴²Ca)⁺⁺, we carefully evaluated the levels of scattered ions from the tails of ⁴⁰Ca⁺ and ⁴⁰CaH⁺ at m/e = 41. The former, which was not accounted for in Srinivasan et al. (1996), was found at ≈3 × 10⁻¹⁰ × ⁴⁰Ca⁺ by measuring in steps of 0.2 amu between masses 40 and 41, whereas the latter was estimated by measuring the signal at mass 41.95 and applying the following relationship (assuming the peak shape of ⁴²Ca⁺ on the low-mass side is the same as that of ⁴⁰CaH⁺):

$${\rm [^{40}CaH^{+}]_{{\rm tail}} = \frac{[41.95]}{[^{42}Ca^{+}]} \times[^{40}CaH^{+}]}.$$

Under our analytical condition, the ratio of scattered ions at m/e = 41 to the intensity of ⁴⁰CaH⁺ was found to be 3 × 10⁻⁶. Such a correction is relatively minor (<1% of the total counts) compared to that for (⁴⁰Ca⁴²Ca)⁺⁺ due to full separation between ⁴⁰CaH⁺ and ⁴¹K. The dynamic background of the counting system was measured for 60 s at the beginning of each analytical cycle, and the typical count rates range from 0.02 to 0.05 counts s⁻¹. This dynamic background was preferred over static background of ∼0.005 counts s⁻¹ measured overnight for 10 hr at 60 s interval because the latter may lead to under correction. The true ⁴¹K/³⁹K ratio of a spot was then obtained after summing up counts over the entire analysis (e.g., Ogliore et al. 2011) and stripping off the interferences:

$$\selectfont\fontsize{7.7}{9.7}{\begin{eqnarray*} &&\rm \left(\frac{^{41}K^{+}}{^{39}K^{+}}\right)_{{\rm true}}\nonumber\\ &&\quad = \frac{[41]_m - \left[\frac{(^{40}{\rm Ca^{43}Ca})^{++}}{^{43}{\rm Ca}^{+}}\right]\,\times \,^{42}{\rm Ca}^{+} -[^{40}{\rm CaH}^{+}]_{{\rm tail}} - [^{40}{\rm Ca}^{+}]_{{\rm tail}} - {\rm bkgd}}{^{39}{\rm K}^{+}}. \end{eqnarray*}}$$

In our analytical protocol, a polished sample was sputtered with a 10 nA ¹⁶O⁻ primary beam, and secondary ions were collected by the axial electron multiplier (EM) in a peak-jumping mode, with the mass sequence of 38.7, ³⁹K⁺, ⁴¹K⁺, ⁴⁰CaH⁺, (⁴⁰Ca⁴³Ca)⁺⁺, (⁴⁰Ca²⁷Al¹⁶O)⁺⁺, ⁴²Ca⁺, and ⁴³Ca⁺. ⁴⁰Ca was not measured to avoid additional uncertainties derived from the cross calibration between a Faraday cup and the axial EM. Before each analysis, ∼25 minute presputtering was applied to the sample surface to minimize the contaminations. The field aperture width was set at 2500 μm to block out scattered K ions from the vicinity of the analysis spot. An energy window of 50 eV was used. To correct for the peak and magnetic field drifts during a long analysis, both mass calibration and surface charging compensation were performed every five cycles. The count time on ⁴¹K⁺ and (⁴⁰Ca⁴³Ca)⁺⁺ was set at 60 s to achieve sufficient counting statistics. Each measurement consisted of 25–50 cycles and required ∼2–4 hr of analysis time. Two terrestrial calcite standards with high ⁴⁰Ca/³⁹K ratios (>10⁶, see Figure 2) were analyzed to ensure that the mass spectrometry and the interference correction scheme were properly performed. Although ⁴⁰K was not measured, normal ⁴¹K/³⁹K ratios within errors (0.072; Garner et al. 1975) obtained in all standard analyses indicated that the instrumental mass fractionation and the matrix effect on K isotope compositions were insignificant and would not affect the determination of ⁴¹K* in extraterrestrial samples.

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The relative sensitivity factor (RSF) of Ca to K was determined to be 2.53 ± 0.01 (2σ) on a NIST 614 glass with known Ca and K concentrations (CaO = 12 wt% and K = 30 μg g⁻¹; NBS Tech Report 1982). Given that Ca isotopes exhibited very limited instrumental mass fractionation in the NBS 614 glass (<2 amu⁻¹), we calculated the true ⁴⁰Ca/³⁹K ratio of a measured phase as follows:

$${\rm \left(\frac{^{40}Ca}{^{39}K}\right)_{{\rm true}} = \left(\frac{^{42}Ca^{+}}{^{39}K^{+}}\right)_{m}\,\times \,\frac{^{40}Ca}{^{42}Ca}\,\times \,RSF},$$

where ⁴⁰Ca/⁴²Ca = 151.03 (Niederer & Papanastassiou 1984).

The results obtained in this study are much lower than the previous value of Srinivasan et al. (1996), probably because the new SIMS enabled better separation between interferences and peaks of interest and more accurate corrections for the scattered ions at m/e = 41. However, it should be noted that the two CAIs could have been thermally processed after their formation, as was implied by their lower-than-canonical ²⁶Al/²⁷Al ratios. Given that K self-diffusivity is only marginally slower than that of Mg in melilite (e.g., 6.74 × 10⁻¹⁹ and 9.43 × 10⁻¹⁹ m² s⁻¹ at 1200 °C, respectively; Ito & Ganguly 2004; the diffusion coefficient of K in fassaite is not available), the extent to which the K isotopes were disturbed should be similar to (or slightly less than) the Mg isotopes. This suggests that the ⁴¹Ca/⁴⁰Ca ratios inferred from our measurements should not represent the true solar system initial. Applying the resetting times of ∼80,000 years and ∼155,000 years to E44 and E65, respectively, as were calculated by scaling their ²⁶Al/²⁷Al ratios back to 5.2 × 10⁻⁵, we obtain converging values of ⁴¹Ca/⁴⁰Ca = 4.55^+2.60_{− 1.57} × 10⁻⁹ and 4.10^+2.04_{− 1.30} × 10⁻⁹. Such ⁴¹Ca/⁴⁰Ca ratios are perfectly consistent with the inferred ⁴¹Ca/⁴⁰Ca = (4.1 ± 2.0) × 10⁻⁹ by Ito et al. (2006) in the EGG3 CAI that is also characterized by the canonical ²⁶Al/²⁷Al of (5.29 ± 0.39) × 10⁻⁵ (Wasserburg et al. 2011). This surprisingly good agreement between CAIs from two different meteorites suggests synchronicity between ⁴¹Ca and ²⁶Al, albeit based on only three CAIs. As ²⁶Al is believed to have been homogeneously distributed at ²⁶Al/²⁷Al = 5.2 × 10⁻⁵ in the solar nebula during the epoch of CAI formation (Jacobsen et al. 2008; Villeneuve et al. 2009), this apparent synchronicity would not only imply a uniformity of ⁴¹Ca/⁴⁰Ca = (4.1–4.5) × 10⁻⁹ at the same time, but render ⁴¹Ca chronology legitimate. Considering the error associated with each value, we propose that ⁴¹Ca/⁴⁰Ca ∼ 4.2 × 10⁻⁹ should be considered the best estimated initial ratio in the early solar system.

The new initial ⁴¹Ca/⁴⁰Ca ratio has important implications for the origin of this radionuclide and the timescale of solar system formation. Earlier explanations for ⁴¹Ca/⁴⁰Ca = 1.4 × 10⁻⁸ involved a last-minute addition to the solar nebula, either by an injection from a stellar source or by in situ early solar system irradiation (e.g., Huss et al. 2009; Gounelle et al. 2001). This is because the expected "average" ⁴¹Ca/⁴⁰Ca value in the interstellar medium (ISM) 4.5 billion years ago is only ∼(2–8) × 10⁻⁸, as can be calculated from Galactic Chemical Evolution (GCE; e.g., Wasserburg et al. 2006; Huss et al. 2009). Given the million-year (or longer) timescale for the formation of a molecular cloud and for a fragment of that cloud to collapse and form the Sun (Hartmann et al. 2001; Glover & Mac Low 2007), ⁴¹Ca directly inherited from the average ISM would have almost decayed away by the time of CAI formation. Even if ⁴¹Ca/⁴⁰Ca = (2–8) × 10⁻⁸ happened to characterize the molecular cloud fragment from which the Sun was formed (which is possible since local ⁴¹Ca abundances in different parts of the ISM could be significantly different from the average value), the time span between the collapse of that fragment and the solar system formation would still make ⁴¹Ca/⁴⁰Ca lower than 1.4 × 10⁻⁸ when CAIs formed.

Our revised initial ⁴¹Ca/⁴⁰Ca ratio of 4.2 × 10⁻⁹ for the early solar system falls below the GCE prediction by about a factor of 4–16, albeit there are large uncertainties associated with such calculations. Although it is impossible to completely rule out a last-minute input of ⁴¹Ca from a dying star or protosolar irradiation, the need is certainly eased. It should also be pointed out that ⁴¹Ca produced by in situ neutron capture on ⁴⁰Ca in the Efremovka parent body due to recent exposure to Galactic cosmic rays (GCRs) is still at least 10-fold lower than the observed ⁴¹Ca abundance (Srinivasan et al. 1996).

4.2.1. A Stellar Origin

4.2.2. Early Solar System Irradiation

4.2.3. Inheritance from the Molecular Cloud