Incorporation of ³⁶Cl into Calcium-Aluminum-Rich Inclusions in the Solar Wind Implantation Model

Abstract

We consider the short-lived radionuclide (SLR) ³⁶Cl in calcium-aluminum-rich inclusions (CAIs) found in primitive meteorites with the solar wind implantation model. In this model, SLRs are produced via nuclear reaction with solar energetic particles (SEPs) interacting with gaseous targets in the protosolar atmosphere in T-Tauri stars. These SLRs are captured by the solar wind and then implanted in CAI precursor materials, which have dropped from the funnel flow leading onto the protostar. This method of incorporating SLRs into solar system materials is currently active in our solar system and has been measured with SLRs from the solar wind being implanted on the lunar surface. T-Tauri stars are capable of SEP fluxes ~10⁵ greater than contemporary SEP fluxes. Here we scale the production rate of ³⁶Cl to the ancient SEP activity. From the enhanced production rates and the refractory mass inflow rate at 0.06 AU from the protosun, we model the ancient ³⁶Cl content in CAIs. We find the initial isotopic ratio of ³⁶Cl/³⁵Cl to range from about 1 × 10⁻⁵ to 5 × 10⁻⁵ and the concentration of ³⁶Cl to range from about 3 × 10¹³ to 1.5 × 10¹⁴ atoms g⁻¹.

1. Introduction

Studies report evidence for the incorporation of the short-lived radionuclide (SLR) (T_1/2 = 0.3 Myr) ³⁶Cl into early solar system materials, including calcium-aluminum-rich inclusions (CAIs). Lin et al. [1] infer an initial ³⁶Cl/³⁵Cl ratio of ≥1.6×10⁻⁴ in sodalite from the carbonaceous chondrite Ningqiang based on Al-Mg systematics. Also, relying upon Al-Mg systematics, Jacobsen et al. [2] report that initial ratio of ³⁶Cl/³⁵Cl in wadalite from Allende would have been >8.7×10⁻³ had the initial ²⁶Al/²⁷Al ratio been the canonical value of ~5×10⁻⁵.

Clues to the source of the ³⁶Cl can be gleaned from this initial ratio. If the initial ³⁶Cl/³⁵Cl had been ~2×10⁻⁴, the source of ³⁶Cl most likely would not have been from a nearby super nova or AGB star [3]. A remaining mechanism for the production of this radionuclide is local irradiation from solar energeticparticle (SEP) born in the protosolar atmosphere. The initial SLR ratios can be used to constrain early solar system evolution and conditions. This is especially true in terms of solar luminosity and flaring characterization.

Bricker and Caffee [4] proposed a solar wind implantation model for incorporation of ¹⁰Be in CAI precursor materials. In this model, ¹⁰Be and possibly other SLRs are produced by SEP reactions in the protosolar atmosphere of a more energetic T-Tauri sun, characterized by SEP fluxes many orders of magnitude greater than contemporary particle fluxes. Studies of the Orion Nebulae indicate that premain sequence (PMS) stars exhibit X-ray luminosity and hence SEP fluxes on the order of ~10⁵ over contemporary SEP flux levels [5]. The SLRs are produced through nuclear reactions with these SEPs, and the irradiation produced SLRs are then entrained in the solar wind and subsequently implanted into CAI precursor material. This production mechanism is operational in the contemporary solar system and is responsible for implantation of solar wind nuclei, including ¹⁰Be [6] and ¹⁴C [7], in lunar material. In this work, we consider ³⁶Cl found in CAIs in primitive carbonaceous meteorites in accordance with a solar wind implantation model. Table 1 characterizes ³⁶Cl found in CAIs.

Table 1 

Characteristics of ³⁶Cl found in CAIs.

2. Solar Wind Implantation Model

2.1. Overview

In the solar wind implantation model, SLRs are produced in the solar nebula ~4.6 Gyr ago by the bombardment of target material in the solar atmosphere by solar energetic particles. These SLRs escape the solar atmosphere entrained in the solar wind. Some fraction of these outward flowing SLRs are incorporated into inflowing material which has fallen from the main accretion flow from the protoplanetary accretion disk. In the region in which the inflowing material and outflowing solar wind intersect, SLRs may be incorporated into the precursor CAI material. The fluctuating 𝑥-wind model of Shu et al. [9–11] provides the basic framework for incorporation of SLRs into CAI-precursor materials and the subsequent transportation of these implanted refractory materials to asteroidal distances. Figure 1 is a cartoon of the basic magnetic field geometry, main accretion flow, and SLRs, including ³⁶Cl outflow.

Figure 1 

Solar wind implantation model of magnetic field geometry for SLRs production via nuclear reactions. The gray area represents accretion flow onto “hot spots” on the PMS star. SLRs produced close to the protosolar surface are implanted into CAI material which has fallen from the accretion flow (figure after Shu et al. [10]).

2.2. Refractory Mass Inflow Rate

The refractory mass inflow rate, that is, the mass that falls from the funnel flow onto the star at the 𝑋-region, is given by 𝑆=𝑀̇_𝐷⋅𝑋_𝑟⋅𝐹, (1) where 𝑀̇_𝐷 is disk mass accretion rate, 𝑋_𝑟 is the cosmic mass fraction, and 𝐹 is the fraction of material that enters the 𝑋-region [12]. For 𝑀̇_𝐷, we adopt 1×10⁻⁷ solar masses year⁻¹. The mass accretion rates can vary from ~10⁻⁷ to ~10⁻¹⁰ solar masses year⁻¹ for T-Tauri stars from 1 to 3 Myr [13]. Embedded class 0 and class I PMS stars can have accretion rates from ~10⁻⁵ to ~10⁻⁶ solar masses year⁻¹ [14]. The value we adopt corresponds to class II or III PMS stars. Following Lee et al. [12], we adopt a cosmic mass fraction, 𝑋_𝑟, and fraction of refractory material fraction 𝐹, of 4×10⁻³ and 0.01, respectively. 𝑋_𝑟 represents the fraction of material that is refractory and 𝐹 represents the fraction of mass that does not accrete onto the protosun. The choice 0.01 is a maximum for 𝐹 and corresponds to all the mass which comprises the planets falling from the accretion flow. If some of the rocky material accreting towards the proto-Sun never reached the edge of the accretion disk, 𝐹 would be smaller by a factor of 20 at most, but this scenario is unlikely. The choice of 𝐹=0.01 is the preferred value of Lee et al. [12] in their model. (See Lee et al. [12] for a detailed discussion of 𝑋_𝑟 and 𝐹.) From (1) and the values described above, we find the rate at which this refractory material is carried into the 𝑥-region, called here the refractory mass inflow rate, 𝑆, is 2.5×10¹⁴ g s⁻¹. On the extremes, 𝑆 could be two orders of magnitude greater if the PMS star was classes 0 or 1; 𝑆 could also be four orders of magnitude less if the mass accretion rate was ∼10⁻⁸ to 10⁻¹⁰ solar masses year⁻¹ and 𝐹∼0.0001.

2.3. Ancient Effective Production Rate

The effective ancient ³⁶Cl outflow rate, 𝑃 in units of s⁻¹, is given by 𝑃=𝑝⋅𝑓, (2) where 𝑝 is the ancient production rate and 𝑓 is the fraction of the solar wind ³⁶Cl that was captured into the CAI-forming region; 𝑓=0.1. (See Bricker and Caffee [4] for a discussion of factor 𝑓.) We calculate the ³⁶Cl production rates assuming that solar energetic particles are characterized by a power law relationship: 𝑑𝐹𝑑𝐸=𝑘𝐸^−𝑟, (3) where 𝑟 ranges from 2.5 to 4. For impulsive flares, that is, 𝑟=4, we use ³He/H = 0.1 and ³He/H = 0.3, and for gradual flares, that is, 𝑟=2.5, we use ³He/H = 0. Contemporary SEP fluxes at 1 AU are ~100 protons cm⁻²s⁻¹ for 𝐸>10 MeV [15]. We assume an increase in ancient particle fluxes over the current particle flux of ∼4×10⁵, yielding an energetic particle flux of 3.7×10¹² protons cm⁻²s⁻¹ for 𝐸>10 MeV at the surface of the protosun.

The production rates for cosmogenic nuclides can be calculated via 𝑝=_𝑖𝑁_𝑖𝜎_𝑖𝑗𝑑𝐹(𝐸)𝑑𝐸_𝑗𝑑𝐸, (4) where 𝑖 represents the target elements for the production of the considered nuclide, 𝑁_𝑖 is the abundance of the target element (g g⁻¹), 𝑗 indicates the energetic particles that cause the reaction, 𝜎_𝑖𝑗(𝐸) is the cross-section for the production of the nuclide from the interaction of particle 𝑗 with energy 𝐸 from target 𝑖 for the considered reaction (cm²), and 𝑑𝐹(𝐸)/𝑑𝐸_𝑗 is the differential energetic particle flux of particle 𝑗 at energy 𝐸 (cm⁻² s⁻¹) [15]. We assume gaseous targets, Cl, K, S, and Ca, of solar composition [16].

The cross-sections we use are from Gounelle et al. [17], with the exception of ^natCa(³He,x)³⁶Cl, which  is a new experimental cross-section from Herzog et al. [18]. The Gounelle et al. [17] cross-sections are a combination of experimental data, fragmentation, and Hauser-Feshbach codes. The uncertainty associated with model codes is at best a factor of two. We have used experimental cross-sections, whenever possible, in order to limit uncertainties associated with the calculations. The reactions we have considered here are the primary production pathways. This takes into account both abundance of target material and cross-sections. Any other reaction would add little to the overall ³⁶Cl production rate. Table 2 shows the cross-sections used in the calculations.

Table 2 

Nuclear reactions considered in this paper.

3. Results

The concentration of ³⁶Cl found in refractory rock predicted by our model is given by 𝑁³⁶𝑃Cl=𝑆=𝑝⋅𝑓𝑀̇_𝐷⋅𝑋_𝑟,⋅𝐹 (5) where 𝑃 is given atoms s⁻¹ and 𝑆 is given in g s⁻¹.

From the value of 𝑆 given above from (1) and calculations of 𝑝 from (4), we calculate the concentration of ³⁶Cl in CAIs using (5) and find the associated isotopic ratio for different flare parameters given in Table 3, and we plot the predicted ³⁶Cl content for spallation production from energetic protons in Figure 2.

Table 3 

Predicted ³⁶Cl content in CAIs.

Figure 2 

Predicted 36Cl content in CAIs from energetic protons as a function of solar flare parameter.

4. Discussion

From the results above, the isotopic ratio predicted by the solar wind implantation model is from a factor of 4 to a factor of 10 below the inferred initial ³⁶Cl/³⁵Cl ratio of ∼2×10⁻⁴. Given the uncertainties in the parameters, that is, 𝑀̇_𝐷, 𝑋_𝑟,𝐹, and 𝑓, the model is viable for ³⁶Cl/³⁵Cl initial ratio of ∼2×10⁻⁴. Jacobsen et al. [2] report that, based on Al-Mg systematics, the initial ³⁶Cl/³⁵Cl ratio may have been >8.7×10⁻³. The model calculations underproduce this value by several orders of magnitude for the flare parameters given here. It is not possible to produce an order of magnitude correct ³⁶Cl/³⁵Cl ratio of ∼1×10⁻² without overproducing ¹⁰Be/⁹Be, ⁴¹Ca/⁴⁰Ca, and ⁵³Mn/⁵⁵Mn by several orders of magnitude.

Clearly, some other mechanism is needed to explain to provenance of ³⁶Cl at the levels described by Jacobsen et al. [2]. A possible scenario is that the irradiation of target material occurred in a volatile rich region away from the protosun. This region would contain much more target materials, that is, Cl, S, and K. Greater target material would lead to greater initial ³⁶Cl content in CAIs. This argument for the enhanced ³⁶Cl found in wadalite samples is also invoked by Jacobsen et al. [2].

Evidence suggests that the distribution of ²⁶Al was homogenous in the solar system, but this is not always the case [3]. Marhas and Goswami [19] found several CAIs that had the “canonical” ¹⁰Be/⁹Be ratio, but were devoid of ²⁶Al, demonstrating a decoupling of ²⁶Al from ¹⁰Be. If ³⁶Cl is also decoupled from ²⁶Al, it is difficult to infer what the initial ³⁶Cl/³⁵Cl ratios were based solely on Al-Mg systems although Jacobsen et al. [2] do report a canonical initial ²⁶Al/²⁷Al ratio for primary minerals in their sample.

The irradiation origin of ²⁶Al found in CAIs is a matter of considerable debate. The proposed region where the enhanced ³⁶Cl production may have taken place could have already been seeded with ²⁶Al from some nonirradiation origin, that is, supernova. Conversely, the origin of ¹⁰Be is likely from SEP irradiation close to the protosun [4, 17]. It would be beneficial to establish a correlation between ¹⁰Be and ³⁶Cl to find if the irradiation that most likely produced ¹⁰Be also produced ³⁶Cl. More studies are needed in this area to establish this relationship.