Early Solar System Solar Wind Implantation of 7Be into Calcium-Alumimum Rich Inclusions in Primitive Meteortites

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1. Introduction

Studies report evidence for the one-time presence of SLRs, through decay product systematics, including ^{10}Be, ^{26}Al, ^{36}Cl, ^{41}Ca, and ^{53}Mn, in CAIs in primitive carbonaceous meteorites at the nascence of the solar system [1] . The possible origins of these SLRs are widely varied and include stellar sources (AGB Stars, Wolf-Rayet stars, nova, and super nova) and energetic particle interaction, from either SEPs, or galactic cosmic rays (GCRs). Bricker & Caffee [2] [3] proposed the solar wind implantation model (SWIM) for the incorporation of ^{10}Be and ^{36}Cl into CAIs early in primitive meteorites.

In the SWIM, the SLRs come into existence via SEP nuclear reactions in the proto-solar atmosphere of the young Sun, characterized by X-ray emissions orders of magnitude greater than main sequence stars. Studies of the Orion Nebulae indicate that pre-main sequence (PMS) stars exhibit X-ray luminosity, and hence SEP fluxes on the order of ~10^{5} over contemporary SEP flux levels [4] . The irradiation produced SLRs are then trapped by magnetic field lines, and these solar wind SLRs eventually impregnate CAI precursors. This mode of production of SLRs, entrainment of SLRs in the solar wind, and implantation of SLR into solar system material is seen in the implantation of solar wind particles, e.g. ^{10}Be [5] [6] and ^{14}C [6] [7] , on the Moon.

^{10}Be is produced via SEP spallation reactions, with oxygen serving as the chief target particle in the SWIM. Similar to ^{10}Be, ^{7}Be, half-life of 53 days [8] , is also primarily produced through SEP nuclear reactions with oxygen as the primary target particle, and ^{7}Be has also recently been detected in stellar photospheres [9] In addition, the one-time presence of ^{7}Be has been measured in CAIs in primitive meteorites (through the study of Li, the decay product of ^{7}Be, systematics) [10] [11] . Owing to the 53 day half-life, local irradiation is the only possible operation pathway for ^{7}Be production. As such, the large difference in half-lives between ^{7}Be and ^{10}Be is of interest in terms of chronological processes associated with early solar system and CAI formation and evolution.

In this work, we consider the possible incorporation of ^{7}Be into CAIs in primitive carbonaceous meteorites in the SWIM. Table 1 below characterizes berylliumisotopes found in CAIs.

2. Solar Wind Implantation Mode

2.1. Synopsis

In the SWIM, SLRs are produced in the solar nebula via SEP nuclear reactions on gaseous target material in the solar atmosphere ~4.6 Gyr, during the formation

Table 1. Beryllium isotopes found in CAIs.

Note: Radionuclide content in g^{−1} calculated from initial isotopic ratio and ^{9}Be content in ppb. The ^{9}Be content in CAIs is estimated 100 ppb [14] [15] .

of the solar system. These newly produced nuclei are incorporated in the solar wind. The SLRs flow along magnetic field lines in the solar wind, and this particle flow intersects with materials which have fallen out of the main accretion flow, which was headed to hot-spots on the Sun. At the intersection of outflowing SLRs, and inflowing fallen CAI precursor material, the SLRs may become impregnated into the inflowing materials. The fundamental geometry for the implantation process described above and transportation of implanted CAIs to the asteroid zone can be gleaned from the X-wind model of Shu et al. [16] [17] [18] . Figure 1 below illustrates of the basic magnetic field geometry, ^{7}Be production via SEP flaring activity, and subsequent implantation into CAI-precursor material from the main funnel flow onto the proto-Sun.

2.2. Refractory Mass Inflow Rate

The effective refractory mass inflow rate, S, i.e. the refractory mass that falls from the main funnel flow which was accreting onto the star at the X-region, is calculated from equation (1):

$S={\stackrel{\dot{}}{M}}_{D}\cdot {X}_{r}\cdot F$ (1)

where
${\stackrel{\dot{}}{M}}_{D}$ is disk mass accretion rate, X_{r} is the cosmic mass fraction, and F is the fraction of material that enters the X-region from the main funnel flow [19] . For
${\stackrel{\dot{}}{M}}_{D}$ , we adopt 1 × 10^{−7} solar masses year^{−1}. Disk mass accretion rates range from ~10^{−7} to ~10^{−10} solar masses year^{−1} for T Tauri stars from 1 - 3 Myr [20] , whereas embedded class 0 and class I PMS stars have mass accretion rates of ~10^{−5} to ~10^{−6} solar masses year^{−1} [21] . Here we adopt for
${\stackrel{\dot{}}{M}}_{D}$ , a rate 1 × 10^{−7} solar masses year^{−1}, corresponding to class II or III PMS stars. From Lee et al. [19] we utilize a cosmic mass fraction, X_{r}_{,} and fraction of refractory material fraction F, of 4 × 10^{−3} and 0.01, respectively, in our model. X_{r} represents the fraction of refractory content in the inflowing material, and F represents the fraction of inflowing mass that does not accrete onto the proto-sun. The choice 0.01

Figure 1. SWIM magnetic field geometry for SLRs production via SEP nuclear reactions. The gray area represents the main accretion flow onto “hot spots” on the PMS star. SLRs produced close to the proto-solar surface are incorporated into CAI precursor material which has fallen from the accretion flow (figure after Shu et al. [17] ).

maximizes F, and corresponds to all the mass which comprises the planets falling from the accretion flow. F = 0.01 is the preferred value of Lee et al. [19] in their model. (See Lee et al. [19] for a detailed discussion of X_{r} and F) Employing Equation (1) and the parameters detailed above, we find the rate at which this refractory material reaches the x-region, called here the refractory mass inflow rate, S, is 2.5 × 10^{14} g s^{−1}. In consideration of the extreme values of, S, S could be two orders of magnitude greater if the accretion rates of ~10^{−5} to ~10^{−6} solar masses year^{−1}, or 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. Effective Ancient Production Rate

The effective ancient ^{7}Be outflow rate, P in units of s^{−1}, is given by:

$P=p\cdot f$ (2)

where p is the ancient production rate and f is the fraction of the solar wind ^{7}Be that enters the CAI-forming region; f = 0.1. (See Bricker & Caffee [2] [3] for a discussion of factor f). The ^{7}Be production rate is calculated assuming that SEPs are characterized by a power law relationship:

$\frac{dF}{dE}=k{E}^{-r}$ (3)

where r ranges from 2.5 to 4. For impulsive flares, i.e. r = 4, we use ^{3}He/H = 0.1 and ^{3}He/H = 0.3, and for gradual flares, i.e. r = 2.5, we use ^{3}He/H = 0. For all spectral indices, we assume α/H = 0.1. Contemporary SEP flux rates at the Sun-Earth distance of 1 AU are ~100 protons cm^{−2}×s^{−1} for E > 10 MeV [22] . We assume an increase in ancient particle fluxes over the current particle flux of ~4 × 10^{5} [2] [4] , yielding an energetic particle flux rate of 3.7 × 10^{12} protons cm^{−2}×s^{−1} for E > 10 MeV at the surface of the proto-Sun.

The production rates for cosmogenic nuclides can be calculated via:

$p={\displaystyle \underset{i}{\sum}{N}_{i}}{\displaystyle \int {\sigma}_{ij}}\frac{dF\left(E\right)}{d{E}_{j}}dE$ (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,
${\sigma}_{ij}\left(E\right)$ 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 (cm^{2}), and
$\frac{dF\left(E\right)}{d{E}_{j}}dE$ is the differential energetic particle

flux of particle j at energy E (cm^{−2}×s^{−1}) [22] . We assume gaseous oxygen target particles of solar composition [23] .

The cross-section we use to calculate ^{7}Be production from protons and ^{4}He pathways is from Sisterson et al. [24] , and the cross-section we use for production from ^{3}He is from Gounelle et al. [25] . The Sisterson et al. [24] cross-section is experimental obtained, and the Gounelle et al. [25] cross-section is a combination of experimental data, fragmentation and Hauser-Feshbach codes. The uncertainty associated with model codes are at best a factor of two. Taking into account both target abundance and nuclear cross-sections, the reaction with oxygen as the target is the primary production pathway. Any other nuclear reaction would add little to the overall ^{7}Be production rate. Table 2 shows the nuclear reactions considered in the calculations.

3. Results

The content of ^{7}Be found in refractory material, in atoms g^{−1}, predicted by SWIM is given by:

${N}^{7\text{Be}}=\frac{P}{S}=\frac{p\cdot f}{{\stackrel{\dot{}}{M}}_{D}\cdot {X}_{r}\cdot F}$ (5)

where P is given atoms s^{−1} and S is given in g×s^{−1}.

Using the refractory mass inflow rate, S, of 2.5 × 10^{14} g×s^{−1} from Equation (1), and calculations of P, the effective ancient ^{7}Be outflow rate, from Equation (2) & Equation (4), we determine the content of ^{7}Be in CAIs in atoms g^{−1} using Equation (5), and find the associated isotopic ratio for different flare parameters given in Table 3. Figure 2 depicts the ^{7}Be isotopic ratio predicted by the SWIM from SEPs.

4. Discussion

Similar to ^{10}Be, the primary target for SEP production of ^{7}Be is oxygen. As such, the SEP origin of ^{7}Be and ^{10}Be are uniquely intertwined. The estimated ^{7}Be/^{10}Be production ratio from MeV SEPs in the early solar system is estimated to be ~70 [14] . Using the production rate from Equation (4) and the production rate for ^{10}Be from Bricker & Caffee [2] from SEP interaction with oxygen targets, we obtain a production ratio of ~50, which is similar to Leya [14] . It would then be expected that the original ratio of ^{7}Be/^{9}Be found in CAIs would be ~50 times greater than the ^{10}Be/^{9}Be ratio, assuming the simple SWIM mechanism described above. Using 9.5 × 10^{−4} [13] as the canonical ^{10}Be/^{9}Be ratio, the ^{7}Be/^{9}Be ratio would scale to 4.8 × 10^{−2}. We find this ratio is reproducible within a factor of ~5, the uncertainty associated with SWIM, for spectral indices r > 3.2. The SWIM can account for the scaled up ^{7}Be/^{9}Be ratio. Figure 3 below details the ratio of ^{7}Be/^{9}Be from SWIM to 4.8 × 10^{−2}.

Experimentally obtained measurements for the original ^{7}Be/^{9}Be ratio in CAIs are limited and a matter of considerable debate. Limited experimentally determined values for the ratio range from about 1.2 × 10^{−3} [11] to 6.1 × 10^{−3} [10] . The experimentally obtained ratios are at least a factor of 10 less than SWIM

Table 2. Nuclear reactions considered in this paper.

Table 3. Predicted ^{7}Be content in CAIs.

Figure 2. Predicted ^{7}Be content in CAIs from energetic protons as a function of solar flare parameter.

Figure 3. Ratio of ^{7}Be/^{9}Be found from SWIM.A ratio of one indicates exact match, a ratio greater than one indicates overproduction, and a ratio less than one indicates underproduction.

calculations, and also a factor of at least 10 less than the scaled up ^{7}Be/^{9}Be found from scaling the canonical ^{10}Be/^{9}Be ratio to ^{7}Be and ^{10}Be production rates. Figure 4 depicts the ratio of SWIM obtained ratio to the canonical ^{7}Be/^{9}Be ratio.

Clearly, some other mechanism is needed to explain the overproduction of the

Figure 4. Ratio of SWIM ^{9}Be/^{10}Be ratio to canonical ^{7}Be/^{9}Be ratio. A factor greater than one indicates overproduction relative to canonical.

Figure 5. Days to canonical ratio vs. spectral index.

^{7}Be/^{9}Be ratio, both in terms of SWIM calculations and the scaling of the ^{10}Be/^{9}Be to relative ^{7}Be and ^{10}Be production rates.

An assumption of SWIM is that radionuclides are produced via SEP interaction and then immediately incorporated into CAI precursor materials. With a half-life of 53 days, it is possible that some temporal evolution occurs before ^{7}Be becomes implanted. Figure 5 shows days to canonical ratio for spectral index.

Figure 5 shows that with a delay on the order of ~100 days from the time of production of ^{7}Be to implantation in to CAI precursor materials, the canonical ratio is replicated. Taking into account the time from production of the radionuclide to implantation into CAI precursors, i.e., two half-lives of ^{7}Be, explains the deficit in ^{7}Be/^{10}Be measured ratio in comparison to the ^{7}Be/^{10}Be production ratio. It is possible and likely for nuclei to have some finite residence time in the photosphere. Calculations of this residence time have not been performed and are beyond the scope of this paper. Our ad hoc choice of two half-lives of residence time for ^{7}Be was to explain the ^{7}Be/^{10}Be measured ratio in comparison to the ^{7}Be/^{10}Be production ratio.

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