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

The one time presence of short-lived radionuclides (SLRs) in Calcium-Aluminum Rich inclusions (CAIs) in primitive meteorites has been detected. The solar wind implantation model (SWIM) is one possible model that attempts to explain the catalogue of SLRs found in primitive meteorites. In the SWIM, solar energetic particle (SEP) nuclear interactions with gas in the proto-solar atmosphere of young stellar objects (YSOs) give rise to daughter nuclei, including SLRs. These daughter nuclei then may become entrained in the solar wind via magnetic field lines. Subsequently, the nuclei, including SLRs, may be implanted into CAI precursors that have fallen from the main accretion flow which had been destined for the proto-star. This mode of implanting SLRs in the solar system is viable, and is exemplified by the impregnation of the lunar surface with solar wind particles, including SLRs. X-ray luminosities have been measured to be 100,000 times more energetic in YSOs, including T-Tauri stars, than present-day solar luminosities. The SWIM scales the production rate of SLRs to nascent SEP activity in T-Tauri stars. Here, we model the implantation of Be into CAIs in the SWIM, utilizing the enhanced SEP fluxes and the rate of refractory mass inflowing at the X-region, 0.06 AU from the proto-Sun. Taking into account the radioactive decay of Be and spectral flare variations, the Be/Be initial isotopic ratio is found to range from 1 × 10 to 5 × 10.


Introduction
G. E. Bricker DOI: 10.4236/ijaa.2019.91002 13 International Journal of Astronomy and Astrophysics uct 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 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.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.

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 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].International Journal of Astronomy and Astrophysics 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.

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): where D M  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].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.

Effective Ancient Production Rate
The effective ancient 7 Be outflow rate, P in units of s −1 , is given by: 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: 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: ( ) 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, ( ) ij E σ 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 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]

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

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   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   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 radio-

Days to Canonical Ratio vs Spectral Index
Days to Canonical Ratio Spectral Index, r International Journal of Astronomy and Astrophysics nuclide 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.

ForDM
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]).

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

Figure 3 .
Figure3.Ratio of7 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.

Figure 4 .
Figure 4. Ratio of SWIM9 Be/ 10 Be ratio to canonical7 Be/9 Be ratio.A factor greater than one indicates overproduction relative to canonical.

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

Table 1 .
Beryllium isotopes found in CAIs.
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.Table2shows the nuclear reactions considered in the calculations.
cross-section is a combination of experimental data, fragmentation and Hauser-Feshbach codes.The un-G.E. Bricker DOI: 10.4236/ijaa.2019.9100216 International Journal of Astronomy and Astrophysics certainty associated

Table 2 .
Nuclear reactions considered in this paper.He, x)7Be International Journal of Astronomy and Astrophysics