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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
^{7}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
^{7}Be and spectral flare variations, the
^{7}Be/
^{9}Be initial isotopic ratio is found to range from 1 × 10
^{−5} to 5 × 10
^{−5}.

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 [^{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 [^{10}Be [^{14}C [

^{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 [^{7}Be has also recently been detected in stellar photospheres [^{7}Be has been measured in CAIs in primitive meteorites (through the study of Li, the decay product of ^{7}Be, systematics) [^{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.

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

Nuclide | Half-life | Initial Isotopic Ratio | Radionuclide (g^{−1}) |
---|---|---|---|

^{7}Be | 53 days [ | 1.2 × 10^{−3} [^{−3} [ | 1.0 × 10^{13 } 5.3 × 10^{13 } |

^{10}Be | 1.36 × 10^{6} yr [ | 9.5 × 10^{−4} [ | 6.4 × 10^{12 } |

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 [

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. [^{7}Be production via SEP flaring activity, and subsequent implantation into CAI-precursor material from the main funnel flow onto the proto-Sun.

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 = M ˙ D ⋅ X r ⋅ F (1)

where 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 [^{−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 [^{−5} to ~10^{−6} solar masses year^{−1} [^{−7} solar masses year^{−1}, corresponding to class II or III PMS stars. From Lee et al. [_{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

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. [_{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.

The effective ancient ^{7}Be 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 ^{7}Be that enters the CAI-forming region; f = 0.1. (See Bricker & Caffee [^{7}Be production rate is calculated assuming that SEPs are characterized by a power law relationship:

d F d E = 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 [^{5} [^{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 = ∑ i N i ∫ σ i j d F ( E ) d E j d E (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 i j ( 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 (cm^{2}), and d F ( E ) d E j d E is the differential energetic particle

flux of particle j at energy E (cm^{−2}×s^{−1}) [

The cross-section we use to calculate ^{7}Be production from protons and ^{4}He pathways is from Sisterson et al. [^{3}He is from Gounelle et al. [^{7}Be production rate.

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

N 7 Be = P S = p ⋅ f M ˙ D ⋅ X r ⋅ 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 ^{7}Be isotopic ratio predicted by the SWIM from SEPs.

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 [^{10}Be from Bricker & Caffee [^{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} [^{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. ^{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} [^{−3} [

^{16}O(p, x)^{7}Be |
---|

^{16}O(^{3}He, x)^{7}Be |

^{16}O(^{4}He, x)^{7}Be |

Flare Parameter | atoms g^{−1} (in CAIs) | Isotopic Ratio |
---|---|---|

p = 2.7, ^{3}He/H = 0 | 1.1 × 10^{16} | 1.6 |

p = 4, ^{3}He/H = 0.1 | 3.8 × 10^{14} | 5.7 × 10^{−2} |

p = 4, ^{3}He/H = 0.3 | 1.1 × 10^{15} | 1.6 × 10^{−1} |

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. ^{7}Be/^{9}Be ratio.

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

^{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.

^{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.

The author declares no conflicts of interest regarding the publication of this paper.

Bricker, G.E. (2019) Early Solar System Solar Wind Implantation of ^{7}Be into Calcium-Alumimum Rich Inclusions in Primitive Meteortites. International Journal of Astronomy and Astrophysics, 9, 12-20. https://doi.org/10.4236/ijaa.2019.91002