Evidence from stable isotopes and 10Be for solar system formation triggered by a low-mass supernova

About 4.6 billion years ago, some event disturbed a cloud of gas and dust, triggering the gravitational collapse that led to the formation of the solar system. A core-collapse supernova, whose shock wave is capable of compressing such a cloud, is an obvious candidate for the initiating event. This hypothesis can be tested because supernovae also produce telltale patterns of short-lived radionuclides, which would be preserved today as isotopic anomalies. Previous studies of the forensic evidence have been inconclusive, finding a pattern of isotopes differing from that produced in conventional supernova models. Here we argue that these difficulties either do not arise or are mitigated if the initiating supernova was a special type, low in mass and explosion energy. Key to our conclusion is the demonstration that short-lived 10Be can be readily synthesized in such supernovae by neutrino interactions, while anomalies in stable isotopes are suppressed.

Supplementary Corresponding percentages of the solar system inventories are given for Case 1 and two other cases with fallback. Note that x(−y) denotes x × 10 −y .

Supplementary Discussion
Core-collapse supernova (CCSN) yields of stable isotopes. Supplementary Table 2 gives the yields of major stable isotopes for the 11.8 M CCSN model assuming no fallback (Case 1). As shown in Fig. 1a of the main text, the yields of stable isotopes increase greatly for CCSNe of 14-30 M . For a stable isotope i E of element E, the percentage of its solar system (SS) inventory contributed by a CCSN is where Y ( i E) is its yield, f is the fraction incorporated into each M of the protosolar cloud, and X ( i E) is its solar mass fraction. The CCSN contributions would introduce shifts in i E/ j E, the number ratio of isotopes i E and j E, for SS materials. The percentage shift for macroscopic samples can be estimated as to those observed in meteorites. As there are few satisfactory explanations of these excesses [4], this provides additional circumstantial support for the thesis that a low-mass CCSN with modest fallback triggered SS formation. We note that Ref. [4] explored a different explanation of these excesses by s-processing in asymptotic-giant-branch (AGB) stars. A crucial distinction between the above two explanations lie in their associated grains that would carry much larger anomalies. Grains from a low-mass CCSN would show excesses of 29 Si/ 28 Si and 30 Si/ 28 Si (see especially Case 2 in Supplementary Table 3), but those from AGB stars would not [4].
CCSN production of short-lived radionuclides (SLRs). Most of the 10 Be production occurs in the C and O shells, where the mass fraction of 12 C is high but that of 4 He is low. A low 4 He abundance is crucial in avoiding 10 Be destruction via 10 Be(α, n) 13 C. For the same reason, neutrino-induced production of 10 Be is self-limiting because spallation of 12 C and 16 O also produces 4 He and protons that can destroy 10 Be via 10 Be(p, α) 7 Li. As long as abundances of 4 He and protons are low, most of the 10 Be survives even when the production zone is heated by shock passage. We note that Ref.
[5] adopted a rate for 10 Be(α, n) 13 C that is orders of magnitude larger than currently recommended [6], and therefore, greatly underestimated the 10 Be yield. In addition, the 16.2 M model used in that work was evolved from a helium core with a fitted hydrogen envelope [7] while each of our models has been evolved selfconsistently as a whole star. We find that the radii of the C/O shell in that 16.2 M model are ∼ 2 times larger than those in our 16 M model. Consequently, the neutrino flux for 10 Be production was significantly smaller in Ref. [5], which also contributed to the much smaller yield reported there.
The SLR 36 Cl can be produced by neutrinos via 36 Ar(ν e , e + ) 36 Cl, where the 36 Ar is observed [8]. Further, both our models overproduce 107 Pd (see Supplementary Table 1 and Table 1 of the main text). No calculation was presented for this SLR in Ref. [1].
With similar yields of 10 Be for CCSNe of 11.8-30 M , production by these sources against decay may maintain an inventory of 10 Be in the interstellar medium (ISM). An upper limit on the corresponding mass fraction can be estimated as where Y ( 10 Be) ∼ 5 × 10 −10 M is the average yield (see Table 1 and Fig. 1b  to give ( 10 Be/ 9 Be) ISM ∼ 6 × 10 −5 at the time of SS formation. This is ∼ 10 times less than the typical value in the early SS (see Table 1 of the main text). As we have shown, the The shock velocities of concern typically occur when the remnant is in the pressure-driven where E is the explosion energy of the CCSN, and n 0 is the number density of hydrogen atoms in the ISM. The remnant evolution during the PDS phase [13] is approximately described by where t * ≡ t/t PDS is the time t since the explosion in units of Using E ∼ 10 50 erg for the low-mass CCSN and n 0 ∼ 100 cm −3 for a typical giant molecular cloud [12], we find that for the above simple case, the remnant reaches v s ∼ 40 km s −1 at t ∼ 2.5 × 10 4 yr. The corresponding R s ∼ 3.4 pc gives f ∼ 2 × 10 −5 . This should be regarded as a lower limit on f because the shock wave can be slowed down more efficiently in a giant molecular cloud with dense clumps . For example, if at the onset of the PDS phase the remnant in the simple case encounters a clump with a hydrogen density of n 0 ∼ 2 × 10 3 cm −3 and a radius of ∼ 1 pc [12], then by momentum conservation relevant for the PDS phase, the shock wave approaches the core of the clump with v s ∼ (n 0 /n 0 )v PDS ∼ 34 km s −1 but its effective radius remains close to R s ∼ 1 pc. In this example, the conditions for triggering the collapse of the core and injecting SLRs into it would be satisfied. Based on the above discussion, we consider our trigger scenario reasonable and urge that simulations of remnant evolution in a giant molecular cloud be carried out to provide more rigorous results. We note that the time of remnant expansion must have been far shorter than ∆ ∼ 1 Myr. Therefore, this interval must reflect the timescales associated with the collapse of the protosolar cloud and the formation of the first solids in the early SS.
Evolution of a CCSN remnant prior to the PDS phase is associated with acceleration of cosmic rays (CRs), which can produce 10 Be [14]. We consider the amount of 10 Be produced by CRs inside the remnant up to the onset of the PDS phase and compare this to the low-mass CCSN yield. Using n 0 ∼ 100 cm −3 but an explosion energy 10 times too high for the low-mass CCSN, Ref. [14] found that CRs can produce 10 Be/ 9 Be ∼ 2. Reference [14] considered a remnant interacting with the protosolar cloud and suggested that CR production of 10 Be inside the cloud might have provided this SLR to the calcium-aluminum-rich inclusions with Fractionation and Unidentified Nuclear isotope effects (FUN-CAIs). However, it is not clear how this production actually took place when the very small size of the cloud relative to the remnant is taken into account. It is highly desirable to extend the study in Ref. [14] to our proposed low-mass CCSN trigger scenario.
Potential tests for a low-mass CCSN trigger: Li, Be, B. In our proposed scenario, a lowmass CCSN trigger provided the bulk of the 10 Be inventory in the early SS as indicated by canonical CAIs. CR production associated with the CCSN remnant might have provided 10 Be to FUN-CAIs [14]. Any 10 Be production by CRs and solar energetic particles (SEPs) [15,16] would be in addition to the injection from the CCSN but generally at subdominant levels consistent with the observed variations of 10 Be/ 9 Be in canonical CAIs [17][18][19][20].
We propose a potential test of the above scenario based on the distinct yield pattern of Li, Be, and B isotopes for the CCSN. Supplementary Table 4 gives the yields of 6 Li, 7 Li, 9 Be, 10 B, and 11 B for the 11.8 M model with no fallback (Case 1). The fallback in Cases 2 and 3 causes little change in these results. It can be seen that the CCSN predominantly produces 7 Li and 11 B, which is a feature of neutrino-induced nucleosynthesis [21]. This is in sharp contrast to the production by CRs or SEPs with much higher energy than CCSN neutrinos. For example, Ref. [14] gave relative number yields of 6 Li : 7 Li : 9 Be : 10 B : 11 B ∼ 1 : 1.8 : 0.11 : 0.43 : 1.1.
The presence of 10 Be in the early SS is established by the correlation between 10 B/ 11 B and 9 Be/ 11 B, from which the initial values ( 10 Be/ 9 Be) 0 and ( 10 B/ 11 B) 0 at the time of 10 Be incorporation are obtained. In our scenario, the low-mass CCSN trigger provided the bulk of the 10 Be and ∼ 5% of the 11 B in the SS (see Supplementary Table 4). Consequently, we expect that samples with higher ( 10 Be/ 9 Be) 0 would have lower ( 10 B/ 11 B) 0 due to the excess of 11 B over 10 B that accompanied the 10 Be from the CCSN. The variations in ( 10 B/ 11 B) 0 should be at the level of ∼ 5%. Such variations are consistent with the data reported in Refs. [19,20]. It remains to be seen if future meteoritic studies with more samples and better precision can establish the above relationship rigorously, thereby providing a test for the low-mass CCSN trigger.
(8.8 ± 0.6) × 10 −4 and interpreted as indicating the presence of the SLR 7 Be in the early SS [22]. If true, the extremely short lifetime of 77 days for 7 Be would almost certainly require irradiation by SEPs for its production, and by association, the same mechanism may also have produced the 10 Be in the sample. However, the above result was disputed and the controversy remains unresolved [23,24]. Here we propose an alternative explanation for the tantalizing correlation between 7 Li/ 6 Li and 9 Be/ 6 Li. We note that the low-mass CCSN trigger also provided ∼ 0.8% of the 7 Li in the SS but a negligible amount of 6 Li. We expect that portions of a sample that received higher amounts of 10 Be from the CCSN would also have higher amounts of 7 Li. For a uniform ( 10 Be/ 9 Be) 0 across the sample, the above relationship would translate into an apparent correlation between 7 Li/ 6 Li and 9 Be/ 6 Li, which nevertheless has nothing to do with the presence of 7 Be in the early SS. This explanation can be tested more directly by checking the relationship between 7 Li/ 6 Li and ( 10 Be/ 9 Be) 0 for a wide range of samples. In our scenario, 7 Li/ 6 Li should increase with ( 10 Be/ 9 Be) 0 .
As only a relatively small amount of 7 Li was added by the low-mass CCSN, high-precision measurements are required to check this relationship. Such measurements would provide an additional test for the low-mass CCSN trigger and also help resolve the controversy over the 7 Be result.