Nucleosynthesis of light trans-Fe isotopes in ccSNe: Implications from presolar SiC-X grains

This contribution presents an extension of our r-process parameter study within the high-entropy-wind (HEW) scenario of corecollapse supernovae (ccSNe). One of the primary aims of this study was to obtain indications for the production of classical p-, sand r-isotopes of the light trans-Fe elements in the Solar System (S.S.). Here, we focus on the nucleosynthesis origin of the anomalous isotopic compositions of Zr, Mo and Ru in presolar SiC X-grains (SNe grains). In contrast to the interpretation of other groups, we show that these grains do not represent the signatures of a ‘clean’ stellar scenario, but rather, are mixtures of an exotic nucleosynthesis component and S.S. material. We further confirm the results of our earlier studies whereby sizeable amounts of all stable p-, sand r-isotopes of Zr, Mo and Ru can be co-produced by moderately neutron-rich ejecta of the low-entropy, charged-particle scenario of ccSNe (type II). The synthesis of these isotopes through a ‘primary’ production mode provides further means to revise the abundance estimates of the light trans-Fe elements from so far favoured ‘secondary’ scenarios like Type Ia SNe or neutron-bursts in exploding massive stars.


Introduction
The nucleosynthetic origin of the stable isotopes in the light trans-Fe region between Zn (Z = 30) and Ru (Z = 44) in the Solar System (S.S.) has been a fascinating subject for astrophysicists, astronomers, nuclear chemists and physicists, and cosmochemists for over 60 years [1 -3]. In this multidisciplinary community, it is commonly believed that these elements are produced by various contributions from three different historical stellar processes: (i) the 'p-process' [4,5], (ii) the 'weak s-process' ( [6,7] and refs. therein), and (iii) the 'weak r-process' ( [8 -10] and refs. therein).
Apart from the bulk S.S. isotopic abundances [11], more recent astronomical observations of elemental abundances in metal-poor halo stars [12 -18] have revived and intensified the general interest in the nucleosynthesis of these elements beyond Fe and have motivated various theoretical studies with increasing realism (see extensive references in [19]). Supplementing these studies are isotopic analyses of meteoritic inclusions such as presolar grains and Ca,Al rich inclusions (see e.g. [20 -24]). In particular, the interpretation of the anomalous Zr, Mo and Ru isotope compositions of SiC-X grains have so far defied a straightforward p-, s-or r-process explanation, requiring alternate nucleosynthesis scenarios. One such favoured process for the production of these light trans-Fe elements is the 'secondary' (i.e. metallicity dependant) neutron-burst (n-burst) occurring in the shocked He-shell of exploding massive stars [25 -27]. Each of these models considered so far, however, are unable to co-synthesise all light p-, s-and r-process isotopes in S.S. proportions [11], and struggle even more so in reproducing the abundance ratio of the two most abundant p-isotopes 92 Mo and 94 Mo.
We offer a solution to these problems by following up on our earlier preliminary results [28,29] exploring the 'primary' production of the light trans-Fe elements in a classical core-collapse supernova (ccSN), low-entropy, neutrino-driven-wind scenario.

Theory: Parametric core-collapse supernova HEW model
The notion of a high-entropy-wind (HEW), or neutrino-driven-wind (NDW), arises from considerations of the newly born proto-neutron star in ccSNe. In this scenario neutrinos interact with matter of the outermost neutron-star layers, leading to proton-rich and moderately neutron-rich HEW ejecta, with initially high entropies [30,31]. In this present paper, as in our earlier publications [28,32,33], the nucleosynthesis calculations up to the charged-particle (CP) freezeout were performed with continuously extended versions of the Basel network code (see [34]), following the description of adiabatically expanding homogeneous mass zones [35].
After CP (α) freezeout, the expanding (and eventually ejected) mass zones from the outer neutron-star layers have different initial entropies (S ≈ T 3 /ρ [k B /baryon]; T: temperature, ρ: matter density ) so that the overall explosion represents a superposition of different entropy 'intervals', correlated with (1) different electron abundances (Y e = Z/A), (2) different ratios of free neutrons to 'seed nuclei' (Y n /Y seed ) for the ensuing r-process, and eventually also with (3) different expansion velocities (V exp ), which determine the respective durations of the α-freezeout (τ α ) and the r-process (τ r ). With the assumption that each equidistant entropy interval contributes an equal amount of ejected matter (see [36] for details), the above correlations within our HEW model can be expressed by a simple 'rprocess strength function', Y n /Y seed ≈ V exp × (S/Y e ) 3 . Using this parameterised approach, our HEW model is able to reproduce the astronomical and cosmochemical observations of different r-process 'components' using different S and Y n /Y seed ranges. The sum total of this multiplicity of r-process types has resulted in our complex S.S. r-process 'blend' composition.
Taking Y e = 0.45 to represent a typical case of a moderately neutron-rich ejecta, the lowest entropy range (S ≤ 50) represents the normal, rapid α-rich freezeout without free neutrons (Y n /Y seed ≈ 10 -14 ), with a primary production of mainly stable or close to stable isotopes in the region of Fe to Sr (see second column of Table 1 in [32]). Moving onto a higher S-range (50 < S ≤ 100; see column 3 of Table 1 in [32], with Y n /Y seed ≈ 1 for S = 100) there are not yet enough free neutrons available to start a real neutron-capture (r-) process. However, under these S-conditions at freezeout, the seed composition is already shifted to the neutron-rich side of β -stability, including the well-known β-delayed neutron isotopes in the 80 < A < 100 mass region. In the next higher S-range (100 < S ≤ 150) of our HEW model, the density of free neutrons (1 ≤ Y n /Y seed ≤ 13) becomes high enough to start a 'weak' r-process up to the rising wing of the A ≈ 130 S.S.-r N peak. Finally, for high entropies of 150 < S ≤ 280, now with Y n /Y seed ≈ 155, our HEW parameter approach predicts quite a robust 'main' r-process starting with the N = 82 r-progenitor isotopes of 43 Tc to 45 Rh , 0 (2020) Web of Conferences https://doi.org/10.1051/epjconf /2020 0 EPJ 227 10 2270100 10 th European Summer School on Experimental Nuclear Astrophysics 9 9 at the onset of the A ≈ 130 peak extending beyond the N ,r peak at the N = 126 shell closure up to the actinide region.
Initially, the HEW model was successfully applied to the light trans-Fe elemental abundance patterns of metal-poor halo stars [32,34] and later the S.S. isotopic abundances [28] whereby we discussed for the first time the possibility of a primary co-production of all p-, s-and r-process isotopes between 64 Zn and 104 Ru within the low-S, CP component of the HEW. As an example, the co-production of all 7 Mo isotopes over different S intervals is illustrated in Fig. 1. Now we focus our attention on a third set of observations: the anomalous isotopic pattern of the three neighbouring even-Z elements Zr, Mo and Ru in presolar silicon carbide X-grains [20,21] building on our earlier work [19,28,37].
In this contribution we focus largely on Mo, due to the increased robustness of the Mo isotope data. Using the standard cosmochemical conventions (e.g. see [19]), the isotopic compositions of the grains ( i x/ k x; x = Mo) are reported as deviations from the S.S. composition ( i x/ k x ) in parts per thousand (δ i x k ), where i represents the target isotope and k represents the normalisation isotope. The grains are characterised by a large range of isotopic deviations from S.S.: i.e. depletions in the classical p-( 92,94 Mo) and r-( 100 Mo) isotopes, enrichments in the largely s-isotopes ( 95,98 Mo), whereas the s-only isotope ( 96 Mo) is present in almost identical abundances as 97 Mo (the normalising isotope). As for Zr, the SiC-X grains are characterised by depletions relative to 90 Zr ( i Zr/ 90 Zr ≤ 0.5, i = 91, 92, 94, 96). The Ru isotope signatures in these grains are more complex and the analysis hindered as Ru isotope data are only available for two SiC-X grains, with relatively large uncertainties. Regardless, we find that the lighter isotopes ( 96,98,99,100 Ru) are on average under-abundant relative to 101 Ru, whereas 104 Ru is present in similar proportions as 101 Ru, , 0 (2020) Web of Conferences https://doi.org/10.1051/epjconf /2020 0 EPJ 227 10 2270100 10 th European Summer School on Experimental Nuclear Astrophysics 9 9 and 102 Ru is over-abundant relative to 101 Ru. In all cases it is evident that the complex isotopic signature of these grains is not representative of a classical p-, s-or r-process. Plotting the isotopic data in cosmochemical three-isotope space (e.g. i Mo/ k Moj Mo/ k Mo; as explained in [19]), the SiC-X grains define a linear correlation for Mo and Zr isotopes (Fig. 2). These linear trends with the S.S. composition at one extreme and the SiC-X grain B2-05 on the other end (see Fig. 2) are interpreted as mixing lines, which strongly suggest that SiC-X grains are admixtures of two distinct nucleosynthetic components (or end members), as already recognised by [22]. Whereas the data support one end-member having a S.S. composition, we do not claim that the composition of B2-05 (other extreme of mixing line) reflects that of the second end-member, but rather B2-05 is the 'purest' grain with the cleanest signature of the SiC-X grain source. Thus we argue that SiC-X grains do not represent pure nucleosynthetic signatures from a single process but are best explained as a mixture of an exotic nucleosynthesis component -SiC-X end-member (SiC-X EM ; approximated by grain B2-05) -with homogenised stardust of S.S. composition. The isotopic compositions of grain B2-05 can thus be used to constrain the isotopic signatures of the stellar source where SiC-X grains formed (see second column, Table 1).

Searching for the stellar source of SiC-X grains
We now consider new and updated classical models (s-, r-, p-, n-burst) alongside our HEW scenario as potential candidates for the exotic SiC-X end-member (SiC-X EM ). Selected isotopic ratios from these stellar sources (described below and in more detail in [19]) are given in Table 1, alongside the experimental constraints on the SiC-X EM composition. Classical and updated s-, r-, p-process: s-process models from [40] through to [41], and the diverse scenarios highlighted in the F.R.U.I.T.Y database [42], are all generally characterised by the absence of 92 Mo, and high 96 Mo/ 97 Mo and 98 Mo/ 97 Mo relative to SiC-X EM , ruling out the s-process as the nucleosynthetic source of SiC-X grains (see Fig. 3). rprocess yields are inferred using the r-residual method using the same aforementioned sprocess models [40 -42]. The resulting r-process signatures are over-abundant in 100 Mo relative to SiC-X grains, and show no signs of 92,94 Mo (classical p-only) or 96 Mo (shielded from the r-process pathway by 96 Zr) making the r-process an unlikely candidate. The improved yields (see [19]) of p-process nucleosynthesis in Type-Ia SNe [43] are preferred over earlier work on electron-capture SNe of AGB stars [44]. Despite the 'secondary' nature of this process, resulting from the use of an enhanced s-seed distribution in the progenitor AGB star, large excesses in the p-nuclides ( 92,94 Mo) and under-abundances of 97 Mo relative to all other Mo isotopes allow us to eliminate p-process nucleosynthesis [43] as the source of SiC-X grains.
, 0 (2020) Web of Conferences https://doi.org/10.1051/epjconf /2020 0 EPJ 227 10 2270100 10 th European Summer School on Experimental Nuclear Astrophysics 9 9 n-burst: as already discussed in [22] and shown in Table 1 and Fig. 3, the n-burst model [25] succeeds to some extent in explaining the anomalous Mo (and Zr) isotope signatures in SiC-X grains, and to a lesser extent Ru (where too little 96,98 Ru is synthesised). However we remind the reader that (1) the concordance for 95 Mo/ 97 Mo between the n-burst model [26,27] and data results solely from SiC-X grains having a close to S.S. 95 Mo/ 97 Mo value and the n-burst model naturally predicting S.S. 95 Mo/ 97 Mo values due to its dependence on an initial S.S. seed composition, and (2) although the 92 Mo/ 97 Mo and 94 Mo/ 97 Mo predictions from the n-burst satisfy the requirements for the SiC-X EM composition (see Table 1), 92 Mo and 94 Mo are ultimately synthesised in very small quantities ( 92,94 Mo/ 97 Mo ≈ 10 -3 ). These points suggest that most of the p-only 92 Mo and 94 Mo present in SiC-X grains arise largely from the S.S. component and not the n-burst component. The same is true for 96 Ru and 98 Ru (see Table 1).
HEW component: Continuing with the analysis initially presented in [19,28,29,34,36] we compute the Mo isotope ratios for cumulative entropy zones (from S = 10 k B /baryon up to ≈ 270 k B /baryon). For each cumulative entropy band, we mix the corresponding (cumulative) isotopic ratios with a S.S. composition to generate mixing lines. A 2D ordinary least squares fit of the mixing lines to the SiC-X data in three-isotope space are used to constrain the optimum values of cumulative entropies (S-range) to consider. The best fit for Mo isotopes is obtained for the case Y e = 0.45 with cumulative-S ≈ 94 k B /baryon. Corresponding Mo isotope ratios are shown in Table 1 (column 3) and Fig. 3. These predictions -'primary' HEW scenario -for 92 Mo/ 97 Mo and 94 Mo/ 97 Mo fall within the range of allowed SiC-X EM compositions and are comparable to the 'secondary' n-burst predictions (Fig. 3). The 95 Mo/ 97 Mo value, which assumes close to S.S. values, is almost reproduced in our model (see Table 1), and the heavier isotopes 98 Mo/ 97 Mo and 100 Mo/ 97 Mo fall within a factor of two of the corresponding SiC-X EM values. Finally, although 96 Mo is under produced ( 96 Mo/ 97 Mo = 6.69×10 -5 ), it does satisfy the SiC-X EM constraint ( 96 Mo/ 97 Mo ≤ 0.638). A similar analysis for Zr reveals that the best fit between HEW theory and SiC-X data occur for slightly different conditions (Y e = 0.43, cumulative-S ≈ 76 k B /baryon), whereas preliminary analyses of Ru require slightly higher electron fractions and entropies (Y e ≈ 0.47, cumulative-S ≈ 120 k B /baryon). Overall, the best HEW model fits for Zr, Mo and Ru occur for the low-S, CP-component of the HEW for a very small Y e -S parameter window, indicating a consistent set of astrophysical conditions in the HEW of ccSNe.  [22,26]. d s-process yields [41]. e r-residuals [11,41]. f p-process yields [43].

Conclusions
, 0 (2020) Web of Conferences https://doi.org/10.1051/epjconf /2020 0 EPJ 227 10 2270100 10 th European Summer School on Experimental Nuclear Astrophysics 9 9 In the present paper we have shown selected results from an extension of our earlier largescale parameter study of the ccSN-HEW scenarios with a focus on its low-entropy (S ≤ 100 -150, Y n /Y seed ≤ 1) charged-particle component. We confirm that for moderate electron abundances in the range 0.44 ≤ Y e ≤ 0.49, all p-, s-and r-process isotopes in the light trans-Fe region between Zn (Z = 30) and Ru (Z = 44) can be co-produced in substantial yields. In this nucleosynthesis scenario, no initial S.S. or S.S.-modulated 'seed' composition (already containing the p-isotopes) is invoked as in e.g. [26,43]. Hence, the low-S component of the ccSN-HEW seems to be the main site of the primary production of the light p-isotopes, even resulting in a fair reproduction of the S.S. abundance ratio of the two most prominent p-isotopes 92 Mo and 94 Mo. Furthermore, particular attention has been directed towards the nucleosynthesis interpretation of the anomalous isotopic compositions of the stable isotopes of Zr, Mo and Ru reported in SiC-X grains. Our geochemical analysis demonstrates that the measured grain data do not represent 'clean' nucleosynthesis signatures, but are a mixture of a minor, initially unknown exotic component with S.S. material. Therefore, discussions about the possible isotopic origins of these admixtures (SiC-X grains), e.g. as presented in [45] are questionable. Only after correcting for this S.S. 'contamination', by way of identifying the purest grain, may we proceed with explaining the isotopic compositions of these grains, which we do so in a consistent and realistic astrophysical way within a narrow band of Y e -S conditions in the charged-particle component of our ccSN-HEW. Finally we postulate that these S.S.-corrected SiC-X grain compositions are probably the only 'clean' signature of a standard ccSN-HEW scenario identified so far -without containing additional rprocess admixtures from other explosive scenarios such as magnetorotational SN-Jets or neutron-star merger events usually observed in metal-poor halo stars. Fig. 3. Mo three-isotope plots for SiC-X grains with mixing lines for various nucleosynthetic endmembers (see main text). Data uncertainties are 2σ. The error bands obtained from the 2D data fits (as in Fig. 2) are displayed as shaded areas. Filled circles indicate end-member compositions.