Slow Neutron-Capture Process: Low-Mass Asymptotic Giant Branch Stars and Presolar Silicon Carbide Grains

Round 1

Reviewer 1 Report

Isotopic abundance anomalies in presolar grains have been measured by many groups. The mainstream SiC grains, Y and Z grains recorded the s-process product in low-mass AGB stars. The measured isotopic abundances of some elements such as Sr and Mo cannot be explained using standard AGB star models. One of the key points to reproduce the abundances is the mechanism of 13C production in He intershell in AGB stars, which is the dominant neutron sources for the s-process. In this paper, the recent progress of AGB star models are reviewed, and some of them reproduce the measured abundances. This review paper is useful for readers of wide fields. When two major problems are revised, I can recommend its publication in the Universe.

Major points:

The authors presented that isotopic abundance ratios of two different elements in presolar grains can constrain 13C distribution of AGB models. As an example, the abundance ratios of 88Sr/86Sr vs 137Ba/135Ba is discussed. This method is useful for improvement the understanding of the AGB s-process. However, the mechanism why the spectral distribution of synthesized 13C in He-rich layers affects their abundance ratios is important. It should be discussed more clearly.

It may be understood by a branch point and neutron density. The abundance ratios are changed by the ratio of the neutron capture rate on a branch point to its beta-decay rate. The neutron capture rate is, in general, proportional to neutron density, although the neutron capture reaction cross section depend also on the temperature. In the magnetic mixing model, 13C distribution is widely spread in height in a He intershell and its density is lower than that of the standard models without the magnetic mixing [for example, see figure 3 in Vescovi, ApJL, 897, 25 (2020) and the same figure in a review paper Vescovi, Universe, 8, 16 (2022)]. As 13C density decreases, neutron density following 13C(alpha, n)16O reactions decreases. As a result, in a branch point where beta decay and neutron capture compete, the fraction of beta decay to the total increases. As pointed out in the later session by the authors, there are many branch points including 85Kr in the s-process flow. The abundance ratio of 88Sr/86Sr depends on the branch point on 85Kr, which is a short-lived unstable isotope with a beta-decay unstable isomer. The main s-process flow is divided to two paths from 85Kr, and these two flows again combine on 88Sr. Thus, the abundance of 88Sr is not affected by the branch point, whereas the abundance of 86Sr is sensitive to the beta-decay fraction on the branch point. Under low neutron density environments, the beta-decay fraction from 85Kr is enhanced and the 88Sr/86Sr ratio decreases.

The authors have proposed an idea that the neutron capture reaction cross section can be estimated from the isotopic abundance ratios in presolar grains using a relationship of sigma x abundance = constant. This relationship was obtained from the solar abundance a few decades ago. Seeger et al. [ApJS, 11, 121S (1965)] pointed out the sigma-N curve that the sigma x abundance shows almost constant but it is an exponential distribution in each region separated by the neutron magic numbers. This empirical approximation has been extended by Clayton and Ward [ApJ, 193, 397 (1974)]. Thus, these backgrounds should be explained, and the fact that sigma N = constant is an approximation different from these formulas should be noted clearly.  Furthermore, the sigma N = constant becomes a good approximation under an assumption that neutron density and temperature are constant in the s-process where a SiC grain is produced. The neutron capture cross section is a function of the neutron energy (temperature). When one evaluates the temperature at which the SiC grains are formed, one can calculate the sigma of an isotope using the sigma N = constant approximation. In typical AGB models, the s-process occurs in two phases of interpulse and He flashes with different temperature and neutron density. Thus, the isotopic abundance anomaly in presolar grains also originates from the two phases. Thus, the obtained sigma from the empirical approximation is an average of sigma at two temperatures, and the fraction of each production and their temperature have been unresolved. This problem should be explained or delete this proposal.

Minor points:

The neutron magic numbers of N=50, 82, 126 are useful.

The definition of [hs/ls]2 and [Pb/Fe] should be clearly presented.

Figure 3 is too small, and the labels of the graphs in figure 4 is too small.

Figure 6 shows the abundance of 92Mo vs 97Mo. Among Mo isotopes, the astrophysical origin of 92 and 94Mo have not been established. As the origin, gamma-process in SNe, Typie Ia SNe and neutrino-p process in Type II SNe have been proposed and its galactic chemical evolution has been discussed [see Sasaki, ApJ, 924, 29 (2022) and references]. Such explanation is kind for readers.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Dear authors,

I was pleased to revise your review that I have found interesting complete and clear. I am sure that it will be useful for the community. In the following I highlight few minor points in order of appearance. I suggest the publication of the paper after their correction.

line 69: "... drops below \sim2500K". I guess it refers to the effective temperature and not the gas (wind) temperature, since condensation temperature for SiC is lower (around 1400 K, e.g. Ferrarotti & Gail 2002). Please, clarify in the text.

Fig. 2: Specify in the caption the meaning for the vertical dashed line. 

Fig. 3: Expand the labels of the left panel

line 217: "... state-of-the-art telescope" add a reference to Fig. 3 like "(see panel d in Fig.3)".

line 284: "help ass" -> "help to ass" ?

line 292: "[83]" there is a "6" as apex but there is no corresponding footnote. 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I think that the method and results described in this review paper are important and that this review paper is worth in publishing in any academic journal including the Universe when it is revised. The authors may be experts for cosmochemistry and astrophysics, but the additional explanation in the revised manuscript in order to answer to my requests shows that they are not expert for nuclear physics, in particular neutron induced reactions. When the paper is published in any journals in the present form, it may give incorrect information for understanding of the s-process. Thus, I recommend to revise again the manuscript for its publication.

The 1/v law for neutron capture reaction cross sections near the thermal energy has been well known. This thermal energy in this formula is approximately 0.025 eV corresponding to the room temperature of 300 K, which is much lower than the thermal energies of T = 10^8-10^9 K in astrophysical environments in the s-process. This 1/v component should be taken into account for the total cross sections. However, the neutron capture has components of resonance capture and direct capture. At a resonance energy, the neutron capture cross section suddenly increases like a peak. The total neutron capture cross sections should be calculated taking the resonances. The 1/v component dominates under the condition that the s-wave neutron capture (the orbital angular momentum of the incident thermal neutron is zero) dominates and the excited energies of neutron capture resonances are higher than the s-process energy. The neutron capture resonances depend on exited states of compound nuclei formed by neutron capture. The level density of excited states in a nucleus in general increases with increasing atomic number. In the light mass region such as C and O, the neutron capture resonances locate in high energy regions of several hundred keV and MeV, whereas in middle-heavy mass nuclides the level density become large and many resonances appear in a typical s-process energies of 1-100 keV. Thus, MCAS should be calculated from these resonances in addition to the 1/v component. Because it is difficult to calculate theoretically the decay widths and energies of resonances on each nucleus, many nuclear experiments to measure resonances (or the total neutron capture cross sections) have been carried out over the last a few decades. For example, in the neutron capture reaction of 88Sr, the first resonance locates at 12.4 keV and there are many resonances low than 100 keV [see P.E. Kochler, Phys. Rev. C 62, 055803 (2000)]. The MACS is a function of energy and the energy dependences of isotopes in the same element are different. Thus, the newly added discussion for the MACS evaluation is not correct.

The explanation for branch points should be also modified. Some of the branch points are not work in specific temperature, where one of beta-decay and neutron capture dominates as pointed out by the authors. However, in most branch points, beta decay and neutron capture compete in the s-process energies. The present explanation may lead misunderstanding for general cases of the branch points.

Beside it, I did NOT suggest that 22Ne(alpha, n)25Mg reaction rate affects the Sr isotopic ratios after the s-process. I have understood that the change of the 13C pockets in the various mixing models in AGB stars affects the s-process 86Sr/88Sr ratios in the previous studies. However, its reason has not been well described in the review paper. In my previous review, I requested the more detailed mechanism of the correlation between the 13C distribution and the Sr ratios. If the branch point in the interpulse phases does not affect the Sr abundance, I hope to know why the different 13C pockets lead the different Sr abundance ratios. The detailed description of the 85Kr branch point is not needed when it does not work.

The figure 6 shows the two isotopic anomalies of 92Mo and 97Mo. The p-isotope 92Mo cannot be, in principle, produced by neutron capture reactions in the s-process because there is no path from any s-isotope to 92Mo, and some nucleosynthesis models have been proposed as the origin of 92Mo as presented in Sasaki, et al. Although the r-process is a typical primary process, the s-process is the secondary process; the s-isotope abundances changes as a complex function of metallicity (time). An AGB star was formed form the interstellar medium which included nucleosynthesis product from early generations of stars. Thus, the AGB star included heavy elements coming from the interstellar medium at the time of the star formation. The 92Mo observed in SiC presolar grains from AGB stars was not newly synthesized in the s-process, but it originated from the interstellar medium. Thus, isotopic abundance of 92Mo (and most of 94Mo) observed in AGB grains is a result of the galactic chemical evolution. Even if the slope of the two Mo isotopes shows the correlation of the MACS as suggested by the authors, the ratios between 92Mo (94Mo) and another Mo isotope does not show such correlation, which is not evidence supporting the proposed method. Even if a AGB model reproduce it, it is meaningless. The figure 6 should be changed to another combination except for 92 and 94Mo.

Furthermore, the fact that the ratio of Si isotopes in SiC grains cannot be explained by the s-process has been well known, and it is explained by the galactic chemical evolution of Si isotopes. Recent studies suggests that a part of presolar grains are formed in the interstellar medium, which are affected by the GCE. This suggests that heavy elements contained in SiC grains may be also affected by the GCE. When the contribution of the GCE is not negligibly small, the proposed MACS method should be modified taking the GCE, but I think that it is out scope of the present review paper.

In summary, the analysis and results in the previous studies by the authors are impressive and give a new insight for AGB s-process. The review paper may be a useful guild for readers, but the explanation for some mechanisms is not correct in the flamework of nuclear physics. The MACS termination method is not one of the main products. When the MACS method is removed, the review paper is worth in publishing. The first draft is better than the present version. I recommend to modify again the manuscript for its publication.

Minor comments:

“beta-minus” should be written by a standard symbol.

Author Response

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Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

The revised manuscript has been much improved from the previous version. As stated in my previous reviews, I think that this is worth in publishing in universe. Although the present manuscript seems to be very nice, I should point out that there have been two major points to be revised.

The equations 1-5 were newly added in the revised manuscript, which are well-known basic formulas for the classical steady flow model. However, there are some mistakes. First, the references [1,2] for these equations are incorrect, which do not present these equations. The basic concept of the classical steady flow model has been developed by D.D. Clayton and his collaborators, and Clayton et al, Annals of Physics, 12, 331 (1961) and Clayton & Ward, ApJ, 193, 397 (1974) are more suitable references for these equations. Second, “the s-process theory” has not been used for the formulas. These equations were derived to explain an empirical correlation for the MACS x abundance = almost constant in a mass region, found in the solar abundances. These equations are NOT in any theory, which is constructed based upon the fundamental law, but it is a model. The difference between theory and model is large in science. It should be change to another description such as “a classical steady flow model for the s-process.” Third, the classical steady model has been used up to now as a primary analysis for nuclear experiments, but the modern AGB s-process calculations discussed in this manuscript do NOT use the steady flow, in which time-dependent network calculations under an evolutional stellar model have been carried out to obtain more precise results. This point should be clearly emphasized for honor of the AGB models.

Other minor points for the equations.

The sigma N curve have been developed by more precise analysis such as Clayton and Ward 1974 as pointed out by the first review. The equation of N sigma = constant has been revised about 50 years ago.

The “v” and “theta” for velocity are confused.

The equation 2 does not used.

Figure 6 shows the abundance correlation between 92Mo and 97Mo and the AGB model calculations with different metallicities are also presented. Because 92Mo in presolar grains originates from the interstellar media, its initial abundance in the s-process calculation should be given by as an input. In typical AGB models, it is adopted as an initial value proportional to the solar abundance indicated by metallicity. On other words, a simple linear function has been assumed for the GCE for 92Mo. This is because the abondance of non-s process isotopes including 92Mo is not one of the main topics in AGB s-process studies. However, 92Mo may have various origins in the galaxy and its GCE is not a simple function (see Sasaki 2022). Thus, when the 92Mo abundance is calculated with an initial value taking GCE, the result is expected to be shifted from the values presented in Fig. 6. This point should be explained to avoid misunderstanding for the AGB models.

Author Response

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