Empirical Abundance Scaling Laws and Implications for the Gamma-Process in Core-Collapse Supernovae

Analyzing the solar system abundances, we have found two empirical abundance scaling laws concerning the p- and s-nuclei with the same atomic number. The first scaling is s/p ratios are almost constant over a wide range of the atomic number, where the p-nculei are lighter than the s-nuclei by two or four neutrons. The second scaling is p/p ratios are almost constant, where the second $p$-nuclei are lighter than the first p-nucleus by two neutrons. These scalings are a piece of evidence that most p-nuclei are dominantly synthesized by the gamma-process in supernova explosions. The scalings lead to a novel concept of "universality of gamma-process" that the s/p and p/p ratios of nuclei produced by individual gamma-processes are almost constant, respectively. We have calculated the ratios by gamma-process based on core-collapse supernova explosion models under various astrophysical conditions and found that the scalings hold for materials produced by individual gamma-processes independent of the astrophysical conditions assumed. The universality originates from three mechanisms: the shifts of the gamma-process layers to keep their peak temperature, the weak s-process in pre-supernovae, and the independence of the s/p ratios of the nuclear reactions. The results further suggest an extended universality that the s/p ratios in the gamma-process layers are not only constant but also centered on a specific value of 3. With this specific value and the first scaling, we estimate that the ratios of $s$-process abundance contributions from the AGB stars to the massive stars are almost 6.7 for the $s$-nuclei of A > 90. We find that large enhancements of s/p ratios for Ce, Er, and W are a piece of evidence that the weak s-process actually occurred before SNe.