Empirical abundance scaling laws and implications for the gamma process in core-collapse supernovae

Analyzing solar system abundances, we have found two empirical abundance scaling laws for p- and s-nuclei with the same atomic number. The first scaling law is that sip ratios are almost constant over a wide range of atomic numbers where the p-nuclei are lighter than the s-nuclei by 2 or 4 neutrons. The second law is that p/p ratios are almost constant where the second p-nuclei are lighter than the first p-nuclei by 2 neutrons. These scalings provide evidence that most p-nuclei are dominantly synthesized by the γ-process in supernova explosions. These scalings lead to a novel concept of the "universality of the γ-process," in that the s/p and p/p ratios of nuclei produced by individual γ-processes are almost constant. We have calculated the ratios produced by the γ-process based on core-collapse supernova explosion models under various astrophysical conditions, and found that the scalings hold for materials produced by individual γ-processes independent of the astrophysical conditions assumed. The universality originates from three mechanisms: the shifting of the γ-process layers in order to keep their peak temperature, the weak s-process in presupernovae, and the independence of the sip ratios from nuclear reactions. The results further suggest an extended universality, that the s/p ratios in the γ-process layers are not only constant but also centered on a specific value of 3. With this specific value and the first scaling law, we estimate that the ratio of s-process abundance contributions from AGB stars to massive stars will be almost 6.7 for the s-nuclei of A > 90. We find that large enhancements of the s/p ratios for Ce, Er, and W are evidence that the weak s-process actually occurred before supernovae.