Annu. Rev. Astron. Astrophys. 1994. 32: 153-90 Copyright © 1994 by Annual Reviews. All rights reserved

5.3. Some Constraints on p-Process Models

As mentioned above, the p-process probably occurs in several places in nature. Any astrophysical setting in which high temperatures but sufficiently short timescales lead to incomplete melting of heavy nuclei can produce p-nuclei. What we really seek is the site that produces the bulk of the p-nuclei. We can attempt to analyze this requirement by means of overproduction factors.

The overproduction factor of an isotope in the product material of some nucleosynthetic process is the ratio of its mass fraction in that material to its mass fraction in the solar system. In order for the process to be responsible for the production of the bulk of the solar system's supply of a given isotope, that isotope must have the largest overproduction factor in the product material. If the process is to be responsible for the bulk of the solar system's supply of two or more isotopes, those isotopes must all have comparably large overproduction factors.

Prantzos et al (1990) found an average overproduction factor of 0.96 for p-nuclei in 15 M of ejecta in their model for SN 1987A. The overproduction factor for ¹⁶O in the same model was 11.5 (Thielemann et al 1990). Since type II supernovae made most of the solar system's ¹⁶O, this would indicate that the type II supernova site could not be responsible for the production of the bulk of the solar system p-process elements. Prantzos et al argue, however, that there are extenuating factors. First, the SN 1987A model used Large Magellanic Cloud metallicities, which are lower than those in our Galaxy. Milky Way metallicities could give enhanced seed abundances and thus higher p-process overproduction factors. Also, it may be that p-nuclei production relative to oxygen could be higher in higher mass stars. Surveys over a range of star masses, such as that of Arnould et al (1992), will be important for understanding the contribution of type II supernovae to the solar system p-process abundances.

As for the type Ia model, Howard et al (1991) noted that besides possibly producing p-nuclei, these supernovae made most of the solar system's ⁵⁶Fe. The requirements that type Ia supernova models make ⁵⁶Fe and p-nuclei in solar proportions and that they produce 0.5 - 1.0 M of ⁵⁶Fe, and the fact that the typical p-process overproduction factors in this model are ~ 10⁴, lead to the conclusion that the zones that produce p-nuclei comprise 0.04 - 0.08 M of the white dwarf. This is in good agreement with the models (e.g. Khoklov 1990). It appears that type Ia supernovae are capable of producing the bulk of the solar system's p-nuclei.

Another important constraint on the p-process is the presence of live ¹⁴⁶Sm in the early solar system (Lugmair et al 1983, Prinzhofer et al 1989). From general galactic abundance evolution arguments, Prinzhofer et al inferred from their measurements that the production ratio of ¹⁴⁶Sm / ¹⁴⁴Sm should be between 0.07 and 0.5. This ratio causes problems for the gamma-process for which the production ratio for these isotopes is typically ~ 0.02 for the type II model (Woosley & Howard 1978) and ~ 0.05 for the type Ia model (Howard et al 1991). The inferred production ratio is in fairly good agreement with that found from proton-capture models (e.g. Audouze & Truran 1975), which led Prinzhofer et al to favor such models for production of p-process elements. As we have seen, however, such models are not astrophysically realistic, so the measurements present a challenge for gamma-process models. Woosley & Howard (1990) found, however, that if the branching ratios for (, n) and (, ) reactions on ¹⁴⁸Gd are varied within experimental uncertainties, the ¹⁴⁶Sm /¹⁴⁴Sm production ratio could be increased dramatically. It is clearly a worthy goal for experimental nuclear physicists to attempt to make accurate measurements of the disintegration rates of ¹⁴⁸Gd. Another important effect that may alleviate the ¹⁴⁶Sm / ¹⁴⁴Sm production problem is galactic infall (Clayton et al 1993).

In summary, plausible models exist that do a good job of satisfying most of the constraints on the p-process. The most vexing puzzle that remains is the underproduction of the light p-nuclei. Perhaps, with more work, we will see that type Ia supernovae can produce these nuclei at the correct levels. On the other hand, it may be that we will need to turn our attention to some other site, such as the -process in the mass cut in type II supernovae (Woosley & Hoffman 1992) or proton-capture reactions in Thorne-Zytkow objects (Cannon et al 1992), to explain the origin of these isotopes.