Sodium production in asymptotic giant branch stars

A new scenario is presented for the production of Na-23 in asymptotic giant branch (AGE) stars. The scenario takes advantage of the periodic third dredge-up episodes characterizing those stars, which mix primary C-12 from their intershell layers to their surface. Two successive interpulse/pulse/dredge-up sequences are then required to produce Na-23. During the first sequence carbon and oxygen are converted into N-14 by the hydrogen burning shell, and subsequently transformed into Ne-22 by the helium burning shell. During the second sequence, Ne-22 is converted into Na-23 by the hydrogen burning shell, which is brought to the surface by the subsequent dredge-up episode. The Na-23 produced by this scenario is thus primary. The efficiency of this scenario is analyzed through standard evolutionary AGE model predictions combined with synthetic calculations for the surface chemical evolution. It is shown that primary Na-23 can efficiently be produced as soon as the surface C+N+O abundance enhancement reaches a certain level depending on the stellar metallicity. The required surface C+N+O abundance enhancement amounts to similar to 0.4 dex in solar metallicity stars, and to similar to 0.8 dex at a metallicity five times less than solar. An analytical study of Na production further reveals that the surface Na-23 abundance asymptotically evolves to a 'line of primary sodium enrichment' (LOPSE) in the [C+N+C] - [Na-23] diagram. That LOPSE represents the Na-23 abundance evolution predicted in zero metallicity AGE stars experiencing third dredge-up episodes. An analytical relation for the surface Na-23 abundance evolution as a function of the surface C+N+O abundance is provided. The predicted surface Na-23 enhancements can exceed 0.5 dex depending on the level of surface C-12 enrichment, and increases with decreasing stellar metallicity. The quantitative prediction of Na-23 surface abundances, however, is presently subject to a high level of uncertainty, partly due to the still poor quantitative prediction of the structural evolution of AGE stars (dredge-up episodes in particular), and partly due to the uncertainties still affecting some nuclear reaction rates (such as Na-23 destruction by proton capture). The case of massive AGE stars in which hot bottom burning occurs is also discussed. The production of secondary sodium in those stars is a natural consequence of Ne-22 burning in their envelope, if the temperature at the base of the envelope exceeds 70 million K. It requires, however, many interpulses to be significant. The production of primary sodium from the dredge-up of primary Ne-22 and its subsequent burning in the envelope, on the other hand, is estimated not to be very efficient, expect maybe in low-metallicity stars. An eventual detection of high Na overabundances in carbon stars or related objects would support the scenario of primary sodium production in AGE stars. Such an observational evidence may have been found in at least one post-AGE star. Further observations of those objects are called for. Observations of Na-23 in planetary nebulae are also encouraged. Finally, the production of primary Na-23 by AGE stars, if confirmed observationally, may have played a non-negligible role in the chemical evolution of our Galaxy.