Gamma-ray line emission from OB associations and young open clusters I. Evolutionary synthesis models

We have developed a new diagnostic tool for the study of gamma-ray emission lines from radioactive isotopes (such as Al-26 and Fe-60) in conjunction w ith other multiwavelength observables of Galactic clusters, associations, a nd alike objects. Our evolutionary synthesis models are based on the code o f Cervino & Mas-Hesse (1991), which has been updated to include recent stel lar evolution tracks, new stellar atmospheres for OB and WR stars, and nucl eosynthetic yields from massive stars during hydrostatic burning phases and explosive SN II and SN Tb events. The temporal evolution of Al-26 and Fe-60 production, the equivalent yield of Al-26 per ionising O7 V star (Y-26(O7 V)), and other observables are pre dicted for a coeval population. The main results are: The emission of the Al-26 1.809 MeV line is characterised by four phases: s tellar wind dominated phase (less than or similar to 3 Myr), SN Ib dominate d phase (similar to 3-7 Myr), SN II dominated phase (similar to 7-37 Myr), and exponential decay phase (greater than or similar to 37 Myr). The equivalent yield Y-26(O7 V) is an extremely sensitive age indicator for the stellar population which can be used to discriminate between Wolf-Raye t star and SN II Al-26 nucleosynthesis in the association. The ratio of the Fe-60/Al-26 emissivity is also an age indicator that const rains the contribution of explosive nucleosynthesis to the total Al-26 prod uction. We also employed our model to estimate the steady state nucleosynthesis of a population of solar metallicity. In agreement with other works, we predic t the following relative contributions to the Al-26 production: similar to 9% from stars before the WR phase, similar to 33% from WR stars, similar to 14% from SN Ib, and similar to 44% from SN II. For Fe-60 we estimate that similar to 39% are produced by SN Tt, while similar to 61% come from SN II. Normalising on the total ionising flux of the Galaxy, we predict total pro duction rates of 1.5 M. Myr(-1) and 0.8 M. Myr(-1) for Al-26 and Fe-60, res pectively This corresponds to 1.5 Mg of Al-26 and 1.7 Mg of Fe-60 in the pr esent interstellar medium To allow for a fully quantitative analysis of existing and future multi-wav elength observations, we propose a Bayesian approach that allows the inclus ion of IMF richness effects and observational uncertainties in the analysis . In particular, a Monte Carlo technique is adopted to estimate probability distributions for all observables of interest. We outline the procedure of exploiting these distributions by applying our model to a fictive massive star association. Applications to existing observations of the Cygnus and V ela regions will be discussed in companion papers.