The chemical evolution of the secondary stars in close binaries, arising from common-envelope evolution and nova outbursts

Using a Paczynski-type stellar evolution code, we have modelled the evolution of secondary stars through the common-envelope and semidetached phases of close binary evolution. Our calculations are aimed at determining the effects of the accretion of red giant envelope material during the common-envelope phase, and the accretion of novae ejecta during the semidetached phase, on the surface composition of the secondary. For the second case, we make use of the results of the calculations of Prialnik & Kovetz, Kovetz & Prialnik and Prialnik, which concern the effects of accretion on to carbon-oxygen white dwarfs with varying white dwarf mass, white dwarf central temperature and mass transfer rate (the defining characteristics of nova outburst behaviour). In this paper we present the results of our calculations of a large grid of models designed to test the effects of these two polluting processes, both individually and together. We find that both processes may significantly affect the surface composition of the secondary, and that in the case of the accretion of novae ejecta, thermohaline mixing is extremely important and cannot be neglected. Our results indicate four phases in the evolution of the surface composition of the secondary during semidetached evolution: (i) the material accreted during the common-envelope phase and that accreted from the novae ejecta are mixed by convection and thermohaline mixing and dominate the surface composition of the secondary; (ii) the material accreted during common-envelope evolution is lost through mass transfer and the surface composition of the secondary is dominated by material accreted from the novae ejecta, which is mixed with the underlying layers of the secondary by convection and thermohaline mixing; (iii) the surface convection zone of the secondary penetrates to deeper layers so that these deeper layers dominate the surface composition of the secondary and thermohaline mixing no longer operates; and (iv) for evolved Population I systems, when the secondary has lost most of its mass, its surface composition is again dominated by material accreted from novae ejecta. We make predictions concerning the abundances of carbon, nitrogen and oxygen and the values of the isotopic ratios C-12/C-13, N-14/N-15 and O-16/O-17 on the surface of the secondary throughout its evolution. With observationally determined abundances and isotopic ratios, we can in principle determine whether or not these two polluting processes operate, and can further differentiate between them.