A MODEL FOR THE SPACE DENSITY OF DWARF CARBON STARS

Recent studies of faint high-latitude carbon stars have shown that a s ignificant fraction of them are not distant asymptotic giant branch (A GB) stars but rather belong to the local population of spheroid dwarfs . In this paper we attempt a theoretical prediction of the local space density of such dwarf carbon stars (dCs) based on the assumption that they are ordinary main-sequence stars that were able to accrete enoug h carbon-enriched material from a binary companion on the AGB to make their C/O ratio larger than unity. A simulated population of dCs is co nstructed by following the evolution of a large number of binaries usi ng simple analytic fits to detailed evolutionary calculations and dete rmining which ones would presently contain a dC. The zero-age paramete rs of the sample are chosen randomly from distributions derived from t he observed properties of unevolved binaries. The space density of hal o dCs that we predict (similar to 2-4 x 10(-7) pc(-3)) is in agreement with current observational constraints. The predicted local space den sity of disk dCs (similar to 1 x 10(-6) pc(-3)) may be somewhat higher than observed. The fraction of binaries that produces dCs depends str ongly on initial metallicity, and virtually no dCs are formed in syste ms with an initial metallicity of more than half solar. Thus, all disk dCs are predicted to be in binaries that formed in the very early pha ses of disk star formation, and their number depends strongly on assum ptions about the age-metallicity relation during this epoch. The predi ctions for the halo are much less model-dependent. The simulated orbit al period distributions are bimodal, with one peak between 10(3) and 1 0(5) days and another peak between 10(2) and 10(3) days. The shorter p eriod component is caused by systems that have gone through a common e nvelope phase. The simulated period distributions bear a strong resemb lance to the observed orbital period distribution of barium and CH gia nts, which may be the evolved descendants of the disk and halo dC popu lations we have modeled.