The carbon star mystery: 40 years later: Theory and observations

In 1981 Icko Iben Jr published a paper entitled "The carbon star mystery: why do the low mass ones become such, and where have all the high mass ones gone?", where he discussed the discrepancy between the theoretical expectation and its observational counterpart about the luminosity function of AGB carbon stars. After more than 40 years, our understanding of this longstanding problem is greatly improved, also thanks to more refined stellar models and a growing amount of observational constraints. In this paper we review the state of the art of these studies and we briefly illustrate the future perspectives.