On the effect of rotation on populations of classical Cepheids I. Predictions at solar metallicity

Context. Classical Cepheids are among the most important variable star types due to their nature as standard candles and have a long history of modeling in terms of stellar evolution. The effects of rotation on Cepheids have not yet been discussed in detail in the literature, although some qualitative trends have already been mentioned. Aims. We aim to improve the understanding of Cepheids from an evolutionary perspective and establish the role of rotation in the Cepheid paradigm. In particular, we are interested in the contribution of rotation to the problem of Cepheid masses, and explore testable predictions of quantities that can be confronted with observations. Methods. Recently developed evolutionary models including a homogeneous and self-consistent treatment of axial rotation are studied in detail during the crossings of the classical instability strip (IS). The dependence of a suite of parameters on initial rotation is studied. These parameters include mass, luminosity, temperature, lifetimes, equatorial velocity, surface abundances, and rates of period change. Results. Several key results are obtained: i) mass-luminosity (M-L) relations depend on rotation, particularly during the blue loop phase; ii) luminosity increases between crossings of the IS. Hence, Cepheid M-L relations at fixed initial rotation rate depend on crossing number (the faster the rotation, the larger the luminosity difference between crossings); iii) the Cepheid mass discrepancy problem vanishes when rotation and crossing number are taken into account, without a need for high core overshooting values or enhanced mass loss; iv) rotation creates dispersion around average parameters predicted at fixed mass and metallicity. This is of particular importance for the period-luminosity relation, for which rotation is a source of intrinsic dispersion; v) enhanced surface abundances do not unambiguously distinguish Cepheids occupying the Hertzsprung gap from ones on blue loops (after dredge-up), since rotational mixing can lead to significantly enhanced main sequence (MS) abundances; vi) rotating models predict greater Cepheid ages than non-rotating models due to longer MS lifetimes. Conclusions. Rotation has a significant evolutionary impact on classical Cepheids and should no longer be neglected in their study.