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Stellar evolution with rotation VII: Low metallicity models and the blue to red supergiant ratio in the SMC

We calculate a grid of models with and without the effects of axial rotation for massive stars in the range of 9 to 60 M$_{\odot}$ and metallicity $Z$ = 0.004 appropriate for the SMC. Remarkably, the ratios $Ω/Ω_{\mathrm{crit}}$ of the angular velocity to the break-up angular velocity grow strongly during the evolution of high mass stars, contrary to the situation at $Z$ = 0.020. The reason is that at low $Z$, mass loss is smaller and the removal of angular momentum during evolution much weaker, also there is an efficient outward transport of angular momentum by meridional circulation. Thus, a much larger fraction of the stars at lower $Z$ reach break-up velocities and rotation may thus be a dominant effect at low $Z$. The models with rotation well account for the long standing problem of the large numbers of red supergiants observed in low $Z$ galaxies, while current models with mass loss were predicting no red supergiants. We discuss in detail the physical effects of rotation which favour a redwards evolution in the HR diagram. The models also predict large N enrichments during the evolution of high mass stars. The predicted relative N-enrichments are larger at $Z$ lower than solar and this is in very good agreement with the observations for A-type supergiants in the SMC.