Stellar evolution with rotation VIII: Models at Z = 10⁻⁵ and CNO yields for early galactic evolution

We calculate a grid of star models with and without the effects of axial rotation for stars in the mass range between 2 and 60 M$_{\odot}$ for the metallicity $Z = 10^{-5}$. Star models with initial masses superior or equal to 9 M$_\odot$ were computed up to the end of the carbon--burning phase. Star models with masses between 2 and 7 M$_\odot$ were evolved beyond the end of the He--burning phase through a few thermal pulses during the AGB phase. Compared to models at $Z=0.02$, the low $Z$ models show faster rotating cores and stronger internal $\Omega$--gradients, which favour an important mixing of the chemical elements. In very low $Z$ models, primary nitrogen is produced during the He--burning phase by rotational diffusion of $^{12}$C into the H--burning shell. The intermediate mass stars of very low $Z$ are the main producers of primary $^{14}$N, but massive stars also contribute to this production; no significant primary nitrogen is made in models at metallicity $Z$=0.004 or above. We calculate the chemical yields in He, C, N, O and heavy elements and discuss the chemical evolution of the CNO elements at very low Z. Remarkably, the C/O vs O/H diagram is mainly sensitive to the interval of stellar masses, while the N/O vs O/H diagram is mainly sensitive to the average rotation of the stars contributing to the element synthesis. The presently available observations in these diagrams seem to favour contributions either from stars down to about 2 M$_{\odot}$ with normal rotation velocities or from stars above 8 M$_{\odot}$ but with very fast rotation.