1 Introduction

Figure 1: Stream lines of meridional circulation in a rotating 20 $M_\odot$model with solar metallicity and $v_{\rm ini}=300$ km s-1 at the beginning of the H-burning phase (see text). The streamlines are in the meridian plane. In the upper hemisphere on the right section, matter is turning counterclockwise along the outer stream line and clockwise along the inner one. The outer sphere is the star surface and has a radius equal to 5.2 $R_\odot$. The inner sphere is the outer boundary of the convective core. It has a radius of 1.7 $R_\odot$.

Stellar rotation modifies all the outputs of stellar evolution for massive stars (Heger et al. 2000a; Heger & Langer 2000; Meynet & Maeder 2000). This is true at solar metallicity. At lower metallicities, like Z=0.004in the SMC, we noticed that the effects of rotation are expected to be larger (Maeder & Meynet 2001). In particular, for similar initial distributions of the rotational velocities, a larger fraction of the stars at lower Z reach break-up velocities. This is a result of the smaller losses of angular momentum by the stellar winds.

In addition, it may be that the initial distribution of the rotational velocities is not the same at lower Z. Indeed, it has been shown (Maeder et al. 1999) that the fraction of Be stars (i.e. stars close to break-up) is much higher in the SMC than in the Milky Way. However, we do not know whether this is just a consequence of the smaller mass loss, as said above, or whether the initial distribution of rotation velocities is also different as a result of processes of star formation at low Z. Whatever the exact origin of the higher fraction of stars close to break-up at lower Z, this shows the need of studies of star models with rotation at low Z.

We consider here star models with metallicity Z=10^-5, which is low enough to correspond to the most extreme metallicity observed in halo stars of the order of $\rm [Fe/H]\simeq -3$ and which nevertheless avoid the particularities of Z = 0 models, which we may consider in a future paper. The main possible comparisons with the observations will concern the chemical evolution of the abundances of the CNO elements and of other heavy elements in halo stars and very low Z galaxies. This is why we put here a particular emphasis on the chemical yields in CNO at very low [Fe/H]. This is a topical point in relation with the problem of primary nitrogen (Edmunds & Pagel 1978; Barbuy 1983; Carbon et al. 1987; Thuan et al. 1995; Izotov & Thuan 1999; Henry et al. 2000). Also, the recent debate around the behavior of the [O/Fe] ratio at very low Z (cf. Israelian et al. 2001; Melendez et al. 2001) shows the need of a better understanding of the CNO yields at very low metallicities.

In Sect. 2, we discuss the model physics. In Sect. 3, we examine the internal rotation and the surface velocities in Sect. 4. The models with zero rotation are briefly mentioned in Sect. 5. The HR diagram and lifetimes are discussed in Sect. 6. The evolution of surface abundances are examined in Sect. 7. In Sect. 8, we discuss the problem of the origin of primary nitrogen and we show how rotation can solve it. The chemical yields in He, CNO and heavy elements are discussed in Sect. 9.