5 Models with zero rotation

Figure 10: Evolutionary tracks for non-rotating (dotted lines) and rotating (continuous lines) models for a metallicity Z = 10-5. The rotating models have an initial velocity $v_{\rm ini}$ of 300 km s-1.

For purpose of comparison, we have computed non-rotating stellar models with the same physical ingredients as for the computation of the rotating ones. The evolutionary tracks are presented in Fig. 10, the lifetimes and various properties of the models are given in Table 2. The models were computed with the Schwarzschild criterion for convection and therefore present the usual differences when compared with models accounting for the effect of overshooting (see Papers V and VII for a more detailed discussion).

With respect to our previous grids of stellar models at solar metallicity (see Paper V), the present models are shifted toward higher effective temperatures, by about 0.15-0.20 dex in log $T_{{\rm eff}}$. The stars are much more compact than at solar metallicity by nearly a factor two (more precisely by a factor between 1.8-1.9 depending on the initial mass). This is a well known consequence of the low opacities in the outer layers of metal poor stars. In Paper VII, we noticed that models at Z = 0.004 with initial masses between 10 and 12.5 $M_\odot$ were showing a behavior in the HR diagram intermediate between the cases of stars presenting a well developed blue loop and the case of more massive stars, which do not produce any blue loop, but begin to burn their helium in their core at a high effective temperature, while they cross the HR diagram for the first time. Here at Z = 10^-5, this transition zone covers a broader range of initial masses, from 2 to about 15 $M_\odot$. This is well consistent with grids of stellar models computed by other authors. Indeed a similar broadening in mass for this transition region can be observed in the grids by the Padova group (compare for instance the grids by Fagotto et al. 1994 at Z = 0.0004 and that of Girardi et al. 1996 at Z = 0.0001).

From Fig. 10, one sees that the 20 $M_\odot$ model does not reach the red supergiant phase at least before the end of the C-burning phase. This feature is also present in zero metallicity stellar models (see e.g. Marigo et al. 2001), but for pop III models, it extends over a broader range of initial masses (from $\sim$10 to $\sim$40 $M_\odot$). Finally, let us note that, when the metallicity decreases, the mass limit for the helium flash decreases (see also Marigo et al. 2001). This is a consequence of the higher central temperatures reached in metal poor stars. Typically a 2 $M_\odot$ model at solar metallicity, computed with the same physical ingredients as used in the present work, undergoes He-flash, while the corresponding model at Z =10^-5 ignites helium in a non-degenerate environment.