which is proportional to the stellar mass. The $M-L$ relation reads

$$L\sim M^{\eta}\; ,$$

where the value of the exponent $\eta$ depends on the mass loss rate. The evolution reaches a given mass with higher luminosity, the lower the value of $N$ is.

Figure  \[bar\_fig7\] shows the Gamma factor during the core hydrogen burning, for pregalactic Population III stars with a mass loss parameter $N=100$.

Galactic, and pregalactic Population III stars evolve during hydrogen burning near the Eddington upper luminosity limit. With and without mass loss, the ratio between the luminosity of the star and its Eddington luminosity is similar.

In Figures  \[bar\_fig8\] and 9, the Gamma factor is plotted as a function of the radius showing the phase when this factor approaches to unity, during the hydrogen burning, for mass losing galactic and pregalactic stars, respectively.

![Mass-luminosity relation for $100\,M_\odot$ galactic and pregalactic Population III stars with metallicity $Z=10^{-6}$ and $Z=10^{-9}$, respectively, and mass loss parameters $N=50$ and $N=100$, during the hydrogen burning.[]{data-label="bar_fig6"}](figure6.eps){width="82mm"}

![The $\Gamma$ factor for pregalactic Population III stars with metallicity $Z=10^{-9}$ and mass loss parameter $N=100$ during the hydrogen burning.[]{data-label="bar_fig7"}](figure7.eps){width="82mm"}

![The $\Gamma$ factor as function of the radius for galactic Population III stars with metallicity $Z=10^{-6}$ 