for evolution with mass loss than for the conservative case. This is because for mass losing stars their initial mass is reduced during the evolution. Figure\[bar\_fig5\] shows the evolution of the convective core size during the hydrogen burning for pregalactic Population III stars and mass loss parameter $N=100$.

![Convective core size for $100\,M\odot$ (solid line), $120\,M_\odot$ (dash-dot-dot-dot-dash), $150\,M_\odot$ (dashes), $200\,M_\odot$ (dash-dot-dash) and $250\,M_\odot$ (dots) pregalactic Population III stars with metallicity $Z=10^{-9}$ and mass loss parameter $N=100$ during the hydrogen burning.[]{data-label="bar_fig5"}](figure5.eps){width="82mm"}

### d) Luminosity and Gamma factors {#d-luminosity-and-gamma-factors .unnumbered}

Luminosity increases or decreases during evolution with mass loss depending on the mass loss rate. The rate of decrease of the luminosity is higher for large mass loss parameters.

In Figure \[bar\_fig6\], the mass-luminosity ($M-L$) relation is shown for $100\,M_{\odot}$ galactic and pregalactic Population III mass losing stars during the hydrogen burning. For low values of the mass loss parameter $N=50$, the luminosity increases during hydrogen burning but decreases for large values of $N=100$. This is because in VMS the opacity is mostly due to electron scattering. Then, as the evolution goes on, the opacity decreases and the mean molecular weight increases. Both of these effects contribute to an increase of luminosity 