relation

$$\label{Zz}
  \dot{M}\sim Z^{\zeta}\; ,$$

where the exponent varies between $0.5-0.8$ for $0.01\leq
Z/Z_{\odot}\leq 1.0$ [@Leitherer1992; @Vink1999; @Vink2000; @Vink2001]. However, [@Kudritzki2002] has found that this relation breaks down below a certain threshold of the metallicity.

[@Krticka2006; @Krticka2009; @Krticka2010b] have studied line-driven winds from the first stars. They showed that weak stellar winds may be due to absorption in lines of CNO elements carried by mixing from the interiors to the atmospheres of the stars.

Rotation
--------

The Population III stars are supposed to be faster rotators than the stars with higher metallicity [@Maeder1999; @Meynet2006b]. The numerical hydrodynamic models of star-formation by [@Stacy2011] also indicate high angular momenta of the first stars, what influences their structure, evolution and final fate. The effects of rotation on the structure and evolution of massive stars were studied by the Geneva Group [@Meynet1997; @Maeder1998; @MaederMeynet2001; @Meynet2000; @Meynet2002]. The rotation may increase the mass loss by several processes:

1.  The rotational mixing enhances the atmospheres with heavier elements which facilitate the radiatively driven winds [@Lamers1995].

2.  The gravitational darkening enhances the radiative flux and the mass loss on poles of the rotationally oblate stars while reducing the angular-momentum loss [@MaederDesjacques2001; @Dwarkadas2002].

3.  The centrifugal force reduces 