We have studied the effects of a hypothetical initial stellar generation ( Population III ) containing only massive ( M > 10 M _ { \odot } ) and very massive stars ( M > 100 M _ { \odot } , Pair-Creation Supernovae ) on the chemical evolution of the Milky Way .
To this purpose , we have adopted a chemical evolution model - the two-infall model from Chiappini et al .
( 1997 ) - which successfully reproduces the main observational features of the Galaxy .
Several sets of yields for very massive zero-metallicity stars have been tested : these stars in fact produce quite different amounts of heavy elements , in particular \alpha -elements and iron , than lower mass stars .
We have focused our attention on the chemical evolution of \alpha -elements , carbon , nitrogen and iron .
It was found that the effects of Population III stars on the Galactic evolution of these elements is negligible if only one or two generations of such stars occurred , whereas they produce quite different results from the standard models if they continuously formed for a longer period .
Also the effects of a more strongly variable IMF were discussed and to this purpose we have made use of suggestions appeared in the literature to explain the lack of metal-poor stars in the Galactic halo with respect to model predictions .
In these cases the predicted variations in the abundance ratios , the SN rates and the G-dwarf metallicity distribution are more dramatic and always in contrast with observations , so we have concluded that a constant or slightly varying IMF remains the best solution .
Our main conclusion is that if very massive stars ever existed they must have formed only for a very short period of time ( until the halo gas reached the suggested threshold metallicity of 10 ^ { -4 } Z _ { \odot } for the formation of very massive objects ) ; in this case , their effects on the evolution of the elements studied here was negligible also in the early halo phases .
In other words , we can not prove or disprove the existence of such stars on the basis of the available data on very metal poor stars .
Because of their large metal production and short lifetimes very massive primordial stars should have enriched the halo gas to the metallicity of the most metal poor stars known ( [ Fe/H ] \sim - 5.4 ) and beyond in only a few million years .
This fact imposes constraints on the number of Pair-Creation Supernovae : we find that a number from 2 to 20 of such SNe occurred in our Galaxy depending on the assumed stellar yields .