We explore how the star formation efficiency in a protocluster clump is regulated by metallicity dependent stellar winds from the newly formed massive OB stars ( M _ { \star } \geq 5 ~ { } M _ { \odot } ) on their main sequence .
The model describes the co-evolution of the mass function of gravitationally bound cores and of the IMF in a protocluster clump .
Dense cores are generated uniformly in time at different locations in the clump , and contract over lifetimes that are a few times their free fall times .
The cores collapse to form stars that power strong stellar winds whose cumulative kinetic energy evacuates the gas from the clump and quenches further core and star formation .
This sets the final star formation efficiency , SFE _ { f } .
Models are run with various metallicities in the range Z / Z _ { \odot } = [ 0.1 , 2 ] .
We find that the SFE _ { f } decreases strongly with increasing metallicity .
The SFE _ { f } -metallicity relation is well described by a decaying exponential whose exact parameters depend weakly on the value of the core formation efficiency .
We find that there is almost no dependence of the SFE _ { f } -metallicity relation on the clump mass .
This is due to the fact that an increase ( decrease ) in the clump mass leads to an increase ( decrease ) in the feedback from OB stars which is opposed by an increase ( decrease ) in the gravitational potential of the clump.The clump mass-cluster mass relations we find for all of the different metallicity cases imply a negligible difference between the exponent of the mass function of the protocluster clumps and that of the young clusters mass function .
By normalizing the SFE s to their value for the solar metallicity case , we compare our results to SFE - metallicity relations derived on galactic scales and find a good agreement .
As a by-product of this study , we also provide ready-to-use prescriptions for the power of stellar winds of main sequence OB stars in the mass range [ 5 , 80 ] M _ { \odot } in the metallicity range we have considered .