Star formation efficiency as a function of metallicity: from star clusters to galaxies

We explore how the star formation efficiency (SFE) in a protocluster clump is regulated by metallicity-dependent stellar winds from the newly formed massive OB stars (M-star >= 5M(circle dot)) on their main sequence. The model describes the coevolution of the mass function of gravitationally bound cores and of the initial mass function 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 SFE, SFEf. Models are run with various metallicities in the range Z/Z(circle dot) = [0.1, 2]. We find that the SFEf decreases strongly with increasing metallicity. The SFEf-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 SFEf-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 SFEs 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-circle dot in the metallicity range we have considered.