Star formation efficiency as a function of metallicity: from star
  clusters to galaxies
  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 (Mstar >5 Msol). 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, SFEf.
Models are run with various metallicities in the range Z/Zsol=[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] Msol in the metallicity range we
have considered
