We study feedback during massive star formation using semi-analytic methods , considering the effects of disk winds , radiation pressure , photoevaporation and stellar winds , while following protostellar evolution in collapsing massive gas cores .
We find that disk winds are the dominant feedback mechanism setting star formation efficiencies ( SFEs ) from initial cores of \sim 0.3 – 0.5 .
However , radiation pressure is also significant to widen the outflow cavity causing reductions of SFE compared to the disk-wind only case , especially for > 100 M _ { \odot } star formation at clump mass surface densities \Sigma _ { cl } \lesssim 0.3 \ > { g\ > cm ^ { -2 } } .
Photoevaporation is of relatively minor importance due to dust attenuation of ionizing photons .
Stellar winds have even smaller effects during the accretion stage .
For core masses M _ { c } \simeq 10 – 1000 \ > M _ { \odot } and \Sigma _ { cl } \simeq 0.1 – 3 \ > { g\ > cm ^ { -2 } } , we find the overall SFE to be \bar { \varepsilon } _ { *f } = 0.31 ( R _ { c } / 0.1 \ > { pc } ) ^ { -0.39 } , potentially a useful sub-grid star-formation model in simulations that can resolve pre-stellar core radii , R _ { c } = 0.057 ( M _ { c } / 60 M _ { \odot } ) ^ { 1 / 2 } ( \Sigma _ { cl } / { g\ > cm ^ { -2 } } ) ^ { -1 / 2 } % \ > { pc } .
The decline of SFE with M _ { c } is gradual with no evidence for a maximum stellar-mass set by feedback processes up to stellar masses of m _ { * } \sim 300 \ > M _ { \odot } .
We thus conclude that the observed truncation of the high-mass end of the IMF is shaped mostly by the pre-stellar core mass function or internal stellar processes .
To form massive stars with the observed maximum masses of \sim 150 – 300 M _ { \odot } , initial core masses need to be \gtrsim 500 – 1000 \ > M _ { \odot } .
We also apply our feedback model to zero-metallicity primordial star formation , showing that , in the absence of dust , photoevaporation staunches accretion at \sim 50 \ > M _ { \odot } .
Our model implies radiative feedback is most significant at metallicities \sim 10 ^ { -2 } Z _ { \odot } , since both radiation pressure and photoevaporation are effective in this regime .