2017ApJ...835...32T

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 ∼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_☉ star formation at clump mass surface densities Σ_cl 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≃10-1000 M_☉ and Σ_cl≃0.1-3 g cm^–2, we find the overall SFE to be {bar}ε_* f_=0.31(Rc_/0.1pc)^–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/60M_☉)^1/2(Σ_cl/gcm^–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_*∼300 M_☉. 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 ∼150-300M_☉, initial core masses need to be 500-1000 M_☉. We also apply our feedback model to zero-metallicity primordial star formation, showing that, in the absence of dust, photoevaporation staunches accretion at ∼50 M_☉. Our model implies radiative feedback is most significant at metallicities ∼10^–2Z_☉, since both radiation pressure and photoevaporation are effective in this regime.