Is feedback-free star formation possible?

It has been suggested that, if the free-fall time of star-forming clouds is shorter than the lifetime ($\approx 3$ Myr) of massive stars exploding as supernovae (SN), a large fraction of the cloud gas can be converted into stars during an allegedly `feedback-free' phase. Here, we show that radiation pressure from Ly$\alpha$ photons produced in the pre-SN phase can instead erase feedback-free conditions, and severely limit the star formation efficiency (SFE). We find that, for a constant star formation rate, all clouds with gas surface density $(37-1.7 \times 10^5)\ M_\odot\ \rm pc^{-2}$ have $\epsilon_* < 0.08$. Higher SFE values can only be reached if Ly$\alpha$-driven shells fragment and form stars. While advanced RHD simulations are required to establish the importance of this effect, adopting an optimistic guess, we find that the SFE increases with cloud surface density, rising from $\epsilon_*=0.023$ at $\Sigma_g = 37\ M_\odot\ \mathrm{pc^{-2}}$ to $\epsilon_*=0.27$ at $\Sigma_g = 1.7 \times 10^5\ M_\odot\ \mathrm{pc^{-2}}$. Given the optimistic assumptions adopted, these numbers should be regarded as upper limits. We conclude that Ly$\alpha$ radiation pressure strongly limits the SFE, even at solar metallicities, erasing the possibility that a feedback-free star formation mode with $\epsilon_* \gtrsim 0.4$ exists in the pre-SN phase. This conclusion remains valid even when other effects such as dust destruction of Ly$\alpha$ photons, presence of HII regions, velocity gradients, atomic recoil, and turbulence are considered.