Turn up the light: Radiative efficiency of protostars at birth

The early stages of stellar birth comprise a two-step process involving the formation of two hydrostatic cores. The second step of gravitational collapse sets the radiative efficiency and accretion rate of the young protostar. These two parameters, which are of prime importance for protostellar evolution, dictate the luminosities and thus play a key role in deciphering the current discrepancy between observational surveys and theoretical models. In this Letter, we provide quantitative estimates on the evolution of the radiative efficiency and accretion rate obtained from self-consistent, high-resolution, radiative hydrodynamic simulations performed using the codes <ns0:monospace>PLUTO</ns0:monospace> and <ns0:monospace>RAMSES</ns0:monospace>. The main highlight of our result is that the radiative efficiency reaches unity, that is, supercriticality, relatively quickly after protostellar birth. Supercriticality at the accretion shock is a necessary condition for cold accretion. Our results thus support a rapid transition to the cold accretion scenario, which is one of the assumptions used in pre-main sequence (PMS) models when working towards solutions to explain observational data. We briefly discuss the implications of the time evolution of the radiative efficiency factor in the context of the luminosity problem, the protostellar luminosity function, PMS evolution, accurate sink properties, and the stellar initial mass function.