In an improved model of protostar mass functions (PMFs), protostars gain mass from isothermal cores in turbulent clumps. Their mass accretion rate is similar to Shu accretion at low mass and to reduced Bondi accretion at high mass. Accretion durations follow a simple expression in which higher-mass protostars accrete for longer times. These times are set by ejections, stellar feedback, and gravitational competition, which terminate accretion and reduce its efficiency. The mass scale is the mass of a critically stable isothermal core. In steady state, the PMF approaches a power law at high mass because of competition between clump accretion and accretion stopping. The power law exponent is the ratio of the timescales of accretion and accretion stopping. The protostar luminosity function (PLF) peaks near 1 L☉ because of inefficient accretion of core gas. Models fit observed PLFs in four large embedded clusters. These indicate that their underlying PMFs may be top-heavy compared with the initial mass function, depending on the protostar radius model.
stars: formation - stars: luminosity function, mass function - stars: protostars