  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 due to competition
between clump accretion and accretion stopping. The power law exponent is the
ratio of the time scales of accretion and accretion stopping. The luminosity
function (PLF) peaks near 1 L_Sun, due to 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 to the IMF, depending on the
model of protostar radius.
