  A long-standing problem in low-mass star formation is the "luminosity
problem," whereby protostars are underluminous compared to the accretion
luminosity expected both from theoretical collapse calculations and arguments
based on the minimum accretion rate necessary to form a star within the
embedded phase duration. Motivated by this luminosity problem, we present a set
of evolutionary models describing the collapse of low-mass, dense cores into
protostars, using the Young & Evans (2005) model as our starting point. We
calculate the radiative transfer of the collapsing cores throughout the full
duration of the collapse in two dimensions. From the resulting spectral energy
distributions, we calculate standard observational signatures to directly
compare to observations. We incorporate several modifications and additions to
the original Young & Evans model in an effort to better match observations with
model predictions. We find that scattering, 2-D geometry, mass-loss, and
outflow cavities all affect the model predictions, as expected, but none
resolve the luminosity problem. A cycle of episodic mass accretion, however,
can resolve this problem and bring the model predictions into better agreement
with observations. Standard assumptions about the interplay between mass
accretion and mass loss in our model give star formation efficiencies
consistent with recent observations that compare the core mass function (CMF)
and stellar initial mass function (IMF). The combination of outflow cavities
and episodic mass accretion reduce the connection between observational Class
and physical Stage to the point where neither of the two common observational
signatures (bolometric temperature and ratio of bolometric to submillimeter
luminosity) can be considered reliable indicators of physical Stage.
