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.
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