Evolutionary Signatures in the Formation of Low-Mass Protostars. II. Toward Reconciling Models and Observations

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. We use as our starting point the evolutionary model following the inside-out collapse of a singular isothermal sphere as presented by Young and Evans. We calculate the radiative transfer of the collapsing core throughout the full duration of the collapse in two dimensions. From the resulting spectral energy distributions, we calculate standard observational signatures (L{sub bol}, T{sub bol}, L{sub bol}/L{sub smm}) to directly compare to observations. We incorporate several modifications and additions to the original Young and Evans model in an effort to better match observations with model predictions; we include (1) the opacity from scattering in the radiative transfer, (2) a circumstellar disk directly in the two-dimensional radiative transfer, (3) a two-dimensional envelope structure, taking into account the effects of rotation, (4) mass-loss and the opening of outflow cavities, and (5) a simple treatment of episodic mass accretion. We find that scattering, two-dimensional geometry, mass-loss, and outflow cavities all affect the model predictions, as expected, but none resolve the luminosity problem. On the other hand, we find that a cycle of episodic mass accretion similar to that predicted by recent theoretical work 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 and stellar initial mass function. Finally, the combination of outflow cavities and episodic mass accretion reduces the connection between observational class and physical stage to the point where neither of the two commonly used observational signatures (T{sub bol} and L{sub bol}/L{sub smm}) can be considered reliable indicators of physical stage.