Resolving the Luminosity Problem in Low-Mass Star Formation

We determine the observational signatures of protostellar cores by coupling two-dimensional radiative transfer calculations with numerical hydrodynamical simulations that predict accretion rates that both decline with time and feature short-term variability and episodic bursts caused by disk gravitational instability and fragmentation. We calculate the radiative transfer of the collapsing cores throughout the full duration of the collapse, using as inputs the core, disk, and protostellar masses, radii, and mass accretion rates predicted by the hydrodynamical simulations. From the resulting spectral energy distributions, we calculate standard observational signatures (bolometric luminosity, bolometric temperature, ratio of bolometric to submillimeter luminosity) to directly compare to observations. We show that the accretion process predicted by these models reproduces the full spread of observed protostars in both Lbol - Tbol and Lbol - core mass space, including very low luminosity objects, provides a reasonable match to the observed protostellar luminosity distribution, and resolves the long-standing luminosity problem. These models predict an embedded phase duration shorter than recent observationally determined estimates (0.12 Myr vs. 0.44 Myr), and a fraction of total time spent in Stage 0 of 23%, consistent with the range of values determined by observations. On average, the models spend 1.3% of their total time in accretion bursts, during which 5.3% of the final stellar mass accretes, with maximum values being 11.8% and 35.5% for the total time and accreted stellar mass, respectively. Time-averaged models that filter out the accretion variability and bursts do not provide as good of a match to the observed luminosity problem, suggesting that the bursts are required.