Low-mass protostars are less luminous than expected. This luminosity problem is important because the observations appear to be inconsistent with some of the basic premises of star formation theory. Two possible solutions are that stars form slowly, which is supported by recent data, and/or that protostellar accretion is episodic; current data suggest that the latter accounts for less than half the missing luminosity. The solution to the luminosity problem bears directly on the fundamental problem of the time required to form a low-mass star. The protostellar mass and luminosity functions provide powerful tools both for addressing the luminosity problem and for testing theories of star formation. Results are presented for the collapse of singular isothermal spheres, for the collapse of turbulent cores, and for competitive accretion.
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