Asymptotic Theory for the Spatial Distribution of Protostellar Emission

In order to facilitate the interpretation of observations of protostellar sources, an analytic theory of protostellar emission is developed, emphasizing submillimeter wavelengths where protostellar sources can be spatially resolved. For a given protostellar envelope an asymptotic expansion for the specific intensity is determined and the convolution of specific intensity profiles with the Gaussian response function of a telescope is calculated. Using these analytic results, the monochromatic luminosity ratio (MLR) is calculated in terms of the underlying physical quantities. Observations of MLR can be used in conjunction with the results of this paper to estimate the physical parameters of protostellar envelopes (particular, the effective power-law indices p and q of the density and temperature distributions).