ASYMPTOTIC THEORY FOR THE SPATIAL-DISTRIBUTION OF PROTOSTELLAR EMISSION

In order to facilitate the interpretation of observations of protostellar sources, we develop an analytic theory of protostellar emission. We focus our discussion on submillimeter wavelengths where protostellar sources can be spatially resolved. For a given protostellar envelope (i.e., given density and temperature distributions), we determine an asymptotic expansion for the specific intensity. We then calculate the convolution of specific intensity profiles with the Gaussian response function of a telescope. Using these analytic results, we calculate the monochromatic luminosity ratio L-nu(R)/L-nu(0)-a directly observable quantity-in terms of the underlying physical quantities. Observations of L-nu(R)/L-nu(0) can be used in conjunction with the results of this paper to estimate the physical parameters of protostellar envelopes (in particular, the effective powerlaw indices p and q of the density and temperature distributions).