V.B.4.e.2.  A Simple Model

For this comparison between the new ALMA data and our experimental results, we adopt a simple model:  Each species is characterized by (1) a column density, with terrestrial isotopic abundances, (2) a single temperature, (3) a lineshape that is characteristic of its velocity distribution within the beam, (4) an optical depth parameter (for the strongest species), and (5) a constant continuum that is subtracted from the astronomical data.

For our simulation in the optically thin case, to convert laboratory absorbance A(n) (Eq. V.B.4.a.3-1) to Jansky/beam,

,                                                                                          (V.B.4.e.2-1)

Where S(n) is a normalized lineshape function based on the numerical lineshape functions derived from the astronomical data.  K’ was adjusted empirically so that the ALMA spectra in units of Jansky/beam matched the intensity of the simulation and was .0025, .002, and .16 for methyl cyanide, ethyl cyanide, and vinyl cyanide respectfully.  This factor, which absorbs nL/Q, is related to the astronomical column density and molecular partition function and has units of Jansky/beam.

If I_max is the intensity for an optically thick line, then

.                                                                                                    (V.B.4.e.2-2)

After we present the results of such a comparison, we will discuss prospects for straightforward extensions of this model.

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