Radiation Bookkeeping: a guide to astronomical molecular spectroscopy and radiative transfer problems with an emphasis on RADEX

This document discusses some terminology necessary to extract chemical/physical information from spectral line observations. Although this is all very basic material, there are at least two astronomers who were often confused about these things. This little guide discusses quantities like brightness temperatures, antenna temperatures, beam dilution, line centre optical depth, flux density, Sobolev approximation, excitation temperature, column density. The general goal is to give the practical steps to compare observations with some types of model calculations. The RADEX software is one of the simplest methods to constrain abundances and physical conditions from observations, and often serves as a useful guideline for using more complex radiative transfer programs. This document tries to explain what assumptions are implicitly made in RADEX, what else can be done, and how we compare this with our data.