How To Use Thermal Dust Continuum Emission To Measure The Physical Properties Of Dusty Astrophysical Objects

Dust grains in the interstellar medium interact with photons across the electromagnetic spectrum. They are generally photon energy converters, absorbing short wavelength radiation and emitting long wavelength radiation. Sixty years ago in 1965, thermal emission from dust grains in the interstellar medium was discovered. This tutorial is a summary of the physics of thermal dust continuum emission and how to use observations of the intensity and flux density of dusty objects to calculate physical properties such as mass, column density, luminosity, dust temperature, and dust opacity spectral index. Equations are derived, when feasible, from first principles with all limits and assumptions explicitly stated. Properties of dust opacities appropriate for different astrophysical environments (e.g. diffuse ISM, dense cores, protoplanetary disks) are discussed and tabulated for the wavelengths of past, current, and future bolometer cameras. Corrections for observations at high redshift as well as the effects of telescope measurement limitations are derived. We also update the calculation of the mean molecular weight in different ISM environments and find that it is 1.404 per H atom, 2.809 per H2 molecule, and 2.351 per gas particle assuming protosolar metallicity and the latest values of the ISM gas phase abundances of metals.