Astronomy Stack Exchange is a question and answer site for astronomers and astrophysicists. It only takes a minute to sign up.
Sign up to join this community
As I understand it astronomers estimate the mass of stars by studying the orbits of their companions (other stars or planets). This helps them to derive relationships between the luminosities and masses of stars. This allows them to infer the mass of stars of known luminosity.
But how do astronomers estimate the mass of cosmic dust in particular clouds or in entire galaxies?
Dust absorbs stellar light (primarily in the ultraviolet), and is heated up. Subsequently it cools by emitting infrared, "thermal" radiation. Assuming a dust composition and grain size distribution, the amount of emitted IR light per unit dust mass can be calculated as a function of temperature. Observing the object at several different IR wavelengths, a Planck curve can be fitted to the data points, yielding the dust temperature. The more UV light incident on the dust, the higher the temperature.
The result is somewhat sensitive to the assumptions, and thus the uncertainties are sometimes quite large. The more IR data points obtained, the better. If only one IR point is available, the temperature cannot be calculated. Then there's a degeneracy between incident UV light and the amount of dust, and the mass can only be estimated to within some orders of magnitude (I think).
If lines from various atomic or molecular transitions are seen as well, the composition can be better constrained. The size distribution can be determined from fitting the theoretical spectrum of a given distribution to observed dust spectra. This information is often not available in a given high-redshift galaxy, so here we can be forced to assume that the dust is similar in nature to "local" dust, i.e. in the Milky Way and our nearest neighbors.
If you're interested in the relevant equations, they can be found many places, e.g. here.
Another way to estimate the dust mass is to measure the metallicity of the gas with which the dust is is mixed, either from emission lines or absorption lines if a background source is available. The dust mass is then found from an assumed dust-to-metals ratio, which is pretty well-established in the local Universe, and to some extend also at higher redshifts.
Even if the accepted answer is well posed and clear, I would mention another method for dust measurements. X-ray spectra can also help to infer the amount of dust, analyzing the absorption at low energy of the observed spectra.
Indeed, the neutral hydrogen column density $N_H$ and the extinction $A(V)$, which is caused by the dust, is found in our Galaxy to be (Guver & Ozel, 2009):
$N_H = 2.2\times 10^{21} A(V)\,$mag
From the extinction one can get the dust optical depth (see here), and from that the volumetric dust density.
A good example of how to obtain $N_H$ is given in the following plot (S. Ikeda et al. 2009, ApJ 692 608):
As it can be seen, the spectra is differently modified by different amounts of neutral hydrogen column density $N_H$. This, of course, can be related to different aboundances, to best-fit the spectra and find the metals amounts.
Also, this method is tightly related to the iron K$\alpha$ line at $6.4\,$keV, which is another measurement of the metals amount (Fabian et al. 2000):
To distinguish among different ionization states, high-resolution spectroscopy is very common.
