observations concerning CDM in our Milky Way galaxy, and other galaxies
The main technique used to estimate the distribution of mass in spiral galaxies, as a function of radius from the centre (nucleus) is to derive a rotation curve from observations of the light (radio, etc; electromagnetic radiation - I'll use 'light' as a synonym) emitted by such galaxies.
One technique involves observing how the line of sight velocity changes with position; here is a concise but accurate summary of how it's done, using a 'long slit' spectrum, and emission lines in the visual waveband.
There are many other ways to obtain a spiral galaxy rotation curve, using different wavebands, different lines; integrated light from sizable chunks of the target galaxy, individual sources (e.g. HII regions, bright stars); and so on.
The results are the same: the curves either keep rising or flatten out, right out (radially) to where no more light seems to be coming from the galaxy.
Using textbook physics, these curves can be interpreted to mean that the mass 'closer in' to the centre of the galaxy (than at any radius) keeps increasing as the radius increases. In fact, no other standard physics textbook interpretation has been proposed, that is also consistent with all the relevant observations.
However, adding up all the mass in these galaxies, estimated from the light emitted (by stars, dust, and gas/plasma) or light absorbed (by dust and gas), gives totals that are just too small ... and the difference (between 'rotation curve mass' and 'stars/dust/gas mass') gets larger as the radius increases.
In addition to spiral galaxy rotation curves, the mass of galaxies can be estimated by several other techniques.
Beyond the faintest (integrated light) edges of galaxies are objects which are moving within the gravitational well of the galaxies. These objects include planetary nebulae, globular clusters, and satellite (dwarf) galaxies. Just as the rotation curves can be interpreted to estimate the total mass 'closer in' (using physics which Newton pioneered), the motions of these more distant objects can also be interpreted, using the same physics, to estimate the total mass 'closer in'. This work is much, much more challenging than rotation curves! However, it probes the mass of galaxies at considerably greater distances than rotation curves can reach, and also gives estimates of the mass of elliptical galaxies, which do not have rotation curves.
These observations can be interpreted as being consistent with the rotation curve observations - galaxies seem to have 'halos' of mass that extend way beyond their 'visible' edges. The density of this (dark) halo mass decreases with radial distance from the nucleus.
Some elliptical galaxies, typically the giants found near the centres of clusters, emit x-rays. The physics of such emission is easily understood from a different part of the standard physics textbook, and the x-ray emission can be interpreted as tracing the (radial) mass distribution in these ellipticals - basically, for the hot plasma that emits the x-rays to be 'trapped' in the giant elliptical galaxy, the galaxy must have a mass that lies between two robust limits. Again, galaxy masses estimated using this technique are consistent with those estimated from motions of globular clusters and planetary nebulae ... and again, the total mass is considerably greater than that estimated from all the light emitted or absorbed by the stars and gas/plasma (ellipticals have essentially no dust).
Some dwarf galaxies, in our Local Group, are close enough that the line of sight velocities of individual stars can be measured, and the distribution of stars within the galaxies accurately measured. Assuming these dwarf galaxies are gravitationally bound, these observations can be interpreted, using standard textbook (Newtonian) physics to give estimates of the total mass of these dwarf galaxies. The results are both astonishing and unambiguous: these galaxies contain far, far more mass than is in the stars whose light we can detect (it's much the same with regard to gas/plasma; note that these galaxies have little dust).
Somewhat in contrast to rotation curves of spiral galaxies, interpretation of the observations using the other techniques I've briefly mentioned does not have to lead to firm conclusions about mass differences ... however, as far as I know, no alternative explanations (based on standard, textbook physics) have been proposed that are also consistent with the 'lensing' observations I will cover next.
So far, the parts of the standard physics textbooks used to interpret the millions of astronomical observations have been many, but have not included General Relativity (GR).
One last technique (two actually) involves estimating mass using GR, and is completely independent of all the techniques briefly described above. It is, to me at least, truly marvelous that 'GR observations' can be interpreted to arrive at conclusions that are completely consistent with the various other observations I've briefly described ... and this consistency across different techniques using different physics is surely one of the strongest indicators that 'unseen mass' is the right interpretation.
