Basically by taking inventory of known systems of baryonic matter (stars), and seeing what is the expected light/mass ratio. See Nereid's thread on dark matter for all the reasons why it is not easy to "hide" baryonic matter, so you need dark matter. Also, look here:
http://apod.nasa.gov/apod/ap060824.html
for very striking evidence that dark matter cannot be normal matter "hidden" in the form of gas.

Ken G - Thanks, you got me on the right track to get an answer from Wickipedia. The answer I needed is that our sun is the basis for inferring a light to mass ratio. It seems to me that it is a risky assumption to use the characteristics of our solar system to infer the characteristics of a galaxy or cluster of galaxies. Of course it is the only data available. If there is considerable error in the likely mass light ratio of clusters and galaxies, then that uncertainty helps me put the non-baryonic conjectures into perspective.

It sounds like you are misinterpreting the Wickipedia data. The Sun may provide a convenient point of comparison, but the mass-to-light ratio of the Sun is not at all characteristic of a galaxy, and is not used. Instead, the known masses and observed luminosities are summed, and a result is determined that way. The main uncertainty comes from the fact that the light comes from the biggest stars, whereas the mass comes from the vast array of small stars. This is the relevant M/L ratio for a galaxy-- note that for the universe as a whole, the dominant "normal" mass comes from the hydrogen gas in galaxy clusters, and that is determined without using the M/L from starlight as it has nothing to do with that. Nevertheless, it emits X-rays because it is very hot, and so it is not counted as dark matter but rather as the normal matter that dominates the universe.

KenG: Thanks for responding. Where outside of our solar system do we get the known masses and luminosities to sum?

We can determine the masses of the component stars in double star systems. We make the assumption that physics (gravitation in this case) works the same around other stars as it does locally, and so far that assumption works reliably.

Enough stars are doubles that we can make good statistical studies about mass and brightness, and include other factors too, such as age and metalicity.

Further, by studying stars in a cluster (which we presume mostly formed at close to the same time as each other, and are the same distance from us as each other), we can find information about how stars of different sizes evolve during their lifetimes. This helps increase the accuracy of our guesses about the masses of single stars. We've done this for many clusters, both open (like the Pleides) and globular.

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