Galaxy Masses and Dark Matter

Methods of Measuring Galaxy Masses

Counting Stars and Addiing Up Their Masses

One does not actually count individual stars; one measures the brightness of the Milky Way or of another galaxy and compares it to the brightness of individual stars to determine how many stars are in the galaxy. With this method we find that the mass of the Milky Way is about 1011 M.

Rotation Curves

A rotation curve is a plot of the velocities of stars or gas in a galaxy versus distance from the center (see illustration in the figure on the right). It can be used to find the mass of spiral galaxies, including the Milky Way. The mass can be found by applying Kepler's and Newton's laws. Note however that the mass that one determines by measuring the velocity of a gas cloud or a star in the disk of a spiral galaxy is the mass contained within the circle made by the orbit of that object. To find the total mass of a galaxy one has to measure the velocity of a gas cloud or star at the edge of the disk of the galaxy. Very often it is much more convenient to measure the velocity of the gas rather than the stars, especially in the case of the Milky Way. In the Milky Way one has to resort to measuring the velocity of the gas because distant stars are obscured by dust in the Galactic plane. The figure below shows the rotation curve of the Milky Way (the parts of the plot are labeled).

The rising part is caused by the fact that orbits that are further away from the center include more mass within them, If one finds gas clouds beyond the edge of a galaxy and measures their velocities they should decrease as the distance from the center increases because the mass should not increase any more as the distance increases. Therefore, the rotation curve should start to drop at distances beyond the visible edge of a galaxy (this is what we would expect from Kepler's laws). However, this is not what we find in practice. The rotation curve of the Milky Way remains flat as far out as we can measure it, up to distances much larger than the visible edge of the Galaxy. This is also the case in just about all other spiral galaxies that we have measured. The flat rotation curves indicate that there is a great deal of unseen matter beyond the visible edge of the Milky Way and of spiral galaxies in general, which we call dark matter. The dark matter in the Milky Way has about twice as much mass as the visible matter. The nature of dark matter is a big puzzle! Not only do we have no idea what it is, but it represents much more mass than we can actually see. In other words, we do not know what 2/3 of the matter in the Milky Way is made of!

Binary Galaxies

Binary galaxies are galaxies that orbit each other just like binary stars orbit each other. The method for measuring their masses is based on Newton's and Kepler's laws. However, there is one important difference: in the case of binary galaxies we cannot wait for them to complete a revolution around each other because that could take up to a billion years. So we measure their instantaneous velocities and their separation and we get a rough estimate of their combined mass.

Clusters of Galaxies

These are large collections of galaxies held together by gravity. By measuring the velocities of all the galaxies in the cluster and the size of the cluster we can get an estimate of its total mass (i.e. combined mass of all the galaxies within it). Measurement of masses of clusters of galaxies by this method confirms that a large fraction of the mass of the cluster is made up of dark matter (i.e., there ius much more mass in the cluster than we would find by just counting the galaxies). In fact, in the case of clusters only 10% of the mass is visible and the other 90% is dark matter. This is a discomforting result because it tells us that we do not know nature if the majority of matter in the universe.

Dark Matter

Ideas About the Nature of Dark Matter

What we call "dark matter" need not be just one of the above possibilities: it can be a combination of many of them.

Since the early 1990s a number of groups have been carrying out long observational campaigns to detect stellar dark objects in the Milky Way. Their methods and results are summarized briefly below.

Attempts to Detect Stellar Dark Matter

The method used to detect stellar dark objects is gravitational (micro-)lensing. The essence of the method is as follows: as a dim object passes in front of a background stars it bends light rays from that star and directs them towards us (just like a black hole bends light, only not to that extreme). So the foreground object effectively acts as a lens and amplifies the brightness of the background star, hence the name. This way we can infer the presence of a dim object even if we cannot see it directly. Because these events require a very large coincidence, the passage of the dim object almost directly in from of the background star, they are quite rare. So, to find them one has to monitor millions of background stars for many years.

The result (after decades of searching) is that many such brightening events have been detected (1 or 2 dozen). From these we are able to draw the following conclusion about dark matter: the dark objects are most likely dim white dwarfs and there are enough of them to make up about half of the dark matter that we think exists in the Milky Way. So we have not solved the problem completely, but we have gone part of the way to solving it.

See also this Wikipedia article that discusses dark matter in more detail.