• Galaxy masses and dark matter Sec. 14.6, 16.2
  • Galaxy classification: 15.1
  • Self-test: 15 in Ch14; 1-2 in Ch15, 4 in Ch16
  • Review: 12-14 in Ch14; 1-2 in Ch15; 10 in Ch16

The Mass of the Milky Way and Other Galaxies

Methods of Measuring Galaxy Masses

  1. Count the stars and add 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 Msun.
  2. 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; adapted from figure 14.18 in section 14.6 of the textbook). 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 as you can see in figure 16.4 in section 16.2 of the textbook. 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!
  3. Binary Galaxies. Binary galaxies are galaxies that orbit each other just like binary stars orbit each other (see the illustration in figure 16.5a in section 16.2 of the textbook). The method for measuring their masses is very similar to the methods described in the context of binary stars in lecture 14 and 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.
  4. 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

Speculations on the Nature of Dark Matter

There are ta number of plausible ideas for what makes up 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 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(see the illustration in figure 14.19 in section 14.6 of the textbook). 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 about 10 years 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.

Normal Galaxies: Morphology and Classification

Galaxies look fuzzy, unlike stars which look like very sharp points (as sharp as our eyes or our telescopes and cameras can make them). The come in a variety of shapes and sizes but there are some very clear trends in their morphologies.

There are many images of galaxies in figures 15.1 through 15.8 in section 15.1 of the textbook. The figure captions have a good description of the galaxies and their morphological characteristics.

The first person to classify galaxies in a systematic way was Edwin Hubble in the mid 1920s. His scheme is still widely used today and its is known as the Hubble classification scheme. It is summarized schematically in his "tuning fork" diagram, which is shown in figure15.9 in section 15.1 of the textbook. He divided galaxies into the following broad classes according to their appearance:




 Spiral  S  Sa, Sb, Sc
 Barred Spiral  SB  SBa, SBb, SBc
 Elliptical  E  E1 thru E7, S0
 Irregular  Irr  Irr I, Irr II

The properties of different types of galaxies are summarized in Table 15.1 in section 15.1 of the textbook.

Spiral Galaxies

They look very much like the Milky Way: they consist of a disk with spiral arms, a bulge in the center of the disk, and a halo surrounding the disk. They are subdivided into Sa, Sb, and Sc (somewhat subjectively) according to the prominence of the bulge and how tightly wrapped the spiral arms are:

The properties of spiral galaxies are also very similar to those of the Milky Way (summarized below; see also lecture 17 for more details)

Barred Spiral Galaxies

These look very much like spirals with one difference: they have a bar of stars going across them and through the bulge, and the spiral arms star at the ends of the bar rather than at the bulge. They are subdivided into SBa, SBb, and SBc by analogy with the Sa, Sb, and Sc subclasses of spirals. Their properties are just like those of spirals.

The Milky Way is, in fact, a barred spiral galaxy (its bulge is elongated like a football).

It is not always easy to tell the difference between a spiral and a barred spiral galaxy. If the galaxy is viewed from the side (edge on), the bar may not be visible even though it may be there (see, for example, the image of the Sombrero galaxy in figure 15.3 in section 15.1 of the textbook).

Elliptical Galaxies

They are called ellipticals because they have no flattened disks (and no spiral arms). They are subclassified into E1, E2, ... E7, S0, according to how spherical they look. E1 are spherical, while larger numbers mean that the galaxy gets progressively more and more elliptical. E7 galaxies are so elongated that they look like cigars.

Elliptical galaxies come in a wide range of sizes and masses, from dwarf ellipticals with a mass of 108 Msun to giant ellipticals with a mass of 1012 Msun. Their properties are different from those of spirals:

As such, elliptical galaxies resemble very closely the haloes of spiral galaxies, although there are many more stars in ellipticals and they are packed more densely together.

S0 galaxies are an intermediate morphology between spirals and ellipticals. They have a small disk of stars, which contains no gas and has no spiral structure. This disk can have a bar, in which case the galaxy will be classified as a barred S0, denoted by SB0.

Irregular Galaxies

As the name suggests the shapes are irregular and they look like nothing in particular. They are still subdivided into two subclasses:

They are rich in gas, they are the sites of vigorous star formation, and they contain a lot of young, blue stars. The orbits of the stars are irregular.

Good examples of irregular galaxies are the Magellanic clouds which are close companion galaxies to the Milky Way (although much smaller). They are called the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC).