Chapter 16: The Expanding Universe

Cepheids in Spiral Galaxy NGC 4603

Individual stellar types are used as distance indicators within the Local Group and out to about 10 Mpc, but they cannot be used at the enormous distances of the most remote galaxies, for two reasons. First, variable stars like Cepheids or RR Lyraes are not luminous enough to be detected at such large distances. Second, the individual stars of a distant galaxy cannot be spatially resolved. The light from an individual star is hopelessly blurred into the overall light of the galaxy. Astronomers, therefore, look for properties of entire galaxies that can serve as distance indicators.

Messier 83, the Southern Pinwheel Galaxy

The Tully-Fisher relation is based on the discovery that the luminosity of a spiral galaxy is correlated with the rotational speed of the gas disk. This relationship can be established using galaxies with distance measurements that specify the luminosity. However, the Tully-Fisher relation can be used out to enormous distances when individual Cepheids cannot be resolved. The observation of rotation speed in a disk is relatively simple; it can be done with a single spectroscopic observation of the 21-cm line, where the velocity width of the line equals twice the rotation speed of the disk. This distance indicator can be calibrated in the local universe and it involves a simple measurement, but does it have a physical basis? In the Milky Way, the disk rotation speed is an indicator of mass. If we assume that the mass-to-light ratio of a spiral galaxy is fixed — that is, the stellar populations are constant — the mass then leads to an estimate of the galaxy's luminosity. The Tully-Fisher relation is thus a good distance indicator. When it is used on galaxies whose distance is known from another technique, it yields distances with a scatter of about 15%. The technique works best when used on galaxies with intermediate inclinations to the line of sight. A face-on spiral shows no Doppler motions due to rotation, because the disk motion is on the plane of the sky, and the total brightness of an edge-on spiral is difficult to measure because of the obscuring effects of dust in the disk.

Elliptical Galaxy NGC 1132 among a field of galaxies

The Faber-Jackson relation for elliptical galaxies is analogous to the Tully-Fisher relation for spiral galaxies. It is based on the fact that the range of stellar velocities of an elliptical galaxy, or the velocity dispersion, is correlated with the size of the galaxy. Once again, the observation is relatively simple. Astronomers use an image to measure the galaxy size (being careful to agree on their definition for objects without sharp edges!) and they use the width of stellar absorption features in an optical spectrum to measure the velocity dispersion. Unfortunately, Cepheids are not found in old stellar populations, so the Faber-Jackson relation cannot be calibrated with Cepheid variables. The physical basis for the Faber-Jackson relation is the fact that old stellar populations in elliptical galaxies are relatively simple. Both the size and the velocity dispersion are good measures of mass. The Faber-Jackson and Tully-Fisher relations are equally good distance indicators, with similar scatter on the measurement for a single galaxy. When galaxies are in a group or a cluster, they are at the same distance. With n measurements of the same quantity, the error on the combined measurement improves by a factor of √n. Astronomers combine measurements of individual galaxies to get a more accurate result.

Supernova 1994d in NGC 4526

Astronomers have had great success with the use of supernovae as distance indicators. A supernova represents the violent death of a massive star. Enormous energy is released, and for a few days, a supernova can rival an entire galaxy in brightness. Single stars with a range in masses do not yield supernovae with a tightly defined luminosity. They are called, for historical reasons, Type II supernovae. However, supernovae that result from mass transfer in a binary system are excellent standard "bombs." They are called Type I supernovae. Here is how it works. If a white dwarf is in a binary system, it can slowly gather gas from its companion. As the white dwarf exceeds the Chandrasekhar limit of about 1.4 solar masses, it must collapse. Carbon and oxygen in the collapsing star are compressed and heated up enough to start fusion. In these reactions, carbon and oxygen fuse to form silicon (₁₂C + ₁₆O → ₂₈Si), and pairs of silicon nuclei fuse into nickel (₂₈Si + ₂₈Si → 56Ni). The rapid energy release blows the star apart; no remnant is left over. It is as if you had a jar of a highly volatile chemical and slowly poured more of the chemical into the jar. As you pass a particular threshold, the chemical becomes unstable and explodes. The result is the same every time — a predictable and standard explosion.

Host Galaxies of Distant Supernovae

Redshifted Spectrum

Redshift can be used as a distance indicator. The Hubble relation allows astronomers to measure the redshift for a galaxy and assign it a distance without measuring the distance directly. Measuring a redshift only requires a spectrum of modest quality, so redshifts have been measured for extremely faint and distant galaxies. However, this distance indicator depends on the assumption that the observed redshift is caused by the expansion of space. In other words, redshift is only a distance indicator in the context of a cosmological model.