16.4: The Extragalactic Distance Scale

Measuring Galactic Distance

To determine many of the properties of a galaxy, such as its luminosity or size, we must first know how far away it is. If we know the distance to a galaxy, we can convert how bright the galaxy appears to us in the sky into its true luminosity because we know the precise way light is dimmed by distance. The same galaxy 10 times farther away would look 100 times dimmer. But the measurement of galaxy distances is very challenging. All galaxies are far away, and most are so distant that we cannot even make out individual stars in them.

For decades, the techniques used to measure galaxy distances were relatively inaccurate, and different astronomers derived distances that differed by as much as a factor of two. In the past few decades, however, astronomers have devised new techniques for measuring distances to galaxies. Most importantly, all of them give the same answer to within an accuracy of about 10%. As we will see, this means we may finally be able to make reliable estimates of the size of the universe.

Variable Stars

Before astronomers could measure distances to other galaxies, they first had to establish the scale of cosmic distances using objects in our own Galaxy. Astronomers were especially delighted when they discovered that they could measure distances using certain kinds of intrinsically luminous variable stars, such as cepheids. Henrietta Leavitt used cepheids as awy to measure distance. Figure \(\PageIndex{1}\) demonstrates how the presence of a cepheid in the galaxy M100 can be used to measure its distance. Over several days, the Hubble Space Telescope was able to measure changes in the star's brightness.

After the variables in nearby galaxies had been used to make distance measurements for a few decades, Walter Baade showed that there were actually two kinds of cepheids and that astronomers had been unwittingly mixing them up. As a result, in the early 1950s, the distances to all of the galaxies had to be increased by about a factor of two. We mention this because we want you to bear in mind, as you read on, that science is always a study in progress. Our first tentative steps in such difficult investigations are always subject to future revision as our techniques become more reliable.

The amount of work involved in finding cepheids and measuring their periods can be enormous. Even though cepheids are fairly luminous stars, they can be detected in only about 30 of the nearest galaxies with the world's largest ground-based telescopes. One of the main projects carried out during the first years of operation of the Hubble Space Telescope was the measurement of cepheids in more distant galaxies to improve the accuracy of the extragalactic distance scale. Recently, astronomers working with the Hubble Space Telescope have extended such measurements out to 108 million light-years.

Figure \(\PageIndex{1}\) : Cepheid Variable Star. Hubble Space Telescope images taken on three separate nights track the changing brightness of a single Cepheid variable star in M100, a method astronomers used to measure the galaxy's distance at 56 million light-years. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Alternative description of Figure \(\PageIndex{1}\).

Nevertheless, we can only use cepheids to measure distances within a small fraction of the universe of galaxies. After all, to use this method, we must be able to resolve single stars and follow their subtle variations. Beyond a certain distance, even our finest space telescopes cannot help us do this. Fortunately, there are other ways to measure the distances to galaxies.

Standard Bulbs

If every light bulb in a huge auditorium is a standard 100-watt bulb, then bulbs that look brighter to us must be closer, whereas those that look dimmer must be farther away. If every star were a standard luminosity, then we could similarly calculate their distances based on how bright they appear to us. Unfortunately, neither stars nor galaxies come in one standard luminosity. Nonetheless, astronomers have been searching for objects out there that do act in some way like a standard bulb. These type of objects are also called standard candles. With the replacement of light bulbs with LED lights, the term will most likely change again, but the concept remains the same: an object that has a consistent luminosity.

A number of suggestions have been made for what sorts of objects might be effective standard bulbs, including the brightest supergiant stars, planetary nebulae, and the average globular cluster in a galaxy. One object turns out to be particularly useful: the type Ia supernova. These supernovae involve the explosion of a white dwarf in a binary system. Observations show that supernovae of this type all reach nearly the same luminosity, about 4.5 × 10⁹ L_Sun at maximum light. With such tremendous luminosities, these supernovae have been detected out to a distance of more than 8 billion light-years and are therefore especially attractive to astronomers as a way of determining distances on a large scale. Figure \(\PageIndex{2}\) includes a Type Ia supernova that can be easily detected because it is brighter than its host galaxy, seen in the upper left region of the large spiral galaxy. 

Figure \(\PageIndex{2}\) : Type Ia Supernova. Near its peak brightness, this type Ia supernova outshines its entire host galaxy, a predictable peak luminosity that lets astronomers use these events as standard bulbs to measure cosmic distances. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Alternative description of Figure \(\PageIndex{2}\).

The Tully-Fisher Relation

Another technique for measuring galactic distances makes use of an interesting relationship noticed in the late 1970s by Brent Tully of the University of Hawaii and Richard Fisher of the National Radio Astronomy Observatory. They discovered that the luminosity of a spiral galaxy is related to its rotational velocity. The more mass a galaxy has, the faster the objects in its outer regions must orbit. A more massive galaxy has more stars in it and is thus more luminous, ignoring dark matter for a moment. We can say that if the mass-to-light ratios for various spiral galaxies are pretty similar, then we can estimate the luminosity of a spiral galaxy by measuring its mass, and we can estimate its mass by measuring its rotational velocity.

Tully and Fisher used the 21-cm line of cold hydrogen gas to determine how rapidly material in spiral galaxies is orbiting their centers. Since 21-cm radiation from stationary atoms comes in a nice narrow line, the width of the 21-cm line produced by a whole rotating galaxy tells us the range of orbital velocities of the galaxy's hydrogen gas. The broader the line, the faster the gas is orbiting in the galaxy, and the more massive and luminous the galaxy turns out to be.

It is somewhat surprising that this technique works, since much of the mass associated with galaxies is dark matter, which does not contribute at all to the luminosity but does affect the rotation speed. There is also no obvious reason why the mass-to-light ratio should be similar for all spiral galaxies. Nevertheless, observations of nearer galaxies, where we have other ways of measuring distance, show that measuring the rotational velocity of a galaxy provides an accurate estimate of its intrinsic luminosity. Once we know how luminous the galaxy really is, we can compare the luminosity to the apparent brightness and use the difference to calculate its distance. A drawback for this system is that it only applies to spiral galaxies.

Table \(\PageIndex{1}\) lists the type of galaxy for which each of the distance techniques is useful, and the range of distances over which the technique can be applied. In order of increasing distance, astronomers use planetary nebulae, cepheid variables, the Tully-Fisher relation, Type Ia supernovae, and redshifts. The majority of them apply to all types of galaxies. However cepheids are not in elliptical galaxies and the Tully Fisher method only works for spiral galaxies. We will discuss measuring distances with redshifts in The Expanding Universe.

Table \(\PageIndex{1}\): Some Methods for Estimating Distance to Galaxies

Method	Galaxy Type	Approximate Distance Range (millions of light-years)
Planetary nebulae	All	0–70
Cepheid variables	Spiral, irregulars	0–110
Tully-Fisher relation	Spiral	0–300
Type Ia supernovae	All	0–11,000
Redshifts (Hubble's law)	All	300–13,000