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Estimating Distances to Galaxies
Magnitude is not the only way to measure relative distances in astronomy. Astronomers also use a galaxy's apparent size as a measure of its distance. The farther away a galaxy is, the smaller it will appear from Earth. Astronomers have also used many other features of galaxies to measure distance.
But even if you use another technique to estimate a galaxy's relative distance, you still may run into the problem you saw in Exercise 7: different galaxies have different properties. Suppose a certain galaxy is twice as large as an average galaxy. On Earth, the only information we could get from that galaxy is what we could see. When we saw the larger image, we would have no way of knowing the galaxy actually was larger: we would assume that it was simply closer to us. Because we didn't know what the galaxy was really like, we would misjudge its actual distance from us. Because we misjudged the galaxy's distance, if we used it in a Hubble diagram, we would not get the correct results. To overcome this problem, we need to look not just at individual galaxies, but also at clusters of galaxies.
Estimating Distances to Clusters
A galaxy cluster is a collection of about a thousand galaxies held together by gravity. Clusters help overcome the problem of galaxy variation because they include so many galaxies. Even if the properties of individual galaxies vary widely, the average properties of all galaxies in the cluster should come close to the average properties of galaxies in the universe. The more galaxies are in a cluster, the more confident we can be that the average properties of all the galaxies in the cluster will match the average properties of all galaxies in the universe.
All the galaxies in the same cluster are effectively at the same distance (both relative and absolute) from us. This means that their magnitudes and apparent sizes have the same ratio as their intrinsic, or "true," brightnesses and sizes. In other words, if galaxy A in a cluster looks 3.5 times brighter than galaxy B, then it really is 3.5 times brighter. By looking at the galaxies in a single cluster, we can get a picture of the different types of galaxies in the universe.
The trick in estimating galaxy distances, however, is knowing which galaxies are actually part of the cluster. Just because two galaxies are in the same area of the sky doesn't mean that they are in a cluster; they could be in the same general direction, but at very different distances.
An analogy might help you figure out how to place galaxies in clusters. Suppose that galaxies are like buildings, and clusters are like cities. Suppose you were standing on a very tall platform at Fermilab in Batavia, Illinois. You look out over the large, flat plains of central Illinois with a telescope. Your job is to survey the landscape for buildings, towns, and cities, and make a map that shows their positions with respect to you at the center. You are not allowed to use any information other than what you can see through your telescope.
In principle, a small town in the relative foreground could look like a large city that is farther away: a one-story building will have the same apparent height as a ten-story building that happens to be ten times farther away. But you probably wouldn't confuse a small town for a large city - there are enough other bits of information at your disposal to get these populations of buildings in their correct relative positions.
Once you know which galaxies are members of clusters, you can compare the properties of individual galaxies in different clusters. For example, the average size of a galaxy in one cluster should be about the same as the average size of a galaxy in another cluster. Or, the brightest galaxy in one cluster should have about the same true brightness as the brightest galaxy in another cluster.
There is no “best” way to measure relative distances to galaxies, but some may arguably be better than others. Edwin Hubble and his co-worker Milton Humason tried a number of ways, mostly related to the magnitude of the brightest galaxies in big clusters. You should also experiment with different ways of finding relative distances to clusters. But you have it easier than Hubble and Humason did - you have much better data!
Because the properties of galaxies vary so widely, you should use the same measure of relative distance for each cluster you examine. Some examples of things that astronomers have tried to find relative distances to clusters are:
1) the apparent sizes, viewed from top or bottom, of spiral galaxies with bright arms
Once you have chosen a measurement of relative distance, you should use it to find how far galaxies are with respect to Earth. To make it easier to understand relative distances between several galaxies and/or clusters, you should "normalize" the distances so that the nearest galaxy or cluster has a relative distance of 1. Then a galaxy twice as far away as the nearest galaxy will have a relative distance of 2.
To normalize the relative distances, set up a ratio between the relative distances of the nearest galaxy (1) and the second nearest (2) so that d1 / d2 = 1 / x, then solve for x: the normalized distance to galaxy 2. Repeat to find the normalized relative distances to farther galaxies. If you normalize all galaxy distances so that the nearest galaxy has a relative distance of 1, you will get an accurate picture of how far away each galaxy is.
Relative Distances for Sample Galaxies
Now that you have identified some of the ways to determine relative distances to galaxies, you are ready to use these ways to find the relative distances to some real galaxies.