The Hubble Diagram and the Expanding Universe

As you examined galaxy clusters and spectra in the last two sections, you went through the same steps that Edwin Hubble went through in 1929. Now, you have only one task left: you must make a Hubble diagram, pulling together your data to learn something about the universe.

Hubble made two important observations that led him from the straight line he saw in his diagram to the picture of the expanding universe. First, the line in his distance-redshift diagram does not depend on direction in the sky - in one direction we see redshifts, as if galaxies are moving away from us, and in the opposite direction we also see redshifts, not blueshifts. Everywhere, galaxies are moving away from us, and the farther they are, the faster they move. Second, counts of galaxies in various directions in the sky, and to various distances, suggest that space is uniformly filled with galaxies. (Although galaxies cluster, the clusters average out over all of space).

From the second observation, we know that our region of space isn't special in any way - we don’t see an edge in any direction. This means that while all galaxies appear to be moving away from us, we are not at the center of the universe - the universe has no center. An observer in any other galaxy would see the same line in a Hubble diagram. This is exactly the picture you get if you assume that all of space is expanding uniformly, and that galaxies ride along on the expanding space. The expanding universe model would not have worked if Hubble had found anything except a straight line in his distance-redshift diagram.

The Big Bang

The term “big bang” implies an explosion somewhere in space, with particles flying through space away from the explosion. If this were true, then with respect to the site of the explosion, the fastest-moving particles will have traveled farthest. If you plot the speed of the particles against the distance they have traveled, you will get a straight line. But this picture is NOT the concept behind the big bang. The explosion model is actually more complex than the big bang model - you need to say why there was an explosion at that point and not some other point; what distinguishes the galaxies at the edge as opposed to closer to the center, etc. In the big bang picture, all locations and galaxies are equivalent - everybody sees the same thing, and there is no center or edge.

Hubble did not measure the redshifts himself. They were already measured for a few dozen galaxies by Vesto Slipher. Hubble’s key contribution was to estimate the distances to galaxies and clusters, and to realize that the data in his diagram could be represented by a straight line.

The line that relates redshift and distance is expressed as

c z = H₀ d ,

where c is the speed of light, z is the redshift, d is the distance, and H₀ is called the Hubble constant. The value of H₀ depends on the units used to measure the distance d. The subscript 0 tells us “evaluated at the present cosmic time,” which suggests that its value may have been different earlier. Note that as we observe galaxies at progressively greater distances, we are seeing them as they were progressively farther in the past, because it has taken the light from them longer to reach us. In other words, larger d means we are looking at things as they were long ago, not as they are now.

If you were to ask an astronomer what the distance to some particular galaxy was, most likely she or he would measure the redshift z and use the formula above to compute d. This is not what we are going to do: we are trying to establish that the formula itself is right, which means that we must estimate d independently from our measurement of redshift.

Absolute and Relative Distances

A quasar found by SDSS at redshift 5.8, or about 28,000 Mpc.

What you measured in this project was relative, not absolute, distance. Having an absolute distance means we know the value of d in inches or meters or something - astronomers use a unit called the megaparsec (Mpc), where 1 Mpc equals about 3,260,000 light-years, or about thirty thousand billion billion meters. If we use such units, then H₀ has units of kilometers per second per Mpc. The currently favored value is H₀ = 70 km/sec/Mpc. The error associated with this number is about 10%, which reflects the uncertainty in measuring absolute distances to galaxies. The inverse of the Hubble constant, 1/H₀, tells us the time since the Big Bang. The value of 1/H₀ is 14 billion years, with the same 10% uncertainty.

Because you could measure only relative distances in this project, you have no information on the value of H₀. But you have still made a significant discovery: the straight line itself is what convinced scientists that the big bang picture was right, not any particular value for H₀. For doing exactly what you did, Hubble nearly won the Nobel Prize in Physics. (Sadly, he died in 1953, just as a committee was set to award him the prize. Nobel Prizes can only be awarded to living scientists.)

Putting it All Together

The data you have so far show a straight line when you plot distance and redshift, which suggests that the universe is expanding. This is an amazing result, but remember that you have only looked at a few galaxies in one tiny part of the sky. Because you looked at so few galaxies, scientists might be skeptical of your conclusions. They might say that something strange was happening in that part of the sky, or that what you found was only a lucky positioning of galaxies.

In fact, Edwin Hubble also had difficulty convincing scientists of his discovery. After he announced it in 1929, he teamed up with astronomer Milton Humason and began looking at more galaxies. They measured the distances and redshifts of thousands of galaxies, trying to prove that all galaxies plotted into a straight line on a Hubble diagram. They succeeded: by 1937, the expanding universe picture was firmly established by these observations.

Project designed by Rich Kron and Jordan Raddick

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