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Hubble Diagram
 A simple diagram
     - The Big Bang
     - Absolute Distance
     - Putting it Together
 Your Diagrams

The Hubble Diagram

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.


The Hubble Diagram and the Big Bang

Click on animation to play

The key breakthrough that led astronomers to the big bang picture was the linear relationship between distance and redshift on the Hubble diagram. Hubble made two important observations that led him to this picture. First, the linear relationship between distance and redshift does not depend on direction in the sky - in one direction we see redshifts, as if galaxies are receding from us, and in the opposite direction we also see redshifts, not blueshifts. Everywhere it seems that galaxies are moving away from us, and the farther they are, the faster they appear to be moving. Second, counts of galaxies in various directions in the sky, and to various distances, suggest that space is uniformly filled with galaxies (averaging over their tendency to cluster).

From the second observation, we can infer that our region of space is not special in any way - we don't see an edge or other feature in any direction. While all galaxies appear to be moving away from us, this does not mean that we are at the center of the universe. All galaxies will see the same thing in a statistical sense - an observer on any galaxy who makes a Hubble diagram would see a linear relationship in all directions. This is exactly the picture you get if you assume that all of space is expanding uniformly, and that galaxies serve as markers of the expanding, underlying space. The expanding universe model would not have worked if Hubble had found anything except a linear relation between distance and redshift.

The term "big bang" implies an explosion at some location in space, with particles propelled through space. If this were true, then with respect to the site of the explosion, the fastest-moving particles will have traveled furthest, leading to a linear relationship between distance and velocity. But this is NOT the concept behind the big bang cosmological picture. The explosion model is actually more complex than the big bang cosmological model - you need to say why there was an explosion at that location and not some other location; what distinguishes the galaxies at the edge as opposed to closer to the center, etc. In the cosmological 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 - those 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 linear relation between redshift and distance is expressed as

c z = H0 d ,

where c is the speed of light, z is the spectroscopic redshift, d is the distance, and H0 is a constant of proportionality called the Hubble constant whose value depends on the units used to measure the distance d. The sub-naught tells us "evaluated at the present cosmic epoch," which suggests that its value may have been different at an earlier cosmic time. 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 at earlier cosmic epochs. (For sufficiently large d, we might expect a departure from the simple linear relation, but that's another story.)

If you were to ask an astronomer what the distance to a 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 valid, 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 2800 Mpc.

What you measured in Section II 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 = 3.1 x 1022 m. (To give you a sense of this distance, the Andromeda galaxy is a bit less than 1 Mpc away.) If we use such units, then H0 has units of km per sec 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.

Exercise 18: Neglecting other elements of the cosmological model, the inverse of the Hubble constant, 1/H0, tells us the time since the Big Bang - the age of the universe. If H0 = 70 km/sec/Mpc, then how old is the universe? This age is subject to the same 10% uncertainty as for H0. Given this uncertainty, what is the range of possible ages? Is this range consistent with the ages of the oldest stars, which are about 11 to 13 billion years old? (Hint: 1 Mpc = 3.06 x 1019 km)

Because you could measure only relative distances in Section II, you have no information on the value of H0. But your work is still a significant accomplishment: the linear relationship is what motivated the big bang picture, not any particular value for H0. For doing exactly what you did in sections II and III, 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 cannot be awarded posthumously.)


Putting it All Together

Exercise 19: In the Distances section, you found relative distances to several galaxies, in three clusters, at one point in the sky. In the Redshifts section, you found redshifts for the same galaxies. Now, use a graphing program to make a Hubble diagram of these galaxies. Graph redshift on the x-axis and distance on the y-axis. Label your axes clearly. Can you fit a straight line through your points?

Question 7: What are the logical steps in the argument that lead from the straight line you see to the concept that the universe is expanding? What assumptions do you need to make to argue this? Can any of those assumptions be tested with SkyServer?

The data you have so far show a relationship between distance and redshift, and imply 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. Scientists need a large amount of data to be convinced, and many of them would 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 statistical coincidence.

In fact, Edwin Hubble also had difficulty convincing scientists of his discovery. After he announced his discovery in 1929, he teamed up with astronomer Milton Humason and embarked on a systematic program to look trace the diagram to larger distances and higher redshifts. They looked at thousands of galaxies, trying to prove that the linear characterization was really valid. They succeeded: by 1937, the redshift-distance relation was firmly established by these observations.

Research Challenge: Return to the SkyServer data and repeat the steps you went through in Sections II and III. Choose galaxies or clusters from the data and use several different methods to find their relative distances. Then, find their redshifts, using either your templates or the redshifts given by SkyServer. The easiest way to examine large numbers of galaxies is to use the Navigation Tool or the SQL Search Tool. For help using the SQL Search Tool, see the Searching for Data tutorial.

Make another Hubble diagram, using all your new data. Try to make the diagram as detailed as you can, and try to make the straight-line fit as accurate as you can. When you finish, E-mail your diagram to us (attach it a .gif or .jpg image, or as a .xls spreadsheet) and we will review your work.


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