A Simple Hubble Diagram

To give you a taste of how to prove that the universe is expanding, and to give you some practice using SkyServer for astronomy research, this page will show you how to make a simple Hubble diagram, with only six galaxies.

Distances

The first step in creating a Hubble diagram is to find the distances to several galaxies. Unfortunately, measuring distances in astronomy is difficult; but fortunately, all you need for a Hubble diagram are relative distances to galaxies, not their actual distances measured in miles or light-years. Relative distances are measured with respect to some standard location, like the Andromeda galaxy or the Virgo cluster. For example, suppose you find that the Perseus cluster is five times further away from Earth than the Virgo cluster. If the Virgo cluster had a relative distance of 1, the Perseus cluster would have a relative distance of 5.

To measure relative distance, astronomers need some way to compare galaxies. Since galaxies are so similar, astronomers assume that they all have the same average properties - that each galaxy is just about as bright and just about as big as any other galaxy. When we assume that two galaxies' intrinsic brightness and size are the same, then any differences in brightness or size between them are due only to their distances from us. If galaxy A is brighter and larger than galaxy B, then it must be closer to us.

Nearby galaxies appear large and bright, while distant galaxies appear small and faint.

One of the easiest ways to compare galaxies is to compare their magnitudes. Magnitude is a measure of how bright a star or galaxy looks to us - how much light from that star or galaxy reaches Earth. In magnitude, higher numbers correspond to fainter objects, lower numbers to brighter objects; the very brightest objects have negative magnitudes.

The scale is set up so that if object A is 2.51 times fainter than object B, then object A's magnitude will be higher by one number. For example, a magnitude five galaxy is 2.51 times fainter than a magnitude four star. The sun has magnitude -26. The brightest star in the Northern sky, Sirius, has magnitude -1.5. The brightest galaxy is the Andromeda Galaxy, which has magnitude 3.5.

The faintest object you can see with your eyes has a magnitude of about 6. The faintest object the SDSS telescope can see has a magnitude of about 23. SDSS measures magnitudes in five wavelengths of light: ultraviolet (u), green (g), red (r), near infrared (i), and infrared (z).

Redshifts

When Slipher looked at the redness of light given off by a galaxy, he was measuring the galaxy's "redshift" - a measure of how fast a star or galaxy moves relative to us. If you have ever stood by the side of the road as a car passed by, you have an idea of what redshift is. As the car moves toward you, its engine sounds higher-pitched than the engine of a stationary car. As the car moves away from you, its engine sounds lower than the engine of a stationary car. The reason for this change is the Doppler effect, named for its discoverer, Austrian physicist Christian Doppler. As the car moves toward you, the sound waves that carry the sound of its engine are pushed together. As the car moves away from you, these sound waves are stretched out.

The same effect happens with light waves. If an object moves toward us, the light waves it gives off will be pushed together - the light's wavelength will be shorter, so the light will become bluer. If an object moves away from us, its light waves will be stretched out, and will become redder. The degree of "redshift" or "blueshift" is directly related to the object's speed in the direction we are looking. The animation below schematically shows what a redshift and blueshift might look like, using a car as an example. The speeds of cars are much too small for us to notice any redshift or blueshift. But galaxies are moving fast enough with respect to us that we can see a noticeable shift.

Astronomers can measure exactly how much redshift or blueshift a galaxy has by looking at its spectrum. A spectrum (the plural is "spectra") measures how much light an object gives off at different wavelengths, from X-rays and ultraviolet light, through visible and infrared light, and into microwaves and radio waves.

The spectra of stars and galaxies almost always show a series of peaks and valleys called "spectral lines." These lines always appear at the same wavelengths, so they make a good marker for redshift or blueshift. If astronomers look at a galaxy and see one spectral line at a longer wavelength than it would be on Earth, they would know that the galaxy was redshifted and was moving away from us. If they see the same line at a shorter wavelength, they would know that the galaxy was blueshifted and was moving toward us.

By the end of its survey, the SDSS will have looked at the spectra of more than one million galaxies. Each spectrum is put into a computer program that automatically determines its redshift. The program outputs a picture like the one below, with spectral lines marked. The "z" number at the bottom of the spectrum (before the +/-) shows the redshift. Positive z values mean the galaxy has a redshift; negative z values mean the galaxy has a blueshift.

Click on the image to see it full size

Spectra of galaxies are stored in the SDSS's "spectroscopic database." The spectra are organized into plates and fibers, as they were when the SDSS telescope measured them.

Making the Diagram

Now that you have magnitudes and redshifts for six galaxies, you are ready to make a Hubble diagram.

Can you really draw a straight line through your data? When scientists try to figure out what data mean, they often talking about making a "model": in this case, the model you are using to relate magnitude to redshift is a straight line. Scientists often speak of the "fit" - how well the model fits the data. The fit can be described with a percentage that shows how close the points lie to the place where they should lie if the model were true. Because every experiment has some error and every observation has some uncertainty, the fit is never 100% accurate. Generally, astronomers consider a fit above 90% to show that the model probably really does describe the data.

Another Hubble Diagram

You have now made a simple Hubble diagram, with six galaxies. The data in the diagram fit well with a straight line. Now, try making the same diagram with six different galaxies.

In Exercise 7, you used the same method you used in Exercises 4 and 5: you graphed magnitude as a function of redshift. So why does the graph you got look so different? When you made both Hubble diagrams, you assumed that magnitude could substitute for distance. When you assumed that magnitude could substitute for distance, you assumed that every galaxy had the same average brightness.

Galaxies do have average properties. But if every galaxy were exactly the same, astronomy would be quite a boring subject. Galaxies come in many different types, and many astronomers make their careers studying the different types of galaxies. Unfortunately, the different types make a Hubble diagram trickier than simply graphing magnitude and redshift.

In the next section, you will learn some other ways astronomers measure relative distance to other galaxies. In the section after that, you will learn more about how to measure redshift. Then, you will use this knowledge to construct a better Hubble diagram, one that does not fall into the trap that this simple diagram fell into.