Redshifts

In the last section, you used SkyServer to look up redshifts of twelve galaxies. In this section, you will learn how to calculate redshifts for yourself.

Astronomers learn an amazing number of things from analyzing spectra. In this section, you will focus on just one application: you will learn how to measure the redshift of a galaxy from its spectrum, and you will learn how to interpret and use the redshift.

Measuring Redshifts

Measuring a redshift or blueshift requires four steps:

1) find the spectrum of something (usually a galaxy) that shows spectral lines
2) from the pattern of lines, identify which line was created by which atom, ion, or molecule
3) measure the shift of any one of those lines with respect to its expected wavelength, as measured in a laboratory on Earth
4) use a formula that relates the observed shift to the object's velocity.

An example will help to show how this works. All spectral lines are created when electrons move around inside atoms. Hydrogen is the most common element in the universe, and it is often seen in galaxies. The spectrum of a hydrogen-containing region shows a pattern of spectral lines called the "Balmer series." The Balmer series is easy to reproduce in a classroom with a hydrogen discharge tube. The force that makes the gas glow is not the same as in galaxies, but the spectrum - the pattern of lines - is the same. Either from your own measurements in the classroom, or by looking the Balmer series up in a table, you know the rest wavelengths of Hydrogen's spectral lines to be as follows: (The wavelengths are given in Angstroms, equal to 100 trillionths of a meter)

Exercise 12: Using the Get Spectra tool, check out the spectrum of the object with ID = 587731512071880746. You can find the spectrum in Plate 401/51788, Fiber 161, and it is reprinted below. This spectrum comes from a galaxy, and like many others, it shows strong spectral lines. The hydrogen lines are already identified for you: the tallest peak is the a line (marked Ha), the second tallest is the b line. The g and d lines are valleys instead of peaks.

Click on the image to see it full size

Read off the wavelengths of the Balmer lines on the x-axis of the spectrum to verify the entries in this table: Wavelengths of Hydrogen - Balmer Series for Object ID # 587731512071880746 Name Color Wavelength (Angstroms) Alpha (a) Red 7220 Beta (b) Blue-green 5360 Gamma (g) Violet 4780 Delta (d) Deep Violet 4500

The redshift is symbolized by z. The definition of z is

 1 + z = l _observed /  l _rest.

For example, taking the Balmer gamma line of galaxy 587731512071880746,

1 + z = 4780 / 4340.5 = 1.1, so

z = 0.1.

If the observed wavelength were less than the rest wavelength, z would be negative - that would tell us that we have a blueshift, and the galaxy is approaching us. But it turns out that only almost every galaxy in the sky has a redshift in its spectrum. 

Choosing the alpha, beta, or delta lines would also give approximately z = 0.1 - the measured redshift does not depend on which line you choose. If you get very different redshifts when you use different lines, then you probably have not correctly identified at least one of the lines.

Interpreting Redshifts

Sometimes we instead want to express a galaxy's redshift as the speed with which the galaxy moves away from us, in units of km/sec.

To convert from redshift z to velocity v measured in kilometers per second, the formula is

v = c z,

where c is the speed of light, c = 300,000 km/sec.

Thus, in this example, galaxy 587731512071880746 appears to be moving away from us at about 30,000 km/sec. This value is typical of the galaxy redshifts found in the SkyServer database.

Since the formula can be rewritten as z = v / c, it shows you how to interpret z: z measures the galaxy's speed away from us relative to the speed of light.

Up to this point things are straightforward, but this definition of z is tricky for two reasons. First, the formula v = c z is accurate only when z is small compared to 1.0 (0.1 would be OK in this sense). For high velocities, those that approach the cosmic speed limit - the speed of light - Einstein's Special Theory of Relativity says that a more complicated formula is needed. Second, while we often speak of the "motion of the galaxies," which implies motion through space, in fact the picture is that space itself is expanding. The galaxies are not moving through space, but just being carried along by space as it expands (see the Conclusion for more about this concept). In this picture, the redshift of a galaxy is not supposed to be interpreted as a velocity at all, even though the observed redshift looks just like a Doppler effect redshift.

Rather, the redshift tells us the size of the universe at the time the light left the galaxy. Because the universe is billions of light-years across, it takes billions of years for light from distant galaxies to reach us. Suppose the distance to galaxy 587731512071880746 was
d(z) at the time the light left it that we are now observing (for z = 0.1, this time was roughly a billion years ago). In those billion years, the space in the universe has expanded, so that now the distance between our galaxy and it is d(0). Then

1 + z = d(0) / d(z).

We interpret this formula to mean this: at the time corresponding to redshift z = 0.1, all galaxies in the universe were 10% closer together. A measured value of z = 0.2 corresponds to a time when galaxies were 20% closer together than they are now, and so on.

Redshifts of Sample Galaxies

Now that you know what redshift is and how to measure it, you are ready to return to the sample galaxies from the last section.