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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 a redshift or blueshift requires four steps:
1) find the spectrum of something (usually a
galaxy) that shows spectral lines
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)
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.
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
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.