10.2 Red-shift and the Big Bang — Learn

Prerequisites: from Chapter 4, that a wave has a wavelength and a frequency; from Chapter 5, that light is an electromagnetic wave and travels at $3.0 \times 10^{8}\,\text{m/s}$ in a vacuum; from Chapter 3, the equation $\text{speed} = \dfrac{\text{distance}}{\text{time}}$ ; and writing very large numbers in standard form.

By the end of this section you can: explain the red-shift of light from a galaxy that is moving away; explain how red-shift is evidence that the universe is expanding; explain how red-shift supports the Big Bang model; describe another piece of evidence for the Big Bang; and calculate how long light takes to reach us from a distant galaxy.

1. Light from a galaxy

A galaxy is a huge group of stars. The Sun is one star in the Milky Way galaxy. Many other galaxies are so far away that their light takes millions or billions of years to reach us.

The light from a galaxy contains a spectrum. The spectrum has a continuous range of wavelengths, crossed by dark lines. Each dark line is at a fixed wavelength, set by the atoms in the stars of the galaxy. The same atoms always give the same pattern, so the pattern acts like a fingerprint.

When astronomers compare the pattern from a distant galaxy with the same pattern made in a laboratory, the whole pattern is moved. It sits at longer wavelengths than in the laboratory. The pattern has moved towards the red end of the spectrum. This is called red-shift.

2. What red-shift shows

Light from a source that is moving away from you has a longer wavelength than light from the same source at rest. The faster the source moves away, the bigger the increase in wavelength. A source moving towards you has a shorter wavelength.

Almost every galaxy shows red-shift. That shows that almost every galaxy is moving away from us.

Watch out. Red-shift does not mean that the galaxy looks red to the eye. The light from the galaxy still contains every wavelength. What moves is the pattern of dark lines. Re-check by comparing the position of one dark line in the laboratory spectrum with its position in the galaxy spectrum. The line moves, not the colour of the whole galaxy.

3. The further away, the faster

Astronomers measure the distance of a galaxy and the size of its red-shift. The size of the red-shift gives the speed at which the galaxy is moving away. The results follow a clear pattern.

Galaxy	Distance from the Earth ( $10^{23}\,\text{m}$ )	Speed away from us (km/s)
A	3	700
B	6	1400
C	9	2100
D	12	2800

The further away a galaxy is, the faster it is moving away. In this table, the distance doubles and the speed doubles with it.

This pattern is evidence that the universe is expanding. The galaxies are not spreading out through space. Space itself is expanding, and it carries the galaxies apart.

4. Try it: shifting the lines

The figure shows two rows of a spectrum. The top row is the light from a laboratory. The bottom row is the same light from a galaxy. The dark lines mark fixed wavelengths.

Predict first. Do not move the slider yet. Write down your answers.

The galaxy is moving away from us. Will the dark lines move towards the blue end or the red end?
If the galaxy moves away faster, what happens to the size of the shift?

Test. Move the slider from left to right. Watch the dark lines in the lower row, and watch the arrow that shows the size of the shift.

Explain. Write two or three sentences. Explain why the wavelength of the light increases when the galaxy moves away from us. Use the words wavelength, crest and speed in your answer.

5. The Big Bang model

The Big Bang model says that the universe began from a very small region that was extremely hot and dense. The universe has been expanding ever since. This happened about 13.8 billion years ago.

Red-shift is the main evidence for the model. The model predicts that distant galaxies move away from us, and the red-shift shows that they do.

There is other evidence too. The cosmic microwave background radiation is a faint microwave signal that comes from every direction in space. It is left over from the hot, dense early universe. Its discovery in 1965 matched a prediction of the Big Bang model.

Before that, some scientists supported a different model, called the Steady State model. Both models could explain red-shift. The Steady State model does not explain the cosmic microwave background radiation, so the Big Bang model became the accepted one.

6. The expansion is speeding up

Since 1998, astronomers have studied very distant supernovae. These explosions are further away than expected, which suggests that the expansion of the universe is speeding up.

No one knows what causes this. The unknown cause is called dark energy. Dark matter is another unknown. Scientists can measure its pull on galaxies, but they do not know what it is. There is still much about the universe that is not understood.

7. How scientists use observations

A model is a set of ideas that explains what we see. Scientists test a model by using it to make predictions. Then they collect observations and check whether the predictions are right.

A model is only kept while the evidence supports it. If new evidence does not fit, the model is changed or replaced. This is how the model of the atom changed from the plum pudding model to the nuclear model. It is also how the Big Bang model replaced the Steady State model.

Worked example 1. Explain what the red-shift of a galaxy shows.

The wavelength of the light from the galaxy is longer than the wavelength of the same light measured in a laboratory. This shows that the galaxy is moving away from the Earth. The further away a galaxy is, the faster it is moving away. That is evidence that the universe is expanding.

Worked example 2. Explain how red-shift supports the Big Bang model.

The Big Bang model says that the universe began from a very small, extremely hot and dense region. The model predicts that the universe has been expanding ever since. Red-shift shows that the galaxies are moving apart, so the universe is expanding. This supports the Big Bang model.

Worked example 3. A distant galaxy is $2.4 \times 10^{25}\,\text{m}$ from the Earth. Light travels at $3.0 \times 10^{8}\,\text{m/s}$ . Calculate how long the light has taken to reach the Earth.

\begin{aligned} t &= \frac{d}{v} \\ &= \frac{2.4 \times 10^{25}}{3.0 \times 10^{8}} \\ &= 8.0 \times 10^{16}\,\text{s} \end{aligned}

The time in seconds is very large. One year is about $3.15 \times 10^{7}\,\text{s}$ , so the time in years is

\begin{aligned} t &= \frac{8.0 \times 10^{16}}{3.15 \times 10^{7}} \\ &= 2.5 \times 10^{9}\,\text{years} \end{aligned}

The light has travelled for about 2.5 billion years. We see the galaxy as it was 2.5 billion years ago.

Progress check

Return to the chapter problem. The telescope photographs a galaxy whose light is red-shifted. State whether the galaxy is moving towards the telescope or away from it. Explain your answer using the word wavelength.

You should now be able to

explain what is meant by the red-shift of light from a galaxy;
explain why the light from a galaxy moving away has a longer wavelength;
explain how the change of a galaxy speed with distance is evidence of an expanding universe;
explain how red-shift supports the Big Bang model;
describe the cosmic microwave background radiation as another piece of evidence for the Big Bang;
calculate how long light takes to travel a given distance, using $\text{time} = \dfrac{\text{distance}}{\text{speed}}$ ;
describe how scientists use observations to test a model.