This note covers how stars form and change, how stars are grouped into galaxies, and what the evidence of redshift tells us about the expanding Universe. It also introduces the Big Bang model and a simple estimate of the age of the Universe.
Key ideas
Stars. A star is a huge ball of hot gas, mostly hydrogen and helium, which gives out electromagnetic radiation across a wide range of wavelengths. Energy comes from nuclear fusion in the core, where hydrogen nuclei join to make helium. The Sun is an average star.
Life cycle of a star.
- Nebula: a cloud of gas and dust. Gravity pulls it together.
- Protostar: as the cloud collapses, it heats up. When the core is hot and dense enough, hydrogen fusion starts and the star is born.
- Main sequence: a long, stable period. The inward pull of gravity is balanced by the outward pressure from the hot gas and radiation produced by fusion. The Sun is in this stage, which lasts for billions of years.
- Red giant (or red supergiant): when the hydrogen in the core is used up, the star expands and cools at the surface. A star of similar mass to the Sun becomes a red giant. A star much more massive than the Sun becomes a red supergiant.
- End stage for a star like the Sun: the outer layers drift off and the core is left as a small, hot, dense white dwarf, which then cools.
- End stage for a massive star: the red supergiant explodes in a supernova. The core left behind becomes a neutron star or, if the star was massive enough, a black hole. A black hole has such strong gravity that nothing, not even light, can escape from it.
The elements heavier than hydrogen and helium were made by fusion in stars. A supernova scatters them into space, where they can become part of new stars and planets.
Galaxies and distances. A galaxy is a very large group of stars (billions of them), held together by gravity. Our galaxy is the Milky Way, and the Sun is one of its stars. The Universe contains billions of galaxies. Distances in space are huge, so a convenient unit is the light-year, the distance that light travels in one year in a vacuum.
The expanding Universe. Light from distant galaxies is shifted to longer wavelengths. This is called redshift. It shows that the galaxies are moving away from us. More distant galaxies show a larger redshift, so they are moving away faster. This suggests that space itself is expanding.
Running the expansion backwards leads to the Big Bang model: all matter and space were once concentrated in a tiny, extremely hot, dense state which expanded about 13.8 billion years ago. A second piece of evidence is the cosmic microwave background radiation (CMBR). This is microwave radiation arriving from all directions in space, which is the leftover radiation from the early Universe, stretched to longer wavelengths as the Universe expanded.
Hubble's law (extended). The recession speed v of a galaxy is directly proportional to its distance d from us: v = H0 × d. The constant H0 is the Hubble constant, with a value of about 2.2 × 10−18 per second. For a small redshift, the fractional change in wavelength is related to the speed: Δλ ÷ λ ≈ v ÷ c, where λ is the wavelength measured in the laboratory, Δλ is the increase in wavelength, and c is the speed of light, 3.0 × 108 m/s.
Because the galaxies move apart at a steady rate in this simple model, the time since the Big Bang is the distance divided by the speed, which is 1 ÷ H0. This gives an estimate of the age of the Universe.
Definitions and formulae
| Term or formula | Meaning / when to use |
|---|---|
| Light-year | Distance light travels in one year, about 9.5 × 1015 m. |
| v = H0 × d | Recession speed of a galaxy (m/s) from its distance (m) (extended). H0 = 2.2 × 10−18 s−1. |
| Δλ ÷ λ ≈ v ÷ c | Redshift and speed for a receding source (extended). |
| Age ≈ 1 ÷ H0 | Estimate of the time since the Big Bang (extended), in seconds. |
| Redshift | Increase in the wavelength of light from a receding source. |
| CMBR | Microwave radiation from all directions, left over from the early Universe. |
Worked examples
Example 1 Light travels at 3.0 × 108 m/s. Find the length of one light-year in metres, taking one year as 3.15 × 107 s. Hence find the distance in metres to a star that is 4.2 light-years away.
Distance = speed × time = 3.0 × 108 × 3.15 × 107 = 9.45 × 1015 m.
For 4.2 light-years: 4.2 × 9.45 × 1015 = 3.97 × 1016 m.
Answer: 1 light-year ≈ 9.45 × 1015 m. The star is 3.97 × 1016 m away.
Example 2 (extended) A galaxy is 2.5 × 1023 m from us. Use H0 = 2.2 × 10−18 s−1 to find its recession speed.
v = H0 × d = 2.2 × 10−18 × 2.5 × 1023 = 5.5 × 105 m/s.
Answer: 5.5 × 105 m/s
Example 3 (extended) A spectral line from hydrogen has a wavelength of 656 nm in the laboratory. In light from a distant galaxy, the same line is measured at 660 nm. Find the galaxy's recession speed and its distance from us.
Increase in wavelength: Δλ = 660 − 656 = 4 nm.
Use Δλ ÷ λ ≈ v ÷ c, so v = c × Δλ ÷ λ = 3.0 × 108 × 4 ÷ 656 = 1.83 × 106 m/s.
Use v = H0 × d, so d = v ÷ H0 = 1.83 × 106 ÷ 2.2 × 10−18 = 8.31 × 1023 m.
Answer: speed 1.83 × 106 m/s, distance 8.31 × 1023 m
Common errors
- Saying the light-year is a unit of time. It is a unit of distance.
- Saying the Big Bang was an explosion at one place in space. It was an expansion of space itself, everywhere.
- Saying that all stars end as black holes. Only the most massive stars do. A star like the Sun ends as a white dwarf.
- Mixing up redshift and the colour of the star. Redshift is a shift of every wavelength towards longer wavelengths, caused by motion away from us.
- Forgetting that the wavelength increase Δλ is the difference between observed and laboratory wavelengths, not the observed wavelength.
Exam tip: When describing the life cycle of a star, name the route for a Sun-like star and the route for a much more massive star separately, so that the two paths do not get mixed up.
Check yourself
- What keeps a main-sequence star stable and not collapsing?
Answer
The inward pull of gravity is balanced by the outward pressure from the hot gas and radiation produced by fusion in the core. - (Extended) A galaxy is 4.0 × 1023 m away. Using H0 = 2.2 × 10−18 s−1, find its recession speed.
Answer
v = 2.2 × 10−18 × 4.0 × 1023 = 8.8 × 105 m/s. - State two pieces of evidence that support the Big Bang model.
Answer
The redshift of light from distant galaxies, showing the Universe is expanding, and the cosmic microwave background radiation. - What are the possible end products of a red supergiant?
Answer
It explodes as a supernova and leaves behind a neutron star or a black hole.