8.4 - Red-Shift & the Doppler Effect

Red-shift in light from distant galaxies

• Every element absorbs its own set of wavelengths of light, producing a fixed pattern of dark lines across a spectrum.
• In light from distant galaxies, these familiar line patterns are shifted towards the red end of the spectrum (longer wavelengths) compared to laboratory measurements.
• This increase in the observed wavelength of light from a galaxy is called red-shift.

What red-shift tells us

• A longer observed wavelength means the source of the light is moving away from us.
• Red-shift is seen in light from galaxies in every direction, showing that distant galaxies are receding from us.
• Red-shift from more distant galaxies is greater than from nearer ones, meaning the more distant a galaxy, the faster it's moving away.

Red-shift is evidence the universe is expanding

• Distant galaxies are receding in every direction, and the further away a galaxy is, the faster it's moving away.
• This is evidence that the whole universe is expanding.

Space itself is stretching

• The expansion happens because space itself is stretching, rather than galaxies flying through fixed space.
• As light travels across expanding space, it's stretched to a longer wavelength.
• Light that has travelled further has crossed more expanding space, which is why more distant galaxies show a greater red-shift.

The balloon model

• As a balloon with spots drawn on it is inflated, every spot moves away from every other spot, and spots that start further apart separate the fastest.
• The surface represents space and each spot represents a galaxy.
• This expansion supports the idea that the universe began from a single hot, dense point.

The Doppler effect

• When a wave source moves relative to an observer, the observed wavelength and frequency change.
• This is called the Doppler effect, and it happens for all waves, including light and sound.

Why the wavelength changes

• The wave speed stays constant, so motion of the source changes the spacing of the wavefronts:
  • Ahead of the source - Wavefronts are bunched together, giving a shorter wavelength and higher frequency.
  • Behind the source - Wavefronts are spread out, giving a longer wavelength and lower frequency.
• For example, a passing siren sounds higher-pitched as it approaches and lower-pitched as it moves away.

The Doppler effect for light

• An object moving away from an observer has its light shifted to a longer wavelength and lower frequency - towards the red end of the spectrum (red-shift).
• An object moving towards an observer has its light shifted to a shorter wavelength and higher frequency - towards the blue end of the spectrum (blue-shift).

The red-shift equation

Where:

• $\mathrm{\Delta }\lambda$ = Change in wavelength, in metres (m)
• ${\lambda }_0$ = Reference wavelength emitted by the source, in metres (m)
• $v$ = Speed at which the galaxy is moving away, in metres per second (m/s)
• $c$ = Speed of light, 3.00 × 10⁸ m/s

Worked example - Recession speed from red-shift

A galaxy emits light with a wavelength of 486 × 10^-9 m. The light is observed on Earth with a wavelength of 502 × 10^-9 m. Calculate the speed at which the galaxy is moving away.