Topic 7.2: The Doppler Effect and Redshift
When an ambulance races toward you, its siren sounds high. As it passes and speeds away, the pitch drops. This is the Doppler effect, named for the Austrian physicist Christian Doppler, who described it in 1842.
Why It Happens
A moving source squeezes the waves in front of it (shorter wavelength, higher pitch) and stretches the waves behind it (longer wavelength, lower pitch). The same thing happens for light:
- A source moving toward you: its light is shifted toward shorter wavelengths, bluer. This is blueshift.
- A source moving away: its light is shifted toward longer wavelengths, redder. This is redshift.
For speeds much less than the speed of light:
(change in wavelength) / (original wavelength) = speed / (speed of light)
or, with z for the fractional shift, z = Δλ / λ = v / c.
A Worked Example
Hydrogen's H-alpha line is at 656.3 nm in the laboratory. In the spectrum of a galaxy it is seen at 662.9 nm.
- z = (662.9 − 656.3) / 656.3 = 0.0101
- v = z x c = 0.0101 x 300,000 km/s = about 3,000 km/s, moving away from us.
The shift is tiny, but a good spectrograph can see a shift of one part in a million.
Using Doppler Shifts
- Speed of stars. Andromeda is blueshifted (about −110 km/s relative to the Milky Way), so it is coming toward us.
- Rotation. One side of a spinning galaxy is blueshifted and the other redshifted. We use this to measure rotation, and to discover dark matter (Topic 7.5).
- Planets around other stars. A planet's gravity makes its star wobble. The wobble shows as a tiny back-and-forth Doppler shift. Michel Mayor and Didier Queloz found the first planet around a Sun-like star, 51 Pegasi b, this way in 1995 (they won the 2019 Nobel Prize).
- Police radar measures the shift of radio waves bounced from your car.
Slipher's Surprise
Between 1912 and the 1920s, Vesto Slipher at Lowell Observatory in Arizona measured the spectra of the "spiral nebulae" (galaxies). He found that most were redshifted, and by large amounts: some were moving away at over 1,000 km/s. Nobody yet knew they were galaxies, or what the pattern meant. The explanation came with Hubble and Lemaitre (Topic 7.3).
Two Kinds of Redshift
- Doppler redshift: the source moves through space.
- Cosmological redshift: the light waves are stretched while crossing expanding space (Topic 7.3). For distant galaxies it is large: a galaxy with z = 1 has its light stretched to twice its original wavelength. The most distant galaxies seen by the James Webb Space Telescope have z above 10.
Worth a Pause
The psalmist wrote, "Day unto day uttereth speech, and night unto night sheweth knowledge. There is no speech nor language, where their voice is not heard" (Psalm 19:2-3). A Doppler shift is a message of this kind: no words, no sound, and yet a precise statement of how fast something is moving, written in a color. It is humbling that we can read it, and that the writing is reliable. That the sky is readable at all is the reason for science, and, for some, the reason for praise. One of the videos says our eyes evolved to see sunlight. Hold that as a theory, and then bring it back around: what about creation? The One who made light also made eyes to read it, and a universe in which its colors carry news from distant stars.
Try It: Expansion Lab. Use Hubble's law to turn distance into speed, find redshift, and estimate the Hubble time. Play Expansion Lab »
Practice Problems
- Explain the Doppler effect using an ambulance siren.
- What is the difference between redshift and blueshift?
- The H-alpha line (656.3 nm) is seen at 659.6 nm in a star. Is the star approaching or receding, and how fast? (z = change / original)
- What does it mean if a galaxy's spectral lines are blueshifted?
- How did astronomers find the first planet orbiting a Sun-like star?
- What surprising thing did Vesto Slipher find about the spiral nebulae?
- What is the difference between a Doppler redshift and a cosmological redshift?