Doppler Effect and Red Shift

The pitch of a passing ambulance siren drops as it speeds away from you — the same effect, applied to light instead of sound, is one of the most powerful tools astronomers have. By reading the tiny colour shifts in starlight, we can measure how fast distant objects are moving without ever leaving Earth.

The Doppler effect for light

When a source of waves moves relative to an observer, the frequency and wavelength the observer detects are shifted from the values emitted at the source. This is the Doppler effect, familiar from sound — a siren sounds higher-pitched as it approaches and lower-pitched as it recedes. The same effect applies to electromagnetic waves, including visible light and radio waves, and it is one of the most important tools in observational astronomy, because it lets us measure the motion of objects we can never physically visit, purely from the light or radio waves they send us.

For a source moving at speed $v$ along the line of sight, with $v$ much smaller than the speed of light $c$, the fractional change in observed frequency is given by

where $f$ is the emitted (source) frequency and $\Delta f$ is the shift between the observed and emitted frequency. Because wavelength and frequency are inversely related for a wave travelling at fixed speed $c$, the same physical shift can equivalently be expressed in terms of wavelength. Astronomers almost always work with the wavelength form, expressed using the quantity $z$, known as the redshift:

Here $\lambda$ is the wavelength emitted by the source, $\Delta\lambda$ is the shift between the observed and emitted wavelength, and the minus sign reflects the sign convention below. This relationship holds equally whether the light being analysed is in the optical part of the spectrum or at radio frequencies — the underlying physics is identical, only the part of the electromagnetic spectrum being observed changes.

Sign convention: red shift and blue shift

The sign of $v$ (and hence of $z$) tells you the direction of motion along the line of sight:

• A receding source (moving away from the observer) has its light stretched to longer wavelength and shifted to lower frequency. Since red light sits at the long-wavelength end of the visible spectrum, this is called a redshift, and $z$ is positive.
• An approaching source (moving toward the observer) has its light compressed to shorter wavelength and shifted to higher frequency. This is called a blueshift, and $z$ is negative.

The quantity $z$ is simply the fractional shift in wavelength — how large the shift is compared with the wavelength that was actually emitted. It gives a single, standardised number that astronomers use to quantify and compare how much any given source's light has been shifted, regardless of which particular spectral line or part of the spectrum is being measured. A spectral line that would be emitted at a precisely known wavelength in a laboratory (for example, a specific absorption line from hydrogen) can be compared against its observed wavelength in a star's or galaxy's spectrum to give $z$ directly.

Redshift in binary star systems

Redshift and blueshift aren't only useful for objects moving steadily away from or toward us — they're just as revealing for objects in orbit. Consider a binary star system viewed roughly edge-on, so that the two stars' orbital plane lies close to our line of sight. As each star orbits the common centre of mass, its velocity component along the line of sight continuously changes: for part of the orbit the star moves toward Earth, and for the other part it moves away.

The result is that the star's spectral lines don't sit at a single fixed shifted wavelength — instead they oscillate periodically between blueshifted and redshifted, cycling once per orbit. Measuring this oscillation gives astronomers a way to detect binary systems that may be too close together to resolve as two separate points of light even in a large telescope, and to work out details of the orbit, such as its period, directly from the pattern of the shift over time. This exact technique — tracking a periodic, orbit-driven Doppler shift in a star's spectrum — reappears later in this module as the basis of the radial velocity method used to detect exoplanets, where it's the star's much smaller companion planet doing the tugging.

Redshift in galaxies and quasars

Beyond individual stars, entire galaxies show redshift in their combined spectra, and — as the next lesson explores — the size of that redshift turns out to increase systematically with a galaxy's distance from us. Some of the most extreme redshifts ever measured, however, come from a class of object called quasars.

Quasars were first identified as unexpectedly bright, compact sources of radio emission, with no obvious visible counterpart at first — the name itself is short for "quasi-stellar radio source," reflecting how star-like they appeared in early optical images despite their strong radio output. When their optical spectra were eventually analysed, quasars turned out to show extremely large redshifts, far larger than those of ordinary nearby galaxies, indicating that they are also extremely distant. Combining an object's large redshift and known distance with how bright it nonetheless appears from Earth implies an almost incomprehensible power output — a quasar can outshine an entire ordinary galaxy of billions of stars from a region not much larger than our Solar System.

Quasars are now understood to be powered by active supermassive black holes at the centres of young, very distant galaxies. As gas and matter spiral inward toward the black hole, they form a swirling accretion disc, are compressed and heated to extreme temperatures by the process, and radiate enormous amounts of energy — mostly before the matter actually crosses the black hole's event horizon. This makes quasars some of the most luminous persistent objects in the universe, visible across enormous cosmological distances precisely because of how much energy this accretion process releases.

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