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Doppler redshift (or redshift for short), is a phenomenon caused by the motion of an object away from the observer due to the Doppler effect, that increases the wavelength of electromagnetic waves such as light, as received by a detector and compared to its original source. It is so-named because in the visible spectrum, orange and yellow light, after being subjected to a redshift, appears to redden as the wavelength increases (and hence the frequency decreases). The opposite shift in wavelength to shorter wavelength is called blueshift.

The Doppler redshift is readily observed in astronomy, where the light from celestial objects moving away from the Earth, appear to be redshifted. The degree of redshifting allows the velocity of such objects to be calculated. Other causes of redshift are also known.

History in astronomy

The Doppler effect as applied to all kinds of waves, is named after Christian Andreas Doppler who proposed the effect in 1842. The hypothesis was tested and confirmed for sound waves by the Dutch scientist Christoph Hendrik Diederik Buys Ballot in 1845.

The first Doppler redshift was independently discovered by French physicist Armand-Hippolyte-Louis Fizeau in 1848. The effect is sometimes called the "Doppler-Fizeau effect".

In 1868, British astronomer William Huggins was the first to determine the velocity of a star moving away from the Earth by this method .

In 1912 American astronomer Vesto Slipher of the Lowell Observatory discovered that the redshift of spectra of spiral and some elliptical nebulae (galaxies) indicated that they were moving at very high radial velocities , questioning their membership in the Milky Way. He was the first person to measure galactic redshifts.

In 1929 Edwin Hubble discovered that the redshift of light from distant galaxies is proportional to their distance, from which was formulated the Redshift Distance Law of galaxies, nowadays known as Hubble's law.

Characteristics of Doppler redshift

If a source of the light is moving away from an observer, then redshift (z > 0) occurs; if the source moves towards the observer, then blueshift (z < 0) occurs. This is true for all waves and is explained by the Doppler effect. Consequently, this type of redshift is also called the Doppler redshift. If the source moves away from the observer with velocity v and this velocity is much smaller than the speed of light c, then the redshift is approximately given by :z ≈ v/c However, it is important to note that this expression is only approximate, and needs modification for speeds close to the speed of light. (For an exact equation for the frequency shift, see the article on the relativistic Doppler effect).

Additionally, there is a special form of Doppler redshift due to time dilation in special relativity where a redshift is seen even when the source is moving at right angles to the detector. The transverse redshift was first observed in the a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the Ives-Stilwell experiment .

Three defining characteristics of the Doppler redshifts, are that it is

1. Full-spectrum, that is, applies to all wavelengths
2. Distortion free, that is, does not produce blurring or splitting of spectral lines. Some broadening of spectral lines is due to thermal effects (see Doppler profile)
3. Frequency independent, that is, affects all wavelengths in a similar manner.

In this respect, the Doppler redshift shares the same characteristics as:

• the cosmological redshift (also called the Hubble redshift)
• the gravitational redshift (also called the Einstein Shift)

Together, these types of redshift are sometimes called Doppler-like redshifts.

Mathematical treatment

Redshift (and blueshift) is represented by the letter z, and is quantified by the equation:

${\displaystyle z={\frac {f_{\mathrm {emitted} }-f_{\mathrm {observed} }}{f_{\mathrm {observed} }}}={\frac {\lambda _{\mathrm {observed} }-\lambda _{\mathrm {emitted} }}{\lambda _{\mathrm {emitted} }}}}$

where f is frequency and λ is wavelength. This quantity is unitless. f_emitted is taken to be that as measured in the laboratory with a spectrometer (for example, the frequency of a specific spectral line), and f_observered is the frequency of the same spectral line as observed from the target object (eg. a celestial object, or another laboratory source).

See also

• Doppler effect
• Redshift as a general phenomenon
• Cosmological redshift (also called the Hubble redshift)
• Gravitational redshift (also called the Einstein Shift)

References

Christian Andreas Doppler, "Über das farbige Licht der Doppelsterne und einige andere Gestirne des Himmels" (On the colored light of the binary star and other stars) (1842) Monograph

Edwin Hubble, "A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae" (1929) Proceedings of the National Academy of Sciences of the United States of America, Volume 15, Issue 3, pp. 168-173

William Huggins, "Further Observations on the Spectra of Some of the Stars and Nebulae, with an Attempt to Determine Therefrom Whether These Bodies are Moving towards or from the Earth, Also Observations on the Spectra of the Sun and of Comet II." (1868) Philosophical Transactions of the Royal Society of London, Volume 158, pp. 529-564

Slipher, V. M., "On the spectrum of the nebula in the Pleiades" (1912) Lowell Observatory Bulletin, vol. 1, pp.2.26-2.27

Slipher, V. M., "The radial velocity of the Andromeda Nebula" (1913) Lowell Observatory Bulletin, vol. 1, pp.2.56-2.57

Ives, Herbert E.; Stilwell, G. R., "An Experimental study of the rate of a moving atomic clock" (1938) Journal of the Optical Society of America, vol. 28, issue 7, p.215

• Doppler effects
• Cosmology