# Redshift

#### What is Redshift?

Astronomers can learn about the motion of objects by looking at the way their color changes over time, or is different from the expected.

Redshift is an example of the the Doppler Effect. As an object moves away from us, the sound or light waves emitted by the object are stretched out, which makes them have a lower pitch and moves them towards the red end of the electromagnetic spectrum. In the case of light waves, this is called redshift. As an object moves towards us, sound and light waves are bunched up, so the pitch of the sound is higher, and light waves are moved towards the blue end of the electromagnetic spectrum. In the case of light waves, this is called blueshift.

The video below demonstrates the concepts of the Doppler Effect and redshift.

#### How Do Astronomers Measure Redshift?

The most accurate way to measure redshift is by using spectroscopy. By looking at the spectra of stars or galaxies, astronomers can compare the spectra they see for different elements with the spectra they would expect. If the absorption or emmission lines they see are shifted, they know the object is moving either towards us or away from us. In the image below, the object is redshifted because the absorption lines are all shifted towards the red end of the spectrum. This object is moving away from us.

For far away objects such as quasars, some of which are too faint to be observed by spectrocopy, astronomers measure photometric redshifts. In this case they observe the peak brightness of the object through various filters. An object that is redshifted will have its peak brightness appear through filters towards the red end of the spectrum.

Astronomers talk about redshift in terms of the redshift parameter z. This is calculated with an equation:

z = (λobserved - λrest)/λrest

where λobserved is the observed wavelength of a spectral line, and λrest is the wavelength that line would have if its source was not in motion.

z is related to the distance of an object. This Cosmological Calculator lets you enter values of z and find the corresponding light travel time. This tells you the number of years the light from the object has traveled to reach us. This is not the distance to the object in light years, however, because the universe has been expanding as the light traveled and the object is now much farther away. The comoving radial distance takes this expansion into account and is the distance to the object now.

The highest known redshifts are from galaxies producing gamma ray bursts. The highest confirmed redshift is for a galaxy called UDFy-38135539 with a z value of 8.6, which corresponds to a light travel time of about 13.1 billion years. This means the light we see now left the galaxy about 600 million years after the Big Bang! The galaxy is now 30.384 billion light years away from us due to the expansion of the universe during the time the light from the galaxy traveled to us..

The table below gives light travel times and distances for some sample values of z:

 z Time the light has been traveling Distance to the object now 0.0000715 1 million years 1 million light years 0.10 1.286 billion years 1.349 billion light years 0.25 2.916 billion years 3.260 billion light years .5 5.019 billion years 5.936 billion light years 1 7.731 billion years 10.147 billion light years 2 10.324 billion years 15.424 billion light years 3 11.476 billion years 18.594 billion light years 4 12.094 billion years 20.745 billion light years 5 12.469 billion years 22.322 billion light years 6 12.716 billion years 23.542 billion light years 7 12.888 billion years 24.521 billion light years 8 13.014 billion years 25.329 billion light years 9 13.110 billion years 26.011 billion light years 10 13.184 billion years 26.596 billion light years

#### What are Some Applications of Redshift?

Astronomers use redshift and blue shift (for nearby objects and measurements this technique is called the radial velocity method) to discover extrasolar planets. This method uses the fact that if a star has a planet (or planets) around it, it is not strictly correct to say that the planet orbits the star. Instead, the planet and the star orbit their common center of mass. Because the star is so much more massive than the planets, the center of mass is within the star and the star appears to wobble slightly as the planet travels around it. Astronomers can measure this wobble by using spectroscopy. If a star is traveling towards us, its light will appear blueshifted, and if it is traveling away the light will be redshifted. This shift in color will not change the apparent color of the star enough to be seen with the naked eye. Spectroscopy can be used to detect this change in color from a star as it moves towards and away from us, orbiting the center of mass of the star-planet system.

More generally, astronomers use redshift and blueshift or radial velocity to study objects that are moving, such as binary stars orbiting each other, the rotation of galaxies, the movement of galaxies in clusters, and even the movement of stars within our galaxy.

#### Cosmological Redshift

Astronomers also use redshift to measure approximate distances to very distant galaxies. The more distant an object, the more it will be redshifted. Some very distant objects may emit energy in the ultraviolet or even higher energy wavelengths. As the light travels great distances and is redshifted, its wavelength may be shifted by a factor of 10. So light that starts out as ultraviolet may be become infrared by the time it gets to us!

As the universe expands, the space between galaxies is expanding. The more distance between us and a galaxy, the more quickly the galaxy will appear to be moving away from us. It is important to remember that although such distant galaxies can appear to be moving away from us at near the speed of light, the galaxy itself is not traveling so fast. Its motion away from us is due to the expansion of the space between us.

#### Example to try:

Use the equation for the z parameter and the table above to answer the following:

Suppose light with a wavelength of 400 nm (violet) leaves a galaxy, and by the time it reaches us, its wavelength has been redshifted to 2000 nm in the infrared.

a. What is the z parameter for this galaxy?

b. How long has the light traveled to reach us?

c. How far is the galaxy from us now?

a. z = 4

b. 12.094 billion years

c. 20.745 billion light years

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