- z = 4
- 12.094 billion years
- 20.745 billion light years
Redshift: Motion and color
Astronomers can learn about the motion of cosmic objects by looking at the way their color changes over time or how it differs from what we expected to see. For example, if an object is redder than we expected we can conclude that it is moving away from us, and if it is bluer we can tell that it is moving towards us. But how do we know this?
Redshift is an example of 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, where light has a longer wavelength.
Doppler effect example: Sound waves from a police car siren. Image credit: Alice Hopkinson, LCO
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, where light has a shorter wavelength. In the case of light waves, this is called blueshift.
The most accurate way to measure redshift is by using spectroscopy. When a beam of white light strikes a triangular prism it is separated into its various components (ROYGBIV). This is known as a spectrum (plural: spectra). Astronomers can look at the spectra created by different elements and compare these with the spectra of stars. If the absorption or emission lines they see in the star's spectra are shifted, they know the object is moving either towards us or away from us.
For far away objects such as quasars, some of which are too faint to be observed by spectroscopy, 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, 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 = (λobserved - λrest) / λrest
z tells you the number of years the light from the object has traveled to reach us, however this is not the distance to the object in light years, because the universe has been expanding as the light traveled and the object is now much farther away.
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|
|0.5||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|
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. As 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.
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 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.
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.