What is Red-Shift?

The light from distant stars and galaxies has distinct spectral features characteristic of the atoms in the gases around the stars. These spectra are found to be shifted towards the red end of the spectrum and this shift being a Doppler shift indicates that they are moving away from us. Analysing these further shows that the more distant ones are moving away from us faster than the nearer ones and is evidence that the universe is expanding. This is the basis for Hubble’s law with the recession speed (redshift) being proportional to the distance. The measured redshifts are usually stated in terms of a z parameter, with the largest z values being associated with quasars.

In other words the redshift z of a galaxy is a measure of the speed v with which it is moving away from us (redshift) or towards us (blueshift). Because the Universe is expanding, due to the Doppler shift the wavelength of the light is longer when it is received on Earth than when it was emitted (thus it is shifted further towards the red end of the spectrum).

So

where ∆𝛌 is wavelength of received light - wavelength of emitted light and  𝛌 is the wavelength of the emitted light, v is the frequency and c is the speed of light.

Calculating v/c from this gives:

Measurements of more than 100 quasars have given a range of redshift of 0.16 to 3.53, corresponding to recession speeds of 0.15c to 0.91c. The z parameter can also be used to imply the scale factor R of the Universe at the time light was emitted from a given object:

where the scale is taken as R0=1 at the present time. So if the redshift of an object yields z=3, then R=1/4. In other words the Universe has expanded by a factor of four since light left that object. At such large values of z the redshift is mainly the cosmological redshift and not a valid measure of the actual recessional velocity of the object with respect to Earth.

The z parameter can be used to calculate mass density compared to the mass density 𝛒mo at the present time.

With z=3 the density is 64 times that of the present density.

Before the James Webb Space Telescope the most distant galaxy was around redshift z=10, however the galaxy with the highest known redshift is now JADES-GS-z13-0 at redshift 13.20, 400 million years after the Big Bang.