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Redshift Tutorial

Calcium H and K

These are very prominent absorption lines is most all galaxies. An example is shown here:

These pair of absorption lines will appear in all the spectra and they should be your principle source for determining the redshift. The rest wavelengths of these lines are 3933 angstroms and 3968 angstrons.

A radial velocity of a galaxy is determined from the redshift as follows:

Vr = cz

where c = speed of light = 300,000 km/s

and z = redshift

To determine the redshift z, you need to calculate from the spectra the ratio of the observed wavelengths of the H and K lines to their rest wavelengths.

For example, suppose the observed wavelengths of these two lines are 3953 and 3988 angstroms.

In this case the redshift z = (3953-3933)/3933 or 0.005.

or

z = (3988 - 3968)/3968 = 0.005.

The velocity of the galaxy would then be 300,000 x .005 = 1500 km/s.

Hydrogen Emission Lines

In addition, some galaxies have emission lines that are principally due to hydrogren recombination. One of these lines that appears in these spectra is H-beta which is shown below:

Suppose that we observe H-beta at a wavelength of 5010 angstroms. We know the rest wavelength is 4861 and therefore the velocity of the galaxy (its redshift, since the line is shifted to longer wavelengths) would be:

(5010 -4861)/4861 = .031

The radial velocity is then .031 * 300,000 = 9300 km/s.