Redshift and Blueshift Explained - How We Know Disance to Far-Off Objects

History of Redshift and Blueshift

The Doppler effect is named after Christian Andreas Doppler who offered the first known physical explanation for the phenomenon 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 described in 1848 by French physicist Armand-Hippolyte-Louis Fizeau, who pointed to the shift in spectral lines seen in stars as being due to the Doppler effect. 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 1871, optical redshift was confirmed when the phenomenon was observed in Fraunhofer lines using solar rotation, about 0.1 Å in the red. In 1901 Aristarkh Belopolsky verified optical redshift in the laboratory using a system of rotating mirrors.

Looking for Redshift in Spectra

The spectrum of light coming from a distant object can be measured through spectroscopy. To determine the redshift features in the spectrum (such as absorption lines, emission lines, or other variations in light intensity) are searched for and if found compared with known features in the spectrum of various elements. A very common element in space is hydrogen.

In the diagram above you can see two spectra. One from out Sun (a known spectra - we know each of the absorption lines) and one from a supercluster of distant galaxies. When we compare the two we see a correlation between the Hydrogen lines of the Sun and of the distant galaxies, the only difference is that the absorption lines in the galaxies are all moved up (towards the red). This indicates a redshift and we can tell that the galaxies are moving away from us (or we are moving away from the galaxies).

Calculation of Redshift and Blueshift

Once we find a known spectral line we can work out it's wavelength in the spectra. We can then use this to calculate the exact redshift.

From the graphic above we can take the Hydrogen Alpha emission line at 656.2 nm. We can then calculate the wavelength from the observed spectra based on the spectrum (for this example the observed line is at 675 nm). We can then use a simple equation to calculate the redshift value.

Equation 27 - Redshift

Plugging in our values for the observed wavelengths gives:

Equation 28 - Redshift example working

z is a dimensionless quantity that is traditionally used. A positive value of z indicates redshift, a negative value represents blueshift.

Calculating Speed and Distance from Redshift

Now we know the redshift of a distant object, we can work out its speed. This is done using the formula:

This equation is actually an approximation that is only valid to describe the redshift of galaxies when the recession velocity v is much smaller than the velocity of light c.

Now we know the speed the object is moving towards or away from us, we can further derive the distance using the Hubble relation. The Hubble relation is a (locally) linear correlation between the redshift of a galaxy and its distance from the Milky Way.

Where v is the velocity and H₀ is the Hubble constant. We can then solve this for d.

Solving the redshift equation for v gives v = z c which we can combine into the Hubble equation which further gives:

Which is how we can calculate distance to an object given its redshift value.

Example Redshifts

Currently the objects with the highest known redshifts are galaxies. The most reliable redshifts are from spectroscopic data and the highest confirmed spectroscopic redshift of a galaxy is that of IOK-1 at a redshift z = 6.96.

The most distant observed gamma ray burst is GRB 080913, which had a redshift of 6.7.