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Redshift or Blueshift Due to Star Rotation

Most stars rotate. During star formation, the gas cloud from which the star is formed contracts. Conservation of anugular momentum means that if the gas cloud was initially rotating, the rate of rotation will speed up.
One side of the star will rotate away from us and the other side will rotate towards us. Light from the side that is rotating away from us will be redhifted and light from the side that is rotated towards us will be blueshifted relative to light from the centre of the star..

Consider our Sun. If the speed of the edge of the star relative to us is  
\[v\]
  the the redshift or blueshift is approximately  
\[\frac{v}{c}\]
  where  
\[c\]
  is the speed of light.
The Sun rotates rougly once every 27 days and has a radius of about 700,000 km.
Hence  
\[v= \frac{Distance}{Time} = {2 \pi r}{T} = \frac{2 \pi \times 700,000,000}{27 \times 24 \times 60 \times 60} =1886 m/s\]

The redshift is then  
\[\frac{1886}{3 \times 10^8} = 6.29 \times 10^{-6}\]

This is very small. For many stars redshift or blueshift due to rotation can be smothered by other factors - notably due to the stars velocity relative to us, and spectral line broadening due to the stars temperature.. Also, distant stars will appear as a prick of light, and the redshift/blueshift due to rotation will mean a broadening of the stars spectrum.