Question

How does a star’s rotation affect the appearance of its spectral lines?

Answer 1

Recall the concept of the doppler effect of light which says that light emitted by a source moving towards us gets blue shifted while that emitted by a source moving away from us gets redshifted. We also know that spectral lines are a result of stellar particles emitting or absorbing part of the light emitted by the star. Now, as the star rotates determine the doppler effect pertaining to such motion relative to an observer, and determine how this would affect the position of the spectral lines as observed by the observer. Remember to account for the broadening of the spectral lines as a consequence of this as well.

Complete answer:
Let us begin by first understanding the concept of the Doppler effect of light.
Doppler effect is the apparent change in the frequency and wavelength of light caused by relative motion between the source and the observer. Now, redshift and blueshift determine how the light shifts towards the longer(red) and shorter(blue) wavelengths of light depending on the nature of the apparent motion between the source and the observer. If the source is moving towards the observer then the light appears to be blue shifted with the observer receiving light of wavelength less than the actual wavelength of the source, and if the source is moving away from the observer, the light appears to be redshifted with the observer receiving light of wavelength longer than the actual wavelength of the source.
Now, keeping in mind that a spectral line is either a dark or a bright line in an otherwise continuous spectrum of light emitted or absorbed by a star as observed by an observer, let us determine how the rotation of a star would influence the position of these spectral lines.
Now, as the star rotates, there is always one side that is rotating towards us and another side rotating away. Due to the doppler effect, the spectral lines in the spectrum of light coming from the side of the start that is rotating towards us are shifted to shorter wavelengths and the lines in the spectrum of light coming from the side of the star that is rotating away from us are shifted towards longer wavelengths.
Additionally, there is also a sort of blurring of the spectral lines that is observed, which is called as Doppler broadening, where the fine spectral lines appear to be unresolved resulting in a cumulative broad spectral line instead. This occurs due to the different velocities of the light-emitting or absorbing particles in the star’s atmosphere as it rotates.
Thus, as the star rotates, the spectral lines get redshifted or blueshifted, accompanied by the broadening of the spectral lines depending on the rotational velocity of the star.

Note:
Astronomers use the above-discussed doppler effect of light and doppler broadening to determine the velocity with which the star rotates. As the star executes multiple rotations, the observed spectrum is cyclically repeated with a periodic broadening of spectral lines. This regularity of broadening can be used to measure the rotational velocity of the star. The larger the broadening, the larger the velocity with which the star rotates, since the spectral lines indicate the cumulative light emitted or absorbed by many stellar particles together. Note that the measurement of the doppler shift in spectral lines also enables us to measure the rotational velocity by measuring the periodicity with which the line shifts occur.