Photons, Spectra of Stars, and the Doppler Effect

How do we know stars are moving? By the Doppler effect.

The Doppler Effect

The Doppler effect is the shift in frequency of electromagnetic radiation when either the observer or the source are moving relative to each other. If the source is moving towards the observer, the frequency of the radiation perceived by the observer will be higher than the one in the frame of reference of the source. Higher frequency means shorter wavelength (recall: frequency = speed of light / wavelength), and the signal is shifted towards the blue part of the spectrum; conversely, if the source is moving away from us, the frequency is lower and thus the wavelength higher - in this case the signal is red-shifted. Mathematically, we can describe the Doppler Effect with the formula:
where n is the frequency of the electromagnetic radiation, n' is the frequency detected from the detector, V is the electromagnetic wave velocity, Vo is the velocity of the source of the radiation. The "-" sign describes the situation in which the source is moving towards the detector and the "+"sign describes the opposite case.
It is easy at this point to understand what happens to the frequency in both situations. It increases when the source moves towars the detector (since it decreases the denominator in the equation) and it decreases when the source moves away from the detector (the denominator increases). In terms of wavelength, the detector measures in the first case a wavelength shifted towards the blue, in the second case a wavelength shifted towards the red as shown in the picture below.

This phenomenon occurs also for sound waves (but remember that sound waves are longitudinal waves and need a medium to propagate in, while electromagnetic waves are trasverse and need no medium); if a train is moving toward you, the pitch (frequency) of its whistle is perceived to be higher than when is moving away from you. There is no magic in it. When the train is moving toward you, the emitted sound wave traverses progressively lesser distances; the crests bunch up (in time) and thus the perceived frequency is higher (number of crests passing per second).


   
The first image shows the waves emitted by a still source while the second image refers to the waves coming from a moving source



The Doppler Effect in Astronomy

How can we use the Doppler's effect in astronomy? If we measure spectral lines, absorption or emission lines of atoms present in the outer envelope of a star, see figure above, then we can see whether these lines are shifted to the right or to the left with respect to reference lines measured in the laboratory. If the lines are shifted towards the higher wavelengths, i.e., towards the red part of the spectrum, the source of radiation is moving away from us; conversely, if they are shifted towards lower values, blue part of the spectrum, the source is moving towards us.

In the early part of the 20th Century, it was found that distant galaxies were all red-shifted. We'll see the implication of this observation in the Secti on "Topics/Cosmology",.