Contents
Introduction
Light from stars contains absorption lines that act as a barcode identifying the elements present in a star’s gaseous atmosphere.
In this post, we’re going to explore how Doppler shifts in these absorption lines can be used to deduce Hubble’s law and the remarkable fact that the Universe is expanding.
Let’s begin!
Starlight contains absorption spectra
Stars produce electromagnetic radiation by nuclear fusion. To a good approximation they are black body emitters, so they generate a continuous spectrum of electromagnetic radiation, the visible part of which looks like this:
However, in their outer atmosphere stars contain cooler gases which absorb characteristic frequencies. When light generated by the star travels outwards through the gaseous atmosphere, these characteristic frequencies are absorbed and subsequently re-emitted.
The re-emission is in all directions. Consequently, the intensity of light now travelling out of the star in the original direction at these special frequencies is greatly diminished. The spectrum emerging from the star’s atmosphere therefore has characteristic frequencies missing (or at least at very low intensities). The emerging spectrum is therefore an absorption spectrum characteristic of the elements in the star’s cooler gaseous atmosphere.
Absorption spectra are usually shown as missing (black) absorption lines in an otherwise continuous spectrum. For example, the absorption spectrum of hydrogen looks like this:
This looks something like a barcode. The absorption spectrum emitted by a star therefore provides a barcode telling us which elements are present in the star’s gaseous atmosphere.
Starlight is subject to the Doppler effect
Like all waves, electromagnetic radiation from stars is subject to the Doppler effect if the star is moving away from or towards the observer.
For example, if a star is moving towards us, its light is compressed so that the wavefronts are bunched up closer together and the wavelengths are shorter. This increases the frequencies, shifting the light towards the blue end of the spectrum.
Conversely, if a star is moving away from us, its light is stretched out so that the wavefronts are further apart from each other and the wavelengths are longer. This reduces the frequencies, shifting the light towards the red end of the spectrum.
Measuring the Doppler shift in starlight
When starlight undergoes a Doppler shift, the absorption lines also shift. We can therefore measure the amount of Doppler shift in starlight by observing how much the characteristic absorption lines have shifted compared with the absorption lines of a stationary sample in the lab.
For example, we might observe a shift of \(\Delta f\) in the frequencies of the absorption lines of hydrogen in starlight compared with a sample of stationary hydrogen in the lab:
Notice how the whole absorption line pattern of hydrogen has shifted towards the red end of the spectrum in the starlight compared with the absorption spectrum of the stationary sample in the lab. In starlight, we can see the characteristic barcode of hydrogen but shifted along.
The change in frequency is related to the change in wavelength by \(\Delta f=\frac{c}{\Delta \lambda}\).
We can define the amount of red shift, \(z\), as the change in frequency (or wavelength) as a fraction of the original that was generated by the star. The red shift is also equal to the velocity of recession of the source divided by the speed of light:
\(z=\frac{\Delta \lambda}{\lambda}=\frac{\Delta f}{f}=\frac{v}{c}\)
This means that by measuring the change in frequency or wavelength of an absorption line, we can calculate the red shift, \(z\), as well as the speed of recession of the star or galaxy from which the starlight came!
Hubble’s law and the expansion of the Universe
Both blue and red shifts have been observed in light from the stars, showing that some stars are moving towards us and some are moving away from us.
However, it turns out that light from all distant galaxies is red shifted. This is significant! It also turns out that the velocity of recession of distant galaxies (calculated from their red shift) is proportional to their distance from us:
This relationship is known as Hubble’s law, where the constant of proportionality, \(H_0\), is the Hubble constant:
\(v=H_0d\)
Hubble’s law has a profound implication. Since galaxies are receding away from us faster and faster the further away they are, the Universe must be expanding. As the Universe expands, it takes distant galaxies with it and stretches all electromagnetic radiation and galaxies in the process. This type of red shift is called cosmological red shift.
A reasonable analogy is to draw dots on a balloon and then blow it up. As you blow up the balloon, the dots will get bigger and further away from each other as the material in which they exist expands.
The cosmological red shift was first discovered in 1929 by Edwin Hubble. It is quite extraordinary to consider that something as small as wavelengths of atomic absorption lines has enabled us to discover something so enormous and significant about the Universe as a whole.
Conclusion
I hope you’ve enjoyed this post on Doppler shifts in starlight! We have seen how starlight contains absorption spectra which are Doppler shifted if the source is approaching or receding from us. We have also reviewed Hubble’s law and the significance of red shifted light from distant galaxies in our expanding Universe.
If you’ve enjoyed this, you might also enjoy the related topics of atomic energy levels and spectra and stellar radiation!
Happy studying!