2.1 Pulsating variables and their light curves

Stars in the instability strip fall into two different but closely related groups, RR Lyrae and Cepheid variables, both of which pulsate on a regular basis. Of these, the Cepheid variables are of particular interest for a couple of reasons. First, their behaviour is consistent with our current theories of how stars work, giving us confidence that we understand the inner properties and workings of stars. Secondly, their pulsations are useful because they have a specific property – that is, the pulsation period depends precisely on the average luminosity of the star (the more luminous a Cepheid variable, the longer the period). This is known as the period-luminosity relationship. This relationship was discovered in 1912 by American astronomer Henrietta Swan Leavitt [Fig 6] and later used by Edwin Hubble in confirming the expansion of the Universe.

Figure 6 American astronomer Henrietta Swan Leavitt.

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Black and white photograph of astronomer Henrietta Swan Leavitt. She is shown as a youngish woman in period dress with long hair tied back.

Figure 6 American astronomer Henrietta Swan Leavitt.

There are two main classes of Cepheid variables. Classical Cepheids are relatively large and luminous, typically resulting from stars much more massive than the Sun and having relatively long periods (a few days to a few weeks). Type II Cepheids are smaller with shorter periods. The RR Lyrae stars are typically older, less massive than the Sun and have shorter periods measured in hours.

Figure 7 The light curve of a Cepheid variable in the Andromeda galaxy (M31). The red dots indicate measurements made by amateur astronomers and used by NASA to make observations with the Hubble telescope at the predicted dimmest and brightest points in the cycle, as indicated by the blue/yellow stars on the curve.

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Diagram depicting the light curve of a Cepheid variable in the Andromeda galaxy (M31). Plotted against a background image of the spiral Andromeda galaxy, a blue curve continues through seven cycles, each time rising sharply and falling rather more slowly. Red dots on the first five cycles from the left indicate individual measurements made by amateur astronomers, and blue/yellow stars on the two cycles at the right indicate predicted values used to guide Hubble telescope observations made by NASA. The vertical scale on the left is labelled as brightness, with the horizontal axis labelled with the dates of observation from July 2010 on the left, to January 2011 on the right.

Figure 7 The light curve of a Cepheid variable in the Andromeda galaxy (M31). The red dots indicate measurements made by amateur ...

Credit: Illustration Credit: NASA, ESA and Z. Levay (STScI). Science Credit: NASA, ESA, the Hubble Heritage Team (STScI/AURA) and the American Association of Variable Star Observers

By taking repeated measurements of the brightness of a Cepheid variable over a period of time and plotting its light curve it is possible to determine its period. Once the period is known, the period-luminosity relationship for Cepheids can be used to work out how intrinsically luminous it is. From telescopic images the apparent luminosity can be measured. Combining these two pieces of information and remembering that the apparent luminosity depends on the intrinsic brightness of the star and its distance, it is possible to determine how far away the star is. Because the Cepheid variables have relatively high luminosities they can even be seen in other galaxies.

This is absolutely crucial information as it allows distance determinations not only of individual Cepheid variable stars, but by extension any star cluster or galaxy that the Cepheid belongs to. The distance to our neighbouring Andromeda galaxy (M31), measured in this way, is 2.2 million light years using the light curves of variables such as the one shown in Figure 7. In turn it has been possible to use the measurement of distances provided by Cepheids as an essential first step in determining a number called Hubble’s constant – a measure of how quickly the Universe is expanding and evidence for the Big Bang. In this way, pulsating stars such as Cepheids not only allow us to test our predictions of how stars work, but are also critical in helping us to understand the very nature and origins of the whole Universe.