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Cepheid variables
Cepheid variables are one particular type of variable star (one whose brightness changes
with time) called after delta Cephei, the first star of this type to be observed. The variation in
brightness of this star was discovered by John Goodricke in 1784. Goodricke lived in York
and was a promising young astronomer but tragically died at the age of twenty one. Since his
discovery many other stars have since been found that vary in a similar way and the group of
stars was called Cepheid variables.
These stars have a period of between one and fifty days and are giant yellow stars with a
mass of between five and twenty times the mass of our Sun. Delta Cephei has a period of
just under 5.4 days.
(There are actually two types of Cepheid variable but we will just consider one type here).
Period
Brightness
Radius
Figure 1
Radial velocity
The brightness (luminosity) of a Cepheid variable changes because the size of the star is
changing. When the star is small its density is large and the temperature and pressure inside
the star increase. This makes the star expand. When the star is large gravity causes it to
contract again and the cycle repeats itself.
The brightness of the star varied in a particular way (see Figure 1) and in 1912 Miss
Henrietta Leavitt of Harvard College observatory discovered an important connection
between the period and brightness. This is now known as the period-luminosity relationship.
The longer the period of luminosity variation the more luminous the star.
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The period-luminosity relation means that if you can measure the period of a Cepheid
variable you can find its luminosity. Knowing how bright the star really is and then measuring
how bright it appears to be will then give the distance of the star from the Earth. The
discovery of Cepheid variables in the Andromeda nebula (M31) enabled its distance from
Earth (over two million light years) to be found.
Two ways of presenting the period luminosity law are shown by the graphs in Figure 2.
Luminosity (Sun = 1)
106
104
Population I Cepheid variables
2
10
1.0
-2.0
-1.0
0.0
1.0
2.0
3.0
log period (days)
Absolute magnitude
-5
-4
-3
-2
Population I Cepheid variables
-1
0
+1
0.1
1
10
100
Figure 2
Period (days)
Of course the period of a variable star in distant galaxies is really difficult to measure and so
yet another method was needed to push back the limits of cosmic distance measurement.
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