Cepheid Variables (造父變星)

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Shakespeare once wrote in his character’s quote, that ‘I am constant as the Northern Star’, or the Polaris. And Aristotle, a renowned ancient philosopher, claimed that stars are eternal and do not change. However, with modern advanced technology and cosmology, the aforementioned are proven wrong.

Today, you will be introduced to a kind of the changing stars ----- the Cepheid Variables. These variables become brighter and dimmer periodically, of which the period of brightness fluctuation may vary from roughly 1-60 days for each variable.

Fact 1 Why are they called Cepheid Variables?

The first star to be observed with a periodic change of luminosity is δ Cephei in the constellation Cepheus in 1784 by John Goodricke. From then on, variable stars that change in luninosity like δ Cephei do are called Cepheid Variables. Famous stars such as the Polaris, η Aquilae, RS Pup and ζ Geminorum are all Cepheid Variables.

Fact 2 What are Cepheid Variables?

Classical Cepheids (Type I) have masses ranging from 5-20 times the mass of our Sun, with luminosity up to 40,000 times the Sun’s. While their average temperature is around 6,000K, which is similar to that of the Sun, they are in fact giants or supergiants. Stars shine as nuclear fusion of elements occur, an energy producing process. When stars almost run out of ‘fuel’, they swell to a gigantic size and are said to have left the ‘main sequence’ and entered an unsteady state.

These are in fact other types of Cepheid Variables such as Type II Cepheids and Anomalous Cepheids, in which quantities like their element compositions, mass and pulsation periods (will be discussed below) differ from each other. Though their details will not be discussed here.

Fact 3 Why do Cepheid Variables vary in brightness?

Giant stars have small cores with high density and large peripheral envelope with low density. The core remains fairly constant. However, the envelope pulsates in and out periodically. Here is the brief mechanism:

He+ <----> He2+ e-
where He+ and He2+ are helium ions with 1 and 2 electrons lost respectively.
Notice that He+ ion is more transparent than He2+ ion.

1)    Under gravitational force, the size of a giant shrinks to a small extent. Thus, pressure increases. As pressure increases, temperature also rises.
2)    As the star heats up, He+ in the peripheral of a giant star loses e- to become He2+.
3)    As He2+ is more opaque, light cannot leave the star effectively, the star dims.
4)    The trapped light energy contributes to a further increment of the temperature of the star.
5)    When the outward push by heat pressure overcomes the gravitational pull, the star swells.
6)    Temperature drops as pressure decreases when the star swells. The less transparent He2+ gains back an e- to give the more transparent He+.
7)    Light can then leave the star and the giant star retrieves a brighter state.

Therefore, we may understand that the luminosity of a Cepheid Variable increases or decreases together with its size based on the above mechanism.

Fact 4 Cepheid Variables are VERY USEFUL

In 1912, Henrietta Swan Leavitt, a worker in Harvard College Observatory whose duty was to take record of stars, has discovered a relationship -------- the relative brightness of Cepheid Variables changes along with the period of changing luminosity (i.e. The brighter it is, the longer the period is). Her curiosity has given rise to one of the most important and groundbreaking discoveries in modern cosmology, granting her an honorable qualification to be an influential astronomer.

Henrietta was curious about the countless variable stars she was recording. She suspected that there is some special relationship between luminosity and period. Thus, she chose Cepheid Variables in the ‘Small Magellanic Cloud’, an object later discovered to be a galaxy, to observe. Originally, the brightness of a star we perceive on the Earth is affected by 1) Distance of it from us 2) Its real luminosity (energy radiated per unit time). As she believed that stars in this ‘cloud’ have roughly the same distances from us, the 1st factor above can be ignored. In other words, the brightness of Cepheid Variables in this ‘cloud’ can be compared. By comparing their brightness and recording their corresponding pulsation period, her suspicion was proven right ------ brightness changes together with period.

With this subtle, yet significant piece of fact, astronomers have made different breakthroughs in the last century. Ejnar Hertzsprung, a Danish astronomer, used the relationship to calculate distances between the Earth and Cepheid Variables far away from us; Harlow Shapley, an American astronomer, used the relationship to measure the size of our Milky Way Galaxy; Edwin Hubble, an American astronomer, discovered that the Universe is expanding by calculating distances of some nearby galaxies (Cepheid Variables in these galaxies) with this relationship. Thus, this exemplifies an axiom ‘We stand on the shoulders of giants’.

Fact 5 Measuring distances with Cepheid Variables

It is not difficult to measure our distances with Cepheid Variables. First, we observe and record the period (time needed for a star to turn dim from bright, and back to bright). Then, by looking at the period-luminosity relation graph, the star’s luminosity (the amount of energy radiated per unit time) is obtained. Next, the apparent brightness of the star (the brightness of it we see on the Earth / the energy received by the Earth per unit area) is measured.
Therefore, with the above equation, the distance of a Cepheid Variable from us is computed. Nonetheless, we may notice that there are 2 distinct lines in Figure 1.1. They belong to 2 different types of Cepheid Variables since their compositions differ from one another. Cepheid I in general has less heavier elements than Cepheid II.


After reading the above, when someone tells you the quote ‘I am constant as the Northern Star’, you may in fact reply him/her that the Polaris is actually a Cepheid Variable which is by no means constant.