What is a Cepheid variable?
This is one of the most important discoveries in astronomy. A Cepheid variable is a special class of pulsating stars that enabled astronomers to determine the distance to nearby star clusters and galaxies. In fact, it was the method that Edwin Hubble used to determine the distance to the Andromeda galaxy, a fact that changed everything.
A Cepheid variable star changes its luminosity (because of changes in its temperature and diameter) with a stable period and amplitude. Delta Cephei in the constellation Cepheus was the first of this type of star to be discovered. Type II Cepheid stars are the ones that astronomers use to determine astronomical distances. They have periods of between 1 to 50 days. There is a relationship between a Type II Cepheid star's luminosity and its pulsation period. Distances to nearby Cepheid II stars have been measured by measuring parallaxes (using triangulation on different dates when the Earth is on opposite sides of the Sun). Using this data allowed astronomers to come up with a luminosity verses period curve for Type II Cepheids, which is used to determine distances to them.
All of this is based on the 'Standard Candle' concept in astronomy. Think of it this way. If you could measure the brightness of a candle at a certain distance, say one foot, you could use this to measure the distance to the candle at distances further than one foot. The reason for this is the fact that the brightness of an luminous object decreases by the square of the distance.
Astronomers use this idea to determine the distance to stars, as long as the type of star is determined by its spectra. The distance to nearby stars of a given type can be measured by parallax.
Astronomers like to use the concept of Absolute Magnitude. This is defined as the logarithm of a star's luminosity as seen from a distance of 10 parsecs (one parsec is 3.26 light years). The equation for this is: 5 x log D = m - M -10. The log of D is to base10. M is Absolute magnitude, m is the apparent magnitude and D is the distance in kiloparsecs (1000 parsecs).
This standard candle method has been used to determine distances to galaxies by means of measuring the brightness of type 1a supernovas. Using this method with type II Cepheid variables is another good way to determine astronomical distances.
A female astronomer by the name of Henrietta Leavitt discovered this period-luminosity relationship of Cepheid variables in the early part of the 20th century and a Danish astronomer, Ejnar Jertzsprung, realized the significance of her data. The result is a method of finding the distance to objects containing Cepheid variables.
The equation used for determining distance using Cepheid variable data is: m - M = 5 x log(d/10) (4.2) or d = 10 to the (m - M + 5) / 5 where m is the apparent magnitude and M is the absolute magnitude. Using a period-luminosity plot for Cepheids and finding the absolute magnitude for the log of the period on the curve, one can determine the absolute magnitude of the Cepheid. After plugging the numbers into the equation, the distance is determined in parsecs.
There are other types of Cepheid variable stars out there in space. The classical Cepheid stars are population I stars and have periods of days to months. These are massive stars, much larger than the Sun. These have been used to determine distances within the Local Group of galaxies, and they are the ones that Hubble used to come up with his Hubble constant, which determined the ratio of Doppler shift in the spectra of a star verses the expansion rate of the universe near it. This has led to a method of determining the distance to deep space objects.
The question you might ask about this is: why do Cepheid stars pulsate? This has to do with k-mechanism. What does this mean? It turns out that helium gas can be singly ionized and doubly ionized (both nuclei have been stripped of electrons). Doubly ionized Helium is more opaque, blocking radiation. The more that Helium is heated the more doubly ionized it becomes. Thus, in the outer layers of the star, this doubly ionized helium blocks radiation, but as it expands (heated gas expands) it cools and becomes singly ionized, thus allowing more radiation to escape. The result is a pulsation in the star's luminosity or brightness. As the gas cools, it is subject to gravity and compresses to heat up again. This process goes on and on at specific period depending on the size of the star. Basically, the star is acting like an engine piston.
I realize that this sounds odd, but Cepheid variable stars have played an important role in the science of astronomy.
Thanks for reading.