We have discussed how the distances to the closest stars may be obtained by measuring their 6 month parallax. A star with a parallax equal to 1" of arc would be a distance of 1 parsec, which amounts to 3.26 light years. A star with a parallax equal to 0.2" would be a distance of 5 parsecs (16.3 light years) and so on.
Stars which are somewhat further away and which are intrinsically not too bright may still permit a determination of their distance if they can be identified as Main Sequence stars, for using the H-R diagram the absolute magnitude of such stars can be determined from their spectral type (or surface temperature). Knowing both the absolute and the apparent magnitude, one can work out the distance to the star.
However, this technique, which is sometimes called the method of spectroscopic parallax, does not permit one to measure distances comparable with the dimensions of our Milky Way galaxy. How then can such large distances be inferred?
Binary stars such as Algol, the demon star, present the appearance of a variable star, as one of the components of the binary eclipses the other. However, certain other stars are truly variable. It is to such stars that we must look for our next yardstick.
The most common type of variable star is the long-period variable such as Mira, the wonder star. In our galaxy about 7000 such stars are known, including some with very irregular periods. Most of the long-period variables are of spectral type M (red). In fact, they possess the spectra characteristic of red giants. Because the red giants are scattered over quite an area of the H-R diagram, and do not simply fall upon a well-defined curve, one cannot use the H-R diagram itself to infer much about the distance to the star. The absolute magnitude is simply not determined well enough by the mere observation that the star is a red giant.
There are about 2500 blue giant variables called RR Lyrae type variables. Such stars are found in the nucleus and corona of our galaxy and invariably in globular clusters such as M13. These RR Lyrae type variables have periods less than one day! Again it is difficult to infer the distance to such a star using an H-R diagram, for you will notice considerable scatter among the points corresponding to luminous blue stars. It is only the lower end of the Main Sequence which is devoid of much scatter. How then is the distance to be determined?
Within a single cluster all the RR Lyrae type variables are found to have about the same apparent luminosity, so it is reasonable to conclude that they have the same absolute luminosity. If one then guesses that such variables in different clusters also have the same absolute magnitude, one obtains a yardstick for determining the relative distances of various clusters. Since the distance to some RR Lyrae type variables can be determined in an independent manner, it is possible to infer that such variables have absolute magnitude about 0.
There are about 700 known Cepheid variables in our galaxy. These stars are yellow supergiants (spectral type F or G). They have periods which range from 3 to 50 days. Polaris, the north star, is a Cepheid variable with a period just under 4 days. Its magnitude doesn't change very much, however, so you must use a photocell to detect the variation. Some other Cepheids are more dramatic, but they all tend to brighten more rapidly than they dim, and thier pulsation is very regular. These are very bright stars.
The variations in luminosity of a Cepheid variable are known to be connected with an actual pulsation of the star. At maximum light the spectral class corresponds to a higher surface temperature than at minimum light. Furthermore, the spectral lines exhibit a Doppler shift of the same period as the light variations. Thus, the radius of the star periodically expands and contracts.
It was discovered by H. Leavitt that for all the Cepheid variables in the large and small Magellanic clouds there is a relation between the apparent luminosity and the period of pulsation. Hence, since these stars are at approximately the same distance, it may be inferred that there is a relation between absolute magnitude and period. From the nearby Cepheids whose distances are known from other considerations, the relationship can be made precise.
By spotting Cepheid variables in the Andromeda galaxy M31 it was determined that M31 was 700,000 light yeaers away. It came as quite a shock when the existence of two types of Cepheid variable was discovered. M31 moved out to 2,000,000 light years almost immediately!
Such revelations as this should make you perpetually suspicious. Try to find out the reasons behind beliefs, in astronomy as well as other things, so you may assess the likelihood of major changes later. This example is not isolated. Until recently the rotation period of Mercury was known to be 88 days, so it kept one face perpetually toward the Sun. Now, since 1965, the period is known to be 50 days.