The Way of Science

3. Cepheid Variables
Here's where it gets interesting, in terms of how science often works. The small-scale device (triangulation) will now be used to calibrate a second yardstick based on a totally different principle. To understand this, the most important and accurate of our measuring techniques, you need background on the concept of "standard candles," and particularly on stars called Cepheid Variables.

First, consider the relationship between how bright an object is, up close (absolute luminosity or absolute magnitude), and how bright it appears to be (apparent luminosity or apparent magnitude) because of the effect of distance. These three variables are mathematically related via an inverse square law: double the distance, and the brightness appears to decrease not by half, but to ¼ of what it was. The critical point is this: if one has three variables mathematically related, and one can determine the values for any two of them, the third can always be calculated. Aha! We can easily measure apparent luminosity for celestial objects; if one just knew how bright they really were (our "standard candle"), we could then calculate distance. Doing that is tricky; we can't journey to a distant star, and hold a fancy light meter a few light years from its surface. Solving that problem means looking at the Cepheid variable stars.

"Variable," when applied to stars, means that their brightness changes. There are many kinds of variable stars, ranging from one-shot exploding versions called novae or supernovae, to those that vary from bright to dim over and over again. The Cepheids vary in a very regular manner, increasing and decreasing their luminosity by factors of two or three. Many Cepheids have periods (time from maximum to maximum) ranging from a few days to about 50 days, and are constant for each star with changes no greater than a fraction of a second. The really critical discovery was that Cepheids with long periods had maximum apparent luminosities much greater than shorter period Cepheids. Better yet, there is a neat mathematical relationship between period and luminosity, with which we will now enrich your life. (It's important, but we do not expect you to "test prep" on the details.)

A cluster of many stars called the Small Magellanic Cloud played a critical role here. We now know that the Cloud is actually a mini-galaxy quite near our own very large Galaxy (the Milky Way). Before this was known, it was still possible to determine that this Cloud was, indeed, a cluster of objects. That is, the contents were all about the same distance from Earth. Any differences in Cepheid luminosities in this cluster must then be due to differences in intrinsic luminosities (not distance). From that bit of logic, it was possible to show a tight mathematical relationship between period and luminosity: the longer the period, the greater the luminosity at maximum. (Modern theory explains why this is so. As the star "burns" its atomic fuel, it increases in size and hence in luminosity. But as it increases its size, it dilutes its fuel, and sputters, as it were. With the loss of energy to continue expansion, gravity pulls the star's mass back to a dense state, and reactions begin again.) Here's the upshot: knowing the luminosity/period relationship allows one to compare any Cepheids, anywhere. If the distance to any one Cepheid could be determined, then the absolute luminosity of that star could be calculated (three variables: apparent luminosity is measured directly, add distance, calculate M, absolute magnitude). If one knew M for that Cepheid, M could be determined for any Cepheid, anywhere, because of that period/luminosity relationship.

All one needs now is to determine the distance to any one Cepheid. That proved to be a long and tedious task, since the nearest Cepheids are just about at the limit of the triangulation/parallax yardstick. The technique used, called spectroscopic parallax, is not to be explained at the level of this course. After about a decade of work, the new yardstick was calibrated using this parallax variant. (Incidentally, we will return to an explanation of spectroscopy for our last yardstick.) Here ends "enrich your life".

The Cepheid yardstick really opened up the Universe for astronomers. It allowed measurements out to 80-90 million ly, and it revealed that the stars were arranged in those enormous clusters called galaxies: millions to hundreds of billions of stars, held together by gravity. (We now know that there are at least 50 billion galaxies out there. That fact should make you realize just how small a part of everything is the Earth and its humans.)

Our Galaxy, the Milky Way, is a rotating disc-shaped aggregation about 100,000 ly in diameter. We (the solar system) are about 30,000 ly from the center. The nearest large disc galaxy, Andromeda, is about 2.3 million ly away. The Small Magellanic Cloud, the critical mini-galaxy that gave us the Cepheid key, is about one-tenth that distance. (These numbers are strictly "enrich your life".) We now know that galaxies are grouped in clusters, and the clusters into superclusters, etc. In other words, the Universe has a very lumpy distribution of matter, and that's of enormous significance for explaining the Evolution of galaxies. (But that's another story that must be omitted here, alas.)

The Cepheid yardstick, though it gave astronomers a revolutionary new tool, still falls short of measuring distances to all those faint patches of light out there. We need a third, even longer yardstick.