Globular Clusters and The Age of the Universe
Usually, when asked how we know the age of the universe, one refers to the expanding of the universe that we see when looking at distant galaxies. When this expanding is tracked back, we arrive at an age of around 15 billion years. But that is not the only method. Here I want to explain an independent method: the age of globular clusters.
Globular Clusters (GCs) are clusters of a huge number (a few hundred thousands) of stars, all at about the same age. They surround our and other galaxies, and were formed at about the same time the galaxies formed, when star formation was much heavier than it is now. Nowadays, GCs do not form any more in our galaxy, but they do in other galaxies where there is much more star formation going on. They should not be confused with Open Clusters, which are much smaller, and contain a lot less stars (a few thousands). Those still do form, and a prominent cluster is for example the Pleiades.
Why are they important to understand the age of the universe? Well, if they are old, than the universe must be at least that old. So their age gives a lower limit to the age of the universe. They are also convenient because all members are of about the same age, and of the same composition. Also, because they are clusters, all members are at about the same distance to us. Now, it happens that the evolution of a star is determined by just two factors: the mass and, to a lesser extent, the composition. A heavy star is relatively short lived, and a lighter star has a much longer life. The sun will live for about 10 billion years in total, but a star with a few tens the mass will live only a few million years. Lighter stars live much longer, even longer than the current age of the universe - so we will not see any of those at the end of their life.
To classify a star, that is to determine its type and therefore its stage in its development, we just need two basic properties: their luminosity, and their color. The color is a more or less direct measurement of the surface temperature. When these observed properties of stars are plotted against each other, we do not see them randomly distributed, but we see a very significant pattern. This is the Hertzsprung-Russell diagram. Follow the link (and others I give here), there is a nice picture (HRD). You see that most stars line up in that diagram in a diagonal line. That is the main sequence. A few others cluster in the upper (brighter), right (cooler) region. In the main sequence, brighter stars are hot and dimmer stars are cool.
Okay, but what about the age now? Well, we can make simulations of the evolution of a star. Simple models assume a spherical symmetry, and use four differential equations. The models also require a lot of input from other sources, for example the opacity of the elements, which are derived in part from nuclear bomb testings. The important thing: the input is not coming from observations of other stars, apart from determining their initial chemical composition, and occasional reality checks. What do we learn from these models? We see that a star on start very quickly moves in the HRD to the main sequence, and spends most of its time there. Its exact position on that line depends just on its mass (and a little bit on its composition). The heavier the star, the brighter and hotter. But also, the heavier the shorter its lifetime. As soon as the end is near, the stars move to the right, upper corner, so it gets cooler and brighter at the same time (which means that it also gets bigger, that's why they are then called giants, but that's another topic).
Okay, to summarize:
- the heavier the star, the shorter its time on the main sequence
- all stars of a GC are of the same age