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In astronomy, an isochrone is a theoretical construct used to determine the age of a star cluster (open clusters and globular clusters both).

The path that an individual star will follow in the Hertzsprung-Russell Diagram differs depending upon the mass of the star. The length of a star's lifetime will also differ, with massive stars only living maybe a few tens of millions of years, and the lowest-mass stars lasting as long as a hundred thousand million years.

If we were to look at the H-R diagram of a star cluster when it is very young, nearly all of the stars would lie on the zero-age main sequence, the diagonal line running from upper left to lower right in madvid's diagram under H-R diagram. As time passes, the more massive stars (at high temperatures and high luminosities) evolve very quickly to the right in the diagram toward cooler temperatures, while the smallest and coolest stars barely evolve at all. As more time passes, smaller and smaller stars evolve off the main sequence toward the red giant branch. Thus, if we were to take snapshots of the distribution of stars in the H-R diagram, we would see the distribution change over time.

One way to determine the ages of star clusters is to build computer models of stars with different masses (say 0.1 to 10 solar masses in steps of 0.1 solar masses), and evolve these models in time. At certain time intervals (say every five million years), you record the temperature and luminosity of each model. You then connect the temperatures and luminosities of the stars with different masses at the same age. This will tell you what the theoretical Hertzsprung-Russell diagram of a cluster of stars at a given age should look like. Each snapshot in time is called an isochrone. By fitting these isochrones to the observed H-R diagrams of real star clusters, you can estimate the ages of the clusters.

In reality, isochrone fitting is a tricky science. For one, isochrones depend not only on the masses of the individual stars, but on their chemical abundances (the amount and ratios of hydrogen, helium, and other elements) as well. For another, it assumes that we fully understand the physics of stellar evolution, and while we have a very good idea of how stars work, our knowledge is incomplete. It also requires that we translate our understanding of stellar interiors (where the evolution occurs) to an observable quantity -- the stellar spectra of cluster stars. Finally, this method also assumes that stars are all born at the same time in a given cluster. This is not a bad approximation, as the period of star formation in a single star-forming region is at most a few tens of millions of years. Since most observed clusters are much older than this anyway, it does not result in a large error.

The science of isochrone fitting first developed around the time when computer simulations of stellar evolution were first practical -- in the late 1950's and early-to-mid 1960's. The first specific reference to this sort of thing I could find was the paper by P. Demarque and R. Larson (both then at the University of Toronto) on "The Age of Galactic Cluster NGC 188" in 1964 (Astrophysical Journal volume 140, 544). (They computed their models on an IBM 7090!) Probably the earliest paper to actually discuss the problem of isochrone fitting in detail was by Allan Sandage and Olin Eggen in 1969 (Astrophysical Journal volume 158, 685).

Isochrones have been an important topic of study since then, particularly as our theoretical understanding of stellar evolution has increased. Today, many research groups compete (in a mostly friendly way) to develop isochrones with improved treatments of stellar physics (for example, improved treatments of convection, rotation, opacities, and so on). One important topic has been the ages of the oldest globular clusters in the universe, and the age of the universe itself. Improvements in our understanding of stellar physics have placed the ages of some of the oldest globular clusters at about 12 gigayears (12,000,000,000 years), in reasonably good agreement with age of the universe determined by cosmologists.

The papers mentioned above (and many others) may be found at the NASA ADS abstract service: adsabs.harvard.edu/abstract_service.html

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