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14.18 Ages of Groups of Stars

Groups and clusters of stars not only teach us about how stars form, but they can also be useful tools for measuring the distances to and ages of their member stars. In this way, we get important clues to the history of the Milky Way galaxy. It is difficult to measure the age of an individual star. Astronomers only have a direct age estimate for one star — the Sun. The 4.6 billion year age of the Sun is based on measurements of radioactive decay rates in Moon and Earth rocks, and on the knowledge that the Sun and the planets formed out of the same collapsing gas cloud. This age agrees with the age calculated from the rate of conversion of hydrogen into helium in the Sun’s core. Ages for other individual stars are far less certain because they depend entirely on stellar models.
 

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Color-magnitude diagram of the globular cluster M55. Click here for original source URL.

Astronomers can measure the ages of groups of stars by constructing an H-R diagram. It is relatively straightforward but time-consuming work; the apparent brightness and surface temperatures of hundreds of stars must be measured. The key to this method is that we assume that the stars in a cluster are at the same distance and that they formed at the same time. If the distance to the cluster is known, the apparent brightness of each star can be converted to luminosity. Astronomers have plotted the H-R diagrams of many clusters. The most massive (and luminous) main sequence stars in a cluster exhaust their hydrogen first. They then change their properties in a way that moves them across the H-R diagram to a position far from the main sequence. As time goes by, less and less massive stars exhaust their hydrogen. So the luminosity at which a star "turns off" the main sequence changes with time. This turn-off point is a chronometer that lets us measure the age of a group of stars.

Astronomers can bring together data on several clusters. The H-R diagrams are superimposed schematically; the sequence for each cluster really represents the combined measurements of hundreds of faint stars. Marked along the main sequence is the age at which various stars evolve off the main sequence. Some clusters, such as NGC 2362, have an age of only 1 or 2 million years. These clusters are so young that few stars have evolved off the main sequence. It is remarkable to realize that a cluster like this is less than 1/1000 the age of the Sun, and its birth was witnessed by the first humans.

Open clusters are young in cosmic terms. Half of the calculated ages for open clusters are less than 100 million years old. The Solar System is nearly 50 times as old as this. These results confirm that star formation is continuing to this day. Many open clusters are associated with dense nebulae where stars are currently forming out of collapsing gas clouds. The brightest stars are hot, blue O and B stars, which formed recently, burn their fuel fast, and cannot last long. There are two nearby groupings in which the least massive stars have not yet even evolved onto the main sequence: the Trapezium association and NGC 2264. They are only about 1 and 3 million years old, respectively. In slightly older clusters some of the more massive stars may have evolved into red giants, adding a colorful contrast.

Stellar motions in a cluster can also indicate youth. Velocities of cluster stars, measured by Doppler shifts, show that some clusters are expanding or losing members, or both. The fastest-moving stars have velocities that exceed the escape velocity of their parent clusters. Thus these clusters are breaking apart as we watch and will disperse after a few hundred million years. This disruption of open clusters occurs by several simultaneous mechanisms. Stellar winds and supernovae disperse the gas in the cluster and thereby reduce its hold on the member stars. The Hyades, for example, are barely stable now, and the outer parts of the Pleiades are already dissipating (although the central, tighter grouping may be stable).

Like open clusters, stellar associations are young. Because of their loose structure, they may break up even faster than ordinary open clusters. Most associations cannot last more than a few tens of millions of years, because of the disruptive tidal forces and the tendency for their stars to follow individual orbits around the center of the galaxy. In many associations there are large masses of neutral hydrogen gas, some of which exceed the mass of the stars. The hydrogen may be debris left over from the formation of incorporated stars, or it may be material ejected from the fastest-evolving stars. Often this gas is carried out of the association by stellar winds and supernovae.

Open clusters and associations are mostly young, but astronomers have found many globular clusters are extraordinarily old. Star formation has ceased in them. All of the gas and dust has dispersed long ago. In the globular clusters of our galaxy, the O, B, and A stars have evolved off the main sequence and have become red giants. The only main sequence stars left are dim and red. For this reason, most bright stars in almost all globular clusters have a reddish color.

For decades, however, there was a problem with the idea that all the stars in a globular cluster had formed together. Most stars fell nicely on a single age path in an H-R diagram as expected, but in some clusters there were stars, called blue stragglers, that inconveniently fell above the main sequence turn-off point as if they were younger than the rest of the cluster. In 1997 the Hubble Space Telescope helped astronomers solve this mystery — it observed a rapidly rotating blue straggler in the cluster 47 Tuc. This suggested that the star was not as young as it seemed, but actually the product of a merger of two older stars whose hydrogen envelopes provided new fuel (and a bluer, brighter envelope) to the resulting star. 
 

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The globular star cluster M80. Click here for original source URL.

Determining the ages of globular clusters can be quite complicated even without having to account for blue stragglers. Spectra show that their stars contain fewer heavy elements than the more familiar stars of the solar neighborhood. Therefore, stars in these clusters display processes of energy generation and transport that are different than those of stars closer to Earth. Astronomers must incorporate these unique properties into a complex model of stellar evolution to date the globular cluster. The models are fed with details such as the heavy-element abundance, the amount of helium diffusion in the stellar cores (that is, the amount of helium that migrates from the cores to layers farther out), and the amount of reddening in the cluster.

Errors in any of the numbers in a stellar evolution calculation could lead to an error in the age estimate. For example, suppose we neglected to account for diffuse interstellar dust between Earth and the globular cluster. The dust dims the light of stars in a globular cluster, so we would underestimate the luminosity of the stars (the clusters contain RR Lyrae stars that are used to measure distance). Since luminosity is related to the energy generation rate in stellar models, we would underestimate the energy generation rate. This in turn would lead to an error in the estimated age of the stars. Distance errors also affect age estimates. A star’s luminosity is proportional to its distance squared, L ∝ d2. Mathematically, this means that a 10% error in distance translates into a 20% error in luminosity. Once again, the age derived from the stellar models depends on the luminosity that is fed in to the models. Thus the difficulties of distance determination affect our knowledge of the age of the oldest stars.  The best techniques set the age of globular clusters at about 9 to 13 billion years. This is a true range and not a measurement uncertainty — globular clusters did not all form at the same time. 

Globular cluster ages are also an important check on theories of how the universe began and evolved. Since the universe should not be younger than the oldest objects it contains, the ages of globular clusters should be less than the age of the universe. This is a completely independent check on the age of the universe derived from the big bang model, which gives a best estimate of 13.8 billion years.