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How do the ages of the globular clusters fit a universe of age 13 x 109 years? Globular clusters are chosen as sounding board because they consist of fairly large groups of about a million stars that must have been formed simultaneously astronomically speaking. Since the stars in such groups are of all manner of masses, their evolutionary paths will, by this time, have progressed varying lengths - the more massive stars would have evolved faster and are now further down the evolutionary track than the lighter stars. Some stars in a cluster will be giants and some dwarfs and others main sequence stars.
In order to determine the position on the Hertzsprung-Russell diagram of any particular star in a cluster, we have to determine the star's absolute magnitude and its spectral class. The spectral class can be determined easily enough by quantifying the various spectral lines of the commoner elements such as hydrogen helium, calcium, iron and others and also their intensities. But the absolute magnitude can only be determined once the distance of the cluster is known. One way of determining the absolute magnitudes is by applying the Period-Luminosity Law to the Cepheid variables found in a cluster. This does not require a knowledge of the distance of the cluster, but the periods of the Cepheid variables have to be measured and this can be done very accurately. The period-luminosity law can then be applied to calculate the absolute magnitudes. In "Unveiling the Universe" I derived the formula:
M = -1,48 -2,7 log P ± 0,32
where M is the absolute magnitude and P is the period in days for classical Cepheids of periods from 1,95 days to 13,62 days, as were measured by A R Sandage and G A Tammann with the 5 metre Hale telescope of Mount Palomar. From this formula the absolute magnitude M can be calculated once the period P is known. So the Cepheid variables in the clusters can be placed in their correct positions on the Hertzsprung-Russell diagram because their spectral classes can be easily determined. By measuring the apparent visual magnitude m of these stars their distances could be determined from the well-known formula:
5 log D = m - M + 5,
where D is the distance in parsecs. The distances of these stars can then be applied to other stars, not only to Cepheid variables and their absolute magnitudes can be calculated when their apparent magnitudes have been measured. The positions of the stars in the H-R diagram revealed the fact that many stars in a cluster, such as Omega Centauri, had left the main sequence long ago and had moved to the giant and super-giant areas, and had returned to the instability region and the horizontal branch where the R R Lyrae stars resort as shown in the diagram.
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HERTZSPRUNG - RUSSELL DIAGRAM
OF GLOBULAR CLUSTER OMEGA CENTAURI
The RR Lyrae stars are Cepheids of very short periods of less than one day. They all have the same absolute magnitude of 0,8 and are largely of spectral class and type A. They serve very well as distance determinants. The difference between the apparent magnitudes m and the absolute magnitude M (12 - -2, or 15 - 1, etc) remains constant at 14 (actually 13,92). This is known as the distance modulus, (m - M) and can be used in the last formula quoted.
The important thing is that the graph reveals the fact that many of the stars of the globular cluster Omega Centauri have long ago left the main sequence and moved to the giant branch, and many have also moved back through the instability strip, where the Cepheids pulsate, and to the horizontal branch. These stars must therefore be very much older than the main sequence stars. The Sun and stars like it have resided on the main sequence for five thousand million years (5 x 109), and can go on residing there for another 5 milliard years. The stars in the Omega Centauri cluster that have left the main sequence, must therefore be very much older than 10 x 109 years. The age of the universe which we calculated as 13 x 109 (13 milliard) years, thus leaves very little time to fit in the stars of the globular clusters. It is not known how much time a star requires to move from the main sequence to the giant area and back to the horizontal strip but it seems that 5 x 109 years would be a fair amount of time. The universe must therefore be at least 15 x 109 (15 milliard years old.) If we had used a value for the Hubble constant of 65 kilometres per second per megaparsec, we would get for the age of the universe:
milliard years
and this would give the globular cluster stars enough time to carry out their evolution.
Jan Eben van
Zyl
13/06/2001
