Absolute Ages of Globular Clusters and the Age of the Universe

The main sequence turnoff luminosity is the best stellar `clock' which can be used to determine the absolute ages of globular clusters. This is due to the fact that it is generally assumed that the luminosity and lifetimes of main sequence globular cluster stars are independent of the properties of stellar convection and atmospheres, two areas of stellar evolution which are poorly understood. Several possible sources of error in this stellar clock are discussed, and isochrones are constructed using a variety of different physical assumptions. The mean age of the oldest globular clusters are determined from these isochrones and it is found that the uncertainties in the input physics can lead to changes in the derived age of $\pm 15\%$. Surprisingly the largest source of error is the mixing length theory of convection. It is well known that uncertainties in the distance scale and chemical composition of globular cluster stars lead to changes of order $\sim 22\%$ in the determination of absolute ages. Combining the various sources of error, the absolute age of the oldest globular clusters are found to lie in the range 11 --- 21 Gyr. This is meant to be a total theoretical range. For the standard inflationary model ($\Omega = 1, \Lambda = 0$), a minimum age of the universe of 11 Gyr requires $H_o \la 60~\kmsmpc$.