arXiv:astro-ph/9808200v1 19 Aug 1998The Age of the UniverseBrian ChaboyeraaHubble Fellow, Steward Observatory, The University of Arizona, Tucson, AZ,USA 85721 e-mail: [email protected] minimum age of the universe can be estimated directly by determining the age ofthe oldest objects in the our Galaxy. These objects are the metal-poor stars in thehalo of the Milky Way. Recent work on nucleochronology finds that the oldest starsare 15.2 ± 3.7 Gyr old. White dwarf cooling curves have found a minimum age forthe oldest stars of 8 Gyr. Currently, the best estimate for the age of the oldest starsis based upon the absolute magnitude of the main sequence turn-off in globularclusters. T he oldest globular clusters are 11.5 ± 1.3 Gyr, implying a minimum ageof the universe of tuniverse≥ 9.5 Gyr (95% confidence level).1 IntroductionA direct estimate for the minimum age of the universe may be obtained by de-termining the age of the oldest objects in the Milky Way. This direct estimatefor the age of the universe can be used to constrain cosmological models, asthe expansion age of the universe is a simple function of the Hubble constant,average density of the universe and the cosmological constant. The oldest ob-jects in the Milky Way are the metal-po or stars located in the spherical halo.There are currently three independent methods used to determine the agesof these stars: (1) nucleochronology, (2) white dwarf cooling curves and (3)main sequence turn-o ff ages based upon stellar evolution models. In this re-view I will summarize recent results from these three methods, with particularemphasize on main sequence turn-off ages as they currently provide the mostreliable estimate for the age of the universe.2 NucleochronologyConceptually, the simplest way to determine the age of a star is t o use the samemethod which have been used to date the Earth – radioactive dating. The a gePreprint submitted to Elsevier Preprint 1 February 2008of a star is derived using the abundance of a long lived radioactive nuclei witha known half-life (see, for example the review [1]). The difficulty in applyingthis method in practice is the determination of the original abundance of theradioactive element. The best application of this method to date has beenon t he very metal-poor star CS 22892 [2]. This star has a measured thoriumabundance (half-life of 14.05 Gyr), and just as importantly, t he abundance ofthe elements from 56 ≤ Z ≤ 76 are very well matched by a scaled solar sys-tem r-process1abundance distribution. Thus, it is logical to assume that theoriginal abundance of tho rium in this star is given by the scaled solar systemr-process thorium abundance. A detailed study of the r-process abundancesin CS 22 892 lead to an age of 15.2 ± 3 .7 Gyr for this extremely metal-poorstar [2]. This in turn, implies a 2 σ lower limit to the age of the universe oftuniverse≥ 7.8 Gyr from nucleochronology. This is not a particularly stringentconstraint at present. However, the uncertainty in the derived age is due en-tirely to the uncertainty in the determination of the thorium abundance in CS22892. The determination of the abundance of thorium in a number of starswith similar abundance patterns to CS 22892 will naturally lead to a reductionin the error. If 8 more stars are observed, then the error in the derived agewill be reduced to ±1.2 Gyr, making nucleochronolo gy the preferred methodof obtaining the absolute ages of the oldest stars in our galaxy.3 White Dwarf Cooling CurvesWhite dwarfs are the terminal stage of evolution for stars less massive than∼ 8 M⊙. As white dwarfs age, they become cooler and fainter. Thus, theluminosity of the faintest white dwarfs can be used to estimate their age.This a ge is based upon theoretical white dwarf cooling curves [3–5]. Thereare a number of uncertaint ies associated with theoretical white dwarf models,which have been studied in some detail. However, the effect of these theoreticaluncertainties are generally not included in deriving the uncertainty associatedwith white dwarf cooling ages.The biggest difficulty in using white dwarfs to estimate the age of the universeis that white dwa rfs are very faint and so are very difficult to observe. Moststudies of white dwarf ages have concentrated on the solar neighborhood, inan effort to determine the ag e of the local disk of the Milky Way. Even thesenearby samples can be affected by completeness concerns. The age determina-tion for these disk white dwarfs is complicated by the fact that the results aresensitive to the star formation rate as a function of time [3]. A recent studyhas increased the sample size of local white dwarfs and concluded that the lo-1The r-process is the creation of elements heavier than Fe through the rapid captureof neutrons by a seed nuclei.2cal disk of the Milky Way has an age of tdisk= 9.5+1.1−0.8Gyr, where the quotederrors are due to the observational uncertainties in counting faint white dwarfs[6]. This implies a 2 σ lower limit to the age of the local disk of tdisk≥ 7.9 Gyr.Recently, with the Hubble Space Telescope it has become possible to observewhite dwarfs in nearby globular clusters2. These observations are not deepenough to observe the faintest white dwarfs and can only put a lower limit tothe age of the white dwarfs. Observations of the globular cluster M4 found alarge number of white dwarfs, with no decrease in the number of white dwarfsat the fa intest observed magnitudes [7]. Based upon the luminosity of thefaintest observed white dwarfs, a lower limit to the age of M4 was determinedto be tglob∼> 8 Gyr [7]. When the advanced camera becomes o perational onHST (scheduled to occur in the year 2000), it will be possible to obtain con-siderably deeper photometry of M4, leading to an improved constraint on theage of M4 from white dwarf cooling curves.4 Main Sequence Turn-off AgesTheoretical models for the evolution of stars provide an independent methodto determine stellar ages. These computer models are based on stellar structuretheory, which is outlined in numerous textbo oks [8,9]. One of the triumphs ofstellar evolution theory is a detailed understanding of the preferred locationof stars in a temperature-luminosity plot (Figure 1).A stellar model is constructed by solving the four basic equations of stellarstructure: (1) conservation of mass; (2) conservation of energy; (3) hydrostaticequilibrium and (4) energy transport via radiation, convection and/or