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The Age of the Universe* Proc. Natl. Acad. Sci. USA Vol. 94, pp. 6579–6584, June 1997 From the Academy This paper summarizes a symposium that was one of the Frontiers of Science symposia held November 2–4, 1995, at the Arnold and Mabel Beckman Center of the National Academy of Sciences and Engineering in Irvine, CA. The age of the universe* DAVID N. SPERGEL†‡,MICHAEL BOLTE§, AND WENDY FREEDMAN¶ †Department of Astronomy, University of Maryland, College Park, MD 20742; ‡Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544; §Lick Observatory, University of California, Santa Cruz, CA 95064; and ¶Carnegie Observatories, Pasadena, CA 91101-1292 The big bang theory is a remarkably simple theory built on two massive than the Sun, is blue and very luminous, whereas pillars: the theory of general relativity and the assumption that Alpha Centauri, which is less massive than the Sun, is red and the universe is isotropic and homogeneous on large scales. This less luminous. theory has had a number of important successes: it can explain The fundamental fuel for a star’s luminosity is mass. In any the observed expansion of the universe; the thermal micro- of the fusion reactions that result in hydrogen conversion to wave background radiation; the observed abundances of deu- helium, a small amount of mass is transformed into energy terium, helium, and lithium; and the rapid evolution seen in in the form of neutrinos and g-rays: the neutrinos flee the distant galaxies (see refs. 1 and 2 for recent reviews). Yet this scene and the g-rays are immediately absorbed, providing successful model faces a potential crisis: the age of the oldest the heat source for the star. Because stars have only a limited stars may exceed the predicted age of the universe. In the first supply of hydrogen in their cores, they have a limited half of the session, Michael Bolte of the University of Cali- lifetime, tMS, on the main sequence. This lifetime is propor- fornia, Santa Cruz, described efforts to measure the age of the tional to iMy^L&, where i is the fraction of the total mass of oldest stars. Because the oldest stars ought to be younger than the star, M, available for nuclear burning in the core, and ^L& the universe, this places a lower bound on t0, the age of the is the time average luminosity of the star on the main universe. In the second half of the session, Wendy Freedman sequence. Because of the strong dependence of luminosity 22.5 of the Carnegie Observatories discussed measurements of the on stellar mass, tMS } M , it is fortunate that our Sun is not more massive because high-mass stars rapidly exhaust Hubble constant, H0, the rate of expansion of the universe. In the simplest and best explained version of the big bang their core hydrogen supply. Once a star exhausts its core theory—a flat, matter-dominated universe—the age of the hydrogen supply, the star becomes redder, larger, and more luminous, and it moves off the main sequence and becomes universe is 2y3H0. The final section of this paper is based on the panel discussion of the implications of their results. The a red giant star. Appendix describes the relationship between the age of the Astronomers find it convenient to represent the properties universe and the Hubble constant in different cosmologies and of stars on a Hertzsprung–Russell (HR) diagram, a plot of a explains why many cosmologists believe that the universe is star’s luminosity and surface temperature. For historical rea- flat. sons, optical astronomers like to plot the magnitude of a star, 22.5 times the base 10 logarithm of its luminosity, on the y axis, Determining the Ages of the Oldest Objects and the temperature of the star on the x axis. To further obscure the field, temperature increases to the left on the Because the first generation of stars formed some time after diagram. the big bang, the age of the oldest known stars places a lower The HR diagram is a particularly useful way to display the limit on the age of the universe. properties of stars in a cluster. A cluster is a dense collection of stars that are thought to have all formed at about the same Theory of Stellar Evolution. Stars are remarkably simple time (give or take a million years). A very young cluster has systems: they are slowly evolving, nearly spherical clouds main-sequence stars over a broad range of masses (and composed mostly of hydrogen and helium that can be accu- luminosities and temperatures). A 2 billion-year-old cluster rately modeled on a computer. The basic physics needed to contains main-sequence stars up to a ‘‘turn-off mass’’ of 2 solar model the structure and evolution of stars is mostly well masses—more massive stars exhaust their core hydrogen sup- understood: nuclear cross-sections, the equation of state of ply in under 2 billion years. A 10 billion-year-old cluster matter, and the physics of hydrostatic equilibrium and radia- contains main-sequence stars up to a ‘‘turn-off mass’’ of 1 solar tion transfer. Although stellar structure does depend some- mass. A 15 billion-year-old cluster would contain no main- what on the physics of convection, which remains poorly sequence star more massive than 0.85 solar mass and no understood, stellar ages are relatively insensitive to the details main-sequence star more luminous than '0.5 times the lumi- of convection. nosity of the Sun. Thus, by determining the maximum lumi- Main-sequence stars are stars, like our Sun, that fuse nosity of a main-sequence star in a cluster, astronomers can hydrogen to helium in their cores. For a given chemical measure its age. composition and stellar age, a star’s luminosity, the total Astronomers, however, cannot measure the luminosity of a energy radiated by the star per unit time, depends only on its star directly; they can only measure the flux from a star, F.If mass. Stars that are 10 times more massive than the Sun are the distance to the cluster, D, can be determined, then energy more than 1,000 times more luminous than the Sun. We should not be too embarrassed by the Sun’s low luminosity: it is 10 Abbreviations: HR, Hertzsprung–Russell; HST, Hubble Space Tele- times brighter than a star of half its mass. More massive scope. main-sequence stars are also bluer (higher surface tempera- *This paper is part of the fourth installment of the new feature, “From tures) than less massive stars. Thus, Sirius, which is more the Academy.” The first installment appeared in the March 4, 1997 issue, the second in the April 1, 1997 issue. “From the Academy” will be presented occasionally as new NRC reports appear and as essays © 1997 by The National Academy of Sciences 0027-8424y97y946579-6$2.00y0 on the NAS are prepared. 6579 Downloaded by guest on September 26, 2021 6580 From the Academy: Spergel et al. Proc. Natl. Acad. Sci. USA 94 (1997) conservation implies that L 5 4pD2F. The challenge, and the Nature offers astronomers a wonderful laboratory for test- major source of uncertainty in age determination, is measuring ing stellar models with double-line, eclipsing binary stars. the distance to stellar clusters. Astronomers can measure the period of these binaries, their Age determinations also depend on the star’s chemical velocities, and the inclination of their orbits. With these composition: a star’s evolution depends on its initial abun- measurements, it is possible to determine their masses to dance of helium, carbon, oxygen, and iron, because these better than 1%. In probably their most stringent test, the elements (and other less common elements) all affect the rate observed mass, luminosities, and temperature are in excellent at which photons can escape from the core of a star and, agreement with the stellar models. Future surveys should be particularly in the case of oxygen, moderate the energy gen- able to detect more of these systems. Their detection and study eration reactions. Because the oldest stars have very low in a globular cluster (see below) would be an important abundances of these elements, stellar age estimates for the confirmation of the inferred ages. globular clusters are, fortunately, not very sensitive to these Observing Old Stars in Old Clusters. Globular clusters are details. thought to be the oldest clusters in the Galaxy. Globular Should We Believe the Models? Stellar models are needed clusters are dense spherical clusters of stars that are on orbits to relate the observed luminosity and surface temperature of that suggest that they were formed in the initial collapse of our a star to its core mass and its time average luminosity, so that Galaxy. Their stellar densities are so high that the Hubble we can determine its main-sequence lifetime. Fortunately, the Space Telescope (HST) was needed to resolve their dense current stellar models are thought to be very reliable in the cores (see Fig. 1). Globular clusters are iron-poor: the relative relevant mass range. The models are less reliable for very abundance of iron to hydrogen in a globular cluster star is only low-mass stars that contain complex molecules in their outer 1y10 to 1y150 of the relative abundance in the Sun. These stars atmospheres and for higher-mass stars, whose cores are altered are also depleted in carbon, oxygen, and all of the other by convection. elements heavier than lithium. Because all of the elements The stellar models correctly predict the age and structure of heavier than lithium are synthesized in stars, these low abun- the Sun.
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