Proc. Natl. Acad. Sci. USA Vol. 95, pp. 18–21, January 1998 Colloquium Paper

This paper was presented at a colloquium entitled ‘‘The Age of the Universe, Dark Matter, and Structure Formation,’’ organized by David N. Schramm, held March 21–23, 1997, sponsored by the National Academy of Sciences at the Beckman Center in Irvine, CA.

The age of the universe from nuclear chronometers

J. W. TRURAN

Department of Astronomy and Astrophysics, Enrico Fermi Institute, The University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637

ABSTRACT An overview is presented of the current sit- constrained by our lack of an adequate knowledge of their uation regarding radioactive dating of the matter of which our nucleosynthesis histories. The long lifetime of 187Re makes the Galaxy is comprised. A firm lower bound on the age from 187Re–187Os chronometer pair an attractive choice for dating nuclear chronometers of Ϸ9–10 Gyr is entirely consistent with galactic nucleosynthesis (11). A major difficulty here, however, age determinations from globular clusters and white dwarf is the fact that 187Os is also produced in the s-process. The cooling histories. The reasonable assumption of an approxi- uncertainties introduced by the subtraction of the s-process mately uniform nucleosynthesis rate yields an age for the contribution to isolate the cosmoradiogenic component are Galaxy of 12.8 ؎ 3 Gyr, which again is consistent with current significant. Further complications are associated with the fact determinations from other methods. that the ␤ decay rate of 187Re in stellar environments is sensitive to temperature. Estimates of the age of the Galaxy, and thereby limits on the Abundance clues to r-process history and the identification age of the Universe, can be obtained by three independent of the astrophysical site of r-process synthesis are reviewed in means: (i) the age of the elements by radioactive dating section 1. Critical input to these chronological studies is (nucleocosmochronology); (ii) the ages of the globular clusters identified and discussed in section 2. The equations of nucleo- (the oldest stars in the halo of our Galaxy); and (iii) the ages cosmochronology are presented in section 3, together with a of white dwarfs from cooling calculations (the age of the model-independent age determination. In section 4, we obtain Galactic disk?). This paper will focus on radioactive dating, an lower bounds on the time scale of galactic nucleosynthesis, with approach that has played a particularly important role histor- the assumption of an early ‘‘single event’’ nucleosynthesis ically. epoch. Observational evidence for a uniform rate of nucleo- The presence of naturally occurring radioactive nuclei in synthesis, and its implications for the age of the Galaxy, is Galactic matter testifies to the fact that the age of the elements presented in section 5. The use of the thorium abundance in an is finite. To the extent that the long-lived nuclear species of extremely metal-deficient halo star for dating purposes is interest are the products of nuclear transformations proceed- considered in section 6. Discussion and conclusions follow. ing in stars and supernovae over the course of our own 1. Abundance Clues to r-Process History. Significant con- Galaxy’s history, they can be used to provide a measure of the straints on the site of r-process nucleosynthesis are provided by duration of star formation activity and concomitant nucleo- observations of the heavy element patterns in halo stars. Early synthesis in the Galaxy. The use of long-lived radioactivities as abundance studies of metal poor stars [see, e.g., the reviews by a mechanism for the determination of a lower limit on the age Wheeler, Sneden, and Truran (12) and McWilliam (13)] of the Galaxy has a history that spans much of the 20th century. showed that abundances of nuclei normally attributable to the An early paper by Rutherford (1) outlined the essential s-process were systematically depleted relative to r-process nuclei. The recognition that the heavy element abundance features of this science. Subsequently, the defining works in ͞ ϷϪ nucleosynthesis theory by Burbidge et al. (2) and Cameron (3) patterns in extremely metal-deficient stars ([Fe H] 3) involve exclusively r-process products (14) is now strongly established the nature of the astrophysical r-process of neutron supported by spectroscopic studies of an increasing number of capture, by which the critical long -lived chronometers 187Re, such stars. This includes the recent study of the star CS 232Th, 235U, and 238U are synthesized. The task, since then, has 22892–052 ([Fe͞H] ϭϪ3.2) by Sneden et al. (15), in which been to identify the astrophysical site for the operation of this thorium also was detected. HST observations (16) have sub- nucleosynthesis process and to calculate the appropriate rates stantiated further this behavior; with the first detection of of production as a function of time over the course of galactic platinum, osmium, and lead in a metal-poor halo star, they evolution. The early developments of the use of the uranium– have shown that nuclei in the r-process peak at mass A Ϸ 195 thorium chronometers by Fowler and Hoyle (4) and Cameron also are formed in solar r-process proportions. In general, (5) were based necessarily on rather simple prescriptions for excellent agreement with the solar r-process heavy element the history of galactic nucleosynthesis. As our understanding abundance pattern is obtained, in metal-poor stars, over the of the processes of stellar and supernova nucleosynthesis entire range of elements from barium to osmium. The level of improved, it became possible to address the problem of nuclear abundance of thorium in the star CS 22892–052 again confirms chronology in the context of increasingly realistic models of the that the r-process occurring in the earliest stages of evolution chemical evolution of the Galaxy (6–10). of our Galaxy was generally consistent with that which formed In this paper, we will be concerned with the determination the bulk of the r-process heavy elements in solar system matter; of realistic age constraints from nucleocosmochronology. We the relative abundance levels in the barium region and imme- will restrict ourselves to the 232Th–238U and 235U–238U chro- Ϸ ␶ Ͼ 9 diately beyond, in the mass region A 195, and in the actinide nometer pairs. The use of such other long-lived ( 1͞2 10 40 87 138 147 176 region are compatible with the corresponding solar ratios. We years) radioactivities as K, Rb, La, Sm, and Lu is note that this is true despite the fact that the r-process͞Fe ratio in the star CS 22892–052 is Ϸ10–50 times the solar system 232 © 1998 by The National Academy of Sciences 0027-8424͞98͞9518-4$2.00͞0 value. This does not, however, guarantee that the Th PNAS is available online at http:͞͞www.pnas.org. abundance in this star can provide a good age estimate.

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The straightforward conclusion to be drawn from these Pi Ϫ␭ ͑ ͒ ϭ ͑ Ϫ it͒ observational behaviors is that r-process nucleosynthesis, and Ni t ␭ 1 e the associated production of the critical actinide nuclear i chronometers we have identified, first occurs during the very The astrophysical input to these equations involves the rate of earliest stages of galactic evolution and, therefore, most likely formation of the range of stellar masses within which r-process is associated with the environments provided by the evolution nucleosynthesis occurs. Although calculations of r-process ϷϾ of massive stars (M 10 MJ) and type II supernovae. This nucleosynthesis have been carried out for a variety of plausible supports the viewpoint that the nucleosynthesis history we are astrophysical sites [see, e.g., the reviews by Hillebrandt (20) probing with the actinide radioactive isotopes is indeed the and Meyer (21)], a firm identification of the appropriate entire history of the Galaxy. The production history of the environment has become possible only recently. Observations 232Th͞238U and 235U͞238U chronometers produced by the of heavy element abundance patterns in metal-deficient halo r-process should trace the rate of star formation activity in the stars point strongly to the identification of r-process nucleo- Galaxy. This implies that 232Th͞238U and 235U͞238U chronom- synthesis with the environments provided by the evolution of eter dating should therefore provide an excellent measure of massive stars and supernovae of Type II. In this context, the the age of the Galaxy. most promising mechanism of r-process synthesis would ap- 2. Age Determinations with r-Process Chronometers. The pear to be that associated with the neutrino-heated ‘‘hot critical input astrophysical quantities required for dating the bubble’’ supernova ejecta (22–23), although an r-process as- epoch of galactic nucleosynthesis include: (i) the abundance sociated with the decompression of cold neutron matter from ratios characterizing the matter that condensed into meteorites neutron star mergers (24) provides a viable alternative. An when the solar system formed and (ii) the production ratios of important consequence of the identification of the r-process the isotopes of uranium and thorium in the relevant (r-process) with such massive stars (M ϾϷ10 MJ) of short lifetimes (␶ Ͻ nucleosynthesis site. Ϸ108 years) is that we can reasonably expect that the age we Abundance determinations for the thorium and uranium determine from r-process chronometer studies is indeed rep- isotopes of interest are provided by analyses of meteoritic resentative of the age of the Galaxy itself. material. The situation for the 232Th–238U pair is complicated The effects of galactic chemical evolution introduce signif- by the chemical differences between the two elements. Anders icant complications for age determinations. There is a very and Grevesse (17) found the present day value of Th͞Utobe substantial literature concerning chemical evolution effects on 3.6, which translates into a primordial solar system ratio age dating, including considerations of varied prescriptions for 232 ͞238 ϭ ( Th U)SS 2.32. This is the value that we have adopted the star formation history, and of the consequences of infall 235 ͞238 ϭ in this paper. We also have used the ratio ( U U)SS and outflow of gas from the star-forming regions. This liter- 0.317 provided by Anders and Grevesse. ature has been reviewed most recently by Cowan, Thielemann The determination of the critical r-process production ratios and Truran (18, 19). In general, such age determinations are 232 ͞238 235 ͞238 ( Th U)r-process and ( U U)r-process is a sensitive func- quite model-dependent. tion of both the input nuclear physics and the physical condi- Meyer and Schramm (25), extending the early work by tions under which the r-process proceeds. There are consid- Schramm and Wasserburg (26), sought to provide a model- erable uncertainties associated with the nuclear properties of independent age determination. In the limit of long-lived the unstable, neutron-rich progenitors of the uranium and chronometers (␭T ϽϽ 1), they derive a simple expression for thorium isotopes of interest. Determinations of these produc- the age that is approximately independent of galactic evolution tion ratios available in the literature [see, e.g., the review effects. In this context, Th͞U can be used to provide a firm articles of Cowan, Thielemann, and Truran (18, 19)] yield lower limit, and Re͞Os can be used to provide a firm upper Յ 232 ͞238 Յ values that span a broad range: 1.40 ( Th U)r-process limit. When account is taken of the additional constraint that Յ 235 ͞238 Յ 1.90 and 0.89 ( U U)r-process 1.89. In our subsequent r-process nucleosynthesis must also produce appropriate levels 232 ͞238 ϭ 244 ␶ ϭ ϫ 7 discussions, we have adopted the values ( Th U)r-process of such shorter lived nuclei as Pu ( 1͞2 8.2 10 years), Ϯ 235 ͞238 ϭ Ϯ 1.65 0.20 and ( U U)r-process 1.35 0.30, which Meyer and Schramm (25) arrive at a very firm lower bound on ϩ ␶ Ͼ represent averages of the values compiled by the above au- the age of the Galaxy (T SS) 9.6 Gyr. thors. 4. Lower Bounds on the Age of the Galaxy. Lower bounds on 3. Basic Equations and a ‘‘Model-Independent’’ Age Deter- the age of the elements can be obtained by considerations of mination. The equations governing the time evolution of the the long-lived actinide chronometers, on the assumption of a abundance of a radioactive nuclear species are straightforward. single event nucleosynthesis history. In this section, we will Assuming a homogeneous interstellar medium and instanta- determine limits based on both the 235U͞238U and the 232Th͞ neous return of the products of stellar nucleosynthesis into the 238U chronometer pairs. 235 ͞238 surrounding gas, the time evolution of species Ni can be written For the case of the U U pair, the appropriate equation is ͑ ͒ dNi t ϭ Ϫ␭ N ͑t͒ ϩ P ␺͑t͒ Ϫ ␻͑t͒N ͑t͒ 235 235 i i i i N P Ϫ͑␭ Ϫ␭ ͒ dt ͩ ͪ ϭ ͩ ͪ 235 238 T 238 238 e N SS P rϪprocess where ␻(t) represents the gain or loss of mass caused by ␺ 235͞ 238 ϭ accretion and winds, (t) is the rate of conversion of mass into where the primordial solar system ratio is (N N )SS ␭ 235͞ 238 ϭ stars, i is the decay rate of species i, and Pi is the production 0.317 and the r-process production ratio is (P P )r-process rate of species i, per unit mass going into stars. 1.35 Ϯ 0.30. This yields a time scale for the epoch of nucleo- Assuming no gain or loss of matter (␻(t) ϭ 0), the simple synthesis of T ϭ 1.75 Ϯ 0.25 Gyr and a limiting age for the ϩ ␶ cases (which we will use in later sections) of (i) a single event Galaxy (T SS)of nucleosynthesis history and (ii) a uniform nucleosynthesis rate ͑ ϩ ␶ ͒ ϭ Ϯ yield the respective solutions: T SS 6.3 0.25 Gyr Ϫ␭ ͑ ͒ ϭ it 232 ͞238 Ni t N0e We can similarly use the Th U ratio to arrive at a lower bound on the galactic age. For the case of the 232Th͞238U pair, and the appropriate equation is Downloaded by guest on September 23, 2021 20 Colloquium Paper: Truran Proc. Natl. Acad. Sci. USA 95 (1998)

232 232 ͞ ϭ N P Ϫ͑␭ Ϫ␭ ͒ pilation of Anders and Grevesse (17), is (Th Eu)SS 0.463. ͩ ͪ ϭ ͩ ͪ e 232 238 T ͞ N238 P238 With the assumption that the primordial ratio Th Eu for CS SS rϪprocess 22892–052 was identical to that of the Sun, we can then obtain ␶ ϭ 232͞ 238 ϭ an age for the star as ( Th 20.27 Gyr) The primordial solar system ratio is (N N )SS 2.32, and the r-process production ratio is (P232͞P238) ϭ 1.65 Ϯ ␶ ͒ ϭ 0.219͞ءr-process 0.463exp͑ϪT 0.20. This yields a time scale for the epoch of nucleosynthesis Th ϭ Ϯ ϩ ϩ4.5 ϭ 15.2 Ϫ Gyr ءof T 3.3 1.20 Gyr, and a limiting age for the Galaxy (T T ␶ 3.7 SS)of ͑ ϩ ␶ ͒ ϭ Ϯ Note that here we have: (i) ignored the uncertainties in the T SS 7.9 1.20 Gyr ͞ Ϯ primordial solar system ratio (Th Eu)SS; (ii) accepted the 20% (Ϯ 0.08 dex) uncertainty quoted by Sneden et al. (15); and We emphasize again that these represent firm lower limits on ͞ the galactic age. (iii) assumed a ‘‘steady-state’’ value for (Th Eu)ISM over 5. Implications of a Uniform Nucleosynthesis Rate. virtually the entirety of galactic history. [That is, we have The ͞ presence of relatively short lived r-process chronometers in assumed no evolution of the (Th Eu)ISM ratio.] Although the primitive solar system matter (e.g., the radioactive isotopes value we obtain [and that quoted by Sneden et al. (15) and 107Pd, 129I, 182Hf, and 244Pu) constrains the history of r-process Cowan et al. (29)] clearly lies in an interesting range, it should synthesis to include significant recent production (a single be recognized that, even with the consideration of only the early r-process event is excluded). The history of star forma- quoted abundance uncertainty, the age can only be constrained tion and nucleosynthesis activity thus becomes a significant the range to 11.5–19.7 Gyr. If we assume a Ϯ10% level of consideration. It was the recognition of this constraint that led uncertainty associated with the Anders and Grevesse (17) ͞ ϭ Ϯ Meyer and Schramm (25) to the determination of a lower value, e.g., (Th Eu)SS 0.463 0.046, we would rather arrive ϩ ␶ Ͼ Յ Յ bound (T SS) 9.6 Gyr. These authors also concluded that at an allowed age range 9.3 T 21.6 Gyr. ͞ ‘‘the effective nucleosynthesis rate was relatively constant over The assumption that the (Th Eu)ISM ratio has remained most of the duration of nucleosynthesis. . . ’’ based on consid- constant over the history of the Galaxy is also considerably erations of 244Pu. Wasserburg, Busso, and Gallino (27) recently uncertain. The fact that the r-process abundances in the metal have argued for such uniform production of the heavy r- poor stars are found to be compatible with solar r-process process nuclei (A Ͼ 140) on observational grounds. They find abundances all of the way from barium to platinum is encour- consistency for 182Hf, 244Pu, 235U, 238U, and 232Th, with a aging. It certainly does not allow us to conclude, however, that uniform nucleosynthesis history. this is true out through the actinide region. Although theo- Given the fact that a rather uniform rate of nucleosynthesis retical models of the operation of the r-process in these regions seems most consistent with observations of short-lived r- can generally reproduce the observed abundance trends, there 232 ͞238 process chronometers, we can use the Th U ratio to remain considerable uncertainties in abundance predictions arrive at an (admittedly) model-dependent age estimate. With past the A Ϸ 190 r-process peak. The fact that the r-process͞Fe the assumption of a constant nucleosynthesis rate over galactic ratio for the star CS 22892–052 is Ϸ10–50 times the solar ratio 232 238 history, the appropriate equation for the case of the Th- U further implies that we are looking at a very early and pair is substantially unmixed phase of galactic evolution; individual Ϫ␭ supernova r-process episodes might be expected to show N232 P232 ␭ ͑1 Ϫ e 232T͒ ͩ ͪ ϭ ͩ ͪ 238 greater dispersion in the Th͞(light r-element) ratio. 238 238 Ϫ␭ ␭ ͑ Ϫ 238T͒ N SS P rϪprocess 232 1 e where, again, the primordial solar system ratio is (232Th͞ DISCUSSION AND CONCLUSIONS 238 ϭ 232 ͞ U)SS 2.32 and the r-process production ratio is ( Th In general, the observational and theoretical considerations 238 ϭ Ϯ U)r-process 1.65 0.20. This yields a time scale for the briefly reviewed in this paper allow the following conclusions: epoch of nucleosynthesis of T ϭ 8.2 Ϯ 3 Gyr and an age for the ϩ ␶ ● Galaxy (T SS)of The important nuclear chronometers are r-process prod- ucts. ͑ ϩ ␶ ͒ ϭ Ϯ T SS 12.8 3Gyr ● The identification of the r-process site with massive stars, supported by the observations of r-process abundance pat- This estimate is intriguingly consistent with galactic age de- terns in halo stars, implies that the critical chronometers for terminations from globular clusters. It also should be noted dating the Galaxy were formed early in galactic history and that an approximately uniform star formation and nucleosyn- were produced at rates proportional to the star formation thesis history are consistent with such other observed galactic rate. abundance trends as the relatively ‘‘flat’’ age–metallicity re- ● lation for disk stars (28). Lower bounds on the age of the elements based on the 6.ATh͞Eu Age for a Halo Star. Considerable interest assumption of a single nucleosynthesis event can be ob- 235 ͞238 232 ͞238 recently has focused on the possibility of a direct determina- tained from both the U U and Th U chronomet- ϩ ␶ Ͼ Ϯ 235 ͞238 tion of the age of an extremely metal deficient (read: extremely ric pairs, yielding (T SS) 6.3 0.25 Gyr for U U ϩ ␶ Ͼ Ϯ 232 ͞238 old) halo field star, from a knowledge of its thorium abundance and (T SS) 7.9 1.20 Gyr for Th U. ● (15, 29). In this case, because we have no observational The very presence of shorter lived r-process chronometers 129 182 244 information concerning the abundances of the isotopes of such as I, Hf, and Pu in primitive solar system matter uranium, it is necessary to consider the abundance of thorium demands some level of recent r-process nucleosynthesis. relative to some stable r-process species. An obvious choice This will necessarily yield longer age estimates for the epoch here is the element europium, the production of which is of galactic nucleosynthesis than are predicted for a single attributed entirely to the r-process (it is an ‘‘r-only’’ element). event model. Meyer and Schramm (25) obtained a firm ϩ ␶ Ͼ The straightforward determination of the age then proceeds lower bound (T SS) 9.6 Gyr. With the assumption of in the following manner. Sneden et al. (15) have found the ratio a constant nucleosynthesis rate over the entirety of Galactic Th͞Eu for the metal deficient ([Fe͞H] ϭϪ3.2) halo star CS nucleosynthesis history, we obtain from consideration of the ϭ 0.219 Ϯ 0.0438. The ratio Th͞Eu 232Th–238U chronometer pair an age estimate for the Galaxy ء(to be (Th͞Eu 052–22892 ϩ ␶ ϭ Ϯ at the time of formation of the solar system, from the com- of (T SS) 12.8 3Gyr. Downloaded by guest on September 23, 2021 Colloquium Paper: Truran Proc. Natl. Acad. Sci. USA 95 (1998) 21

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