Stellar origin of the 182Hf cosmochronometer and the presolar history of solar system matter

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Science  08 Aug 2014:
Vol. 345, Issue 6197, pp. 650-653
DOI: 10.1126/science.1253338

Relocating a heavy-metal factory

We can learn about the solar system's past by measuring heavy radioactive isotopes in meteorites—the extraterrestrial equivalent of carbon dating on Earth. Elements heavier than iron are mainly synthesized in supernovae or asymptotic giant branch (AGB) stars. Knowing exactly which element is produced where, is key to dating the solar system. Lugaro et al. found that AGB stars generated more of a nuclide called 182Hf than previously thought (see the Perspective by Bizzarro). Its abundance indicates that it was produced about 30 million years before the Sun's formation.

Science, this issue p. 650; see also p. 620


Among the short-lived radioactive nuclei inferred to be present in the early solar system via meteoritic analyses, there are several heavier than iron whose stellar origin has been poorly understood. In particular, the abundances inferred for 182Hf (half-life = 8.9 million years) and 129I (half-life = 15.7 million years) are in disagreement with each other if both nuclei are produced by the rapid neutron-capture process. Here, we demonstrate that contrary to previous assumption, the slow neutron-capture process in asymptotic giant branch stars produces 182Hf. This has allowed us to date the last rapid and slow neutron-capture events that contaminated the solar system material at ∼100 million years and ∼30 million years, respectively, before the formation of the Sun.

Radioactivity is a powerful clock for the measurement of cosmic times. It has provided us the age of Earth (1), the ages of old stars in the halo of our Galaxy (2), the age of the solar system (3, 4), and a detailed chronometry of planetary growth in the early solar system (5). The exploitation of radioactivity to measure time scales related to the presolar history of the solar system material, however, so far has been hindered by our poor knowledge of how radioactive nuclei are produced by stars. Of particular interest are three radioactive isotopes heavier than iron: 107Pd, 129I, and 182Hf, with half-lives of 6.5 million years (My), 15.7 My, and 8.9 My, respectively, and initial abundances (relative to a stable isotope of the same element) in the early solar system of 107Pd/108Pd = 5.9 ± 2.2 × 10−5 (6), 129I/127I = 1.19 ± 0.20 × 10−4 (7), and 182Hf/180Hf = 9.72 ± 0.44 × 10−5 (8). The current paradigm is that 129I and 182Hf are mostly produced by rapid neutron captures (the r process), in which the neutron density is relatively high (>1020 cm−3), resulting in much shorter time scales for neutron capture than for β-decay (9). The r process is believed to occur in neutron star mergers or peculiar supernova environments (10, 11). In addition to the r process, 107Pd is also produced by slow neutron captures (the s process), in which the neutron density is relatively low (<1013 cm−3), resulting in shorter time scales for β-decay than for neutron capture, the details depending on the β-decay rate of each unstable isotope and the local neutron density (9). The main site of production of the s process elements from Sr to Pb in the Galaxy is in asymptotic giant branch (AGB) stars (12), the final evolutionary phase of stars with initial mass lower than ∼10 solar masses (M). Models of the s process in AGB stars have predicted marginal production of 182Hf (13) because the β-decay rate of the unstable isotope 181Hf at stellar temperatures was estimated to be much faster (14) than the rate of neutron capture leading to the production of 182Hf (Fig. 1).

Fig. 1 Section of the nuclide chart including Hf, Ta, and W.

Stable isotopes are shown as gray boxes, and unstable isotopes are shown as white boxes (with their terrestrial half-lives). Neutron-capture reactions are represented as black arrows, β-decay as red arrows, and the radiogenic β-decay of 182Hf as a green arrow. The production of 182Hf is controlled by the half-life of the unstable 181Hf, which precedes 182Hf in the s process neutron-capture isotopic chain. The probability of 181Hf to capture a neutron to produce 182Hf is >50% for neutron densities >4 × 109 cm−3 or >1011 cm−3, using a β-decay rate of 42.5 days (terrestrial) or of 30 hours at 300 million K (14), respectively.

Uniform production of 182Hf and 129I by the r process in the Galaxy, however, cannot self-consistently explain their meteoritic abundances (1517). The simplest equation for uniform production (UP) of the abundance of a radioactive isotope in the Galaxy, relative to a stable isotope of the same element produced by the same process, is given byEmbedded Image (1)where Nradio and Nstable are the abundances of the radioactive and stable isotopes, respectively; Pradio/Pstable is the ratio of their stellar production rates; τ is the mean lifetime of the radioactive isotope; and T ∼ 1010 years is the time scale of the evolution of the Galaxy. Some time during its presolar history, the solar system matter became isolated from the interstellar medium characterized by UP abundance ratios. Assuming that both 129I and 182Hf are primarily produced by the r process, one obtains inconsistent isolation times using 129I/127I or 182Hf/180Hf: 72 My or 15 My, respectively, before the solar system formation (17). This conundrum led Wasserburg et al. (15) to hypothesize the existence of two types of r process events. Another proposed solution is that the 107Pd, 129I, and 182Hf present in the early solar system were produced by the neutron burst that occurs during core-collapse supernovae (1820). This does not result in elemental production, but the relative isotopic abundances of each element are strongly modified because of relatively high neutron densities with values between those of the s and r processes.

We have updated model predictions of the production of 182Hf and other short-lived radioactive nuclei in stars of initial masses between 1.25 and 25 M (table S1). Stars of initial mass up to 8.5 M evolve onto the AGB phase and have been computed by using the Monash code (2124). Stars of higher mass evolve into core-collapse supernovae and have been computed by using the KEPLER code (25, 26). The estimates of β-decay rates by Takahashi and Yokoi (14) were based on nuclear-level information from the Table of Isotopes (ToI) database, which included states for 181Hf at 68, 170, and 298 keV. The 68-keV level was found to be responsible for a strong enhancement of the β-decay rate of 181Hf at s process temperatures, preventing the production of 182Hf during the s process (Fig. 1). More recent experimental evaluations (27), however, did not find any evidence for the existence of these states. Removing them from the computation of the half-life of 181Hf in stellar conditions results in values compatible with no temperature dependence for this isotope (fig. S2), within the uncertainties.

The removal of the temperature dependence of the β-decay rate of 181Hf resulted in an increase by a factor of 4 to 6 of the 182Hf abundance predicted by the AGB s process models. The effect was milder on the predictions from the supernova neutron burst, with increases between 7% for the 15 M model and up to a factor of 2.6 for the 25 M model. Some production of 182Hf, as well as of 129I and 107Pd, is achieved in all the models, with 182Hf/180Hf ranging from ∼0.001 to ∼0.3 (Fig. 2). In terms of the absolute 182Hf abundance, however, only AGB models of mass ∼2 to 4 M are major producers of s process 182Hf in the Galaxy, owing to the combined effect of the 13C(α,n)16O and the 22Ne(α,n)25Mg neutron sources (20, 22). Only in these stars is the production factor of the stable 180Hf with respect to its solar value well above unity.

Fig. 2 Stellar model predictions as function of the initial stellar mass.

(A) The production ratios of the radioactive isotopes of interest with respect to the stable reference isotope of the same element. (B) The production factors with respect to the initial solar composition of each stable reference isotope. Stars below 10 M evolve through the AGB phase and associated s process, whereas stars above 10 M evolve through a core-collapse supernova and associated neutron burst. All the models were calculated by using no temperature dependence for the half-life of 181Hf and with initial solar abundances updated from (34), corresponding to a metallicity 0.014.

When using Eq. 1 with the updated s+r production rate ratio for 182Hf/180Hf, we still have the problem that the time of isolation of the solar system material from the average interstellar medium is much shorter than the value obtained by using 129I/127I (Table 1). For the nuclei under consideration, however, it is likely that their mean lifetimes are smaller or similar to the recurrence time, δ, between the events that produce them. In this case, the granularity of the production events controls the abundances, and the correct scaling factor for the production ratio is the number of events, T/δ. Because the cosmic abundances of these nuclei result from two different types of sources, the r process and the s process, it necessarily follows that the precursor material of the solar system must have seen a last event (LE) of each type—a r process LE and a s process LE. After each of these LEs, the abundance of a radioactive isotope in the Galaxy, relative to a stable isotope of the same element produced by the same process, is given by Embedded Image (2)where pradio/pstable are the production ratio of each single stellar event; the second term of the sum accounts for the memory of all the previous events (16). Using simple considerations on the expansion of stellar ejecta into the interstellar medium and the resulting contamination of the Galactic disk (18), one can derive δ ∼ 10 My for supernovae and ∼50 My for AGB stars in the mass range of 2 to 4 M. Because these values are first approximations, and because the r process probably does not occur in every supernova, in Table 1 we present the results obtained using δ = 10 My to 100 My. The time of the r process LE as derived from 129I/127I is 80 My to 109 My (Table 1), which is in agreement (within the uncertainties) with the 95 My to 123 My values derived from the early solar system 247Cm/235U ratio, which can only be produced by the r process and whose initial abundance needs confirmation. This r process LE time is in strong disagreement with the r process LE times derived from 107Pd/108Pd and 182Hf/180Hf, which should be considered upper limits, given that the abundances of 108Pd and 180Hf have an important (70 to 80%) s process contribution that is not accounted for when considering r process events only. A natural explanation is to invoke a separate s process LE for 107Pd and 182Hf. When calculating the time of this event under the approximation that the stable reference isotopes 108Pd and 180Hf are of s process origin, which is correct within 30%, we derive concordant times from 107Pd and 182Hf of ∼10 My to 30 My (Table 1). Our derived timeline for the solar system formation is schematically drawn in Fig. 3.

Table 1 Production ratios and inferred time scales.

Pradio/Pstable are the ratios of the stellar production rates (s+r processes), and pradio/pstable are the production ratios of each single stellar event (s or r process, as indicated). The UP and LE ratios are calculated by using Eq. 1 and Eq. 2, respectively. For 247Cm/235U in Eq. 1, T is substituted with the mean lifetime of 235U (τ = 1020 My), and in Eq. 2, δ/T is removed and pradio/pstable is multiplied by the ratio of the summation terms derived for 247Cm and for 235U. The UP and LE times are the time intervals required to obtain the initial solar system ratio starting from the UP and LE ratios, respectively. For the initial 247Cm/235U, we assume the average of the range (1.1 − 2.4) × 10−4 given by (33). Meteoritic and nuclear uncertainties result in error bars on the reported times of the order of 10 My (20).

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Fig. 3 Schematic timeline of the solar system formation.

The r process LE contributed 129I to the early solar system, the s process LE contributed 107Pd and 182Hf, and self-pollution of the star-forming region contributed the lighter, shorter-lived radionuclides, such as 26Al.

Our timing of the s process LE that contributed the final addition of elements heavier than Fe to the precursor material of the solar system has implications for our understanding of the events that led to the formation of the Sun. This is because it provides us with an upper limit of the time before the solar system formation when the precursor material of the solar system became isolated from the ongoing chemical enrichment of the Galaxy. This isolation time scale can represent the time it took to form the giant molecular cloud where the proto-solar molecular cloud core formed, plus the time it took to form and collapse the proto-solar cloud core itself. It compares well to the total lifetime (from formation to dispersal) of typical giant molecular clouds of 27 ± 12 My (28). In this context, other radioactive nuclei in the early solar system of possible stellar origin (table S2), such as 26Al, probably result from self-pollution of the star-forming region itself (20, 2931). This is not possible for the radioactive nuclei of s process origin considered here because their ∼3 M parent stars live too long (∼400 My) to evolve within star-forming regions. Our present scenario implies that the origin of 26Al and 182Hf in the early solar system was decoupled, which is in agreement with recent meteoritic analysis that has demonstrated the presence of 182Hf in an early solar system solid that did not contain 26Al (32).

Supplementary Materials

Supplementary Text

Figs. S1 and S2

Tables S1 and S2

References (3546)

References and Notes

  1. Supplementary text is available for further discussion as supplementary materials on Science Online.
  2. Acknowledgments: We thank M. Asplund for providing us updated early solar system abundances, D. Price and C. Federrath for comments, and M. Pignatari for discussion. The data described in the paper are presented in fig. S2 and table S1. M.L., A.H., and A.I.K. are Australian Research Council (ARC) Future Fellows on projects FT100100305, FT120100363, and FT10100475, respectively. This research was partly supported under ARC’s Discovery Projects funding scheme (project nos. DP0877317, DP1095368, and DP120101815). S.G. acknowledges financial support from the Fonds National de la Recherche Scientifique, Belgium. U.O. thanks the Max Planck Institute for Chemistry for use of its IT facilities.
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