The straightforward conclusion to be drawn from these observational behaviors is that r-process nucleosynthesis, and the associated production of the critical actinide nuclear chronometers we have identified, first occurs during the very earliest stages of galactic evolution and, therefore, most likely is associated with the environments provided by the evolution of massive stars (M≈>10 M⊙) and type II supernovae. This supports the viewpoint that the nucleosynthesis history we are probing with the actinide radioactive isotopes is indeed the entire history of the Galaxy. The production history of the 232Th/238U and 235U/238U chronometers produced by the r-process should trace the rate of star formation activity in the Galaxy. This implies that 232Th/238U and 235U/238U chronometer dating should therefore provide an excellent measure of the age of the Galaxy.
2. Age Determinations with r-Process Chronometers. The critical input astrophysical quantities required for dating the epoch of galactic nucleosynthesis include: (i) the abundance ratios characterizing the matter that condensed into meteorites when the solar system formed and (ii) the production ratios of the isotopes of uranium and thorium in the relevant (r-process) nucleosynthesis site.
Abundance determinations for the thorium and uranium isotopes of interest are provided by analyses of meteoritic material. The situation for the 232Th-238U pair is complicated by the chemical differences between the two elements. Anders and Grevesse (17) found the present day value of Th/U to be 3.6, which translates into a primordial solar system ratio (232Th/238U)ss=2.32. This is the value that we have adopted in this paper. We also have used the ratio (235U/238U)ss= 0.317 provided by Anders and Grevesse.
The determination of the critical r-process production ratios (232Th/238U)r-process and (235U/238U)r-process is a sensitive function of both the input nuclear physics and the physical conditions under which the r-process proceeds. There are considerable uncertainties associated with the nuclear properties of the unstable, neutron-rich progenitors of the uranium and thorium isotopes of interest. Determinations of these production ratios available in the literature [see, e.g.. the review articles of Cowan, Thielemann, and Truran (18, 19)] yield values that span a broad range: 1.40 ≤ (232Th/238U)r-process≤ 1.90 and 0.89 ≤(235U/238U)r-process≤1.89. In our subsequent discussions, we have adopted the values (232Th/238U)r-process= 1.65±0.20 and (235U/238U)r-process=1.35±0.30, which represent averages of the values compiled by the above authors.
3. Basic Equations and a “Model-Independent” Age Determination. The equations governing the time evolution of the abundance of a radioactive nuclear species are straightforward. Assuming a homogeneous interstellar medium and instantaneous return of the products of stellar nucleosynthesis into the surrounding gas, the time evolution of species Ni can be written
where ω(t) represents the gain or loss of mass caused by accretion and winds, ψ(t) is the rate of conversion of mass into stars, λi is the decay rate of species i, and Pi is the production rate of species i, per unit mass going into stars.
Assuming no gain or loss of matter (ω(t)=0), the simple cases (which we will use in later sections) of (i) a single event nucleosynthesis history and (ii) a uniform nucleosynthesis rate yield the respective solutions:
The astrophysical input to these equations involves the rate of formation of the range of stellar masses within which r-process nucleosynthesis occurs. Although calculations of r-process nucleosynthesis have been carried out for a variety of plausible astrophysical sites [see. e.g., the reviews by Hillebrandt (20) and Meyer (21)], a firm identification of the appropriate environment has become possible only recently. Observations of heavy element abundance patterns in metal-deficient halo stars point strongly to the identification of r-process nucleosynthesis with the environments provided by the evolution of massive stars and supernovae of Type II. In this context, the most promising mechanism of r-process synthesis would appear to be that associated with the neutrino-heated “hot bubble” supernova ejecta (22–23), although an r-process associated with the decompression of cold neutron matter from neutron star mergers (24) provides a viable alternative. An important consequence of the identification of the r-process with such massive stars (M>≈10 M⊙) of short lifetimes (τ< ≈108 years) is that we can reasonably expect that the age we determine from r-process chronometer studies is indeed representative of the age of the Galaxy itself.
The effects of galactic chemical evolution introduce significant complications for age determinations. There is a very substantial literature concerning chemical evolution effects on age dating, including considerations of varied prescriptions for the star formation history, and of the consequences of infall and outflow of gas from the star-forming regions. This literature has been reviewed most recently by Cowan, Thielemann and Truran (18, 19). In general, such age determinations are quite model-dependent.
Meyer and Schramm (25), extending the early work by Schramm and Wasserburg (26). sought to provide a model-independent age determination. In the limit of long-lived chronometers (λT≪1), they derive a simple expression for the age that is approximately independent of galactic evolution effects. In this context, Th/U can be used to provide a firm lower limit, and Re/Os can be used to provide a firm upper limit. When account is taken of the additional constraint that r-process nucleosynthesis must also produce appropriate levels of such shorter lived nuclei as 244Pu (τ1/2=8.2×107 years), Meyer and Schramm (25) arrive at a very firm lower bound on the age of the Galaxy (T+τss)>9.6 Gyr.
4. Lower Bounds on the Age of the Galaxy. Lower bounds on the age of the elements can be obtained by considerations of the long-lived actinide chronometers, on the assumption of a single event nucleosynthesis history. In this section, we will determine limits based on both the 235U/238U and the 232Th/ 238U chronometer pairs.
For the case of the 235U/238U pair, the appropriate equation is
where the primordial solar system ratio is (N235/N238)ss= 0.317 and the r-process production ratio is (P235/P238)r-process= 1.35±0.30. This yields a time scale for the epoch of nucleosynthesis of T=1.75±0.25 Gyr and a limiting age for the Galaxy (T+τss) of
We can similarly use the 232Th/238U ratio to arrive at a lower bound on the galactic age. For the case of the 232Th/238U pair, the appropriate equation is