Influence of nuclear physics inputs and astrophysical conditions on the Th/U chronometer

The productions of thorium and uranium are key ingredients in $r$-process nucleo-cosmochronology. With the combination of improved nuclear and stellar data, we have made a detailed investigation of the $r$-process abundance pattern in the very metal-poor halo stars based on the classical $r$-process approach. It is found that the results are almost independent of specified simulations to observed abundances. The influence from nuclear mass uncertainties on a Th/U chronometer can approach 2 Gyr. Moreover, the ages of the metal-poor stars HE $1523-0901$, CS $31082-001$, and BD $+{17}^{°}3248$ are determined as $11.8\pm 3.7$, $13.5\pm 2.9$, and $10.9\pm 2.9$ Gyr, respectively. The results can serve as an independent check for age estimates of the Universe.

Figure 1

${\sigma }_{\mathrm{rms}}$(abund.) and ${\sigma }_{\mathrm{rms}}(S_n)$ for different mass models. The line is plotted to guide the eyes. For details refer to the text.

Figure 2

Historical time and corresponding abundance ratio Th/U. The solid line between the present and the time when the Solar System became a closed system can be deduced from the radioactive decay of Th and U. The predictions from the assumptions of sudden and uniform synthesis are shown by the dashed and dotted curves, respectively. The predicted zero-age Th/U ratios using different mass models are calculated based on fit III and are marked in the corresponding curves. The dash-dotted lines represent the age of the Solar System (4.6 Gyr [47]) and the age of the Universe (13.7 Gyr [48]). For details refer to the text.

Figure 3

Calculated $r$-process abundances (scaled to Eu) using various mass models. The $\beta$-decay properties are taken from the FRDM$+$QRPA model. The simulations from fits I, II, and III are denoted by the solid, dashed, and dotted curves, respectively. The filled circles represent the scaled average element abundances of CS 31082-001 and CS 22892-052 in the region $Z<82$. The abundances for Pb, Th, and the upper limit (open circle) on U are taken from CS 22892-052. We adopt the usual notation that $\log {}_{10}\varepsilon (A)\equiv \log {}_{10}(N_A/N_H)+12.0$ for element $A$, where $N$ represents abundance.

Figure 4

Calculated $r$-process abundances using the $\beta$-decay rates predicted in the FRDM$+$QRPA (solid curve) and ETFSI$+$CQRPA (dashed curve) methods. The calculated abundances (scaled to Eu) for the RMF and DZ28 mass models are shown in (a) and (b), respectively. The filled and open circles are the same as in Fig. 3.

Figure 5

Ages of the metal-poor stars HE 1523-0901 and CS 31082-001 determined using various mass models and fits. The circles (squares, diamonds) denote ages determined using fit I (II, III). The average ages with all mass models and the three mass models DZ10, DZ28, KTUY are labeled as Aver1 and Aver2, respectively. The thick horizontal line corresponds to the age of the Universe [48].