$\mathrm{R}\mathrm{e}/\mathrm{O}\mathrm{s}$ Constraint on the Time Variability of the Fine-Structure Constant

We argue that the accuracy by which the isochron parameters of the decay ${}^{187}\mathrm{R}\mathrm{e}\to {}^{187}\mathrm{O}\mathrm{s}$ are determined by dating iron meteorites may constrain the possible time dependence of the decay rate and hence of the fine-structure constant $\alpha$, not directly but only in a model-dependent manner. From this point of view, some of the attempts to analyze the Oklo constraint and the results of the quasistellar-object absorption lines are reexamined.

Figure 1

An exponential fit (16) to the QSO result [7] shown as a binned fit, though the minimizing of ${\chi }^2$ itself has been made with respect to the original 128 data points. The minimum ${\chi }_{\mathrm{r}\mathrm{d}}^2=1.069$ is obtained for $a=-0.354$ and $b=1.39$. The horizontal long-dashed line represents the average $y=-0.54$. A flat distribution of the data is obvious. The Oklo time $u_{\mathrm{o}\mathrm{k}\mathrm{l}\mathrm{o}}=0.14$ and the meteorite time $u_{\mathrm{m}\mathrm{e}\mathrm{t}}=0.33$ are shown by upward arrows.

Figure 2

The 68% and 95% confidence regions around the minimized ${\chi }^2$ of the fit corresponding to Fig. 1, as indicated by a cross.

Figure 3

A tentative fit with a fixed $a=-0.025$ but with $b=7.28$ that minimizes chi-squared, resulting in ${\chi }_{\mathrm{r}\mathrm{d}}^2=1.13$. Notice too sharp a fall of the curve toward the higher $u$.