3 Equivalent widths

The equivalent widths (EWs) were measured by direct integration under the continuum using the subroutine SPLOT of the IRAF package. They were determined independently by three of us to minimize the effects of a subjective location of the continuum. The finally adopted EWs and the quoted errorbars result from a critical discussion of these determinations. Table 2 presents the resulting LiI EWs with the estimated 95% confidence limit error bars. The uncertainties are in general $\le 5$ mÅ. The table also lists previous measurements by other authors giving 95% confidence limit error bars.

For about 40 stars of the sample this represents the first spectroscopic study in the region of the LiI feature. The rest have been observed by other authors (mainly by Pilachowski et al. 1993, and Thorburn 1994). The common stars among these works allow a comparison between measurements, constituting a test of consistency and on the validity of the observations. On the measurements presented in Table 2 there are 16, 9 and 3 stars with 2, 3 and 4 independent observations respectively, adding in total 49 pairs of measurements to compare. For a couple of measurements ($x_i \pm \sigma_{x_i}$) and ($y_i\pm \sigma_{y_i}$) of the i-star, the difference is ($a_i,\sigma_{a_i}$), being a_i=x_i-y_i and $\sigma_{a_i}=\sqrt{\sigma_{x_i}^2+\sigma_{y_i}^2}$. The quantity $\sum_i^{49} a_i^2/\sigma _{a_i}^2$ follows approximately a $\chi ^2$ distribution with 49 degrees of freedom. The variance of the distribution is $\sim 2\times 49$ which defines the $1\sigma$ and the $2\sigma$ level as the ranges $38\le \chi ^2\le 59$ and $31\le \chi ^2\le 71$, respectively. In our case $\chi ^2=116$, which is not in the mentioned ranges and a value extremely unlikely if all measurements were consistent. To test the possible presence of systematic errors in some of the measurements, we have removed from the above comparison the measurements in which $\vert a_i\vert/\sigma_{a_i}\ge 2.5$.Doing the same analysis than above, the value obtained now is $\chi ^2=52$ for 41 pairs of measurements, which is in good agreement with the statistical expectations. This seems to indicate that in $\sim 20$% of the common pairs of measurements there are additional sources of error not included in the uncertainty provided by the quoted errorbars. Other statistical tests give the same conclusion. Explicitly we suspect of the following stars:

• G205-42: There are two additional measurements by Pilachowski et al. (1993) and Thorburn (1994). For this star our measurement is in disagreement with the other two.
• HD 111721 and HD 163810: For these stars there is only one additional measurement by Pilachowski et al. (1993), clearly in disagreement with the values reported in this work.
• G88-32: Our measurement (19 $\pm$ 5 mÅ) is discrepant with two previous measurements by Hobbs & Thorburn (1991; 26 $\pm$ 4.4 mÅ) and Thorburn (1994; 28 $\pm$ 5.8 mÅ).
• G166-45: This is a very intriguing double lined spectroscopic binary. While Hobbs & Thorburn (1991) and Thorburn (1994) measure 29 $\pm$ 3.6 mÅ, our determination gives 36 $\pm$ 3 mÅ, in agreement with the measurement by Rebolo et al. (1988; 35 $\pm$ 3 mÅ). In the spectrum obtained by Rebolo et al. (their Fig. 1b) it is possible to appreciate a small asymmetry in the red wing of the LiI line. The new spectrum recorded in 1991 January also shows this asymmetry, possibly indicating that the secondary star also has a LiI line.
• BD -13^_$^\circ _ \cdot$3442: Here we report 22 $\pm$ 2 mÅ, which presents a serious discrepancy of 8 mÅ with the measurement of Thorburn (1994; 30 $\pm$ 6.8 mÅ). However, our measurement is in better agreement with that obtained by Ryan et al. (1996; 19 $\pm$ 2 mÅ).
• LP815-43: We report here 25 $\pm$ 6 mÅ. The situation here is confused with several measurements giving around 25 mÅ and others close to 15 mÅ.

Removing these stars from the statistical analysis, we found $\chi ^2=26$ for the remaining 31 pair of measurements indicating that the inconsistency of the sample is due to the stars removed. Previous work on this have been done by Ryan et al. (1996) and Deliyannis et al. (1993). For instance, applying the above analysis to the sample analyzed by Ryan et al. we obtain $\chi ^2=248$ for 148 pair of measurements. Removing 5 stars (Ryan et al. recognized problems in 4 of them) involving in total 10 pair of measurements, the value obtained for $\chi ^2$ is now compatible with the value expected from the quoted noise of each measurement.

  

Figure 2: Comparison between our measurements of the LiI $\lambda 670.8$ nm equivalent widths and those by Pilachowski et al. (1993; top) and Thorburn (1994; down). The error bars represent the estimated 95% confidence limits

The comparison between our measurements and those by Thorburn (1994) and Pilachowski et al. (1993) is summarized in Fig. 2. Defining $\rm \Delta _P$and $\rm \Delta _T$ as the mean differences between our measurements and the ones by these authors, respectively, we obtain $\rm \Delta _P=+0.7$ and $\rm \Delta _T=$ -0.9 mÅ, values which show the absence of significant systematic effects between the three sets of measurements. The rms of the differences are 4.4 and 4.6 mÅ for the comparison with the samples of Pilachowski et al. and Thorburn, respectively, values which are slightly larger than the expectations in terms of the error bars ($\sim 2.7$ and $\sim 3.5$ mÅ, respectively). If we remove in the comparison with Thorburn the stars G88-32, G166-45, G205-42, BD $-13^\circ$ 3442, and do the same with HD 111721, HD 163810 and G205-42 in the comparison with Pilachowski et al., we found that the rms of the differences were now in perfect agreement with expectations in terms of noise. These results confirm our claims on the inconsistency in $\sim$20% of the common measurements.

We conclude that for $\sim\! 20$% of the stars there are systematic effects not taken into account in the reported uncertainties, and we shall bear in mind that any conclusion inferred from the global sample should be robust against rejection of subsamples comprising this fraction of the stars. Repeated independent observations may guarantee a sufficient number of reliable determinations along the ${\rm Li}-T_{\rm eff}$ and ${\rm Li}-{\rm [Fe/H]}$ planes to solve the scatter problem. It would be particularly useful to conduct such programme in photometric and spectroscopic twin halo dwarf stars. One possible case of twin stars is that of G64-37 and G64-12. These are the two stars in our sample with the largest number of determinations, all of them being consistent. Our new measurements are in agreement with the best previously estimated values. When our own values are taken into account the new best estimated LiI EWs are 25.2 $\pm$ 1.2 and 15.4 $\pm$ 0.9 mÅ for G64-12 and G64-37, respectively. This LiI EW difference between both stars was noted by Ryan et al. (1996) and is reinforced by our new measurement. Given the strong similarity in their V-K and c₁ indices (see Table 2) we could expect very similar $T_{\rm eff}$ and gravity and therefore rather different lithium abundances. However, as we can also see in Table 2, when the reddening is taken into account, the stars do not look as similar as was thought. This question will be addressed in more detail in a forthcoming paper.

Acknowledgements

We thank A. Magazzú, J.E. Beckman and E.W. Barnett for their help with the IACUB observations and their support to the project. We also thank C. Pilachowski for providing the S/N of their spectra. Finally we wish to thank F. Spite for his support to this project and his useful comments on the manuscript. This work has used the

SIMBAD database. This work has been partially supported by the Spanish DGES under projects PB92-0434-C02 and PB95-1132-C02-01. This article has been corrected for English and style by Terry Mahoney (Research Division, IAC).

This paper is dedicated to the memory of C.D. McKeith, who contributed much to this work before his untimely death in September 1996.