3 Correction to a uniform zero point

3.1 Data that define the zero point

The values of [Fe/H] for the zero-point stars may be thought of as an initial zero-point data base. To expand that data base, a search is made for literature results whose zero points appear to be reasonably secure. Acceptable results may be referred to the Sun directly or through the zero-point stars listed above. Data for which T91 has noted some special problem are set aside for the moment. Data are also set aside if they have been derived from the Holweger-Müller (1974) solar model and a stellar model from a published grid. This combination will be referred to here as a "non-uniform'' grid of model atmospheres. Data derived with non-uniform grids require corrections ranging from -0.05 dex to +0.25 dex (see Sect. 6 of Paper I).

There appears to be a belief among some astronomers that the history of [Fe/H] analysis has been dominated by external zeroing (see Kuroczkin & Wisniewski 1977; Twarog & Anthony-Twarog 1996). If this were true, presumably it would not be possible to find enough differential values of [Fe/H] to form an adequate zero-point data base. In fact, the expanded version of that data base contains results for 193 stars. Given the data for these stars, one can produce a final set of averages that does not depend on an adopted solar value of log (Fe/H).

Alternative ways of setting the zero point include use of the Hyades as well as external zeroing. One could assume that the Hyades giants and dwarfs have the same mean value of [Fe/H] (again see Twarog & Anthony-Twarog 1996). By contrast, the approach adopted here is to test this assumption instead of adopting it at the outset. It is found that at 95% confidence, no difference as large as 0.049 dex exists between the values of [Fe/H] for the Hyades dwarfs and giants (see Sect. 7.6 of Paper II).

3.2 Expanding the data base

The reader is now invited to inspect Table 1. The description given to this point has reached stage 2 of the analysis (see the second line of Table 1). Details about each remaining data group considered here are given in the table. Reasons for not including the added data in the initial zero-point data base are given in footnotes to the table. The data groups are sequenced so that larger groups are added before smaller groups. This is done to make it as likely as possible that "overlap'' stars can be found in both the zero-point data at a given stage and the data group to be added at the next stage. If the number of overlap stars is as large as possible, the correction to the added data will be as precise as possible. An adequate number of overlap stars is found at each step.

  

Table 1: Grouping the input values of [Fe/H]

$^{\mathrm{a}}$ Corrections given in papers themselves are not considered here. Only corrections derived by comparing data from different papers are listed.
$^{\mathrm{b}}$ When necessary, data are referred to the Sun through the Paper II standard stars.
$^{\mathrm{c}}$ This number includes only HD stars, since only data for such stars are used to rezero results in subsequent steps in the analysis.
$^{\mathrm{d}}$ From Williams 1971, 1972 and Gustafsson et al. 1974. No lower limits from Williams 1972 are used. The Williams data are re-scaled and corrected to the Gustafsson et al. zero point by using Eq. (1). T91 found that an overall zero-point correction for the collected photometric data was required.
$^{\mathrm{e}}$ These data are based on a non-uniform grid of model atmospheres. T91 found that a zero-point correction was required. Before averages are formed, rms errors are set to 0.07 dex if they are less than 0.07 dex.
$^{\mathrm{f}}$ T91 found that a B-V-based correction was required.
$^{\mathrm{g}}$ From Luck 1991, Luck & Wepfer 1995, and Luck & Challener 1995. These data are based on a non-uniform grid of model atmospheres. Results using spectroscopic values of log g are adopted.
$^{\mathrm{h}}$ Literature sources for these data will be given in a subsequent paper in this series.

A search is now made for discrepant zero-point data. A few such data are found and deleted. In addition, a search is made for results that are added at stage 6 but should be included earlier. An example of such a data set is from Cottrell & Sneden (1986). Their results are initally included at stage 6 because they are based on a non-uniform grid. However, a zero-point correction derived for them turns out to be effectively zero, so they are included at stage 2 instead. Once any required editing is done, the analysis is repeated, and it is iterated until no further editing is necessary.

As each part of the analysis beyond stage 1 is performed, a number of values of [Fe/H] for the Paper II zero-point stars are encountered. Those results have not been used to calculate the mean values of [Fe/H] given in Paper II for the zero-point stars. As a result, one might conceivably find a discrepancy that could signal that the Paper II mean values should be modified. Reassuringly, no discrepancy as large as $2\sigma$ is found.

3.3 Special correction techniques

Sometimes data require more than a simple zero-point adjustment before being added to the data base. As noted in Table 1, four additional correction algorithms are required.

1) U-B corrections. Suppose that values of [Fe/H] from a given paper have a systematic error that varies with temperature. If the cause is continuum misplacement, the error will increase if temperature decreases or if metallicity increases. By using a parameter that does the same things, one can correct for the error. U-B fits these requirements, and since it also has a large dynamic range, it should be a good choice of correction parameter. The adopted correction equation then has the following form:

$$F = F \mkern1mu {\rm (uncorrected)} + S(U-B) + Z,$$ (1)

with $F \equiv$ [Fe/H] and S and Z being constants.

This technique can be tested by applying it to the results of Gratton et al. (1982). Those authors derived high-dispersion values of [Fe/H] from the blue-violet spectral region. They give convincing evidence that their results suffer from continuum-placement error. The technique described above detects the results of this error at a confidence level exceeding 99.99%. (For more information about this test, see T91, Sect. 2.6, paragraphs 1, 2, and 4.)

2) B-V corrections. These corrections are applied to data from Brown et al. (1989), using a counterpart to Eq. (1). The Brown et al. equivalent widths were measured to the red of 6600 Å, so they are unlikely to suffer from continuum misplacement. It seems more likely that in this case, the systematic error depends on temperature alone. Ideally, one would use some version of R-I or a similar low-blanketing color index in the correction equation. B-V is chosen instead because it is readily available. The resulting correction equation appears to be quite adequate. (See T91, Sect. 3, entry for Brown et al.)

3) Corrections based on $\theta \equiv 5040/T_{\rm eff}$. These corrections are applied to the data of Zacs (1994). Values of $\theta$ derived by Zacs are the only convenient data on which to base the corrections. Again, the correction equation is a counterpart to Eq. (1).

4) Rescaling. Spectrum-synthesis results given by Williams (1971, 1972) are included in the analysis. Those results are known to suffer from a scale-factor error. The adopted procedure for correcting that error is to transform the Williams data so that they correspond to spectrum-synthesis results from Gustafsson et al. (1974). The correction equation applied here is

$$F = 0.691F\rm _W - 0.001,$$ (2)

with F now representing the data of Gustafsson et al. and $F\rm _W$ denoting the Williams data. No rescaling of the combined Williams and Gustafsson et al. data seems to be necessary. (For further discussion of this problem, see Sect. 2.5 and Appendix A of T91.)

It may be noted that when Eq. (1) and its counterparts are derived, one must find out whether the resulting values of S differ significantly from zero. If they do not, it is appropriate to assume that S=0 and derive a zero-point correction Z alone. To solve this problem, a least-squares routine that returns rms errors for derived coefficients is employed. The ratio of S to its derived error is then calculated. This ratio is the t statistic, and it may be used with standard tables to find out whether S differs from zero at 95% confidence or better. A similar procedure may be used if S=0 is assumed and one suspects that Z does not differ significantly from zero.

3.4 Data that are not added to the data base

Some published metallicities for evolved K stars are not included in the data base. The number of such data is not disturbingly large; one finds that even without them, the final catalog includes results for 1118 stars. Data may be set aside because of continuum-placement problems or other good reasons to suspect that they suffer from systematic errors. Other reasons for setting data aside include a lack of pertinent information about the analyses used to produce them. A complete list of omitted data bases and the reasons for omitting them will be given with the catalog (see Taylor 1999).