The prevalence of differential analysis is a first indication that a reliable zero point may be found for the catalog data. The first step in calculating those data may now be taken by sorting the extended sample in a somewhat different way. Two classes of accepted results are established, with one class including results from all analyses for which extrinsic zero points can be calculated (again see Sect. 3.2). Some results in this class have small values of $N_{\rm L}$ , while others contribute to the fourth through the seventh lines in Table 1. The other class considered here includes only results from differential analyses relative to the Sun for which the $N_{\rm L}$ limits given above are always satisfied. No distinctions among these results are made which are based on their input solar equivalent widths (EWs) This procedure will be justified in Sect. 3.4.

The second step is to edit the extended sample. Papers are deleted from that sample for reasons given in Table 2. After the deletions are performed, the remaining sample is augmented by adding data from Nissen (1981). Nissen's results are from photometry of one cluster of weak lines and a second cluster of moderately-saturated lines.

Table 2: Reasons for deleting analyses from the extended sample.
Reason

DCOG result-not used for certain metal-poor stars

EWs from a blanketed wavelength region

$\rm [Fe/H]$ zero point cannot be determined adequately

Few or no lines on linear part of curve of growth

Further analysis of program stars may not take place ${\rm ^a}$

Noisy EWs

Only one result in catalog $\rm [Fe/H]$ range

Only previously published stellar EWs used

Results superseded by improved analysis

Subsequent analysis indicates systematic error

Values of $\rm [Fe/H]$ not given numerically

$^{{\rm a}}$
Cunha et al. (1995) have derived metallicities for stars in the Orion association. The cautious assumption made here is that those stars are less likely than field stars to be the objects of further analysis. This issue is deemed to be important because rms errors are determined from the scatter in multiple data for given stars. It is not clear that errors derived in that way should be applied if there is a minimal prospect for further analyses.

**Table 2:** Reasons for deleting analyses from the extended sample.
Reason
DCOG result-not used for certain metal-poor stars
EWs from a blanketed wavelength region
$\rm [Fe/H]$ zero point cannot be determined adequately
Few or no lines on linear part of curve of growth
Further analysis of program stars may not take place ${\rm ^a}$
Noisy EWs
Only one result in catalog $\rm [Fe/H]$ range
Only previously published stellar EWs used
Results superseded by improved analysis
Subsequent analysis indicates systematic error
Values of $\rm [Fe/H]$ not given numerically

The third step in the analysis is to apply an initial set of corrections to the data. These corrections are made only if they can be based on published numerical results. When necessary, solar values of [Fe/H] are corrected to the Liège EW system (see Delbouille et al. 1973; Rutten & van der Zalm 1984a, 1984b). Corrections are also applied if incompatible solar and stellar model atmospheres have been used (see examples (5) and (6) in Appendix A). The entire data base is also corrected to a temperature scale which is described in a companion paper (see Taylor 2003). This part of the correction procedure is described in more detail in Sects. 3.4 through 3.6 of T94.

For each data set which requires an extrinsic zero point, a special reduction procedure is adopted. One or more stars with data in the set are designated as ad hoc standard stars. Averaged values of [Fe/H] for those stars are then calculated from data sets with reliable zero points. Finally, corrections for the problem data sets are derived, with a "comparison algorithm'' being applied if necessary (see Taylor 1999a, Sect. 4.3).

3.3 Data averaging and input rms errors

The fourth step in the analysis is to calculate overall averages from the data. For each star considered, this averaging yields a mean value of [Fe/H], an rms error of the mean, and a number of effective degrees of freedom. Each input datum is weighted by the inverse square of an input rms error. The integrity of the resulting mean values of [Fe/H] must be checked by performing a zero-point analysis, and that test will be described in the next section. For the moment, attention is focused on the input rms errors.

Each block of input data is assigned to rms error class S, N, or W. Class N contains data which are quoted in the literature without errors from EW scatter, while class W data are quoted with such errors. For the most part, older papers are in class N, while more recent papers are in class W. Data are assigned to class S if there are reliable rms errors for them in the literature. They are also assigned to this class if special rms errors have been derived for them by using the comparison algorithm. Further discussion of class S data is given in Sect. 4.1 of T94.

For all data without reliable published rms errors, those errors are derived from scatter in residuals from averaged values of [Fe/H]. A sample of such scatter is given in Fig. 1, where residuals for part of the Edvardsson et al. (1993) data are depicted. The procedure for deriving class N errors is adopted unchanged from Sect. 3.8 of T94. An improved procedure for deriving the counterpart class W error is described in Appendix B of this paper. The resulting values of the two errors are as follows:

with V_w being defined in Appendix B. V_w is added to a contribution from EW scatter to obtain errors for class W data (again see Appendix B).

$\begin{figure} \par\includegraphics[angle=-90,width=8.8cm,clip]{MS2858f1.eps} \end{figure}$

Figure 1: For the data of Edvardsson et al. (1993), residuals from averaged values of [Fe/H] (in dex) are plotted against HD number. Only data for HD numbers which equal 99 999 or less are plotted. The solid line applies for a residual of zero, while the dashed line is the mean residual. The adopted reduction of the Edvardsson et al. data is that of the authors themselves, not the subsequent reduction by Gratton et al. (Table 3).

The rms errors in Eqs. (2) and (3) contribute to useful insights about the input catalog data. An F test shows that $\sigma_N > \sigma_W$ at a confidence level C > 99.9%. One might think this to be an expected result, since it implies that more recent values of [Fe/H] are more precise than their older counterparts. However, no comparable trend can be found for evolved stars (see Sect. 4.6 of Taylor 1999a). In addition, if $N_{\rm L}$ is about 10 or greater, $\sigma_{\rm W}$ is substantially larger than the error contribution from EW scatter. Again, a similar result holds for evolved stars (see Sect. 5.3 of Taylor 1999a). Apparently most of the scatter in the input data is from one or more sources other than EW scatter.

3.4 Statistical testing for systematic offsets

The zero-point assessment referred to above is performed by searching for papers whose data yield precise average residuals. These averages are calculated by using an interim solution in which no corrections have yet been made for the non-zero mean residuals which will ultimately be found. To estimate the statistical significance of each averaged residual, a t test is used to derive a value of

with C being the confidence level for rejecting the null hypothesis that the true average is zero. The resulting values of P are given with the averaged residuals in Tables 3-5.

Table 3: Acceptable mean residuals from interim [Fe/H] solution.
No. of No. of Mean

Source papers stars $\phantom{{\rm ^a}}$ residual ${\rm ^a}$ $\phantom{{\rm ^b}}P{\rm ^b}$

Boesgaard ${\rm ^c}$ 6 62 $+14 \pm 13$ -

Cayrel de Strobel ${\rm ^d}$ 13 33 $+\phantom{0}7 \pm 14$ -

Gratton (group 1) ${\rm ^e}$ 6 83 $+\phantom{0}2 \pm \mkern2mu 9\mkern8mu$ -

da Silva ${\rm ^f}$ 6 18 $-22 \pm 19$ -

Chen et al. (2000) 1 43 $-18 \pm 14$ -

Favata et al. (1997) 1 30 $-10 \pm 14$ -

Feltzing; Neuforge-Verheecke &

Magain ${\rm ^g}$ 3 15 $+10 \pm 18$ -

Fuhrmann (1998) 1 46 $+\phantom{0}3 \pm 10$ -

Santos et al. (2001) 1 42 $-10 \pm 11$ -

Edvardsson et al. (1993) ${\rm ^h}$ 1 137 $-20 \pm 6\phantom{0}$ 2.94

Nissen (1981) ${\rm ^j}$ 1 111 $-34 \pm 12$ 2.24

$^{{\rm a}}$
The listed numbers are mean residuals multiplied by 1000. Units are dex.
$^{{\rm b}}$
$P \equiv -\log_{10} (1-C)$ , with C being the confidence level.
$^{{\rm c}}$
Included papers: Boesgaard (1987, 1989), Boesgaard et al. (1988), Boesgaard & Friel (1990), Friel & Boesgaard (1992), Deliyannis et al. (2000).
$^{{\rm d}}$
Included papers: Cayrel de Strobel (1968), Cayrel et al. (1977), Cayrel de Strobel et al. (1981), Cayrel et al. (1985, 1988), Perrin et al. (1988), Cayrel de Strobel & Bentolila (1989), Cayrel de Strobel & Cayrel (1989), Cayrel de Strobel et al. (1989), Chmielewski et al. (1992), Friel et al. (1993), Cayrel de Strobel et al. (1994), Chmielewski et al. (1995).
$^{{\rm e}}$
Included papers: Gratton & Ortolani (1986), Gratton & Sneden (1987), Gratton et al. (1989), Gratton et al. (1996), Clementini et al. (1999), Randich et al. (1999).
$^{{\rm f}}$
Included papers: da Silva (1975), da Silva & Foy (1987), Porto de Mello & da Silva (1997a, b), Castro et al. (1999), del Peloso et al. (2000).
$^{{\rm g}}$
Included papers: Neuforge-Verheecke & Magain (1997), Thoren & Feltzing (2000), Feltzing & Gonzalez (2001). The zero points for the first and third papers should be similar (see Sect. 4.2 of Feltzing & Gonzalez 2001).
$^{{\rm h}}$
Data source: reduction by Gratton et al. (1996).
$^{{\rm j}}$
Nissen's metallicites have been derived from photomultiplier measurements of clusters of weak lines.

**Table 3:** Acceptable mean residuals from interim [Fe/H] solution.
	No. of	No. of	Mean
Source	papers	stars	$\phantom{{\rm ^a}}$ residual ${\rm ^a}$	$\phantom{{\rm ^b}}P{\rm ^b}$
Boesgaard ${\rm ^c}$	6	62	$+14 \pm 13$	-
Cayrel de Strobel ${\rm ^d}$	13	33	$+\phantom{0}7 \pm 14$	-
Gratton (group 1) ${\rm ^e}$	6	83	$+\phantom{0}2 \pm \mkern2mu 9\mkern8mu$	-
da Silva ${\rm ^f}$	6	18	$-22 \pm 19$	-
Chen et al. (2000)	1	43	$-18 \pm 14$	-
Favata et al. (1997)	1	30	$-10 \pm 14$	-
Feltzing; Neuforge-Verheecke &
Magain ${\rm ^g}$	3	15	$+10 \pm 18$	-
Fuhrmann (1998)	1	46	$+\phantom{0}3 \pm 10$	-
Santos et al. (2001)	1	42	$-10 \pm 11$	-
Edvardsson et al. (1993) ${\rm ^h}$	1	137	$-20 \pm 6\phantom{0}$	2.94
Nissen (1981) ${\rm ^j}$	1	111	$-34 \pm 12$	2.24

Table 3 contains the most encouraging results found. For the last two entries in the table, $P \geq 1.3$ (C > 0.95). However, the listed mean residuals are small, and it seems probable that their nonzero status would not have been recognized if unusually large numbers of contributing data had not been available. For the remaining entries, P < 1.3. In these cases, the null hypothesis stating that the averages are zero is maintained. Note that each of the first four entries in Table 3 is from a series of six or more papers produced by a given author and collaborators.

Table 4: Probably acceptable mean residuals from interim [Fe/H] solution.
No. of No. of Mean

Source papers stars $\phantom{{\rm ^a}}$ residual ${\rm ^a}$ $\phantom{{\rm ^b}}P{\rm ^b}$

Balachandran (1990) ${\rm ^c}$ 1 63 $-81 \pm 15$ > 6

Boesgaard & Lavery (1986) ${\rm ^d}$ 1 11 $+98 \pm 20$ 3.28

Clegg (1977) ${\rm ^e}$ 1 11 $-162 \pm 25\phantom{0}$ 4.15

Gratton (group 2) ${\rm ^f}$ 2 16 $+42 \pm 18$ 1.46

Pasquini et al. (1994) ${\rm ^g}$ 1 26 $-146 \pm 16\phantom{0}$ > 6

Thévenin et al. (1986) ${\rm ^h}$ 1 10 $-173 \pm 33\phantom{0}$ 3.27

Varenne & Monier (1999) ${\rm ^j}$ 1 19 $-262 \pm 25\phantom{0}$ > 6

$^{{\rm a}}$
The listed numbers are mean residuals multiplied by 1000. Units are dex.
$^{{\rm b}}$
$P \equiv -\log_{10} (1-C)$ , with C being the confidence level.
$^{{\rm c}}$
Only results with $N_{\rm L} = 6$ are used. Stellar and solar EWs are from different spectrographs.
$^{{\rm d}}$
Only results with $N_{\rm L} = 9$ are used. Stellar and solar EWs are from the same spectrograph.
$^{{\rm e}}$
The source of solar EWs is unknown. For stellar EWs, $4200 \mkern6mu {\rm\AA}\ \leq \lambda \leq 4700 \mkern6mu {\rm\AA}$ .
$^{{\rm f}}$
Included papers: Gratton (1989), Sneden et al. (1991). For each paper, stellar and solar EWs are from different spectrographs.
$^{{\rm g}}$
$N_{\rm L} = 2$ for all results. The description of the zero-point procedure in this paper is incomplete.
$^{{\rm h}}$
For stellar EWs, $4200 \mkern6mu {\rm\AA}\ \leq \lambda \leq 4700 \mkern6mu {\rm\AA}$ . The description of the zero-point procedure in this paper is incomplete.
$^{{\rm j}}$
The zero point for this paper is from external zeroing.

**Table 4:** Probably acceptable mean residuals from interim [Fe/H] solution.
	No. of	No. of	Mean
Source	papers	stars	$\phantom{{\rm ^a}}$ residual ${\rm ^a}$	$\phantom{{\rm ^b}}P{\rm ^b}$
Balachandran (1990) ${\rm ^c}$	1	63	$-81 \pm 15$	> 6
Boesgaard & Lavery (1986) ${\rm ^d}$	1	11	$+98 \pm 20$	3.28
Clegg (1977) ${\rm ^e}$	1	11	$-162 \pm 25\phantom{0}$	4.15
Gratton (group 2) ${\rm ^f}$	2	16	$+42 \pm 18$	1.46
Pasquini et al. (1994) ${\rm ^g}$	1	26	$-146 \pm 16\phantom{0}$	> 6
Thévenin et al. (1986) ${\rm ^h}$	1	10	$-173 \pm 33\phantom{0}$	3.27
Varenne & Monier (1999) ${\rm ^j}$	1	19	$-262 \pm 25\phantom{0}$	> 6

In Table 4, results with P > 1.3 are listed if they can be attributed plausibly to a known source of possible zero-point error. The following sources are considered.

Like Table 4, Table 5 contains entries with $P \geq 1.3$ . However, none of the explanations listed above will work for those entries. They show that even when zero-point procedures with every appearance of rigor are applied, the resulting values of [Fe/H] can sometimes have appreciable offsets.

Table 5: Problem mean residuals from interim [Fe/H] solution.
No. of No. of Mean

Source papers stars $\phantom{{\rm ^a}}$ residual ${\rm ^a}$ $\phantom{{\rm ^b}}P{\rm ^b}$

Bikmaev et al. (1990) 1 15 $-132 \pm 36\phantom{0}$ 3.77

Edvardsson et al. (1993) ${\rm ^c}$ 1 186 $-52 \pm 6\phantom{0}$ > 6

Fulbright (2000) 1 38 $-95 \pm 12$ > 6

Gonzalez ${\rm ^d}$ 6 21 $+59 \pm 14$ 3.31

Hartmann & Gehren (1988) ${\rm ^e}$ 1 4 $-330 \pm 34\phantom{0}$ > 6

$^{{\rm a}}$
The listed numbers are mean residuals multiplied by 1000. Units are dex.
$^{{\rm b}}$
$P \equiv -\log_{10} (1-C)$ , with C being the confidence level.
$^{{\rm c}}$
Data source: Edvardsson et al. reduction.
$^{{\rm d}}$
Included papers: Gonzalez (1998), Gonzalez & Vanture (1998), Gonzalez et al. (1999), Gonzalez & Laws (2000), Gonzalez et al. (2001), Laws & Gonzalez (2001). Data from Feltzing & Gonzalez (2001) may be on a different zero point, and that paper is therefore included in a separate entry (see Table 3).
$^{{\rm e}}$
The authors give a datum for HD 59984 which yields a discrepant residual and has therefore been omitted.

**Table 5:** Problem mean residuals from interim [Fe/H] solution.
	No. of	No. of	Mean
Source	papers	stars	$\phantom{{\rm ^a}}$ residual ${\rm ^a}$	$\phantom{{\rm ^b}}P{\rm ^b}$
Bikmaev et al. (1990)	1	15	$-132 \pm 36\phantom{0}$	3.77
Edvardsson et al. (1993) ${\rm ^c}$	1	186	$-52 \pm 6\phantom{0}$	> 6
Fulbright (2000)	1	38	$-95 \pm 12$	> 6
Gonzalez ${\rm ^d}$	6	21	$+59 \pm 14$	3.31
Hartmann & Gehren (1988) ${\rm ^e}$	1	4	$-330 \pm 34\phantom{0}$	> 6

Overall, one can say that Tables 3 through 5 do not support extreme conclusions. Tables 4 and 5 show that there is more zero-point diversity than might have been hoped. On the other hand, Table 3 suggests that a meaningful zero point may nevertheless be found in the data. To see whether this is the case, corrections are first made by subtracting the listed offsets from the data to which the offsets apply. This is done if P > 1.3. Corrections $\vert\Delta F\vert < 0.06$ dex are applied to 18% of the input data. For an additional 18% of the data, $\vert\Delta F\vert > 0.06$ dex.

A revised version of the catalog is now produced, and check statistics are calculated. Numerical values for those statistics are listed in Table 6. One set of tests is applied to data of classes N and W which were not obtained by using solar EWs derived from stellar spectrographs. No detectable offset is found. In the fourth row of the table, the overall zero points for data of classes N and W are compared. Again no detectable offset is found, suggesting that the older data are on the same zero point as their more recently derived counterparts. It seems fair to assume that such results are obtainable only because the data are on a common zero point.

Table 6: Test statistics for accepted [Fe/H] solution.
Mean

$\phantom{{\rm ^a}}$ Statistic ${\rm ^a}$ $\phantom{{\rm ^b}}\nu{\rm ^b}$ $\phantom{{\rm ^c}}$ residual ${\rm ^c}$

N(no) - W(yes) 42 $+9 \pm 19$

W(no) - W(yes) 91 $-8 \pm 7\phantom{0}$

Net correction ${\rm ^d}$ 113 $-5 \pm 6\phantom{0}$

N(all) - W(all) 135 $-5 \pm 9\phantom{0}$

$^{{\rm a}}$
"N'' and "W'' designate rms error classes (see Sect. 4.4). "No'' denotes data whose zero points may be uncertain because solar EWs were not measured with stellar spectrographs. "Yes'' denotes data with zero points that are deemed to be reliable, and "all'' denotes a combination of data of both kinds.
$^{{\rm b}}$
$\nu$ is the number of degrees of freedom that would be used in a t test of the listed mean residual.
$^{{\rm c}}$
The listed numbers are mean residuals multiplied by 1000. Units are dex.
$^{{\rm d}}$
This is the net correction for data with uncertain zero points, and has been averaged from the two entries just above.

3 Producing the catalog

3.1 Choosing analyses

3.2 Initial corrections

3.3 Data averaging and input rms errors

3.4 Statistical testing for systematic offsets

		Mean
$\phantom{{\rm ^a}}$ Statistic ${\rm ^a}$	$\phantom{{\rm ^b}}\nu{\rm ^b}$	$\phantom{{\rm ^c}}$ residual ${\rm ^c}$
N(no) - W(yes)	42	$+9 \pm 19$
W(no) - W(yes)	91	$-8 \pm 7\phantom{0}$
Net correction ${\rm ^d}$	113	$-5 \pm 6\phantom{0}$
N(all) - W(all)	135	$-5 \pm 9\phantom{0}$