Testing TGMET

The first test was to remove one by one each reference star of the library, treat it like an anonymous object, then compare the estimated parameters and the true ones. This test was performed iteratively to adjust the atmospheric parameters of the reference star as described in paper II. The overall resulting standard deviation of the estimated versus ``true'' parameters for this high S/N sample is respectively 86 K, 0.28 dex, 0.16 dex for $T_\mathrm{eff}$ , $\log g$ and [Fe/H].

Several phenomenae influence the results. In metal-rich stars, the amount of spectral information is greater than in almost line free stars. In the same way, stars cooler than 5000 K are losing the Stark profile of the wings of their hydrogen lines. Therefore the uncertainities on the determination of the parameters is greater for the cool and metal-deficient stars than for the hot and metal-rich stars. To take this effect into account, the library was divided in four zones (from A to D, see figure 7) and the mean error was calculated as well as the dispersion in each zone and for each parameter. The results are listed in Table 1.

Because our ultimate goal is to use low S/N ( $\sim$ 10) spectra, the spectra of the library were degraded at S/N = 10 by adding a random (Poisson) noise. The mean error and the dispersion in each zone were recalculated. The results are listed in table 2.

To be sure that no bias has been introduced with the artificial noise (such as correlation between pixels), the software was tested with 30 stars of well known parameters (some of them already belonging to the library), observed willingly at low S/N. Figure 8 shows the difference between the true and the estimated parameters as a function of the S/N of the object star.

Table: Statistics on the self-concistancy of the library at mean S/N = 100.
Zone sum A B C D

number of star 211 87 63 33 28

$<\Delta T_\mathrm{eff}\gt$ 17 11 9 54 11

$\sigma_{T_\mathrm{eff}}$ 86 74 63 131 87

$<\Delta \log g\gt$ 0.04 0.03 0.03 0.06 0.06

$\sigma_{\log g}$ 0.28 0.25 0.20 0.43 0.28

$<\Delta$ [Fe/H]> 0.02 0.00 0.00 0.07 0.04

$\sigma_{[Fe/H]}$ 0.16 0.14 0.14 0.20 0.19

**Table:** Statistics on the self-concistancy of the library at mean S/N = 100.
Zone	sum	A	B	C	D
number of star	211	87	63	33	28
$<\Delta T_\mathrm{eff}\gt$	17	11	9	54	11
$\sigma_{T_\mathrm{eff}}$	86	74	63	131	87
$<\Delta \log g\gt$	0.04	0.03	0.03	0.06	0.06
$\sigma_{\log g}$	0.28	0.25	0.20	0.43	0.28
$<\Delta$ [Fe/H]>	0.02	0.00	0.00	0.07	0.04
$\sigma_{[Fe/H]}$	0.16	0.14	0.14	0.20	0.19

Table: Statistics on the self-concistancy of the library at S/N = 10.
Zone sum A B C D

number of star 211 87 63 33 28

$<\Delta T_\mathrm{eff}\gt$ 10 12 -4 50 -9

$\sigma_{T_\mathrm{eff}}$ 102 84 78 158 99

$<\Delta \log g\gt$ 0.03 0.00 0.04 0.08 0.05

$\sigma_{\log g}$ 0.29 0.24 0.21 0.45 0.31

$<\Delta$ [Fe/H]> 0.02 0.00 0.00 0.07 0.08

$\sigma_{[Fe/H]}$ 0.17 0.14 0.14 0.22 0.18

**Table:** Statistics on the self-concistancy of the library at S/N = 10.
Zone	sum	A	B	C	D
number of star	211	87	63	33	28
$<\Delta T_\mathrm{eff}\gt$	10	12	-4	50	-9
$\sigma_{T_\mathrm{eff}}$	102	84	78	158	99
$<\Delta \log g\gt$	0.03	0.00	0.04	0.08	0.05
$\sigma_{\log g}$	0.29	0.24	0.21	0.45	0.31
$<\Delta$ [Fe/H]>	0.02	0.00	0.00	0.07	0.08
$\sigma_{[Fe/H]}$	0.17	0.14	0.14	0.22	0.18

**Figure:** Difference between true and estimated parameters ( $T_\mathrm{eff}$ : upper part, $\log g$ : center part, [Fe/H] : lower part) versus S/N for 30 well-known stars used as test stars. Star symbols flag the stars already belonging to the library and which have been reobserved for the purpose of this test at a lower S/N.
$\begin{figure} \resizebox {8cm}{!}{\includegraphics{paper1fig8.ps}}\end{figure}$

The computing time for TGMET is about 10 min, when run in parallel with the aquisition and reduction softwares, on the SUN-sparc 20 station devoted to the observations with ELODIE.