5 Quality control

To check the reliability of our data and reduction we used the following tests: (1) analyze the inter-comparison of repeated observations and analyze internal consistency, (2) compare fully reduced spectra with other libraries and (3) compare Lick indices for stars with published measurements.

We investigated three possible sources of discrepancy: (1) errors on the instrumental response and/or correction of atmospheric extinction are likely to result in low and intermediate spatial frequencies variations. (2) inaccurate subtraction of the diffuse light may be diagnosed as significant mismatch of the strongest lines and (3) inaccurate correction for the blaze will lead to oscillations with a one-order period.

5.1 Internal consistency

5.1.1 Multiple observations of the same star

There are in total 358 repeated observations for 104 stars in the archive. After giving a double weight to the observations in the runs for which the run-dependent response was computed from primary calibration and half weight to the observations done with an airmass larger than 1.5 (their photometric quality is lower because of the differential refraction), we find a global rms dispersion for the pairwise comparison of about 3.5%, see Fig. 4. Without weighting, the dispersion is 4% and the difference was a hint of the lowest photometric quality of high airmass observations, hence leading to suspicion about the refraction corrector. Since it is a pairwise comparison, the mean photometric error on individual observations is: $3.5 / \sqrt{2} = 2.5\%$. (Note that this error does not account for possible systematic errors affecting uniformly the whole archive, this will be discussed in Sects. 5.2 and 5.3).

Most of the photometric errors lie in the residual "curvature'' of the spectra. After subtracting a third degree polynomial from each pairwise comparison, the rms dispersion becomes 0.7%, corresponding to a mean photometric precision of 0.5%, in full agreement with the mean S/N ratio. No hint for a modulation at the scale of one order of the echelle spectra is found.

5.1.2 Modeled spectra

Random errors on the strengthening of the spectra are probably on average smaller than 0.5% because otherwise they would increase the dispersion of the pairwise internal comparison (after the third degree polynomial is subtracted).

The new version of the TGMET program that will be described in a separate paper allowed us to generate interpolated spectra for a given position in the ( $T_{\rm eff}$, $\log~g$, [Fe/H]) space. The difference between the spectra in the archive and these modeled spectra can potentially uncover possible random errors on the strengthening.

Therefore we computed and averaged the differences to the modeled spectra for all the spectra in the archive. The mean residuals were searched for a modulation at the scale of one order, either in the spectrum or in its Fourier transform. We did not detect any signal. We made simulations that suggested that a 0.5% (rms) modulation would probably have been detected, but a 0.2% modulation would not.

5.2 External comparisons

The comparisons between our physically calibrated spectra and other libraries were used in the previous section to compute the correction to the instrumental response. The goal was to determine the variation of the response at the scale of 1 to 5 nm that was not constrained by the primary calibration. Therefore, by construction, the mean external comparison is flat (i.e. may only vary smoothly with the wavelength). A careful analysis of the individual comparison could assess the level of stability of the instrumental response.

The patterns in the correction to the instrumental response were consistently found in the different individual comparisons and no significant effect was found after this correction was applied. However, the scarcity of the available comparisons did not allow us to measure a photometric precision.

5.3 Comparison of Lick indices

The Lick indices (see e.g. WO97) measure equivalent widths of features defined in bands of 2 to 5 nm (hence of the width of about 1/2 or 1 order of the echelle spectra). Their measurements are then sensitive to both incorrect strengthening of the spectra and errors in the instrumental response.

The spectral range of the Elodie archive allowed us to measure most of the Lick indices. Only the blue CN indices are missed as well as the H$\delta$indices (H $\delta_{\rm A}$ and H $\delta_{\rm F}$) defined in WO97.

We used the definitions from WO97 or Cardiel et al. (1998) to measure the indices for all the spectra in the archive. The results are reported in Table 1 (given in the electronic version only).

The measurement errors computed from the photon noise (see e.g. Prugniel et al. 2001) is in the present case negligible because of the extremely high S/N per Å. The main source of error is due to the photometric calibration and may be systematic. The comparison of the Lick indices measured in WO97 constrain the magnitude of these systematic errors.

The archive has 102 stars which have been previously measured in WO97. The comparisons are reported in Table 2.

 

 

Table 2: Comparison of Lick indices: Col. 1: Name of the Lick index Col. 2: Number of spectra used for the comparison Col. 3: Mean value of the index Col. 4: Mean shift (Elodie) - (WO97) Col. 5: rms dispersion of the comparison Col. 6: Majorant of photometric error

Index	#	Mean	Shift	rms	Error
Ca4227	101	0.689	-0.091	0.278	-0.0073
G4300	102	3.858	0.083	0.464	0.0024
H $\gamma _{\rm A}$	102	-1.765	0.392	0.527	0.0089
H $\gamma_{\rm F}$	99	0.678	0.177	0.337	0.0084
Fe4383	102	2.715	-0.341	0.692	-0.0067
Ca4455	101	0.723	-0.267	0.250	-0.0118
Fe4531	101	2.299	-0.078	0.335	-0.0017
Fe4668	102	2.214	-0.183	0.712	-0.0021
H$_\beta$	103	2.706	0.061	0.192	0.0021
Fe5015	102	3.393	-0.197	0.449	-0.0026
Mg1	103	0.040	0.003	0.011	0.0030
Mg2	103	0.125	-0.005	0.011	-0.0054
Mgb	100	2.335	0.117	0.247	0.0036
Fe5270	100	1.777	-0.088	0.254	-0.0022
Fe5335	102	1.515	-0.035	0.279	-0.0009
Fe5406	103	0.895	0.076	0.279	0.0028
Fe5709	101	0.505	-0.046	0.187	-0.0020
Fe5782	101	0.313	-0.095	0.168	-0.0047
NaD	103	1.415	-0.165	0.408	-0.0051
TiO1	103	0.006	-0.006	0.011	-0.0057
TiO2	103	0.011	0.005	0.009	0.0054

We do not find systematic effects that would result from errors in the instrumental errors and the residual dispersions are compatible with the errors in the WO97 measurements (the internal error due to the photon noise in the archive is totally negligible).

The systematic shifts are always smaller than the dispersion except for Ca4455 (where it is equal) and for Fe4383 the shift may be significant. However, we cannot attribute this to an error in our measurements and in particular we note that the shift for Fe4383 is similar to the one found by WO97 when they compared the original Lick measurements with the spectra of the Jones library (note that our flux calibration is not fully independent from the Jones library since this latter was used among others to correct the instrumental response). The Ca4455 index is not in the range of the Jones spectra and we cannot comment of the shift we found. Figure 5 presents the distributions of the differences (us - WO97) for two indices: Mg₂ and H $\gamma _{\rm A}$. The first one is very important for extragalactic studies, it is defined on a broad region (53 nm between the extrema of the red and blue side-bands). Though it is potentially sensitive to the uncertainties on the flux calibration described above, the agreement between us and WO97 is excellent. The second index presented in Fig. 5, H $\gamma _{\rm A}$, is narrower (14 nm) but it is located in the blue region of our spectra where our calibration is probably less accurate. There is a systematic shift with respect to WO97, but the rms residual is fully accounted for by the errors on WO97.

Figure 5: Comparison of Lick indices Mg2 and H $\gamma _{\rm A}$ with WO97. The abcissae are the difference (Elodie - WO97) between the Lick indices. The top panels show the distribution as a function of the value in WO97, and the bottom panels the histograms of the differences