3 Atmospheric parameters

3.1 Input parameters

The vast majority of the reference stars which form the library were selected in the catalogue of [Fe/H] determinations (Cayrel de Strobel et al. 1997). A few others are from the list of proper motion stars of Carney et al. (1994). The [Fe/H] catalogue provides near 6000 determinations of ($T_\mathrm{eff}$, $\log g$, [Fe/H]) from detailed analyses of high resolution, high S/N spectra for 3248 stars. For each star, several different values are listed for their atmospheric parameters. The difficulty of finding the "true" parameters for a given star can be illustrated by the case of the well-known deficient sub-giant HD 140283. Its first detailed analysis was performed by Chamberlain & Aller (1951), and since then 28 detailed analyses have been reported, quoting $T_\mathrm{eff}$ from 5362 K to 6300 K, $\log g$ from 3.2 to 4.8 and [Fe/H] from -1.04 to -3.06, with standard deviations of 111 K, 0.39 and 0.23. A simple average is not correct since all the analyses do not have the same weight. It is also worth noting that $T_\mathrm{eff}$ and $\log g$ quoted in detailed analyses are often the values of the model atmosphere chosen to deduce the iron abundance and are not obtained directly from spectroscopy. It is thus quite difficult to know which parameters should be adopted for a given star. The [Fe/H] catalogue is complete up to december 1995, and several recent references including new atmospheric parameters have been added to our list of determinations: Carney et al. (1994), Alonso et al. (1996b), Pilachowski (1996), Gratton et al. (1997), Nissen & Schuster (1997), Nissen et al. (1997), Thévenin (1998). The sample of Carney et al. is not in the [Fe/H] catalogue because the metallicity estimations rely on low S/N spectra. The sample of Nissen et al. includes photometric metallicities and surface gravities derived from Hipparcos parallaxes. The study of Alonso et al. is not based on spectroscopy but concerns only effective temperatures calibrated with the InfraRed Flux Method. As temperature is the parameter which shows the largest scatter between the authors, two independant calibrations of $T_\mathrm{eff}$ were also used: $T_\mathrm{eff}$ versus V-K and [Fe/H] and $T_\mathrm{eff}$ versus b-y, c₁, [Fe/H] (Alonso et al. 1996a). The V-K colour indices were found for 70 stars in the catalogue of Morel & Magnenat (1978). Both b-y and c₁ were found for 143 stars in the catalogue of Hauck & Mermilliod (1998). The references which appear the most often for this sample are Thévenin (1998) for 128 stars, Gratton et al. (1997) for 70 stars, McWilliam (1990) for 62 stars, Alonso et al. (1996b) for 64 stars, Axer et al. (1994) for 32 stars, Pilachowski (1993) for 27 stars, Edvardsson et al. (1993) for 24 stars, Tomkin et al. (1992) and Luck & Challener (1995) for 19 stars. The determinations of these different authors were compared to uncover any systematic offsets in the various photometric and spectroscopic data sets. There were none: values for individual stars present scatter, but there are no systematic trends between these authors.

  

Figure 1: Histogram of the rms of the determinations of $T_\mathrm{eff}$ from the literature and photometry for the 211 standards

We first computed a weighted mean of the different determinations with higher weight for recent determinations (after 1990) and lower weight for old ones (before 1980 when solid state detectors were not yet available). The weighted root-mean square (rms) of the different determinations measures their agreement. The histogram of the rms for each parameter is shown respectively in Figs. 1 to 3. Figure 4 shows the histogram of the number of [Fe/H] determinations per star. For the majority of the standards the determinations are in a reasonable agreement, but large discrepancies can also be seen for several stars. The situation is particularly worrisome for temperatures which appear to be that parameter the most delicate to determine. As it is difficult to find an objective criterion to keep some determinations and to eliminate others, we had to think of another way to find the best parameters for the reference stars. The availability of high S/N spectra at the same resolution for all these stars provided a useful support to perform an internal check of the library by comparing standards of the same type, and to adjust their parameters until reaching the self-consistency of the library. The method TGMET developed for the on-line determination of atmospheric parameters of anonymous stars, presented in Paper I, offered the opportunity to realise the comparison between the spectra in a quantitative way.

  

Figure 2: Histogram of the rms of the determinations of $\log g$ from the literature for the 211 standards

  

Figure 3: Histogram of the rms of the determinations of [Fe/H] from the literature for the 211 standards

  

Figure 4: Histogram of the number of [Fe/H] determinations per standard

3.2 Final parameters

The TGMET software, presented in Paper I, provides a criterion of resemblance between two spectra and an estimation of the atmospheric parameters of a target star. The estimation is performed by comparing the target spectrum to each reference spectrum following three steps. The first one is the convolution of all spectra to exactly the same resolution. The degradation of the resolution is performed to eliminate the effects of different projected rotational velocities when comparing two stars, and slight modifications of instrumental resolution between observational runs. A value of 13 $\mathrm{km~s}^{-1}$ (FWHM) was chosen because it corresponds to the reference star having the lowest resolution (instrumental + intrinsic). The wavelengths of the reference spectrum are then shifted to make its absorption lines coincide with those of the target spectrum. The third step is a flux adjustment, order by order (on the 15 most significant ones), pixel by pixel, by the least square method. We use a criterion of resemblance, which is equivalent in practice to the reduced $\chi^2$. The reference stars presenting the lowest reduced $\chi^2$ are kept for the solution. The estimated parameters of the target star are given by the weighted mean of the parameters of the best reference stars. The aim of the method is eventually to find in the library a twin of the target star, or several standards with very similar spectra.

When testing each reference spectrum against the rest of the library, it was found in a few cases that spectra with significantly different atmospheric parameters were found to be very similar. As the atmospheric parameters of the reference stars are the result of the weighted mean described in the previous paragraph, it is not surprising to have such discrepancies. Standard deviations of 145 K in $T_\mathrm{eff}$, 0.35 in $\log g$ and 0.18 in [Fe/H] were obtained for the distribution of the "mean literature" parameters versus "TGMET" parameters, with extreme discrepancies reaching 421 K, 1.27 and 0.49. The discrepancies have two main sources. The first one is the inhomogeneity of the parameters from the literature, the mean of which can lead to erroneous values, as described in the previous section. The second one is the inhomogeneity of the distribution of the reference stars in the 3D space of the parameters. The library is not a perfect 3D grid with equal spacing between the points. There are several sparse parts, especially among metal-poor stars and cool dwarfs. These holes in the library correspond to the absence of certain kinds of stars in the [Fe/H] catalogue which are difficult to observe or to analyse. When it occurs in these parts of the library, a given star might not have an analogue, and its nearest "neighbour" might be quite far. If this source of discrepancy can only be eliminated by filling the library with new reference stars of various parameters, the problem of inhomogeneous parameters can be partially solved by using TGMET iteratively on each standard. By slightly modifying the parameters of the reference stars, step by step, identical parameters should be found for twin spectra. The correction which can be applied to the initial parameters depends on the consistency of the determinations in the literature and on the proximity of the neighbours. No correction was applied in three cases. The first one concerns the only star which is supposed to have perfectly known parameters: the Sun. The second case concerns 22 stars which do not have close neighbours in the library, or whose parameters put them at the edges of the 3D space. The third case concerns stars for which the solution given by TGMET was satisfactory, that is the difference between the solution and the library parameters was smaller than 100 K, 0.5 and 0.3 respectively for $T_\mathrm{eff}$, $\log g$ and [Fe/H]. These values were adopted as a reasonable scatter inherent to the method and the library. A limit to the correction was also fixed, depending on the reliability of the initial parameters. A level of quality was attributed to the starting point: high for many recent determinations in a good agreement, medium for several determinations with a significant scatter or very few recent ones, poor for old determinations or large scatter. There are only 8 standards of high quality, with at least 6 recent determinations showing a dispersion lower than 75 K, 0.4 and 0.15 in $T_\mathrm{eff}$, $\log g$ and [Fe/H]. The corresponding limit of correction in $T_\mathrm{eff}$ was 100 K for good reference stars, 200 K for medium ones and 250 K for poor ones. In all cases the maximal correction in $\log g$ was 1. and 0.5 in [Fe/H] with respect to the initial values. The corrections were performed step by step by computing the difference between the input parameters and the output parameters. The steps were respectively 50 K, 0.1 and 0.05 for $T_\mathrm{eff}$, $\log g$ and [Fe/H]. The parameters converged after 6 iterations. Among the high quality standards, only 3 were slightly corrected by an amount of 50 K in $T_\mathrm{eff}$. Figures 5 to 7 show the distribution of the input parameters versus final parameters.

  

Figure 5: Final $T_\mathrm{eff}$, obtained after 6 iterations of TGMET, versus input $T_\mathrm{eff}$, deduced from the literature, for the 211 standards of the library

  

Figure 6: Final $\log g$, obtained after 6 iterations of TGMET, versus input $\log g$, deduced from the literature, for the 211 standards of the library

  

Figure 7: Final [Fe/H], obtained after 6 iterations of TGMET, versus input [Fe/H], deduced from the literature, for the 211 standards of the library

Some 44% of the temperatures were corrected, 11% of the gravities and 7% of the metallicities. This confirms that temperature is a very delicate parameter to estimate in spectroscopy and that its influence on the spectral profile is predominant. On the contrary, the correction of metallicities was insignificant, showing that the weighted mean of the determinations found in the literature was satisfactory. Figure 7 in Paper I shows how the 211 standards of the library are distributed in the plane ($T_\mathrm{eff}$, [Fe/H]) by intervals of gravity. The run of TGMET on the standards showed that the best solar analogue in this sample is HD 186427.

The final parameters are listed in Table 1 which includes the following columns: identifiers BD/HD and HIP, spectral type, equatorial coordinates (ICRS, epoch J1991.25), V magnitude, parallax and standard error in mas, ICRS proper motions and standard error in mas/yr, ELODIE radial velocity, final atmospheric parameters ($T_\mathrm{eff}$, $\log g$, [Fe/H]), level of reliability of the atmospheric parameters from 1 (poor) to 4 (high), bolometric (or visual) absolute magnitude, distance (if the relative error on parallaxe is lower than 30%), distances at plus and minus one sigma, components of the spatial velocity (U, V, W) with respect to the Sun.

Acknowledgements

Our thanks go to all the observers who let us include in the library their spectra taken with ELODIE. We are grateful to Claude Catala and Jean-Claude Bourret for making some observations especially for this program.