2. Definition of spectral criteria
Our study is based on spectra obtained with the photoelectric spectrum scanner designed at Astronomisches Institut at Bochum (used with a resolution of about 10Å, the wavelength range about 3500-8500Å). The scanner has been attached to the 61cm Cassegrain telescope of the University of Bochum, which is located at the European Southern Observatory at la Silla, Chile. An available sample of 54 F-G-K MK standard stars are used in our analysis (some peculiar or binary stars according to Hoffleit, 1982, have been excluded). Table 1 contains the list of our stars together with the most reliable published data. The main source of MK types is the catalogue of Garcia (1989) where the MK data were compiled in accordance with the recommendations by the authors of the MK system (Morgan and Keenan). Other MK sources are (in order of preference) the following: a) recent refined MK classification by Keenan and McNeil (1989), Gray and Garrison (1989) and Gray (1989); b) MK types selected in the Simbad database, operated at Strasbourg Centre de Donnees Stellaires. All photometric data were taken from the Simbad database. The source of [Fe/H] is the catalogue of Cayrel de Strobel et al. (1992) with an extension compiled by Malyuto (1994). As in Paper I, each measurement in our analysis refers to an area confined by the border wavelengths for an interval, the spectral energy distribution and the zero level. To choose the intervals for measurements and to define criteria for our analysis, the following sources were consulted:
Table 1. The list of the MK standard stars used in the analysis
1) Many strong lines and bands measured by means of narrow-band photoelectric photometry and used by different authors as temperature and gravity criteria (the references were taken from the lists by Straizys, 1992).
2) Classification criteria chosen from an analysis of those objective prism spectra (Seitter, 1975, Bartaya, 1979, Jimsheleishvili, Malyuto, 1981) whose resolutions (3-10Å) are similar or somewhat higher than in the case of our data.
3) Intervals chosen by visual inspection of our own spectral scans of MK standard stars revealing a clear dependence on spectral or luminosity class.
4) The intervals chosen by a similar inspection as in the previous paragraph, but of spectra (resolution about 6Å) obtained with a CCD camera (Corral et al., 1994).
We chose the intervals for measurements in a such way that the sensitivity to spectral and/or luminosity effects were different for two adjacent or near-by intervals. The ratios of measurements in such intervals may then serve as classification criteria (indices) with minimum contamination by interstellar extinction. The differences in the mean wavelengths for each ratio do not exceed 90Å, l and the appropriate reddening effects in the ratios reach 2% only in a few extreme cases. Table 2 contains the border wavelengths for the intervals with indications of the principal measured features. We used the Catalogue of Solar Spectrum (Moore et al., 1966) to identify the features. An example is presented in Figs. 1a-1b. Each interval includes at least four channels of 10Å each. Table 3 contains the list of classification indices. Two of them (No. 2 and 4) are the same as the quantities and in Paper I, respectively.
Table 2. The border wavelengths for the intervals in Å
Table 3. The classification indices (the ratios of measurements in the intervals)
The internal accuracy of the indices was estimated from repeated measurements (two stars have been measured four times, four stars have three times and three stars two times). The averaged rms errors of one measurement for each index (expressed in percent) are given in Table 3. The accuracies of these errors have been estimated, too. We see that these estimates seem to be real and show good internal consistency (about 1 per cent on the average). Table 4 contains the averaged values of the classification indices used in our analysis.
To analyse our measurements as a function of MK classification, the discrete values of MK spectral and luminosity classes were transformed into numerical codes which vary continuously. The numerical spectral codes for spectral classes were the same introduced earlier by West (1970): F0 = 4.0, G0 = 5.0, K0 = 6.0. For MK luminosity classes we used the following luminosity codes : V = 7.0, IV = 6.0, III = 5.0, II = 4.0, Ib = 3.0, Iab = 2.0, Ia = 1.0, IaO = 0.5. To check how these codes are connected with the continious main physical parameters, we plotted effective temperatures against spectral codes for MK luminosity classes V, III and I (Fig. 2), and absolute magnitudes against luminosity codes for MK spectral classes F0, G0 and K0 (Fig. 3) from the MK calibration by Schmidt-Kaler (1982). These figures show that the dependences are different but they are rather smoth. It means that, if necessary, one may relate codes with these main physical parameters. However we prefer to use here the MK types which are directly determined physical parameters. The diagram "Spectral codes against luminosity codes" for our standard stars is presented in Fig. 4. We see that the stars are rather uniformly distributed along the spectral and luminosity classes.
Our standards are classified in the literature as normal stars in the MK system (see Table 1); therefore we may suggest that these stars have nearly normal metallicities. In fact the [Fe/H] values are known from the literature for the majority of them (see the same Table) and indeed a few stars only have moderate metal deficiency ([Fe/H] between -0.3 and -0.6). We found no metallicity effects in our diagrams. Therefore with good reason the metallicity parameter may be ignored in the present analysis.
The results of measurements were presented in the form of diagrams "indices against spectral codes". Two examples may be found in Paper I. Some indices are sensitive mainly to spectral class, whereas other ones are responsive also to luminosity class. It seems reasonable to combine the indices which behave similarly respect to spectral and luminosity classes. Judging from the diagrams "indices against spectral codes", the indices 3. 4 and 6 (see Table 3) were averaged (each of them is sensitive to spectral class but only slightly dependent on luminosity class), the quantity
is treated as the spectral class index. In Fig. 5 the index was plotted against spectral classes (codes). We see that this index is connected very tightly with spectral class except for supergiants which deviate slightly and are more scattered.
We found unreasonable to combine the indices sensitive to luminosity class because of their different behaviour in the diagrams "indices against spectral codes" and we treated them individually. For three indices (No. 1, 2 and 5 in Table 3, which are most sensitive to luminosity effects) the quantities
were calculated and are considered here as luminosity class indices.
Our experience with classification indices (Malyuto, Oestreicher, Schmidt-Kaler, 1996) has shown that two-index diagrams (one index against the other) are well suited for classification purposes, if a luminosity sensitive index is plotted against a temperature sensitive one (the luminosity effects are more pronounced and the data scatter are smaller than in case of diagrams "indices against MK spectral codes"). In two-index diagrams both measurements are performed almost simultaneously and therefore possible spectral variations only slightly influence these diagrams. One uncertain physical parameter (MK spectral class) is not involved in diagrams if we are interested only in determination of luminosity classes.
In Figs. 6, 7 and 8 the two-index diagrams are given where luminosity sensitive indices , and , respectively, were plotted against the spectral type indice . We see that the two-index diagram in Fig. 6 are useful only in separating supergiants from other stars. The luminosity effects are more pronounced in Figs. 7 and 8 and the corresponding diagrams may be used in determining luminosities if (for G-K spectral classes if we judge from Fig. 5).
© European Southern Observatory (ESO) 1997
Online publication: April 28, 1998