Clustering spectra according to the factor coefficients . 76

First inspection of the stars in the{a₁;a₂}plane shows three major groups.

The biggest one, however, may be splitted into two smaller ones. We ordered our stars, therefore, into four groups. In order to find the members of the groups we carried outk-means clustering (see e.g. Murtagh and Heck, 1987).

After finding the group members we computed the average spectra within the groups.

Since similar spectra mean similar factor coefficients the average spectra within the groups may serve as templates for further classification. Fig.

5.3a-d show the template spectra obtained in this way.

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Figure 5.1: The first (solid line) and second (dotted line) most significant factors resulted from the principal components analysis. The two factors are orthogonal i.e. ^R e₁(λ)e₂(λ)dλ = 0. The observed spectra can be represented as linear combinations of the factors: S(λ) =a₁e₁(λ) +a₂e₂(λ). The factors are normalized to unit standard deviation and zero mean value and this explains the range and scale on the vertical axis in the Figure.

a2

a1

0 .2 .4 .6 .8 1

0 .2 .4 .6 .8 1

Figure 5.2: Distribution of the factor coefficients on the {a1;a2} plane. If the spectra are well represented by the first two factors a²₁ +a²₂ is close to the unity. The Figure clearly shows that the vast majority of the points approaches closely the unit circle confirming the validity of the two-factor representation of the original spectra. Some points, however, are well inside this circle. Inspection them individually reveals that they are underexposed noisy spectra.

5.4.3 Classification of the mean spectra

To identify different features on our mean spectra obtained in the previous paragraph we used templates given in the Bonner Spectral Atlas (Seitter, 1975). In order to get accurate spectral types for the template spectra we compared them with the spectra listed in the spectral library of Jacoby and Hunter (1984). Spectra in the library having similar strength of the char-acteristic lines to those of our program stars have intensity maxima shifted systematically towards shorter wavelengths. The shift of the intensity max-ima of the template spectra in comparison with the library spectra of similar line strength can be accounted for the effect of interstellar reddening. Mul-tiplying the library spectra with the Whitford’s reddening law (Whitford , 1958) and varying the value of the visual absorption A_V gives a much better fit for our template spectra.

Spectrum of group 1: A conspicuousHβline is visible in absorption. Nev-ertheless, one cannot recognize Hαbecause it would be near to the red edge of the spectrum which is somewhat underexposed. Otherwise the spectrum is dominated by neutral metallic lines (FeI, MgI,). There is some suspect for the NaI/5890−96˚A doublet. The best matching library spectrum is A8.

Spectrum of group 2: TheHβ line is nearly as conspicuous as atgroup 1..

In the contrary, the FeI and MgI lines in the 5160−90˚A range are definitely stronger than in the previous case. The NaI/5890−96˚A doublet is clearly visible. Following the same procedure as before we obtainedF6spectral type.

Spectrum of group 3: The strength of the neutral metallic lines increases in comparison with the previous groups. There is some hint for theHβline in absorption. The NaI/5890−96˚A doublet is very pronounced. The resulted spectral type is G9.

Spectrum of group 4: The appearance ofHβ is similar togroup 3but the characteristic metallic lines are more enhanced. The shift of the intensity maximum towards the red corresponds to the enhancement of the neutral metallic lines so it might be accounted for the differences of effective temper-atures between the template spectra of groups 3 and 4. Applying the same procedure as in the case of previous groups we gotK8 for this template.

Fig. 5.3 shows the mean spectra obtained by averaging within the groups obtained.

The spectral type and effective temperature of the template spectra and the mean values of factor coefficients within the four groups define a relation-ship which enables us to assign spectral types and effective temperature to all of the program stars, after obtaining the coefficients from factor analysis.

Based on the spectral types obtained and the V and BV data of Kun and P´asztor (1990) we calculated the interstellar reddening for our program stars.

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Figure 5.3: a-d: Spectra obtained by averaging within the groups defined by clustering the stars on the {a₁;a₂} plane. The physical parameters of the spectra are summarized in Table 5.2.

Table 5.2: Physical parameters of the groups obtained Group Tef f(K^o) Sp B−V EB−V a1 a2

1 7500 A8 0.70 .47 .90 .36

2 6000 F6 1.03 .53 .85 .49

3 5300 G9 1.78 .98 .64 .71

4 3920 K8 2.04 .90 .36 .87

Averaging the interstellar absorption within the spectral groups defined we got the mean reddening for the template spectra. Table 5.2 summarizes the spectral type, effective temperature and interstellar absorption of the tem-plate spectra obtained and Table 5.3 gives these data for the program stars, along with α, δ and V listed in the paper of Kun and P´asztor (1990).

Inspecting the data of Table 5.2 reveals that the reddening is lower in groups 1 and 2 and higher in groups 3 and 4. This means that the ba-sic phyba-sical parameter responsible for the differences between the template spectra is a combined effect of the reddening and the effective temperature.

It is worth mentioning that the reddening obtained from fitting the templates with the library spectra is systematically lower by about 0.2 mag than those obtained from the V and BV photometric data.

Although all of our program stars were picked up in previous surveys by some suspectedHαemission on small scale spectra the template spectra show no definitive evidence forHαemission. However, it is quite usual at repeated small scale spectral surveys on the same field that stars which were detected at the first coverage do not show any remarkable evidence of emission on the next occasion. Repeated small scale spectral observations revealed that the correlation length in time of the suspectedHα emission is in the order of few days (Bal´azs et al., 1987). Among our 35 program stars only Kun 193 shows very strong Hydrogen emission (Fig. 5.4).