2 Technique of the spectral classification

The process of spectral classification of O-M stars on the basis of UBV data is carried out as follows. First of all it is necessary to construct a reliable dependence of colour excesses of stars on intrinsic distance modulus along a given direction. The practice of research of interstellar light absorption (e.g. Urasin et al. 1989) proves that for construction of such a dependence towards the Galactic periphery it is enough to know magnitudes and spectra of stars up to V=15 mag only. Of course this absorption curve like the one shown in Fig. 1 can be successfully used not only for spectral classification of stars brighter than V=15 mag, but also for fainter stars. The present technique is based on the Q-method which is equally applicable for classifying both bright and faint stars with a difference caused by the different level of photometric measurements errors.

Figure 1: Individual (dots) and smoothed (solid line) colour excesses E(B-V) versus intrinsic distance module V0 - MV for stars brighter than V=14 mag in a direction of NGC 2244

Thus, using absorption curves derived from photometric values and spectra of one or two hundred stars brighter than 14-15 mag, it is possible to extend spectral classification on many hundreds and even thousands of stars taking advantage of a sharp increase of star numbers with a growth of star magnitudes. For the determination of bright star spectra it is possible to use either photometric (e.g. Strayzis 1977; Urasin 1973; Urasin et al. 1989) or spectrographic methods (e.g. Voroshylov et al. 1985; Kuznetsov 1978; Kharadze & Bartaya 1960; Johnson & Morgan 1953; Walker 1956; Young 1978). The most simple is a photometric method whose features are described by Urasin (1973), Urasin et al. (1989). In this case the spectra of O-B6 stars to be used later for absorption curve construction are determined unequivocally by the Q-method. This gave an opportunity to investigate interstellar absorption in the Milky Way in an interval of galactic longitudes 7 - 222⁰ and distances up to 10 kpc from the Sun using UBV photometry data alone (Urasin et al. 1989).

In some rare cases, construction of absorption curves towards the periphery of the Galaxy meets certain difficulties and can appear inconvenient. The origins of these difficulties should be studied and used for elaboration of criteria useful for spectral classification. For example, according to the data by Williams & Cremin (1969), a dense dust cloud is located just beyond the open cluster NGC 2264 along a line of sight, shielding light of background stars. At shorter distances stars are practically not subject to absorption. Average colour excess E(B-V) of these stars is 0.08 mag (Arshutkin et al. 1990). At the same time, according to Arshutkin et al. (1990), Khalandadze et al. (1986), Cohen & Kuhl (1979), on distances between the cluster and the cloud there exist stars with large colour excesses which are one order higher than E(B-V). The method of the spectral classification described in the present study allows us to take advantage of such features in distribution of absorbing matter thus excluding multiplicity in spectral estimates of stars at fixed Q_UBVvalue.

For construction of reliable absorption curves the open cluster members should be excluded from the analyzed sample of stars because random errors of determination distances to the cluster members can exceed a linear size of the cluster by one or two orders. As a consequence E(B-V) and (V₀ - M_V) values for members instead of being concentrated in practically one point on absorption curves are found to be rather heavily scattered along the axis of the intrinsic distance module (Kuznetsov 1978). This circumstance markedly biases behaviour of the absorption curve which is the principal element of the present method of spectral classification based on UBV photometry. Due to the influence of cluster members on the character of the absorption curve plot, the latter can go almost horizontally for some distance. This so called effect of the "horizontal bar'' was earlier explaining only by the influence of observational selection (Voroshylov & Khalandadze 1983).

Rather strong influences on absorption curve plot are caused by existing distinctions in scales of absolute magnitudes of main sequence (MS) and zero-age-main-sequence (ZAMS) stars. In practically all previous studies on research of the Galaxy structure in directions of young open clusters, star-forming regions, and OB-associations, the absolute magnitudes of these stellar group members were determined the same way as for field stars, that is using the MS scale.

In Table 1 absolute magnitudes M_V(ZAMS) were determined on the ZAMS scale and these values for members of young stellar groups are compared with those given in the MS scale available for field stars. For the spectral interval O-A0 we used Schmidt-Kaler (1982) data. One can see that the differences of absolute magnitudes $\Delta M_V=M_V\mbox{(ZAMS)} - M_V\mbox{(MS)}$ are positive and vary from +0.5 to +1.0 mag. In the plot of the absorption curve the (V₀ - M_V) values of young stellar group members will be systematically shifted on 0.5 - 1.0 mag larger distances, which substantially increases the scale of distances in the Galaxy. Using the Schmidt-Kaler (1982) tables of intrinsic distance module transformation to linear distances it is easy to calculate systematic errors in distances r (Table 2). Calculations show that a maximum "stretching'' of the scale of distances up to 60% is expected at M_V =+0.5 and M_V = +1.0 mag.

 

 

Table 1: Differences $\Delta M_V=M_V\mbox{(ZAMS)} - M_V\mbox{(MS)}$of absolute magnitudes M_V(ZAMS) and M_V(MS) related to the ZAMS and MS distance scales correspondingly, for O-A0 stars

Sp	$M_V\mbox{(ZAMS)}$	$M_V\mbox{(MS)}$	$\Delta M_V$
O4	-5.2	-5.9	+0.7
O9,5	-3.6	-4.25	+0.65
B0	-3.25	-4.0	+0.75
B0,5	-2.6	-3.6	+1.0
B1,5	-2.1	-2.8	+0.7
B2,5	-1.5	-2.0	+0.5
B3	-1.1	-1.6	+0.5
B6	-0.2	-0.9	+0.7
B8	+0.6	-0.25	+0.85
B9,5	+1.1	+0.4	+0.7
A0,5	+1.5	+0.8	+0.7

 

 

Table 2: Systematic errors $\Delta r_1$ and $\Delta r_2$ of distance r determination caused by $\Delta M_V=+0.5$ and $\Delta M_V=+1.0$ errors of the absolute magnitudes scale correspondingly

V0-MV	r,pc	$\Delta r_1$,pc	$\Delta r_2$,pc
8.0	400	100	200
9.0	630	160	370
10.0	1000	250	500
11.0	1600	400	900
12.0	2500	700	1500
13.0	4000	1000	2300
14.0	6300	1600	3700

Thus, presently developed observational knowledge on absorbing medium and star distribution in space can essentially differ from a real picture of the Galaxy structure. This short analysis substantiates a conclusion that for the increase in accuracy of interstellar dust and star distribution studies in the Galaxy cluster, members are to be preliminary excluded before the analysis started. The member selection can be carried out with one of the commonly used methods, or with those presently developed by authors (Kuznetsov 1988; Kuznetsov et al. 1989; Kuznetsov et al. 1993) for various initial sets of observational data on kinematic, photometric and spectral characteristics of stars. Certainly, this discussion concerns also a case of researching interstellar light absorption and spatial star distribution in directions of more extended stellar groups (star-forming regions and OB-associations).

In Fig. 1 the observed dependence E(B-V) versus (V₀ -M_V) for NGC 2244 is shown, derived here in a way described.

Once a reliable dependence E(B-V) versus (V₀ -M_V) in a given direction is found, it is possible to proceed directly to realization of the spectral classification. First of all it is necessary to calculate Q_UBV values for each star under the commonly used formula given e.g. by Strayzis (1977), Holopov (1981), and Johnson (1958):

Q_UBV=(U-B) - [ E(U-B) / E(B-V)](B-V). (1)

At E(B-V) < 1 a relation E(U-B)/E(B-V) = X+ SE(B-V) with factors X and S depending on the spectral class of a star takes place. Because for the Cepheus-Perseus-Monoceros law the E(U-B)/E(B-V) value varies mainly in the limits 0.70-1.00 (Strayzis 1977; Sudjus 1974), its average value 0.85 may be used as a good initial approximation for computing Q_UBV. Knowing the dependence of Q_UBV on spectra Sp (Strayzis 1977), it is easy to determine a set of Npossible spectral classes $Sp_1, Sp_2,\ldots Sp_N$ of any star at fixed Q_UBV. Then, using the Schmidt-Kaler (1982) tables, these spectra are transformed to normal colour parameters (B-V)₀ and absolute magnitudes M_V. Supplementing this information with observed BV values of stars, we find colour excesses, light absorption A_V = 3.2 E(B-V), and intrinsic distance module (V₀ -M_V). The last values should be computed two ways, using the ZAMS scale for open cluster members, and the MS scale for field stars.

Computed pairs of E(B-V) and (V₀ -M_V) values of the studied star are then put in the diagram of colour excess dependence versus intrinsic distance modulus, for example in a diagram shown in Fig. 1. Of all possible sets of E(B-V) and (V₀ -M_V) values the most real is that pair which is in best agreement with the absorption curve in view of errors of observations. Normally deviations of colour excesses and the distance module from the mean absorption curve should not exceed $3\sigma \{ E(B-V)\}$ and $3\sigma \{ (V_0 -M_V)\}$ accordingly. All spectra which do not satisfy the above-stated criterion are discarded and as a result a preliminary spectrum $\overline{Sp}$ of a star is determined. According to Kuznetsov (1978) the errors of E(B-V) and (V₀ -M_V) determination are $\sigma \{ E(B-V)\} =0.10$ mag and $\sigma \{ (V_0 -M_V)\} = 0.60 - 0.80$ mag accordingly. Therefore scattering of the data points in the plot of colour excess versus intrinsic distance modulus within areas where absorption is constant, should not exceed 0.20 - 0.25 mag (Voroshylov et al. 1972). In directions of NGC 2244 and NGC 2264 it does not exceed $3\sigma \{ E(B-V)\} =0.30$ mag (Fig. 1; Arshutkin et al. 1990; Khalandadze et al. 1986; Kuznetsov 1978).

Once the star spectrum $\overline{Sp}$ is determined, more accurate E(U-B)/E(B-V) and Q'_UBVvalues are recomputed and a final spectral type Sp_UBV of the star is determined with the help of transition tables by Strayzis (1977). In the cases to be discussed below, when two spectral estimates $\overline{Sp}$are equally possible for a star, it is necessary to use auxiliary data, for example, the probability of the star to be a cluster member.