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4. Results

The analysis was performed separately for each photometric region. The method was applied several times using as variables the observed Strömgren-Crawford indices ((b-y), m1, c1 and tex2html_wrap_inline1471) and the bracket, reddening free, indices ([m1], [c1] and tex2html_wrap_inline1471). So, each analysis yielded different definitions of the p coordinate.

4.1. Early region

From a photometric point of view, a star belonging to the early region is a star located in a specific zone of the diagrams tex2html_wrap_inline1681 and tex2html_wrap_inline1683 (Strömgren 1966). For normal stars this corresponds approximately to spectral types B0-B9. However, since peculiar stars are bluer than normal stars, some A0-A2 peculiar stars are also classified into the early region.

In general, a linear combination of the tex2html_wrap_inline1475 colours will not be reddening free. Although standard calibrations to compute reddening are not suitable for CP2 stars, we dereddened them as if they were normal stars since the uncertainties are of about 0.010 mag (Maitzen 1980) and we will come back to this problem in Sect. 6 (click here). The number of stars as a function of the computed reddening is shown in Fig. 1 (click here). 59 (13%) CP2 stars and 277 (21%) normal stars have a colour excess greater than 0.10 mag. To avoid the effect of the reddening, we built a subsample of almost unreddened stars, removing all those with E(b-y) > 0.10 mag, and we performed the discriminant analysis.

The MDA yielded the following value for p:

Figure 1: Histogram of colour excess for normal (dashed line) and CP2 (solid line) stars classified into the early region

the zero point being introduced in order that tex2html_wrap_inline1691 for normal stars. To estimate the order of the errors of the coefficients, we built different subsamples of normal and CP2 stars by randomly reducing the whole samples in 10% of stars. The MDA applied to these subsamples shows that the coefficients vary by about 2-3%.

A polynomial was fitted to the normal stars:

and a tex2html_wrap_inline1695 was defined. So, p0 gives a standard relation for normal stars (tex2html_wrap_inline1699) and tex2html_wrap_inline1701, for a given star, is the difference between its p coordinate and the p coordinate of a normal star with the same [u-b]. The polynomial was fitted as a function of [u-b], in order to avoid the reddening in the x-axis, following Maitzen & Vogt (1983). Figure 2 (click here) shows the p coordinate for the normal and CP2 samples and the standard relation of normal stars.

As a threshold value for peculiarity, we defined tex2html_wrap_inline1715 above which 50% of the CP2 stars are located. The percentage of normal stars with respect to the total number of stars with tex2html_wrap_inline1717 shows the associated "contamination''. This contamination is an indicator of the capability of tex2html_wrap_inline1701 to separate CP2 from normal stars. In the present case, a threshold of tex2html_wrap_inline1715 = 1.50 yields a contamination of about 2%. The percentage of contamination increases quickly as the threshold decreases.

Figure 2: p vs. [u-b] for the stars of the early region with tex2html_wrap_inline1727 mag. The ordinate p resulted from the application of the Multiple Discriminant Analysis using (b-y), m1, c1 and tex2html_wrap_inline1471 as variables describing the behaviour of both populations: peculiar and normal stars. Dots represent normal stars and full circles CP2 stars. The solid line is the adopted standard relation for normal stars and the dashed line indicates the threshold above which 50% of the CP2 stars are placed

Table 6 (click here) shows the efficiency of tex2html_wrap_inline1701 as a function of the [u-b] (i.e. temperature). The best segregation is obtained for high values of [u-b], whereas for the hottest stars
([u-b]<0.7) it is poor. This is due to the decreasing sensitivity of the v-band to indicate higher opacities among hotter B-type stars.

A fraction of the contamination can be explained by the presence of undetected binaries. The binary nature can increase the value of p of the primary component up to 0.1 for a B5-type star and by up to 0.6 for an A0-type star. The maximum increase is obtained when the secondary is an A3-A5 type star. So, in some combinations of spectral types, normal binary stars could be misclassified as CP2 stars. On the other hand, p is not reddening free: following Eq. (1) and applying the common extinction curve we obtain E(p)= -4.7E(b-y), so reddening decreases p and tex2html_wrap_inline1701, and we cannot differentiate a very reddened peculiar star from an unreddened normal star.

For the total sample, including reddened stars, the value of the contamination is about 3%, while the detection remains around 50%.

In order to analyze the effect of the peculiarity in each filter, it is useful to rewrite the Eq. (1) as follows:

The contribution of y-band to p is due to the feature at tex2html_wrap_inline1515, whereas v is modified by the tex2html_wrap_inline1767 feature. The coefficient of u shows that this band does not play any significant role in p. The negative sign of the tex2html_wrap_inline1471 coefficient is due to the fact that the tex2html_wrap_inline1471 index for CP2 stars is lower than for normal stars. The contribution of b, in spite of its coefficient, is small, because it lies in a region only slightly affected by the peculiarity.

The use of bracket, reddening free, indices to characterize the populations in the MDA yielded to a contamination of 13%. The effectiveness is smaller than with observed indices, probably because we are removing part of the information contained in the (b-y) colour.

As mentioned above and since the peculiar stars are bluer than the normal stars, some CP2 stars with spectral types A0-A2 are photometrically classified into the early region. We also carried out a discriminant analysis with a sample limited by spectral type from B0 to B9, i.e. instead of classifying the stars into the early region by their photometry we classified the stars by their spectral type. The contamination indicator is higher than before (15%), very probably because we excluded stars (see Fig. 2 (click here)) which exhibit the largest p values from our sample.

Since tex2html_wrap_inline1701 inferred from Eqs. (1) and (2) yield the lowest level of contamination, this peculiarity parameter is the one adopted from now on.


[u-b] CP2 normal % %
range stars stars detection contamination
0.5-0.7 35 232 9 0
0.7-0.9 129 217 49 2
0.9-1.1 87 204 52 4
1.1-1.3 92 267 62 0
1.3-1.5 70 104 41 2
0.5-1.5 413 1024 50 2
Table 6: Detection and contamination for tex2html_wrap_inline1785


The tex2html_wrap_inline1701 parameter defined by Eqs. (1) and (2) is only able to detect CP2 stars. A sample of 71 CP3 stars extracted from Renson et al. catalogue showed a mean value of tex2html_wrap_inline1701 equal to 0.16 (s.d. 0.41). This is because tex2html_wrap_inline1701 is mainly sensitive to the tex2html_wrap_inline1515 depression, not present in the CP3 stars.

Figure 3: The same as Fig. 2, but for the intermediate region

Table 7 lists 60 stars extracted from HM catalogue that we consider likely to be peculiar (i.e. with tex2html_wrap_inline1809). To build the table we considered all early stars with complete photometry in the HM catalogue and removed the stars belonging to Renson et al. catalogue, all those having tex2html_wrap_inline1533 or Geneva photometry (which are more effective to detect CP2 stars than tex2html_wrap_inline1475 system, see Sect. 5) and the stars having a quoted peculiar spectra in SIMBAD data base.

4.2. Intermediate and late regions

A similar analysis was applied to the intermediate and late regions, with subsamples of stars with tex2html_wrap_inline1727 mag. Unfortunately, the tex2html_wrap_inline1701's obtained are less efficient (Figs. 3 (click here) and 4 (click here)) than in the early region.

The calculated values of p and the standard relation for normal stars are, for the intermediate region:

and for the late region:

Figure 4: The same as Fig. 2, but for the late region

50% of detection is at tex2html_wrap_inline1715 = 1.25 and 2.00 mag, with contamination levels of 29% and 17%, for intermediate and late regions, respectively. Due to the small size of the samples, the errors of the coefficients are larger than for the early region: around 6% for the intermediate region and 4% for the late region.

Several authors have pointed out the similarity between cool CP2 stars, mainly Sr stars, and metallic stars, also named CP1 stars. To test this point, we applied the MDA to a sample of metallic stars extracted from The General Catalogue of Ap and Am stars by Renson et al. (1991). The sample contains 494 stars classified into the late photometric region according to the same algorithm used above. Considering two populations, normal stars and metallic stars, the MDA yielded:

The efficiency of this p is shown in Fig. 5 (click here). With
tex2html_wrap_inline1831 the contamination is equal to 1.1%. The dependence of p on each colour does not differ excessively from the p obtained for cool CP2 stars. So, the MDA confirms the mentioned similarity between CP1 and cool CP2 stars. Cameron (1967) already noticed that cool CP2 stars are placed on a c1 vs. m1 diagram at the same location as Am stars. All attempts at separating both types using these indices were unsuccessful.

Figure 5: The same as Fig. 2, but for Am stars

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