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2. Walraven photometry

2.1. The observations

The photometric observations were made during 11 nights in 1989 between June 21 and July 29, with the Walraven photometer on the 90 cm Dutch telescope at the European Southern Observatory. This photometer (Lub & Pel 1977) provided simultaneous measurements of the stellar brightness in five passbands (called tex2html_wrap_inline1116), between 3250 and 5500 Å. All measurements were made using a diaphragm with a 16 arcsecond diameter. An observation of each star consisted of four integrations of 16 seconds each, followed by two such integrations on the sky background. Most stars were observed during more than one night. The number of observations for each star (ranging from 1 to 7, with one exception of 12 observations) are listed in Table 2.

The observations were tied to the Walraven photometric system by measurements of (typically 7) standard stars at the beginning, middle and end of each night.

The visual brightness (tex2html_wrap_inline1118) and colour indices (tex2html_wrap_inline1120, tex2html_wrap_inline1122, tex2html_wrap_inline1124 and tex2html_wrap_inline1126) of the programme stars were obtained, using linear fits to the standard-star observations, as a function of tex2html_wrap_inline1128 (z is the zenith distance):
eqnarray799
where SV and QV are the (sky-corrected) signal and zero point in the V channel, respectively. Similar expressions were used for the other colour indices. (As is customary in the Walraven system, the brightness and colours of a star are given on a tex2html_wrap_inline1138 scale, and not in magnitudes.)

   

nf(n)g(n)nf(n)g(n)nf(n)g(n)
21.841.4961.111.07101.061.04
31.321.2071.091.06111.051.03
41.201.1381.081.05121.051.03
51.141.0991.071.04
Table 3: The correction factor f(n) to the uncertainty in the mean value and the correction factor g(n) to the standard deviation for a small number of observations n

The Walraven V and colours obtained for each star during different nights, have been averaged. The uncertainties in the mean values, as listed in Table 2, have been estimated as follows. The square root of the sample variance, tex2html_wrap_inline1166, is not a good estimate of the standard deviation for small numbers of observations, and tex2html_wrap_inline1168 (n being the number of observations), is not a good estimate of the error in the mean value (Burington & May 1970). We have estimated a correction factor f(n) to the error tex2html_wrap_inline1174 in the mean value tex2html_wrap_inline1176 and a correction factor g(n) to the standard deviation s, as a function of the number of measurements using a computer simulation. From a normal distribution with mean tex2html_wrap_inline1182 and standard deviation tex2html_wrap_inline1184 we have drawn 106 times n random numbers, each time calculating the sample standard deviation s and the sample mean value tex2html_wrap_inline1176. The 106 standard deviations found in this way for each n are averaged. The correction factor g(n) is the standard deviation of the parent population divided by the average sample standard deviation derived from the simulation. The correction factor f(n) is the standard deviation of the 106 values for tex2html_wrap_inline1204. The correction factors are listed in Table 3 (click here). The uncertainties in the Walraven brightness and colours have been estimated using the corrected formula tex2html_wrap_inline1206.

If an observation deviated from the corresponding mean value by more than four times the standard deviation (derived from the other observations of the same source) for all colours, it was excluded from the analysis. Only two observations were excluded in this way.

   

tex2html_wrap_inline1208tex2html_wrap_inline1210
tex2html_wrap_inline1212tex2html_wrap_inline1214
tex2html_wrap_inline1216tex2html_wrap_inline1218
tex2html_wrap_inline1220tex2html_wrap_inline1222
tex2html_wrap_inline1224tex2html_wrap_inline1218
Table 4: The average standard deviations of the observations with their spread

A measure of the accuracy of the photometry is given by the standard deviation of consecutive observations of the brightness and colours of each star, provided that the star is not intrinsically variable. Table 4 (click here) lists the average standard deviations tex2html_wrap_inline1228 (corrected for small n as described above) of the brightness and colours and their spread tex2html_wrap_inline1232. In the present sample, it is found that the average standard deviation does not depend on brightness. In calculating this average, we left out 12 stars which appeared to be variable in brightness or in one or more colours, having standard deviations significantly larger (more than tex2html_wrap_inline1234) than the average standard deviation. These stars are indicated in Table 2 with an asterisk. The average standard deviation and its spread was used to assign uncertainties to the brightness and colours of stars, that were only measured once. These uncertainties, as listed in Table 2, were taken equal to tex2html_wrap_inline1236 (from Table 4 (click here)).

  figure282
Figure 1: Colour-colour diagram of the Walraven colours tex2html_wrap_inline1122 and tex2html_wrap_inline1120. The error bars indicate the uncertainties in the colours as listed in Table 2, the arrow indicates an interstellar reddening of 0.1 dex in tex2html_wrap_inline1120

A diagram of tex2html_wrap_inline1122 against tex2html_wrap_inline1120 is shown in Fig. 1 (click here). All stars, but five, lie in a narrow band with a width of about 0.06 in log (flux) (tex2html_wrap_inline1248 mag). The three sources that lie above this band are: HR 6843, HR 8646 and HR 8917. The deviation of these three stars could be caused by large interstellar or circumstellar reddening (the spectral classification of these stars also predicts a much smaller colour index than observed). The two stars that lie below this band are HR 5356 and HR 8181.

2.2. Comparison with Johnson's photometric system

The difference between the Walraven apparent brightness tex2html_wrap_inline1118 and the apparent brightness obtained from Johnson's apparent visual magnitude tex2html_wrap_inline1258 appears to depend slightly on colour tex2html_wrap_inline1120. Johnson's apparent visual magnitudes have been obtained from the Bright Star Catalogue (BSC) (Hoffleit & Jaschek 1982). For the stars in our sample, excluding the five deviating stars from Sect. 2.1, the best-fit linear relation is given by:
 equation803

  figure301
Figure 2: A comparison of Johnson's tex2html_wrap_inline1262 with the Walraven colour tex2html_wrap_inline1120. The error bars indicate the uncertainties in the colours, as listed in Table 2. For tex2html_wrap_inline1262 an uncertainty of 0.01 is assumed. The solid line is given by Eq. (4)

The Walraven tex2html_wrap_inline1120 colour and Johnson's tex2html_wrap_inline1262 are tightly related (Fig. 2 (click here)). The best linear fit for our sample (excluding the five deviating stars from Sect. 2.1) is given by:
 equation807
The relations 3 and 4 are consistent with those derived by Van Paradijs et al. (1986) for a sample of OB-type stars.

One star, HR 7126 with tex2html_wrap_inline1272 and tex2html_wrap_inline1274, has a large deviation from this relationship, which is probably due to an error in the BSC value for tex2html_wrap_inline1262. For instance, the Hipparcos input catalogue (Turon et al. 1992), lists for this star tex2html_wrap_inline1278, which puts it right on the relationship defined by Eq. (4 (click here)).


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