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
), 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 () and colour indices (
,
,
and
) of the programme stars
were obtained, using linear fits to the standard-star observations, as a
function of
(z is the zenith distance):
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 scale, and not in magnitudes.)
n | f(n) | g(n) | n | f(n) | g(n) | n | f(n) | g(n) |
2 | 1.84 | 1.49 | 6 | 1.11 | 1.07 | 10 | 1.06 | 1.04 |
3 | 1.32 | 1.20 | 7 | 1.09 | 1.06 | 11 | 1.05 | 1.03 |
4 | 1.20 | 1.13 | 8 | 1.08 | 1.05 | 12 | 1.05 | 1.03 |
5 | 1.14 | 1.09 | 9 | 1.07 | 1.04 |
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,
, is not a good estimate of the
standard deviation for small numbers of observations, and
(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
in the mean value
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
and standard deviation
we have drawn 106 times n
random numbers, each time calculating the sample standard deviation s and the
sample mean value
. 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
. 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
.
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.
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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 (corrected for small
n as described above) of the brightness and colours and their spread
. 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
) 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
(from
Table 4 (click here)).
Figure 1: Colour-colour diagram of the Walraven colours and
. 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
A diagram of against
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) (
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.
The difference between the Walraven apparent brightness and the
apparent brightness obtained from Johnson's apparent visual magnitude
appears to depend slightly on colour
. 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:
Figure 2: A comparison of Johnson's with the Walraven colour
. The error bars indicate the uncertainties in the colours, as
listed in Table 2. For
an uncertainty of 0.01 is assumed. The
solid line is given by Eq. (4)
The Walraven colour and Johnson's
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:
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 and
, has a
large deviation from this relationship, which is probably due to an error in
the BSC value for
. For instance, the Hipparcos input catalogue
(Turon et al. 1992), lists for this star
, which puts it
right on the relationship defined by Eq. (4 (click here)).