For all programme stars we made additional spectral classifications from photometry by dereddening all programme stars in the (U-B) versus (B-V) diagram (Fig. 3 (click here)), assuming a normal extinction law, i.e. E(U-B)/E(B-V) = 0.72. When available the new UBV data were used in this diagram. In other cases we used the photometry by Chini & Neckel (1981) or by Sagar & Joshi (1981). As can be seen from Fig. 3 (click here) as well as from the colour-magnitude diagrams (shown in Fig. 4 (click here)), it is not possible to distinguish giants from main-sequence stars using this (U-B) versus (B-V) diagram. Therefore we assumed all stars to be of luminosity class V in this classification. The resulting spectral classifications using UBV data from literature are listed in the second column of Table 5, whereas the resulting classifications using the new UBV data from Table 2 are listed in the third column. A dash in these columns indicates that UBV data was available, but the corresponding reddening line did not intersect the main sequence.
For the stars with photometric data in the Walraven system we calculated the
reddening-free parameters [B-U], [U-W] and [B-L], defined as:
In this method the extinction law is again assumed to be normal.
The resulting [B-U] versus [B-L] and [B-U] versus [U-W] diagrams are
shown in Fig. 5 (click here). In these diagrams we also plotted lines of
constant 
and 
, derived from Kurucz
(1991) models in a similar way as was done for the Kurucz
(1979) models by Brand & Wouterloot (1988). Our new
[B-U] versus [B-L] diagram agrees well with theirs, whereas clear
differences can be seen between the [B-U] versus [U-W] diagrams. As can
be seen from Fig. 5 (click here), the data points fall reasonably well within
the grid of Kurucz models for the [B-U] versus [B-L] diagram, whereas
for the [B-U] versus [U-W] diagram a fair amount of data points are
plotted outside the grid. This same effect was also noted by Brand &
Wouterloot (1988), who attributed this to the failure of the Kurucz
(1979) models to reproduce the absorption line strengths in the W
band. We conclude that although the Kurucz (1991) models do
give better results than the ones from 1979, this still is the case.
Following Brand & Wouterloot (1988), we only used the [B-U]
versus [B-L] diagram (Fig. 5 (click here)b) to derive a two-dimensional
spectral type by obtaining values for 
and 
by
interpolation between the lines of constant 
and 
, and
converting these to two-dimensional spectral types, adopting the absolute
calibrations by Schmidt-Kaler (1982). The resulting spectral
classifications are listed in the fourth column of Table 5. As can be seen
from Fig. 5 (click here)b a small number of points fall outside the scope of the
grid covered by the Kurucz models in the [B-U] versus [B-L] diagram as
well. The programme stars for which this is the case are indicated in
Table 5 by dashes in the fourth column. Deviations in both the [B-U] and
[B-L] directions may be due to the assumption of a normal extinction law
in deriving the reddening-free parameters [B-U] and [B-L]. Since the
Walraven L band is heavily influenced by the Balmer lines in this band,
the deviations in the [B-L] direction may very well be explained by the
presence of hydrogen emission lines in the stellar spectrum, either
intrinsic or due to poor sky subtraction. In retrospective, it is of course
not surprising that the unsophisticated sky subtraction procedure offered by
our aperture photometry often fails, for bands heavily influenced by
hydrogen emission lines, when even the sophisticated sky subtraction
procedures used for the reduction of our CCD long-slit spectra are probably
not always successful in removing all emission from the surrounding
nebulosity.
Figure 3: The U-B versus B-V two colour diagram for programme stars in
NGC 6530. Probable members (
) are indicated by circles.
Possible members (
) are indicated by squares. The
diamonds indicate programme stars not included in the proper motion survey
by van Altena & Jones (1972).
The solid line shows the intrinsic colours for main-sequence stars (luminosity
class V). Those for luminosity class III (giants) are indicated by the dashed
line. The arrow indicates the reddening direction for a normal extinction law,
with E(U-B)/E(B-V) = 0.72
In comparing the spectral types listed in Table 5 found using the different
methods we notice that generally there is good agreement between the spectral
types obtained from spectroscopy and photometry, indicating that the
assumption of a normal extinction law in obtaining the spectral types from
photometry was not too far off. In individual cases we can notice large
differences between the spectroscopic and photometric (especially from the
Walraven data) spectral types, however. This could e.g. be due to the
presence of unresolved binaries. In such cases we adopted the spectroscopic
spectral type for the programme stars if this was well-determined. In all
other cases we took the spectral types from the Walraven or Johnson
photometry, when available and in agreement with the rough spectroscopic
spectral types. These adopted spectral types are listed in the 7
column of Table 5. Colour excesses E(B-V) were determined from the
observed (B-V), adopted spectral types, and the intrinsic (B-V) colours
from Schmidt-Kaler (1982) and are also listed in Table 5.
Spectral Energy Distributions (SEDs), from the ultraviolet to the infrared wavelength ranges, were constructed for all programme stars using the new photometric data assembled in Table 2, photometric data from literature and ultraviolet spectrophotometric data extracted from the IUE archives. Observed magnitudes/intensities were converted to fluxes using the flux calibrations by Wesselius et al. (1982), de Ruiter & Lub (1986), Johnson (1966), Bessell (1979) and Berrilli et al. (1992) for the ANS, Walraven, Johnson, Cousins and Near-IR data, respectively.
These observed SEDs were corrected for interstellar plus circumstellar
extinction by comparing the observed fluxes (
) to the
theoretically observed fluxes (
) at earth:
In this formula 
is the flux emitted by the star per surface
unit, 
is the stellar radius, d is the stellar distance,
is the total extinction at a given wavelength (in magnitudes)
and 
is the transmission function of the photometric filter.
was taken from the Kurucz (1991) models for the
adopted spectral type, assuming a solar abundance of the elements.
was taken from Schmidt-Kaler (1982) for the
Walraven, Johnson and Cousins photometric systems, from Wesselius et al.
(1982) for the ANS data and from Fluks et al. (1996)
for the Near-IR data, after which we normalized these transmission functions
so that 
. 
(as
a function of the ratio of total to selective extinction 
) was
obtained from the extinction laws by Steenman & Thé
(1991), using the relation 
= 
. Since
and d are not accurately known, the parameters
were obtained by fitting 
to 
in each SED. This fitting procedure was applied only up to 1.3 
m
(J-pass band), because beyond this wavelength the SED could be influenced
by thermal emission of circumstellar dust grains in which case the Kurucz
model does not represent the true system flux anymore. Examples of the
resulting observed and extinction-free SEDs are shown in Fig. 6 (click here).
With this method it is also possible to correct for anomalous extinction,
characterized by a value of 
, by fitting 
to 
for different values of 
using the method described above, until, by
trial and error, a best fit is obtained, according to the 
-test. If
a value significantly different from the one found for interstellar matter,
, is found the extinction law is called anomalous, which indicates
a different size distribution or chemical composition of the dust grains
responsible for the extinction than those in interstellar matter. If the
extinction is anomalous (
> 3.1), the error in the 
-value is
0.2, whereas for 
= 3.1 this error is 0.1, provided that data points
over a sufficient wavelength interval were used. Note that the obtained
extinction laws are in fact a mixture of an interstellar, normal, and a
possible circumstellar, potentially anomalous, component. So, in the case
of anomalous extinction the 
-values for the circumstellar matter will
in fact be higher than the ones derived using this method.
Note that above procedure to analyze the SED is very similar to the one employed by Steenman & Thé (1989), but has been improved by the use of the new extinction laws by Steenman & Thé (1991), and the use of the new Kurucz (1991) models. Furthermore, we used fluxes integrated over the response curve of the photometric band, instead of monochromatic fluxes.
Figure 4: a) V versus (U-B) colour-magnitude diagram for
programme stars in NGC 6530. Plot symbols have the same meaning as in
Fig. 3. The solid line shows the colour-magnitude relation for stars of
luminosity class V with a distance modulus of 1128 and corrected for
reddening and extinction with E(B-V) = 030 (see Sect. 4). The relation
for luminosity class III (giants) is indicated by the dashed line.
b) V versus (B-V) colour-magnitude diagram for programme stars in
NGC 6530. Plot symbols and lines have the same meaning as in a)
Figure 5: a) The Walraven [B-U] versus [U-W] two colour diagram
for our programme stars in NGC 6530 with Walraven photometric data. Probable
members (
) are again indicated by circles, whereas possible
members (
) are again indicated by squares.
Lines of constant 
and 
, according to the Kurucz
(1991) models, are also shown.
b) The Walraven [B-U] versus [B-L] two colour diagram for our
programme stars in NGC 6530 with Walraven photometric data. Plot symbols
and lines have the same meaning as in a)
Figure 6: Examples of observed (squares) and extinction-free (circles) SEDs
for our programme stars. The solid line is the Kurucz (1991)
model fitted through the extinction-free SED
For most programme stars we obtained good fits of the extinction-corrected fluxes to the Kurucz model. However, there are a number of stars in which the JHK photometry lies above the Kurucz model, and thus exhibit infrared excesses, probably due to remnants of a circumstellar disk or dust shell left over from star formation. The stars for which this is the case are marked with "Yes'' in the last column of Table 5, whereas for stars in which we obtain a good fit of the JHK bands to the Kurucz model, this column contains "No''. The dashes in this column indicate that not enough data were available to draw any definite conclusions. It is unlikely that these infrared excesses are due to the presence of red companions because: (a) the shape of most of these infrared excesses are not compatible with stellar colours; (b) unperturbed late-type stars will not have had time to loose enough circumstellar material to become even visible in the near infrared (Palla & Stahler 1993), so it is very unlikely that such an infrared excess is due to optical binaries; (c) in case an early type star has a late-type companion, it sweeps out its circumstellar environment very rapidly (e.g. Hester et al. 1996; Pérez et al. 1996), after which the difference in brightness between the primary and the secondary will be so large that this would not show up in our study. Furthermore, if an infrared excess would be due to a late-type companion, we would expect that it would be bright enough to detect its presence in our spectra.
After applying our SED-fit method, stellar luminosities were computed by
integrating over the Kurucz (1991) model, fitted to the
extinction-free SED:
with 
the Kurucz model flux, fitted to the extinction-corrected
SED. For wavelengths longer than the largest one covered by the Kurucz
(1991) model (
), 
was taken equal to a
Planckian in the Rayleigh-Jeans limit, fitted to the Kurucz model, and the
analytical solution of the resulting integral was used to perform the
integration to infinity. A distance 
was derived for each
programme star by comparing this stellar luminosity with the absolute
luminosity calibration assembled by Schmidt-Kaler (1982). The
above method to derive distances of individual objects gives similar
results as the more familiar distance modulus method. However, our method
will give more accurate results because it does not rely on the accuracy of
only one photometric measurement (mostly V) and on often poorly estimated
bolometric corrections. The computed values of E(B-V), 
and 
, as well as 
and 
, adopting a
distance of 
(see Sect. 4), for each star are listed
in Table 5. A dash in the column with 
values or the infrared excess
indicates that not enough data was available to draw any definite
conclusions on this. A colon indicates uncertain values.