To obtain an upper limit to our resolution we tried to estimate the Rbrightness of the cool companion by fitting the available photometric data of those stars that have sufficient measurements. In order to disentangle the flux of the hot star from that of the cool star we analyse the composite spectral energy distribution. For this purpose ultraviolet, optical and infrared (spectro-) photometry is collected from literature and archives (IUE, 2MASS). To determine the contribution of the hot star we fit synthetic spectra (Kurucz 1992) to the bluest part of the observed spectral range, i.e. IUE data plus u or u/U plus v/B (if no UV data were available) and determine the effective temperature of the sdB star. In doing so we assume that the companion does not contribute to the flux in this wavelength range (cf. Fig. 5). While this is probably true for the IUE data, some contamination may be present in the u/U- and v/B-band and consequently the temperature determination for the sdB star can be compromised.
However, for some stars photometric data are so incomplete that no
meaningful fit can be obtained.
Aside from the F675W measurements discussed here PG 0942+461
and HE 2213-2212 have only JHK photometry from 2MASS, which
are insufficient for a fit.
While HE 0430-2457 has BVR photometry
it is still not possible to constrain the sdB star's temperature with these
data as B-V is insensitive to
at sdB temperatures.
To convert the magnitudes into flux values we used the data given in
Table 3.
filter | flux |
![]() |
[erg/(cm2 s Å)] | [Å] | |
u |
![]() |
3500 |
v |
![]() |
4110 |
b |
![]() |
4670 |
y |
![]() |
5470 |
U |
![]() |
3600 |
B |
![]() |
4400 |
V |
![]() |
5500 |
![]() |
![]() |
6400 |
![]() |
![]() |
7900 |
![]() |
![]() |
12510 |
![]() |
![]() |
16280 |
![]() |
![]() |
22030 |
![]() |
![]() |
12500 |
![]() |
![]() |
16500 |
![]() |
![]() |
22000 |
By comparing the measured flux in the R band to the model flux of the
sdB star we derive the flux ratio of the hot vs. the cool star in the
system.
For those systems
which should have a rather bright companion according to their photometric
data we verified the flux ratio in R between sdB and cool companion
from
two colour diagrams similar to those used by
Ferguson et al. (1984), which is best
suited for components of comparable brightness (for details see Ferguson et al. 1984).
With this method
we found that the companion of TON 1281 is bright enough to affect also the
u filter, yielding a temperature of 25000K to 27000K for the sdB
instead of the 22000K given in Table 4 and a brightness
difference
of
to
.
Also for PG 1601+345
we find a much smaller brightness difference (
)
and higher
temperature (29500 K) from this method than from our photometric fits. In
this case the B filter is already affected by the cool companion.
For reasons of consistency we keep the values from the photometric fits for
these two stars in Table 4.
For all other stars
with brightness differences
the results from both methods
were the same.
To correct for interstellar
reddening we used the reddening-to-infinity maps
of Schlegel et al. (1998) which give
somewhat higher values than the older data of Burstein & Heiles
(1982).
KPD 2215+5037, PG 1558-007, and
PG 2259+134 all lie in regions of quite high reddening according
to Schlegel et al. (1998) and show no spectroscopic evidence
for a cool companion (see Appendix A). The observed apparent
infrared excess can be explained by high interstellar reddening alone,
without invoking the presence of a cool companion. We also find no
evidence for a companion from available photometry of PG 1656+213,
although there is spectroscopic evidence (Ferguson et al. 1984).
However there are are no flux measurements
redwards of V available and B and V fluxes
are inconsistent. Therefore we keep PG 1656+213 as a programme star.
Star |
![]() |
AR |
![]() |
![]() |
![]() |
d | ![]() |
![]() |
![]() |
[K] | [pc] | [AU] | |||||||
PB 6107 | 23000 |
![]() |
![]() |
![]() |
![]() |
870 |
![]() |
0
![]() |
87 |
PG 0105+276 | 32000 |
![]() |
![]() |
![]() |
![]() |
1100 |
![]() |
0
![]() |
110 |
PHL 1079 | 25000 |
![]() |
![]() |
![]() |
![]() |
630 |
![]() |
0
![]() |
63 |
PG 0749+658 | 22000 |
![]() |
![]() |
![]() |
![]() |
580 |
![]() |
0
![]() |
116 |
TON 1281 | 22000 |
![]() |
![]() |
![]() |
![]() |
1150 |
![]() |
0
![]() |
80 |
TON 139 | 20000 |
![]() |
![]() |
![]() |
![]() |
950 |
![]() |
0
![]() |
48 |
PG 1309-078 | 24000 |
![]() |
![]() |
![]() |
![]() |
910 |
![]() |
0
![]() |
91 |
PG 1421+345 | 24000 |
![]() |
![]() |
![]() |
![]() |
2100 | 0
![]() |
210 | |
PG 1449+653 | 28000 |
![]() |
![]() |
![]() |
![]() |
830 |
![]() |
0
![]() |
58 |
PG 1511+624 | 31000 |
![]() |
![]() |
![]() |
![]() |
1200 |
![]() |
0
![]() |
84 |
28000 |
![]() |
![]() |
![]() |
1200 |
![]() |
0
![]() |
84 | ||
33000 |
![]() |
![]() |
![]() |
1260 |
![]() |
0
![]() |
88 | ||
PG 1558-007 | 23000 |
![]() |
![]() |
![]() |
910 | ||||
PG 1601+145 | 25000 |
![]() |
![]() |
![]() |
![]() |
1100 |
![]() |
0
![]() |
77 |
PG 1636+104 | 20000 |
![]() |
![]() |
![]() |
![]() |
1200 |
![]() |
0
![]() |
84 |
PG 1656+213 | 17000 |
![]() |
![]() |
![]() |
1800 | ||||
TON 264 | 26000 |
![]() |
![]() |
![]() |
![]() |
870 |
![]() |
0
![]() |
174 |
PG 1718+519 | 27000 |
![]() |
![]() |
![]() |
![]() |
950 |
![]() |
0
![]() |
48 |
PG 2148+095 | 26000 |
![]() |
![]() |
![]() |
![]() |
520 |
![]() |
0
![]() |
52 |
KPD 2215+5037 | 35000 |
![]() |
![]() |
![]() |
480 | ||||
PG 2259+134 | 30000 |
![]() |
![]() |
![]() |
1000 | ||||
BD ![]() |
29000 |
![]() |
![]() |
![]() |
![]() |
320 |
![]() |
0
![]() |
64 |
Aznar Cuadrado & Jeffery (2001) present an extensive discussion
of sdB parameters derived from energy distributions, which also includes
some of the stars discussed in this paper. In Table 5 we
present the temperatures given in their paper and other values collected
from literature in comparison to the ones derived here. As can be seen from
Table 5 differences of 10% in
between
different authors are quite common.
star |
![]() |
|||||
this paper | ACJ01 | T93 | A94 | T95 | UT98 | |
PB 6107 | 23000 | 25000 | ||||
PG 0105+276 | 32000 | 35850 | 32000 | |||
PHL 1079 | 25000 | 26350 | 30000 | 30000 | ||
PG 0749+658 | 22000 | 25050 | 23500 | |||
TON 1281 | 22000 | 23275 | 29500 | |||
TON 139 | 20000 | 18000 | ||||
PG 1449+653 | 28000 | 28150 | 28000 | |||
PG 1511+624 | 31000: | 33000 | ||||
PG 1636+104 | 20000 | 21000 | ||||
TON 264 | 26000 | 28500 | ||||
PG 1718+519 | 27000 | 29950 | 23500 | 25000 | 30000 | |
PG 2148+095 | 26000 | 22950 | 26000 | 25000 | ||
KPD 2215+5037 | 35000 | 24500 | ||||
PG 2259+134 | 30000 | 28300 | 28500 | 22500 |
The temperatures derived from the photometric data and from line profile fits for the stars in regions with high reddening agree moderately well (compare Tables 4 and A.1). The discrepancies may be due to small scale variations in reddening that affect the temperatures derived from photometry but not those derived from line profile fits.
From the photometric fit we can derive the apparent
R magnitudes of the sdB and of
the cool star and correct both for interstellar extinction. The
uncertainty in
of about
10% evident from
Table 5 causes an estimated uncertainty in the derived
brightness for both components of
.
Knowing the absolute Rmagnitude of the sdB stars then allows to determine their distance. We use
the mean MV derived by Moehler et al. (1997) for hot subdwarfs
in the globular cluster NGC 6752. They found two groups of hot subdwarfs, a
cooler one with a mean effective temperature of 22000K and <MV> =
(5 stars), and a hotter one with <
> = 29000K and
<MV> =
(12 stars). From Kurucz (1992) model
atmospheres for [M/H] = 0 we find V-R =
for
=
22000K and
for 29000K. We therefore use MR =
for stars cooler than 25000K and MR =
for
hotter stars.
Using the archive point spread functions we estimated the minimum separation
that we can resolve for a given brightness difference by adding two PSFs
with a defined brightness difference and angular separation and examining
the resulting image by eye. We find the following resolution limits:
(
)
= 0
2 (
), 0
1
(
), 0
07 (
), 0
05 (
). Using the
distances determined above we can now derive upper limits for the linear
separation of the unresolved binaries (cf. Table 4), ranging
from 50 AU to 210 AU.
Table 2 shows that the brightness differences between the components
in TON 1281 and HE 0430-2457 are too large to reproduce the spectral
energy distribution of TON 1281 and the photometry of HE 0430-2457,
respectively.
The large
brightness difference of
(from the WFPC2 data) for PG 1558-007 agrees with the lack
of photometric and spectroscopic
evidence for a companion.
In the remaining two cases
(PG 1718+519, TON 139)
the brightness differences in Table 2 are somewhat larger than
those derived from the spectral energy distribution.
To see
whether we can in principle accommodate the HST observations by fits to the
photometric data we repeated the fits, this time enforcing the brightness
difference in the R band obtained from the HST data. The results are
shown in
Fig. 5 (in comparison to the original fits). Obviously the
companion of PG 1718+519 is sufficiently bright to affect also the u
filter, thereby rendering our assumption that this filter is unaffected by
the cool companion obsolete. The fits for TON 139 do not show much
difference. We conclude that the spectral energy distribution of TON 139
and PG 1718+519 are consistent with the R band flux ratio measured with
the HST WFPC2 camera.
![]() |
Figure 5: Fits of ATLAS9 model spectra (Kurucz 1992, [M/H] = 0) to the photometric data of PG 1718+519 (left panel, including IUE spectra) and TON 139 (right panel). The upper panels show the fits obtained assuming that the bluest photometric data points (IUE spectra and u for PG 1718+519, u and v for TON 139) are not affected by the cool companion. The lower panels show fits that reproduce the brightness differences measured on the WFPC2 images. |
Since the He-sdO PG 0105+276 does not
belong to the programme sample, we discuss it
separately. It is the only programme star that is resolved into three
components. However, the two companions are quite distant from the primary
(3
37 and 4
48, respectively).
The light of these companions can explain at least qualitatively
the IR excess observed by ground based aperture photometry. The spectrum of
PG 0105+276, however, does not show any signature of a cool companion,
probably because
due to the orientation and the small width of the slit no light of the
distant companions was included.
The diaphragm used in the photometry was large
(18
)
and included the companions' light.
The brightness differences measured on the WFPC2 image (
,
)
for PG 0105+276
are smaller than the one derived from the photometric fit
(
), i.e. one companion is brighter than expected. However,
as discussed in Appendix A,
the true temperature (from line profile fitting) is much
higher than the one obtained from the spectral energy distribution
(63000K vs. 35000K)
making the companion's luminosity obtained from photometry a lower limit
only.
Copyright ESO 2002