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Mon. Not. R. Astron. Soc. 000, 000--000 (0000) Printed 18 February 1998 (MN L A T E X style file v1.4)
The detection of binary companions to subdwarf B stars ?
C. Simon Jeffery 1 and Don L. Pollacco 2
1 Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland
2 Isaac Newton Group, La Palma
Accepted . Received ; .
ABSTRACT
Intermediate dispersion spectroscopy of a sample of 40 hot subdwarf B stars between
5500 š A and 9000 š A has been obtained. The sample includes a large fraction of targets
which have been studied photometrically. Seven targets show strong lines due to the
infrared Ca ii triplet, the unequivocal signature of a cool companion. The positive
Ca ii identifications include known photometric binaries and new targets; all are as­
sociated with a photometric red excess. Assuming a canonical value for the subdwarf
luminosity, all of the detected companions are overluminous compared with the main­
sequence. The detection procedure indicates an improved and more secure method for
the measurement of the binary frequency of hot subdwarfs.
Key words: Stars: early­type, subdwarfs, binaries: spectroscopic.
1 INTRODUCTION
Hot subdwarfs are O and B­type stars which may be found,
on an Hertzsprung­Russell diagram, below the upper main
sequence. They dominate old stellar populations as reflected
by the ultraviolet excesses observed in giant elliptical galax­
ies (Brown et al. 1997, Yi et al. 1997) and by their ubiquity
in galactic populations. Over 50% of all targets detected
in surveys of blue objects (U \Gamma B ! ¸ \Gamma0:46; typically hot­
ter than ¸ 25 000K) are subdwarf B stars (sdBs: Green et
al 1986). sdBs are considered to be the archetypal extreme
horizontal branch star, being low­mass stars (¸ 0:5M fi ) on
the helium main­sequence (Heber et al. 1984, Heber 1986).
That is, they consist of a helium core sustaining nuclear fu­
sion via the 3ff cycle surrounded by a very thin hydrogen
envelope (M ! ¸ 0:01 M fi ). The problem they present is an ex­
treme form of the classical horizontal­branch problem: how
can a red­giant of a given mass lose a substantial fraction
(i.e.¸ 100%) of its hydrogen­rich envelope at or soon after
the moment when helium­burning is ignited in the core?
If all sdBs were binaries, mass transfer through Roche­
lobe overflow could provide a solution; however at one time
very few sdBs were known to be binaries. Conversely, the ab­
sence of binarity in sdBs would support an argument that
they be formed as the consequence of a merger between two
white dwarfs (Iben & Tutukov 1986); the long gravitational
radiation timescale for such products is in stark conflict with
their numbers. Recent advances in understanding the phys­
ical processes of stellar evolution, in particular the mixing
? Based on observations made with the Isaac Newton Telescope,
La Palma
of helium in the stellar interior, have pointed to more di­
rect means of producing very blue horizontal branch stars
(Sweigart 1997). Whether they are created through a sin­
gle evolutionary channel or through several, it is imperative
to understand precisely the r“ole and hence the incidence of
binarity amongst sdBs.
The first major effort in this direction was a spectropho­
tometric study of the original Palomar­Green sdB sample
(Ferguson et al. 1984), in which a few dozen sdBs with
composite spectra were identified, from which a binary fre­
quency of ¸ 50% was deduced. Following a photometric
survey of a carefully selected sample of sdBs, Allard et al.
(1994) identified some 31 composites and assigned spectral­
types to the unseen companions. After allowing for binaries
excluded from the sample because their companion is too
hot and luminous or too cool and underluminous, Allard et
al. concluded that the incidence of sdB binarity lies in the
range 54--66%. This figure may now need to be revised in
view of more recent measurements of the Galactic luminos­
ity function (Gould et al. 1996) which show that previous
studies overestimate the number of low­luminosity stars on
the main­sequence. An estimated binary frequency of 64--
100% based on a balloon ultraviolet survey (Bixler et al.
1991) should be viewed with some caution in view of the
small number (8) of composites involved. In reviewing these
photometric studies, it was noted that the binary detection
criteria may be subject to target contamination by back­
ground sources. It was also noted that for those sdB stars
with composite spectra, the apparent luminosity ratio re­
quired the cool star to be a giant or subgiant (Allard et al.
1994, Theissen et al. 1995). Since the binary frequency es­
timates were calculated assuming that the companions are
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fl 0000 RAS

2 C.S.Jeffery & D.L.Pollacco
main­sequence stars, Theissen et al. (1995) concluded that
these estimates are likely to be in error.
In view of the major uncertainties surrounding previous
work on this important topic, it was decided to seek direct
spectroscopic confirmation of the binary nature of the com­
posite sdB stars, to search for evidence of main­sequence
companions to sdB stars and ultimately to re­measure the
sdB binary frequency. This paper reports on the first phase
of this project, namely the definition of suitable criteria for
the identification of binary sdBs and of methods for estimat­
ing effective temperature and luminosity ratios.
2 OBSERVATIONS
Given previous evidence that cool companions of spectral
types K and early M can be detected photometrically from
their small colour excess in the red, it was proposed to ob­
serve a large sample of sdBs at moderate resolution and high
S/N in the wavelength interval –5500 \Gamma 9000 š A. The object
was to detect spectroscopic features (e.g.TiO bands) which
could only be attributed to a cool companion.
Spectra of 40 sdBs were obtained with the intermediate
dispersion spectrograph (IDS) on the Isaac Newton Tele­
scope (INT) during the bright moon nights 1997, Febru­
ary 24 ­ 27, using a R300V grating and the No.3 Tektronix
CCD. In most cases the slit was aligned at the parallactic
angle to enable relative spectrophotometry, and its width
was matched to the instrumental resolution. In a very few
cases, the slit was rotated so as to include a faint nearby
companion, in order to eliminate it as a possible photomet­
ric contaminant. Spectra of spectrophotometric calibration
standards BD+25 ffi 2534, BD+33 ffi 2642, HZ 15 and G191--
B2B were also obtained.
The spectra were reduced in a uniform way using IRAF.
The subtraction of telluric absorption and nigh­sky emission
features caused the greatest difficulties, and for the faintest
targets could not be carried out completely satisfactorily.
The spectra were calibrated photometrically, but since a nar­
row slit was used, only relative fluxes are useful.
3 BINARY DETECTION
The observed sample included eight sdBs which had been
reported to have composite spectra by Ferguson et al. (1984,
3 stars) and/or Allard et al. (1994, 6 stars) and five sdBs
observed by Allard et al. and not reported as composite.
The sample overlaps were largely determined by telescope
scheduling.
The most striking discovery was that a significant frac­
tion of the sample (seven) showed strong Ca ii lines due
to the infrared triplet at –8498; 8542; 8662 š A (CaT; Fig. 1).
Since at the resolution of our observations the CaT lines are
only measurable in stars later than ¸F0 (Jones et al. 1984),
it represents an unequivocal signature of a cool compan­
ion. The CaT lines all lie close to hydrogen Paschen series
members (–8502; 8545; 8665 š A), which could arise in the sdB
spectrum. However the measured wavelengths, the relative
strengths of the lines and the absence of absorption due to
Pa13 (–8598 š A) are sufficient to remove any ambiguity.
The question posed by the photometric surveys, and one
Figure 1. Spectra of seven sdB stars in the region of the Ca ii
infrared triplet. The spectra have been normalized and offset,
but have not had any velocity corrections applied. Pixels badly
affected by a cosmic ray (cr) have been removed.
which the current work seeks to address, is whether any de­
tected companion is physically associated with the sdB star.
The largest angular separation between the sdB and any
companion is constrained by the seeing­disk of the sdB (in
the dispersion direction) and the slit­width (perpendicular
to this). For each target, a Palomar sky survey image 5'\Theta5'
was retrieved from the Digitized Sky Survey (DSS) held
at Space Telescope Science Institute. These were inspected
for possible nearby background sources. The distance of the
nearest detectable object to the sdB were measured for tar­
gets reported as composite in at least one survey. With two
exceptions, there was no evidence of a contaminating com­
panion.
PG1049+013 was identified as a composite candidate by
Allard et al. (1994). The DSS image shows a galaxy centred
9'' from the sdB star. The galactic limb overlaps the centre
of the sdB star; our spectrum shows the galactic nucleus
to be active with strong emission lines. PG1049+013 shows
no evidence for CaT and, in our spectra, does not show a
red excess. Hence it should not be considered a composite
system. PG1033+201 is discussed below.
4 THE CALCIUM TRIPLET AND COLOUR
EXCESS
A cool companion will redden the observed flux distribu­
tions. Four spec­
tral windows centred at – = 6050; 6700; 7050; 8650 š A with
widths \Delta– = 300; 300; 200; 200 š A respectively were identi­
fied as being relatively free of stellar and telluric absorption
and night­sky emission. The mean flux from each target in
each spectral window was measured and combined to give
colour indices f6700 =f6050 and f7050 =f6700 (Table 1). The
colour f8650 =f6700 gave similar results but is substantially
noisier. The colours are closely correlated (Fig. 2). This is be­
cause, at these wavelengths, the subdwarf effective temper­
ature TsdB has little effect on the flux gradient and because
the effect of interstellar reddening is similar to the addition
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Detection of subdwarf binaries 3
Table 1. Subdwarf colours. Two spectra of the same object are
labelled a and b.
Star f6700 =f6050 f7050 =f6700
CBS115 0.684 0.846
CBS129 1 0.786 0.861
CBS20 0.716 0.879
LB1941 0.801 0.931
LB2392 0.716 0.881
TON1273a 0.676 0.866
TON1273b 0.671 0.833
TON183 0.682 0.881
TON299 0.842 0.959
TON62 0.684 0.850
TON943 0.654 0.852
UV 01032+40a 0.661 0.847
UV 01032+40b 0.663 0.859
KUV 0411+1434 0.796 0.924
KPD 0422+5421 0.733 0.899
KUV 0511+176 0.693 0.860
KPD 0640+1412 0.741 0.883
KPD 0716+0258 0.700 0.857
PG 0757+425 0.869 0.941
PG 0823+465 0.682 0.858
PG 0825+428 0.811 0.918
PG 0837+401 0.689 0.856
PG 0838+164 0.636 0.857
PG 0839+399 2 0.689 0.849
PG 0850+170 0.651 0.831
PG 0856+121 0.651 0.840
PG 0907+123 0.679 0.862
PG 0934+186 0.669 0.847
PG 1012+008 0.651 0.857
PG 1033+201 0.734 0.919
TON1281 1040+234 0.793 0.919
PG 1047+003 0.641 0.838
PG 1049+013 3 0.671 0.856
PG 1051+501a 0.674 0.839
PG 1051+501b 0.635 0.834
Feige 36 1101+249 0.644 0.829
PG 1104+243 0.757 0.885
PG 1230+052 0.642 0.844
Feige 65 1233+426 0.684 0.864
PG 1244+113 0.657 0.843
PG 1248+374 0.760 0.931
HZ 40 1311+372 0.681 0.868
PG 1338+481 0.692 0.870
Feige 87 1338+611 0.755 0.902
PG 1449+653 0.765 0.922
PG 1458+423 0.688 0.865
1 : saturated – ! 6800 š A
2 : visual double
3 : AGN 9''
of a cool companion. The majority of sdB stars have colours
clustered in the interval 0:63 ! f6700 =f6050 ! 0:70. Experi­
mental error, variations of \Sigma5000K in TsdB and, principally,
reddening by 0:0 ! EB\GammaV ! 0:2 are sufficient to account for
the observed spread, but cannot be disentangled using the
current data alone. Redder colour indices imply excessive
extinction or the presence of a cool companion, as shown by
Allard et al. (1994).
There is an excellent correlation between colour excess
and the detection of CaT in our sample (Fig. 2). We find
a critical value f6700 =f6050 = 0:75. In the present sample,
Figure 2. The two­colour diagram for subdwarf B stars, as de­
scribed in the text. Triangles represent sdB stars which show the
Ca ii triplet (CaT). Squares represent sdB stars which do not
show CaT. Open symbols represent reported composite objects.
Filled symbols have not previously been reported as composite.
The reddening vector is shown. Labelled stars are discussed in
the text.
five stars redder than f6700 =f6050 ? 0:77 show CaT. Two of
these were previously reported composite. Two stars with
f6700 =f6050 ? 0:77 do not show CaT. CBS129 was satu­
rated at – ! 6500 š A, f7050 =f6700 indicates the true colour
to be unreddened. KUV0411+1434 shows strong Paschen
lines which inhibit detection of CaT (at the resolution ob­
tained) and may indicate a relatively early­type compan­
ion. All sample sdBs with 0:75 ! f6700 =f6050 ! 0:77 have
been reported composite, two show CaT. Only one sdB with
f6700 =f6050 ! 0:75, PG1033+201, has been reported com­
posite. There is a 12th magnitude star (GSC0142401026)
30'' distant which, being 3 magnitudes brighter, may have
affected aperture photometry.
5 NATURE OF THE COMPANION
For composite systems the entire flux distribution may to
first order be characterized by four parameters, TsdB , TK ,
EB\GammaV , and the luminosity ratio of the two stars LsdB=LK .
Determination of all of these requires, at least, blue­visual
and/or ultraviolet photometry and blue­visual spectroscopy.
However, it is still possible to deduce some general properties
of the CaT binary systems detected in this investigation.
Initially we assume EB\GammaV = 0.
5.1 Relative Luminosity
In particular, it is possible to determine the relative lumi­
nosities of the two components, albeit as a function of their
effective temperatures. Composite spectra are constructed
by adding fluxes derived from Kurucz' (1991) model atmo­
spheres in such proportion that synthetic indices f6700 =f6050
match those observed. The proportion required provides
LK=LsdB as a function of the effective temperatures TsdB
and TK . In practice, TsdB has little effect on the result. TK
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4 C.S.Jeffery & D.L.Pollacco
Figure 3. An observed colour (such as f6700 =f6050 ) defines a re­
lation between the luminosity ratio and effective temperature of
the cool companion in sdB composites. LK (T K ) relations for CaT
systems in the current sample are shown (solid lines), labelled
from top to bottom. The locus of the main sequence (ms -- bold
line) assumes a canonical value L sdB ú 27 L fi . T sdB is assumed to
be 30 000K. The effect of changing T sdB from 25 000 \Gamma 35 000K is
demonstrated for PG0757+425 and Feige 87 (dashed lines). Lu­
minosity ratios and spectral types (converted to T eff ) derived
from BVRI photometry by Allard et al. (1991) are marked for
comparison (asterisks).
is constrained by the absence of strong molecular features,
implying TK ? 4 000K, and the presence of CaT, implying
a spectral type later than F0. The luminosity ratio implied
for the seven CaT detections are shown in Fig. 3, together
with values inferred by Allard et al. (1994) from broad­
band BVRI photometry. Representative synthetic spectra
are compared with the observations for a range of TK in
Fig. 4.
The influence of TsdB on these ratios is modest (see
figure). The effect of metallicity is negligible. A systematic
problem is the normalization of the mean observed value
hf6700 =f6050 i ú 0:66 for apparently unreddened `single' sdB
stars with the value hf6700 =f6050 i ú 0:68 obtained from a
30 000 K sdB model atmosphere. This was removed by sub­
tracting a correction factor (0.02) from the theoretical colour
indices. Increasing this factor to 0.03 has a similar effect to
reducing the sdB temperature by 5 000 K.
Figure 4. Synthetic spectra for two composite sdBs. Each figure
shows the observed flux­calibrated spectrum for an sdB showing
the CaT triplet, together with synthetic spectra comprising the
sum of an sdB star (T eff = 30000K) and a cool companion with
T eff = (4000; 4500; 5000)K and relative luminosities selected to
match the colour f 6700 =f 6050 (see Fig. 3) The coolest model shows
strong molecular bands. There is little to distinguish between the
4500 K and 5000 K models.
In order to make further inferences about either com­
ponent without additional data, it is necessary to make
an assumption. For example, if the sdB stars are assumed
to have the canonical mass 0.55 M fi and log gsdB ¸ 4:4 +
0:04(TsdB=1000) (cf. Saffer et al. 1994), then all of the ob­
served companions are overluminous compared with the
main sequence, being giants or subgiants. Conversely, if the
cool components are assumed to be on the main sequence,
the hot star must be less luminous than normally assumed
for a `single' sdB star, possibly being a helium white dwarf
(cf. Jeffery et al. 1992).
The addition of broad­band photometry does not fully
remove this ambiguity. A similar conclusion regarding the
luminosity ratio of sdB composites was also obtained by Al­
lard et al. (1991), and by Theissen et al. (1995).
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Detection of subdwarf binaries 5
5.2 Absolute luminosity
The detection of CaT lines suggests an elegant means to
determine TK and LK uniquely. In cool stars of all spectral
types from F to mid­M the total equivalent width of CaT
(WCaT ) correlates strongly with log g (Jones et al. 1984)
such that log g ú 10:32 \Gamma 0:89WCaT , or WCaT = W(g). The
flux contribution due to the cool star relative to the total
flux at –8500 š A is a function of TK and LK and is denoted
here by fK;8500 =fsdB+K;8500 = F(TK ), since LK = L(TK)
is provided by the observed colour f6700 =f6050 if MsdB is
assumed. The surface gravity of the cool star is simply a
function of effective temperature and mass, g = G(TK ; MK ).
The apparent equivalent width of CaT W obs =
fK;8500 =fsdB+K;8500 :WCaT can thus be written as
W obs = F(TK )W(G(TK ; MK ))
and depends only on TK and weakly on MK . Thus, in prin­
ciple, a measurement of the total equivalent width of the
CaT lines W obs and a photometric colour index such as
f6700 =f6050 should be sufficient to determine both the ef­
fective temperature and luminosity of the cool companion.
Equivalent widths for each of the CaT components iden­
tified were measured, but found to be between 25% and
100% smaller than predicted from the observed colours. It
is likely that at the resolution of our observations the line
profile and continuum are insufficiently defined (see Fig. 1).
Higher resolution spectra will be required to pursue this
technique.
5.3 Radial velocities
The discovery of CaT in certain sdB spectra reveals a new
group of double­lined spectroscopic binaries (Feige 87 bina­
ries ?). One question is whether the orbital separations are
sufficiently small for the orbits of either star to be measured.
Evidence for this could be provided by velocity differences
between Balmer or Paschen (sdB) and calcium (K star) lines,
but is not accessible at the resolution of the current obser­
vations.
Evidence for short periods would also be provided
by the detection of variable radial velocities. Orosz et al.
(1997) recently reported a velocity study of composite sub­
dwarfs selected from the sample identified by Ferguson et
al. (1984). They have identified significant velocity changes
(? 3oe) for PG1224+309 and marginal velocity changes
for PG0825+428 (1:6oe) and PG1210+429 (1:3oe). Of these,
PG0825+428 is a known CaT binary, the others were not
observed in our sample. Orosz et al. (1997) failed to find
velocity changes in nine other stars (! 0:9oe), including
the CaT system PG1104+243 and the non­CaT system
PG1248+375.
A second important conclusion of the work by Orosz et
al. (1997) is that most secondaries of sdB composites in the
Ferguson et al. (1984) sample are late G dwarfs, rather than
early K stars. By deconvolving the composite spectra, they
derived the flux contribution of the secondaries in the wave­
length interval 5400 \Gamma 6600 š A, being in the range 10 \Gamma 51%.
However, assuming a 30 000 K sdB primary, with M and
log g given by Saffer et al. (1994), it is easy to show that in
order to provide the flux contribution cited, the secondaries
must be substantially overluminous compared with the main
sequence.
5.4 The detectability of main­sequence
companions
One aim of this investigation was to detect the main­
sequence secondaries of binary sdB stars. Spectroscopic fea­
tures have been detected only in sdB's which also show
a colour excess. Given a canonical sdB star, what is the
faintest main­sequence companion that would be detectable
via a colour excess or via the calcium infrared triplet?
The first can be determined by considering both stars
as black body emitters. Introducing appropriate model at­
mospheres has a small effect on this argument in that the
Paschen continuum affects the relative fluxes by slightly dif­
ferent amounts. The excess in a given colour f– 2 =f– 1 emitted
by a system containing two stars with effective temperatures
TB , TK and luminosities LB , LK is
f– 2 =f– 1 (B +K)
f– 2 =f– 1 (B) = 1 + r 2 \Theta (e h 0 =– 2 TK \Gamma 1)(e h 0 =– 1 TB \Gamma 1)
1 + r 2 \Theta (e h 0 =– 1 TK \Gamma 1)(e h 0 =– 2 TB \Gamma 1) ;
where h 0 = hc=k and
r 2 = ( LK
LB )( TB
TK ) 4 :
Values for LK can be obtained from TK by adopting
suitable main­sequence mass­radius and mass­luminosity re­
lations:
RK ¸ M ff
K ; ff ú 0:75;
and
LK ¸ M fi
K ; fi ú 2:0
for M ! ¸
1M fi , where RK ; RB are the radii of the two stars.
For the subdwarf, LB has already been defined by
M ú 0:55M fi ; log gsdB ¸ 4:4 + 0:04(TsdB =1000)
Under these constraints, an excess of ? 5% in the colour
f6700 =f6050 will only occur for main­sequence companions
with TK ? 5800K. For a slightly larger wavelength interval,
f8500 =f6050 for example, this limit drops to TK ? 5300K,
but thereafter is virtually unchanged over longer baselines,
including the photometric colour index V­I. Such an excess
is difficult to disentangle unambiguously from any excess
caused by interstellar reddening. For example, EB\GammaV = 0:1
produces a ¸ 3% excess in f6700 =f6050 . Note that our CaT
detections all have f6700 =f6050 colour excesses of more than
10%.
The question of detection via CaT is similar, but con­
cerns only the relative flux at 8500 š A and is independent
of reddening. The total equivalent width of CaT in main­
sequence stars is ¸ 6 š A, or ¸ 3 š A in the strongest compo­
nent, –8542 š A(Jones et al. 1984). The equivalent width of
Ca ii –8542 š A in the composite spectrum is then
W8542;B+K = W8542;K \Theta R 2
K :f –;K)
R 2
B :f –;B +R 2
K :f –;K
= W8542;K \Theta
R 2
K =(e h 0
=8542T K \Gamma 1)
R 2
B =(e h 0 =8542T B \Gamma 1) +R 2
K =(e h 0 =8542T K \Gamma 1)
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6 C.S.Jeffery & D.L.Pollacco
With the same assumptions as above for luminosities,
Ca ii –8542 š A should therefore show an equivalent width
greater than 100mš A for all main­sequence companions. Our
current observations cannot detect Ca ii –8542 š A with an
equivalent width less than about 800mš A. However the use
of CaT as a diagnostic tool for the exploration of binarity
amongst sdB stars exhibits great potential. In particular it
provides the only likely means of detecting M­type compan­
ions which are unlikely to be evolved or, as we have illu­
trated, to be identified from infrared photometry.
6 THE BINARY FREQUENCY OF
SUBDWARF B STARS
The overall aim of this investigation remains to deter­
mine securely the incidence and characteristics of binarity
amongst sdB stars. In this paper, the binary nature of sys­
tems identified as composite from their photometric indices
has been confirmed by the detection of lines due to the cool
companion. It has also been confirmed that, if the primaries
are true subdwarf B stars, then these cool companions are all
more luminous than main sequence stars of the same effec­
tive temperature. However the sample could not be used to
measure the binary frequency directly because it is strongly
biased towards known composite systems.
We have shown that our current observations are not
sensitive enough to detect the main­sequence companions
of sdB stars, either photometrically if the companions are
cooler than ¸ 5800K, or from Ca ii for all spectral types.
Indeed, it is unlikely that any photometric measure would
detect main­sequence companions cooler than ¸ 5000K, un­
less the interstellar contribution can be determined reli­
ably. However Ca ii lines due to main­sequence companions
should be observable with an equivalent width ¸ 100mš A.
Our primary conclusions enforce a re­evaluation of es­
timates of the binary frequency amongst sdB stars made by
Allard et al. (1994) and others. Allard et al. assumed that
the companions follow a standard main­sequence luminosity
function and that all companions with spectral types G8 to
M0 had been detected. Supplementing the detection of 31
composite systems in a sample of 100 stars with a number
of less luminous companions appropriate to a Schmidt­Kaler
(1982) main­sequence luminosity function, Allard et al. in­
ferred a binary frequency of the order of 54% -- 66%. It
is generally true for all stellar populations that the num­
ber of main­sequence stars of a given spectral class exceeds
the numbers of giants and sub­giants. Therefore the current
conclusion that all detected sdB companions are giants or
sub­giants implies that the Allard et al. measurement seri­
ously underestimates the overall binary frequency amongst
sdB stars.
Two questions remain: i) Do the companions to sdB
stars follow the same distributions in luminosity class and
spectral type as single stars? ii) Are the primaries of sdB
stars with composite spectra typical of apparently `normal'
sdB stars, or are they underluminous for some reason? Three
types of investigation are necessary: i) a detailed study of the
atmospheric parameters of both components in a number of
composite sdB stars, ii) a reliable measurement of the inci­
dence of the CaT triplet amongst sdB stars, together with
accurate photometry of those systems, iii) a wider search for
velocity changes in both normal and composite sdB stars.
These investigations are being pursued.
Acknowledgments
The authors acknowledge time allocated by the United
Kingdom Particle Physics and Astronomy Research Council
(PPARC) Panel for the Allocation of Telescope Time on the
Isaac Newton Telescope, La Palma, which is operated by the
Isaac Newton Group on behalf of PPARC, data analysis fa­
cilities provided by the Starlink Project which is run by the
Council for the Central Laboratory of the Research Councils
on behalf of PPARC, software provided by PPARC's Collab­
orative Computational Project No. 7 for the Analysis of As­
tronomical Spectra, and use of the Digitized Sky Survey pro­
duced at the Space Telescope Science Institute (see WWW
http://stdatu.stsci.edu/dss/dss acknowledgments.html).
REFERENCES
Allard F., Wesemael F., Fontaine G., Bergeron P., Lamontagne
R., 1994. AJ 107, 1565
Bixler J.V., Bowyer S., Laget M., 1991. AA 250, 370
Brown T.M., Ferguson H.C., Davidsen A.F., Dorman B., 1997.
ApJ 482, 685
Ferguson D.H., Green R.F., Liebert J., 1984. ApJ 287, 320
Gould A., Bahcall J.N., Flynn C., 1996. ApJ 465, 759
Green R.F., Schmidt M., Liebert J., 1986. ApJS 61, 305
Heber U., 1986. AA 155, 33
Heber U., Hunger K., Jonas G., Kudritzki R.P., 1984. AA 130,
119
Iben I., Jr., Yutukov A.V., 1986, ApJ 311, 742
Jeffery C.S., Simon T., Lloyd Evans T., 1992. MNRAS 258, 64
Jones J.E., Alloin D.M., Jones B.J.T., 1984. ApJ 283, 457
Kurucz R.L., 1991a. in 'Precision Photometry: Astrophysics of
the Galaxy', eds. A.G.Davis Philip, A.R.Upgren, K.A.Janes,
L.Davis Press, Schenectady
Orosz J.A., Wade R.A., Harlow J.J.B., 1997. AJ 114, 317
Saffer R.A., Bergeron P., Koester D., Liebert J., 1994. ApJ 432,
351
Schmidt­Kaler T.H., 1982. in Landolt­Bornstein New Series Vol.
2b, eds. K.Schaifers & H.H. Voigt (Springer, New York).
Sweigart A.V., 1997. ApJ 474, L23
Theissen A., Moehler S., Heber U., Schmidt J.H.K., de Boer K.S.,
1995. AA 298, 577
Yi S., Demarqu P., Oemler A., Jr., 1997. ApJ 486, 201
c
fl 0000 RAS, MNRAS 000, 000--000