Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/~csj/papers/journal/H3269.PS Äàòà èçìåíåíèÿ: Fri Jan 18 19:36:56 2002 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 07:47:45 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: massive stars

Astronomy & Astrophysics manuscript no.
(will be inserted by hand later)
Physical parameters for subdwarf B stars with composite
spectra ?
R. Aznar Cuadrado and C. S. Jeery
Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland
Abstract. New intermediate-resolution spectra have been obtained for a number of subdwarf B stars having both
single and composite spectra. Physical parameters have been determined for the sdB stars and, in composite-
spectrum systems, their cool companions. For these binaries, we have developed a method which uses the blue-
optical spectrum to determine the eective temperatures of both stars, the surface gravity of the hot stars and
the radius ratio of the system. The surface gravity of the cool star is measured using the infrared calcium triplet.
The surface gravities of these cool companions identify them as main-sequence stars with masses in the range 0.8{
1.2 M , conrming a previous energy distribution analysis. There is also evidence that the composite-spectrum
sdBs are more helium-poor than single-spectrum sdBs.
Key words. Stars: formation, early-type, subdwarfs, fundamental parameters, binaries: spectroscopic.
1. Introduction
Subdwarf B (sdB) stars are the most extreme of hor-
izontal branch stars, being predominantly helium stars
of approximately half a solar mass overlaid by a
hydrogen-rich veneer (Heber 1986). Common in both our
own galaxy (Green et al. 1986) and in giant ellipticals
(Brown et al. 1997), they present a problem for stellar
evolution theory: how does a red giant star dispose of its
entire hydrogen-rich envelope prior to core helium igni-
tion?
From an initial supposition that sdB stars were pre-
dominantly single, models including enhanced mass-loss
rates (e.g. D'Cruz et al. 1996), and white dwarf merg-
ers (Iben 1990, Saio & Jeery 2000) have been investi-
gated. However a signicant fraction of sdB stars are
known to have composite spectra (Ferguson et al. 1984,
Allard et al. 1994, Jeery & Pollacco 1998), leading to
suggestions of a binary fraction between 50% and 100%.
Recent radial velocity studies (Saer et al. 2001) have
identied three distinct groups: 1) single-spectrum sdBs
with small or negligible velocity variations, 2) single-
spectrum sdBs with large velocity variations and likely
periods of hours to days and 3) composite-spectrum sdBs
with small velocity variations and relatively long periods.
Another recent investigation nds that the second group
comprises some 60 8% of all sdBs (Maxted et al. 2001).
Send oprint requests to: C. S. Jeery, e-mail:
csj@star.arm.ac.uk
? Based on observations made with the Isaac Newton and
William Herschel Telescopes.
The clear conclusion is that binary evolution plays a sig-
nicant r^ole in the formation of sdB stars.
For the group (2) sdBs, the binary companion is invisi-
ble. Radial velocity and, in some cases, light curve studies
will yield vital clues about the overall dimensions of these
binary systems, and hence about their previous evolution.
For group (3), dynamical information is less accessible {
although very careful observations over a long time base
will be an important tool in this endeavour. Fortunately
and by denition, the binary companion in a composite
spectrum can be seen.
We have already examined the ux distributions
for a number of binaries (Aznar Cuadrado & Jeery
2001: Paper I) and concluded that the companions are
main sequence stars. This contradicted previous analyses
(Allard et al. 1994, Jeery & Pollacco 1998) which sug-
gested that the companions were overluminous. Therefore
it is important to verify the results spectroscopically.
Such an approach carries an additional bonus. The near-
infrared triplet lines of ionized calcium are very strong
in late-type stars and provide a sensitive diagnostic
of surface gravity, providing the eective temperature
and metallicity are known (Cohen 1979, Jones et al. 1984,
Smith & Drake 1987, Jrgensen et al. 1992). If both sur-
face gravities and the radius ratio can be measured, the
mass ratio can be determined directly and provides a very
important tool for exploring the previous evolution of this
group of sdB stars.
In this paper we introduce the methods used to analyse
the spectra of composite-spectrum sdB stars, and present
results for an initial sample. The methods are tested by

2 Aznar Cuadrado and Jeery: Physical parameters for composite sdB stars
Table 1. Instrumental congurations.
Dates Telesc. Spec. Grating Dichroic Slit Detector R =  A
1997 Sep 4 INT IDS R1200R { 1.6" TEK3 5000 8000{8800
1997 Sep 12,13 WHT ISIS R1200B 5700 1.2" TEK1 4000 4200{4650
R600R 5700 1.2" TEK2 4300 8000{8850
1998 Oct 3,4 WHT ISIS R1200B 5300 1.2" TEK1 4000 4200{4650
1999 Mar 26,27 INT IDS R1200B { 1.2" TEK5 2500 3800{4700
R1200R { 1.2" TEK5 5000 8000{8850
Table 2. Spectroscopic observations of single and com-
posite sdB stars.
Star Telesc. HJD cen exp S/N
(-2450000) (  A) (s)
PG 0004+133 WHT 705.704 4400 1200 80
PG 0110+262 WHT 704.639 4400 1800 92
WHT 705.733 8400 1800 74
PG 0229+064 WHT 1091.702 4400 200 140
PG 0240+046 WHT 1091.721 4400 850 140
PG 0342+026 WHT 705.748 4400 900 93
PG 0749+658 INT 1264.399 4250 300 70
INT 1264.538 8400 600 48
PG 0839+399 INT 1265.387 4250 600 50
PG 1104+243 INT 1265.667 4250 300 52
INT 1264.596 8400 300 65
PG 1233+427 INT 1265.591 4250 150 60
PG 1701+359 WHT 704.359 4400 900 150
WHT 704.359 8400 900 73
PG 1718+519 WHT 705.377 4400 1200 80
WHT 705.378 8400 1200 60
PG 2110+127 WHT 704.399 4400 1200 100
INT 696.543 8400 900 90
PG 2135+045 WHT 1090.366 4400 900 70
INT 696.580 8400 1800 35
PG 2148+095 WHT 705.427 4400 1200 170
WHT 705.426 8400 1200 100
PG 2259+658 WHT 704.454 4400 1800 65
providing independent analyses for a number of single-
spectrum sdB stars.
2. Observations and data reduction
The observations used in this analysis have been col-
lected from the William Herschel (4.2m) and the Isaac
Newton (2.5m) Telescopes at the Roque de los Muchachos
Observatory on La Palma between 1997 and 1999.
Instrumental setups for each observing run are given in
Table 1.
The stars in the current analysis were all selected be-
cause they had been observed with IUE and their ux dis-
tributions were well understood (Aznar Cuadrado 2001).
The possibility that composite spectrum systems might be
chance alignments has also been examined for these stars
(ibid.). The sample included a number of stars known to
have composite spectra or to have an infrared colour ex-
cess, as well as a comparable number considered to be
`single-spectrum' systems. The log of observations is given
in Table 2.
All stellar spectra were bias subtracted, at-elded,
sky subtracted and one-dimensional spectra were ex-
tracted using standard iraf packages. Copper-argon-neon
comparison spectra were used to provide a wavelength cal-
ibration corresponding to each stellar observation. Spectra
were normalized with respect to the local continuum.
The blue spectra are dominated by the hydrogen
Balmer series, which are both temperature and gravity
sensitive. Other prominent features present in both single
and composite-spectrum subdwarfs are the He i 4388  A
and He i 4471  A lines, the magnesium doublet at 4481
 A, the silicon triplet at  4553, 4568 and 4575  A, and the
C ii 4267  A doublet, amongst others. The near-infrared
spectra of composite sdBs are dominated by the cal-
cium triplet at  8498, 8542 and 8662  A. There are
many weaker unidentied features. Several broad hydro-
gen Paschen lines come from the hot subdwarf. These
are eectively invisible because the subdwarf spectrum is
swamped by the cool star. However, they have the eect of
depressing the apparent continuum in this spectral range.
3. Radial velocities
The spectra in our sample included both single and com-
posite systems. Their radial velocities were measured by
cross-correlation with theoretical models for both hot and
cool star spectra.
This process includes the subtraction of the continuum
and the conversion of the wavelength scale to logarith-
mic units, before calculating the cross-correlation func-
tion (ccf). Several spectral regions were excluded from
the ccf, including wavelengths corresponding to bad CCD
columns, cool-star features in composite systems (e.g. the
G-band at  4200  A), broad Balmer lines, or strong lines
from the observed spectrum that didn't appear in the syn-
thetic spectrum. The ccf was then converted to velocity
units and the position of its peak was measured by tting
a Gaussian.
The cross-correlation templates used for measuring the
radial velocities v rad of each observed spectrum were taken
to be the best-t model spectrum for the total system
as described below. Hence, for single spectrum sdBs, we
obtain a single radial velocity. For composite systems, the

Aznar Cuadrado and Jeery: Physical parameters for composite sdB stars 3
Table 3. Heliocentric radial velocity measurements of sin-
gle and composite sdB stars.
Star HJD sdB K star
(-2450000) v v ôv
Single
PG 0004+133 705.704 {20.64
PG 0229+064 1091.702 7.64
PG 0240+046 1091.721 63.42
PG 0342+026 705.748 13.48
PG 0839+399 1265.387 25.78
PG 1233+427 1265.591 65.58
PG 2259+658 704.454 {14.46
Composite
PG 0110+262 704.639 1.06 |{ 35.9
705.733 |{ 36.92
PG 0749+658 1264.399 {21.07 |{ 0.2
1264.538 |{ {21.22
PG 1104+243 1265.667 {4.68 |{ 8.4
1264.596 |{ {13.04
PG 1701+359 704.359 {121.93 |{ 13.9
704.359 |{ {135.82
PG 1718+519 705.377 {63.33 |{ 14.7
705.378 |{ {48.61
PG 2110+127 704.399 27.01 |{ 1.1
696.543 |{ 25.91
PG 2135+045 1090.365 {30.01 |{ 2.0
696.580 |{ {28.02
PG 2148+095 705.427 {152.71 |{ 34.8
705.426 |{ {117.92
blue spectrum is dominated by lines from the hot star
and so provides the sdB star velocity. The red spectrum is
dominated by calcium lines from the cool companion and
hence gives the cool star velocity.
The heliocentric velocities measured from each obser-
vation are given in Table 3. Errors on individual velocities
are the formal errors given by the least squares Gaussian
t to the ccf peaks. The actual errors are probably much
larger, but diôcult to determine quantitatively (the typi-
cal ccf width is 200-400 km s 1 ). The standard deviation
about the mean (14 km s 1 ) may be a better indication.
In composite systems, the dierence ôv between the
two component radial velocities would be a measure of the
lower limit to the orbital velocity of the sdB star. Systems
with large velocity dierences between hot and cool com-
ponents could be short-period systems, i.e. PG 0110+262,
PG 1701+359, PG 1718+519 and PG 2148+095.
In the interim, other groups have used radial velocity
studies to detect binary sdB stars (Maxted et al. 2001,
Saer et al. 2001). From our sample, the single-
spectrum sdB PG0839+399 is a radial velocity binary
(Maxted et al. 2001), while the composite-spectrum sdBs
PG0749+658 and PG 1701+359 do not show detecTable
velocity variations (ibid.). Consequently, our conclusions
may be subject to unidentied systematic errors. In
the case of PG0229+064 heliocentric radial velocities of
+8 2 and +8 3 km s 1 measured on 1998 July 20 and
September 13 respectively (Ramspeck et al. 2001) are es-
sentially identical with our own measurement. Additional
velocities for PG 1233+427 (53  2 km s 1 : 2000 January
30 and 31), PG 0342+026 (15  2 km s 1 : 1998 Sep
11, 14  2 km s 1 : 2000 Jan 30) and PG 0749+658
( 11  2 km s 1 : 2000 Jan 31) have also been communi-
cated to us (Edelmann & Heber, private communication).
These are not suôciently dierent from our own mea-
surements to make us suspect that any are short-period
spectroscopic binaries.
Prior to analysis, the wavelengths of the observed spec-
tra were corrected to the laboratory rest frame by applying
these measured radial velocity shifts.
4. Spectral analysis
The aim of this study is to measure the various phys-
ical parameters, including eective temperature ( T e ),
surface gravity ( log g), chemical composition and, for bi-
nary stars, the radius ratio directly from optical and near-
infrared spectra. This is achieved by nding the best-t
model spectra within a grid of theoretical models using
the method of  2 minimization.
The methods for hot single stars have been de-
scribed in detail (Jeery et al. 2001), including the gen-
eration of model atmospheres (sterne), the synthesis of
model spectra (spectrum) and the least-squares min-
imization (sfit). These techniques have been extended
to model binary stars which consist of both a hot and
a cool component. Although they have already been in-
troduced (Jeery & Aznar Cuadrado 2001), the method
is described more formally here.
The fundamental assumption is that both cool and hot
absorption sources are primarily stellar. We consider the
observed normalized spectrum S  . Our aim is to recon-
struct the best-t model spectrum
s  =  2
1 f 1 +  2
2 f 2
 2
1 f c1 +  2
2 f c2
where  are the stellar angular diameters, f  is the theo-
retical emergent ux, f c is the continuum ux and sub-
scripts 1 and 2 refer to the individual stellar compo-
nents. The uxes are functions of each star's properties:
f 1 = f 1 ( T e1 ; log g 1 ; : : :) and f 2 = f 2 ( T e2 ; log g 2 ; : : :).
The angular diameters cannot be solved for explicitly from
S, but their ratio gives R 2 =R 1 =  2 = 1 .
The principal free parameters which govern the mea-
sured spectrum are thus:
{ T e 1 ; T e 2 : eective temperature,
{ log g 1 ; log g 2 : surface gravity,
{ R 2 =R 1 : radius ratio,
{ v sin i 1 ; v sin i 2 : rotational velocity,
{ v 1 ; v 2 : radial velocity,
{ v t1 ; v t2 : microturbulent velocity,
{ y 1 ; y 2 : helium abundance 1 ,
1 The helium abundance is measured from models in which
the fractional abundance by number nHe is specied. Several

4 Aznar Cuadrado and Jeery: Physical parameters for composite sdB stars
Table 4. Atmospheric properties of single-spectrum sdB stars measured spectroscopically using sfit and previously.
Star T e log g y Reference
PG0004+133 y 25 025 400 4.970.10 0.010.01 sfit
(Fig. 1) 25025 400 Paper I
24 7001300 4.50.2 0.028 Moehler et al. 1990a
PG0229+064 18 0001025 4.350.10 0.330.01 sfit
20100 400 Paper I
19000 950 4.550.10 0.16 Ramspeck et al. 2001
22 0001000 4.650.15 0.137 Heber et al. 1999
PG0240+046 36200 400 6.250.10 1.940.02 sfit
34 8001850 Paper I
37 0002000 5.30.3 1.222 Thejll et al. 1994
PG0342+026 24000 375 5.170.10 0.010.01 sfit
27900 975 Paper I
24 0001200 4.900.20 0.003 Heber et al. 1999
25 0002500 5.250.20 0.000 Theissen et al. 1995
26 2201000 5.670.15 0.004 Saer et al. 1994
22 3001000 5.000.30 0.000 Lamontagne et al. 1987
PG0839+399 37300 500 6.020.10 < 0.010.01 sfit
35 6001800 Paper I
36 1001000 5.910.15 0.002 Saer et al. 1994
PG1233+426 25560 550 5.520.10 < 0.010.01 sfit
28750 900 Paper I
26 5001000 5.600.15 0.005 Saer et al. 1994
26 2001500 5.300.30 0.000 Lamontagne et al. 1985
PG2259+134 28500 600 5.930.10 0.020.01 sfit
28350 750 Paper I
22 5002500 5.000.20 0.000 Theissen et al. 1995
28 5001600 5.300.20 0.022 Theissen et al. 1993
y T e assumed from Paper I.
{ [Fe=H] 1 ; [Fe=H] 2 : metallicity 2 ,
The radial velocities have already been discussed. Ideally,
stellar composition entails many more free parameters
than metallicity and helium abundance alone, but requires
high-resolution spectroscopy to measure, as does the mi-
croturbulent velocity. Helium abundance cannot be mea-
sured directly for cool sources. Tests showed that [Fe=H] 2
cannot be uniquely determined from the given data.
Similarly, given the magnitude of errors in T e 1 , it is not
practical to measure [Fe=H] 1 in detail. Thus the follow-
ing assumptions are made. The abundances of all elements
other than hydrogen and helium are in proportion to their
cosmic abundances, with [Fe=H] 1 = [Fe=H] 2 = 0. The he-
lium abundance of the cool star is normal: y 2 = y . The
adopted microturbulent velocities are typical for early-
type stars v t1 = 5 km s 1 and main-sequence late-type
stars v t2 = 2 km s 1 . The latter assumption is very impor-
authors give the number ratio y = nHe= nH instead. We give
the latter in Tables 4 and 5 and elsewhere.
2 Providing the stars are hydrogen-rich, the metallicity
( [Fe=H]) represents the logarithm of the value relative to the
solar metal abundance, assuming a solar distribution of ele-
ments heavier than helium.
tant as it aects both the metallicity [Fe=H] 2 (see above)
and the derived radius ratio R 2 =R 1 . We have adopted
v t2 = 2 km s 1 in order that the latter quantity as de-
rived from spectral tting be as consistent as possible with
 2 = 1 derived from spectrophotometry (Paper I) where we
used cool star models computed with v t2 = 2 km s 1 .
Secondary eects on T e2 and log g 2 are not signicant
here.
4.1. Model grids
The model atmospheres and ux distributions used to
analyse the hot star were computed with the line-
blanketed plane-parallel LTE code sterne. The high-
resolution spectra were calculated with the LTE code
spectrum (see Jeery et al. 2001).
The model atmospheres were calculated on a
three-dimensional rectangular grid dened by T e =
18 000(2 000)40 000 K, log g = 4:5(0:5)7:0, and com-
position nH= 1- n He , n He = 0:01; 0:10(0:10)0:60 and
[Fe=H]=0. The larger value of nH or n He is reduced to
compensate for trace elements.
Synthetic spectra were calculated on wavelength in-
tervals 3800 5020  A (blue) and 8450 8670  A (CaT).

Aznar Cuadrado and Jeery: Physical parameters for composite sdB stars 5
Table 5. Atmospheric properties of composite sdB stars measured spectroscopically using sfit and previously.
Subscript 1 refers to the hot subdwarf, subscript 2 refers to the cool companion.
Star T e 1 log g 1 y 1 T e 2 log g 2 R 2 =R 1 Ref. y
PG 0110+262 21 000 750 5.170.17 < 0.010.01 5 250800 4.530.21 3.21.9 sfit
21 050 575 5 485200 4.20.2 1
21 0001000 < 5:900.10 5 000500 6.0 2
22 0001000 < 5:500.10 5 500500 4.4 3
22 0001500 4 500500 7.8 4
PG 0749+658 25 400 500 5.700.11 < 0.010.02 5 000500 4.580.24 3.51.2 sfit
25 050 675 5 600300 3.90.3 1
24 6001000 5.540.15 0.004 5 
23 5001500 4 125500 6.3 4
PG 1104+243 32 8501550 5.400.12 0.010.02 6 4001000 4.300.31 5.91.1 sfit
28 000 875 5 735150 6.10.2 1
27 5001500 4 300500 10.6 4
27 2001500 5.500.30 6
28 0005000 4 6001000 9.8 7
PG 1701+359 32 5001325 5.750.12 < 0.010.01 6 0001000 4.600.23 2.71.8 sfit
36 075 700 6 450230 4.80.2 1
30 0002500 5.000.20 0.000 8
28 5001500 4 000500 6.2 4
26 2501250 5.800.20 9
PG 1718+519 29 0001550 6.000.14 < 0.010.01 5 200400 4.550.23 4.81.6 sfit
29 9501100 5 92570 8.20.3 1
30 0002500 5.000.20 0.000 5 125500 8
25 0001500 4 300500 10.7 4
23 3001000 4.250.20 9
PG 2110+127 26 5001700 5.200.18 < 0.010.06 5 400400 4.400.24 4.71.1 sfit
(Fig. 2) 24 9006500 5 500575 5.50.3 1
30 0002500 5.000.20 0.000 5 375500 8
33 7001000 5.330.15 0.004 5
26 0001500 4 500500 10.4 4
PG 2135+045 28 400 800 4.800.22 < 0.010.01 5 000500 4.400.30 3.10.5 sfit
26 3259950 4 3751790 4.70.6 1
32 1001000 4.790.15 0.016 5 
27 0001500 4 400500 6.5 4
PG 2148+095 30 000 860 4.900.16 < 0.010.01 5 700400 4.400.31 3.00.8 sfit
(Fig. 4) 22 950 825 4 375200 5.00.2 1
25 0001000 < 5:800.10 5 000500 6.0 2
26 0001500 4 300500 7.9 4
y References: 1 = Paper I; 2 = Ulla & Thejll 1998; 3 = Thejll et al. 1995; 4 = Allard et al. 1994;
5 = Saer et al. 1994; 6 = Lamontagne et al. 1987; 7 = Ferguson et al. 1984; 8 = Theissen et al. 1995;
9 = Theissen et al. 1993.
 Saer et al. 1994 did not recognise the composite nature of these stars.
Linelists comprising some 142 absorption lines of hydro-
gen, helium, carbon, magnesium and silicon were taken
from the list of assessed data for hot stars lte lines
(Jeery 1991). Microturbulent velocity v t = 5:0 km s 1
and solar abundances for all elements other than hydro-
gen and helium were assumed (see above).
Model atmospheres and ux distributions used to
analyse the cool star were taken from the Kurucz'
standard grid of atlas models (Kurucz 1993a), for
T e = 3500(500)8000, log g = 2:0(0:5)4:5, [Fe=H] =
0:5; 0:3; 0:0 and v t = 2:0 km s 1 .
Grids of high resolution spectra were calculated in the
same spectral regions as for the hot star using Kurucz'
code synthe (Kurucz 1993b, Jeery et al. 1996) assum-
ing a microturbulent velocity v t = 2 km s 1 .

6 Aznar Cuadrado and Jeery: Physical parameters for composite sdB stars
4.2. SFIT
For a given observation, an optimum t was obtained by
minimizing  2 ,
 2 =
X

(S  s  ) 2
 2

; (1)
the weighted square residual between the normalized ob-
served spectrum, S  , and the theoretical spectrum,
s 0
 = s  ( T e ; log
g)
I(
)
V (v sini; ); (2)
where I(
) and V (v sini; ) represent the instrumen-
tal and rotational broadening, respectively. Instrumental
broadening is measured from the width of the emission
lines in the copper-argon comparison lamp. The  2 mini-
mization was carried out using a variant of the algorithm
amoeba (Press et al. 1989, Jeery et al. 2001).
In the construction of  2 , each wavelength point was
given a weight w  = 1=  , the inverse of the standard
deviation of the mean normalized ux in line-free regions.
In our spectra    0:01. Some spectral regions needed
to be excluded from the t (e.g. bad columns or strong
lines missing from the theoretical spectrum). In sfit, such
defects are masked by increasing  in appropriate wave-
length intervals. We used   = 0.1.
In any such tting procedure, the normalization of
the observed spectrum can be of crucial importance
(Jeery 1998). The problem is to normalize the observed
spectrum correctly without, for example, compromising
the wings of broad absorption lines. This is particularly
diôcult when there is an unknown contribution to the
line opacity from metal lines in a cool star companion, so
that there may be no \true" continuum anywhere in the
observed spectrum.
The initial normalization was performed by tting a
low-order spline function to a series of pseudo-continuum
points, usually the highest points in the spectrum. sfit
includes two re-normalization algorithms which may be
used to optimize the t (cf. Jeery et al. 1998). One com-
putes a low-order polynomial t to the residual, the other
applies a low-pass Gaussian lter. A second order polyno-
mial was used to renormalize the spectrum in wavelength
ranges 4200 { 4650  A and 8000 { 8850  A while a third or-
der polynomial was used in the region of high order Balmer
lines (H 9 , H 8 , H  , etc). Because low-order polynomials are
used, individual line proles are unaected.
In principle and for suitable data with negligible noise,
sfit can solve simultaneously for as many parameters as
required. In practice, it is necessary to restrict the free
solution to between two and three parameters at a time,
keeping others xed, and to iterate until the optimum so-
lution is obtained. sfit requires a set of initial estimates
for the free parameters. Results from the ux distribution
analysis (Paper I) were used for T e1 ; T e 2 and the radius
ratio. Standard values were assumed for log g 1 ; log g 2 and
y 1 .
4.3. Analysis: single stars
For single sdB stars, sfit was applied to the blue spectra.
The rst parameter derived was the composition y of the
sdB star. Within the T e range of sdB stars, the strength
of helium lines depends far more on helium abundance
than T e or log g. T e and log g were found next by
nding the best t to the Balmer lines. Rotational broad-
ening is small compared with the instrumental proles in
these spectra.
Table 4 presents the results of the spectral analysis of
single sdB stars (labeled sfit), together with the results
of the ux distribution analysis (Paper I) and results from
literature.
4.4. Analysis: binary stars
For composite sdB stars, sfit was applied separately to
both blue and red spectra. Again, the rst parameter to
be xed from the analysis of the blue spectrum is the
composition of the sdB star, i.e. y 1 . Afterwards, T e 1 ,
log g 1 of the sdB star and R 2 =R 1 are found by tting the
observed Balmer lines. The lower limit of the model grid
was occasionally too large to t the observed helium lines.
In these cases only an upper limit to y 1 can be given.
The radius ratio R 2 =R 1 is directly related to the eec-
tive temperatures of both components, so must be a \free"
parameter whenever either T e is free. The contribution
of the cool companion in the blue spectrum is re ected
in the presence and strength of some metallic lines, being
good indicators of the temperature of the cool star and the
radius ratio of the system. Therefore, the blue spectrum is
also used to x T e 2 and R 2 =R 1 . It was frequently diôcult
to nd a solution for T e1 , T e 2 and R 2 =R 1 consistent
with the ux distribution analysis (Paper I). In cases of
con ict, we attempted to keep R 2 =R 1 consistent between
the two studies, although even this was not always possible
(Table 5).
In the initial analysis of the blue spectrum, the cool
companion is assumed to have log g 2 = 4:5 (cf. Paper I).
Applying sfit gives new values, rst for y 1 , then for T e1 ,
log g 1 , T e 2 and R 2 =R 1 .
With these improved estimates for the sdB star prop-
erties, the red spectrum is analyzed. In particular, log g 2
is determined by tting the calcium triplet.
A second analysis is now performed in the blue in or-
der to rene the t to the hot star spectrum, using the
new parameters for the cool star. The above procedure is
repeated until the solutions converge.
Table 5 presents the results for composite spectrum
sdB stars, together with previous results from the liter-
ature. Solar metallicity was adopted for all stars except
PG 1104+243, for which we adopted [Fe=H] 2 = 0:5.
The instrumental prole is large compared with any ro-
tational broadening except in the cases of PG 1701+359
and PG 1718+519, where v sin i = 5 and 10 km s 1 , re-
spectively, were adopted.

Aznar Cuadrado and Jeery: Physical parameters for composite sdB stars 7
Table 6. Comparison of binfit and sfit for a test binary.
Parameter Model binfit sfit
T e 1 ( K) 24 000 24 060260 24190300
log g 1 6.0 6.020.05
y 1 0.10 0.110.01
T e 2 ( K) 4 500 4 550150 4 500200
log g 2 4.5 4.540.05
R 2 =R 1 6.29 5.900.16 6.270.20
Table 5 includes values for R 2 =R 1 for some previous
papers. These have been computed from cited ux ratios
at 5500  A, eective temperatures and/or spectral types
and an appropriate bolometric correction.
4.5. Errors
The formal errors associated with the best t parameters
x i are given by the diagonal elements ô i = ( 1 ) ii of the
inverse of the covariance matrix , whose elements are
given by
 ij =
X

 @s 
@x i
@s 
@x j
= 2


: (3)
Since sfit is never run with all parameters free, the full
covariance matrix is never computed. Thus the total errors
 i need to be obtained from a careful analysis of the partial
errors ô i .
For a single-star spectrum, only the derivatives be-
tween T e , log g and y need to be calculated. In the case
of a binary system, the derivatives between the physical
parameters of both components of the system are required.
These have to be evaluated numerically, e.g.
@x 1
@x 2
= x 1 0 x 1

x 2
; (4)
where x 1 represents parameters of the sdB star and x 2
represents parameters of the cool star.
x 2 is an increment
used to compute a change in x 1 , usually 1% of x 2 . x 1 0 are
parameters derived when using x 2 +
x 2 as input to the
t.
The errors given in Tables 4 and 5 are total errors. For
example the total error  in T e 1 is given by
 2
T e 1
= ô 2
T e 1
+
 @ T e 1
@ log g 1
 2
ô 2
log g 1
+
 @ T e 1
@ y 1
 2
ô 2
y1 +
 @ T e 1
@ log g 2
 2
ô 2
log g 2
+
 @ T e1
@ (R 2 =R 1 )
 2
ô 2
R2=R1 : (5)
In addition to the formal errors cited, there are ad-
ditional systematic errors. Principal amongst these are
in the metallicity of the cool star, [Fe=H] 2 . This has a
strong in uence on the measurement of log g 2 from the
Fig. 1. Normalized blue spectrum of the single sdB star
PG 0004+133 (histogram) together with the best t model
spectrum (polyline). The symbol  marks a CCD defect.
calcium triplet, and hence on the radius ratio R 2 =R 1 be-
cause the latter is primarily xed by the strength of the
metal-lines relative to Balmer lines in the blue spectrum.
High-resolution spectra will be required to address this
problem.
There are also systematic dierences between the
methods used to obtain R 2 =R 1 in this paper and in
Paper I. To compare these methods we have constructed a
simple test. The energy distribution and normalized spec-
trum of a binary system containing a typical sdB star
and a main-sequence star were computed. These were re-
sampled to mimic the observational data available to us
in each investigation. The data were then analyzed using
binfit (to t the ux distribution, Paper I) and sfit in-
dependently. The model parameters and the results of the
 2 analysis are shown in Table 6. The results are all consis-
tent with the test model except the value of R 2 =R 1 given
by binfit. The errors associated with this parameter are
possibly underestimated, since they are only derived from
the formal error in the angular diameters.
5. Results
5.1. Single-star spectra
Fig. 1 shows the best t model for the single sdB star
PG 0004+133. In addition to results reported in Table 4,
the following individual remarks are noted.
PG 0004+133: Since only the H line is available, we
have assumed T e from Paper I.
PG 0229+064: with y = 0:33, this is a helium-rich sdB
star (Heber et al. 1999). The metal lines imply a higher
metal abundance than assumed in the model. This has also
been found by Ramspeck et al. (2001) who, in particular,
nd C and N overabundant by nearly one dex.

8 Aznar Cuadrado and Jeery: Physical parameters for composite sdB stars
Fig. 2. Normalized blue spectrum of the composite
PG2110+127 (a) together with the best t composite
model spectrum (b) formed by adding models with (c)
T e 1 =26 500 K, log g 1 =5.20, y = 0:01, v t1 = 5 km s 1
and (d) T e 2 =5400 K, log g 2 =4.40, [Fe=H] = 0:00,
v t2 = 2 km s 1 with radius ratio R 2 =R 1 = 4:7. The model
spectra have been velocity shifted and degraded to match
the observations. The symbol  marks a CCD defect.
PG 0240+046: an even more helium-rich sdB star with
66% of He abundance, consistent with a previous abun-
dance of 55% (Thejll et al. 1994).
PG 0342+026: C, Si and Mg appear to be underabun-
dant relative to the assumed solar composition.
PG 0839+399 and PG 1233+426: the helium abun-
dance is below the measurement threshold, and metals
are underabundant.
PG 2259+134: C appears to be underabundant.
5.2. Composite spectra
Results for sdB stars with composite spectra are shown
in Table 5. Figs. 2 and 3 show best ts for the composite
sdB star, PG 2110+127. The radius ratios (R 2 =R 1 ) and
Fig. 3. Normalized red spectrum of the composite
PG 2110+127 around the infrared calcium triplet (his-
togram) together with the best t model spectrum (poly-
line).
Fig. 4. As in Fig. 1 but for the composite sdB star
PG 2148+095.
hence, by implication, the radii of the cool stars (R 2 ) are
all smaller than measured previously.
In nearly all cases, the He i lines are weaker than pre-
dicted by models with n He1 = 0:01, implying hot star
He abundances below this value. In addition, metal lines
from the hot star, (e.g. silicon, carbon and magnesium),
appear to be too strong in the model compared with the
observations. Since we assumed [Fe=H] 1 = 0:0, this im-
plies that metals are generally underabundant in the sdB
stars in our sample. This requires conrmation from high-
resolution spectroscopy. In addition to results reported in
Table 5, the following individual remarks are noted.
PG0110+262 and PG 0749+658: C underabundant
PG 1104+243: with y = 0:01  0:01, this is the most
helium-rich composite sdB in our sample. The strength
of the Ca K line and other metallic lines in the blue
spectrum indicates T e 2 = 6400 K, log g 2 = 4:3, and
R 2 =R 1  6. However, assuming the same radius ratio and
[Fe=H] 2 = 0:0, the red spectrum gives T e2 = 4500 K
and log g 2 = 4:6. Since the blue spectrum provides very
strong constraints on T e 2 and R 2 =R 1 , it was necessary

Aznar Cuadrado and Jeery: Physical parameters for composite sdB stars 9
to adopt a reduced value for [Fe=H] 2 = 0:5 to maintain
consistency with Paper I.
PG 1701+359 and PG 1718+519: C, Mg and Si under-
abundant. R 2 =R 1 signicantly smaller than in Paper I.
This could be due to the adoption of too high metallicity
[Fe=H] 2 .
PG 2110+127: C, Mg and Si underabundant.
PG 2135+045: C, Mg and Si underabundant. R 2 =R 1
signicantly smaller than in Paper I. This is probably due
to the absence of IUE LW and JHK photometry which led
to particularly large errors in the Paper I T e measure-
ments.
PG 2148+095: C, Mg and Si underabundant. R 2 =R 1
signicantly smaller than in Paper I probably due to sig-
nicant dierences in T e . The latter are probably due
to the absence of an IUE LW spectrum and a possible
anomaly in the J-band photometry.
Signicant dierences between the results of the
spectroscopic (sfit) and photometric (Paper I) analyses
have been discussed above. Tables 4 and 5 also include
the results of earlier photometric and spectroscopic
analyses. The current results agree well with pre-
vious spectroscopic analyses (Moehler et al. 1990a,
Saer et al. 1994, Heber et al. 1999) in the cases
of PG 0342+026, PG 0839+399, PG 1233+426 and
PG 0749+658. They do not agree well in the cases
of PG 0004+133, PG 0229+064, PG 2110+127 and
PG 2135+045.
The high helium abundance may contribute to the T e
discrepancy in PG 0229+064, a cool He-rich subdwarf with
a relatively low surface gravity. Saer et al. (1994) did
not recognize the composite nature of PG0749+658 and
PG 2135+045, and it is not clear how they modelled the
spectrum of PG 2110+127. When deriving the sdB param-
eters, Theissen et al. (1993, 1995) corrected for the con-
tinuum light of the cool companions, but not the (weaker)
Balmer lines from the cool stars. Therefore these results
may not be fully reliable.
5.3. ( log g - T e ) diagram and helium abundances
Fig. 5 compares the sdB stars analysed here with an homo-
geneous sample of sdB stars (Moehler, private communica-
tion) and the location of the helium main sequence (He-
MS) and zero-age extreme horizontal branch (ZAEHB)
(Moehler et al. 1990a). The surface gravities of hot stars
in composite sdBs lie in the range 4:80  log g  6:00,
while our sample of single sdB stars have 4:35  log g 
6:25. Although both log g and T e ranges for compos-
ite sdBs are slightly smaller than for the single-spectrum
stars, there is essentially no dierence between their distri-
bution in the log g- T e diagram and that of larger sam-
ples of sdB stars analyzed previously.
A striking result of this study is that the majority
of single-spectrum sdB stars have helium abundances of
y=0.01 or higher, while the composite stars have y < 0:01
(the minimum currently available in our model grid).
Fig. 5. Position of single sdB stars (lled circles) and com-
posite sdB stars (lled triangles) in the ( log g 1 { T e1 ) di-
agram as derived from the spectral analysis sfit. Open
circles represent the position of an homogeneous sample
of sdB stars (Maxted et al. 2001). The position of the He-
MS and ZAEHB are represented as solid and dash-dotted
lines, respectively (Moehler et al. 1990a).
Low surface He abundances are expected in sdB stars
because of the competition between gravitational settling
and radiative levitation acting on dierent ions. The same
diusive processes may be responsible for the apparently
low abundances of carbon, silicon and magnesium in our
sample (cf. Bergeron et al. 1988).
It has already been noted that sdB stars with compos-
ite spectra and, hence, F-, G- or K-type companions form
a distinct group from those with no or unseen companions
(Saer et al. 2001). With a separate evolutionary history,
a distinct surface abundance might be anticipated, but
remains to be explained.
Two single-spectrum sdB stars (PG0229+064 and
PG 0240+046) have y >> 0:01. It is interesting that these
particular examples lie at the extremities of our sam-
ple. Recalling the three groups of sdBs introduced ear-
lier (Saer et al. 2001), such helium-rich sdBs may form
a completely separate subgroup. They were identied in
the PG survey (Green et al. 1986: spectral classes sdB-O,
sdOA and sdOD) and subsequently (Moehler et al. 1990a:
HesdB, Saer et al. 1994). The latter found most of the
He-rich sdBs to have T e > 30 000 K, and commented
that it was diôcult to reconcile these stars with time-
dependent diusion calculations.
We do not currently know whether any He-rich sdB
stars are members of short-period binary systems. The
latter is particularly important { one scenario for the pro-
duction of sdBs is the merger of two helium-white dwarfs

10 Aznar Cuadrado and Jeery: Physical parameters for composite sdB stars
Fig. 6. Position of the cool companion in composite
sdB stars in the ( log g 2 { T e2 ) diagram as derived
from the spectral analysis. The position of the ZAMS
and TAMS from stellar models with solar composi-
tion (Girardi et al. 2000) are plotted as dash-dotted and
dashed lines, respectively. Labels refer to identication
numbers in Table 7.
(Iben 1990, Saio & Jeery 2000). The surface layers of the
product may be so helium-rich that diusive processes
could not completely remove the surface helium. A sig-
nicant number of He-rich binary sdBs would demand an
alternative explanation.
5.4. Composite sdB companions in the HR diagram
The cool companions in binary sdB stars have surface
gravities in the range 4:30  log g 2  4:58. Fig. 6 shows
the position of the cool companion in binary sdB stars in
the ( log g { T e ) diagram as derived from sfit together
with the location of the ZAMS and TAMS from stellar
models with solar composition (Girardi et al. 2000). The
observations are consistent with surface gravities of main-
sequence stars. This comparison may be taken further by
assuming a canonical 0.5 M for the masses of the sdB
stars. Using the sdB surface gravities and the measured
radius ratios, the luminosities of both components can be
calculated (Table 7).
Table 7 presents the luminosities, eective tempera-
ture and masses of the cool companions of composite sdB
stars. These results reinforce our conclusion (Paper I) that
the cool companions in composite sdB systems are main-
sequence stars with M  1:0  0:1 M .
5.5. Mass ratios in composite sdB systems
The mass ratio of a binary system containing a hot sdB
star and a cool companion is given by q = M 2 =M 1 . From
g = (GM)=R 2 and the radius ratio R 2 =R 1 , the mass ratio
can be expressed as
q = (R 2 =R 1 ) 2 (g 1 =g 2 ): (6)
This method of measuring q is subject to the normally
quite large errors in measuring log g. Mass ratios for com-
posite systems analysed by us lie in the range 0:52 < q <
3:83.
Assuming the cool companions in our sample to be
main-sequence stars with eective temperatures 4500 <
T e2 = K < 6500, then their masses should be in the range
0:75  M=M  1:32 (Gray 1992). Hence, assuming
that the hot components of the binary systems are sdB
stars with typical masses of  0:5M (Heber et al. 1984,
Heber 1986), then the mass ratios should be in the range
1:50  q  2:65. Clearly, the surface gravity ratio method
is not yet suôciently sensitive to yield the mass ratio di-
rectly.
6. Discussion
Green et al. (2001) have discussed the evolutionary ori-
gin of subdwarf B stars in view of ndings regarding the
distribution of binary periods and companions found in
other surveys (Saer et al. 2001). They deduce that sdB
stars with spectral lines from a cooler companion invari-
ably have periods longer than a year, while very short-
period sdBs have essentially invisible companions. The de-
duction is that both groups are produced by Roche lobe
over ow/mass transfer from low-mass stars near the tip
of the red giant branch. If the initial binary is suôciently
wide and the secondary is suôciently massive and able
to accept the dynamic mass transfer of the rst couple of
tenths of a solar mass without lling its Roche lobe, then
the initial mass ratio may be reduced suôciently to allow
stable mass transfer and avoid a common-envelope phase.
In this case the orbital period would remain long, and
the secondary would increase in mass, becoming a blue
straggler (BS) with >  1 M , as observed by ourselves. An
important question will be to determine accurately the
upper and lower limits on both masses and periods for
such sdB+BS binaries. Green & Liebert (2001) suggest
that binaries with less massive secondaries would form a
common-envelope and end up either merging or as short-
period sdB+MS systems.
The division of sdBs into long- and short-period bina-
ries suggests a reason for the dierence in helium abun-
dance between the two samples. While low-helium (and -
metal) abundances are known to be a result of atmospheric
diusion in high-gravity stars within a certain tempera-
ture range, external forces may partially disrupt these.
Tidal interaction due to a binary companion will be much
stronger in a short-period than in a long-period system.
Unless the sdB star is rotating completely synchronously,

Aznar Cuadrado and Jeery: Physical parameters for composite sdB stars 11
Table 7. Spectroscopically determined luminosities and masses for composite sdB star companions compared with the
photometric analysis (Paper I). The luminosities assume 0.5 M for the sdB stars (Heber et al. 1984, Heber 1986).
Star sfit Paper I
L 2 = L T e2 = K L 2 = L T e2 = K
1 PG0110+262 0:64  0:40 5250  800 0:19  0:04 5485  200
2 PG0749+658 0:19  0:08 5000  500 0:18  0:07 5600  300
3 PG1104+243 2:85  1:78 6400  1000 4:90  0:77 5735  150
4 PG1701+359 0:21  0:14 6000  1000 0:48  0:10 6450  230
5 PG1718+519 0:21  0:06 5200  400 1:02  0:15 5925  70
6 PG2110+127 1:45  0:44 5400  400 0:03  0:02 5500  575
7 PG2135+045 1:17  0:48 5000  500 0:31  0:54 4375  1790
8 PG2148+095 1:47  0:44 5700  400 0:11  0:03 4375  200
tidal eects will operate on timescales shorter than diu-
sion ( 10 5 years) and may dilute the chemical separation.
Extremely low-hydrogen abundances would therefore be
seen preferentially in long-period sdB binaries.
The presence of sdBs within the sample with he-
lium abundances signicantly greater than normal (e.g.
PG 0229+064, PG 0240+046) may be a consequence of
their belonging to sdB group (1) { apparently single
stars (Saer et al. 2001). It is interesting that no sdB
star with y > 0:03 is known to be a short-period binary
(Maxted et al. 2001). Since sdB stars are known with ex-
tremely high helium abundances (cf. Jeery et al. 1987),
we suggest that these could have an entirely separate
origin, being the products of helium plus helium white
dwarf mergers (Iben 1990). Evidence for such a conclu-
sion is provided by the extreme helium star V652Her
(Jeery et al. 2001), considered to be strong evidence for
such a merger product evolving to become an isolated he-
lium main-sequence star (Saio & Jeery 2000). When it
becomes a subdwarf, diusion will inevitably modify the
initially helium-rich atmosphere. However, with a much
more limited reservoir of hydrogen, extremely low helium
abundances will be diôcult to achieve. Consequently sdBs
produced by mergers could be expected to show a very
wide range of helium abundances.
7. Conclusions
We have analysed representative samples of sdB stars
having apparently single or composite spectra. The at-
mospheric properties of the sdB stars were measured by
comparing moderate-resolution blue spectra with theoret-
ical models. In the case of sdBs with composite spectra,
the atmospheric properties of the cool companions were
measured from the blue spectra and from near-infrared
spectra, where the infrared calcium triplet provides an in-
valuable surface gravity indicator.
Both samples covered a similarly wide range in T e
and log g. However the composite sdB stars invariably
have lower helium abundances in their atmospheres than
the single-spectrum sdBs. Although we cannot entirely ex-
plain this phenomenon, we suggest that it may be due to
tidal eects disrupting diusive separation in short-period
systems more than in long-period systems. Some of the
composite sdB stars also showed depletions of metals in-
cluding silicon, carbon and magnesium.
Assuming a typical surface luminosity representing
all subdwarf B stars of log(L sdB = L ) = 1.400.13, the
majority of the companions of composite sdBs have lu-
minosities in the range 0:4  L cool = L  2:6, consis-
tent with being main-sequence stars of about 1  0:2 M .
This supports the hypothesis that composite sdB stars
are the result of Roche lobe over ow near the red-giant
tip in a low-mass binary with nearly equal initial masses
(Green et al. 2001).
This is the rst time that an attempt has been made
to model accurately the spectra of composite subdwarf B
stars and to measure the cool star luminosity using the
infrared calcium triplet. Although successfully executed,
higher resolution spectra will be needed to measure the
metallicity of the cool star and hence the radius ratios
with greater accuracy.
Acknowledgements. This research is supported by a grant
to the Armagh Observatory from the Northern Ireland
Department of Culture, Arts and Leisure and by the UK
Particle Physics and Astronomy Research Council through the
award of telescope time and travel grants. We are particularly
grateful to Prof Philip Dufton and Drs Sabine Moehler and
Betsy Green for helpful discussions and to Dr Don Pollacco for
obtaining some of the observations.
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