Issue |
A&A
Volume 519, September 2010
|
|
---|---|---|
Article Number | A25 | |
Number of page(s) | 27 | |
Section | Stellar structure and evolution | |
DOI | https://doi.org/10.1051/0004-6361/201014465 | |
Published online | 08 September 2010 |
Hot subdwarf stars in close-up view
I. Rotational properties of subdwarf B stars in close binary systems and nature of their unseen companions![[*]](/icons/foot_motif.png)
S. Geier1 - U. Heber1 - Ph. Podsiadlowski2 - H. Edelmann1 - R. Napiwotzki3 - T. Kupfer1 - S. Müller1
1 - Dr. Karl Remeis-Observatory & ECAP, Astronomical Institute,
Friedrich-Alexander University Erlangen-Nuremberg, Sternwartstr. 7, 96049 Bamberg, Germany
2 - Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
3 - Centre of Astrophysics Research, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK
Received 19 March 2010 / Accepted 26 May 2010
Abstract
The origin of hot subdwarf B stars (sdBs) is still unclear. About
half of the known sdBs are in close binary systems for which common
envelope ejection is the most likely formation channel. Little is known
about this dynamic phase of binary evolution. Since most of the known
sdB systems are single-lined spectroscopic binaries, it is difficult to
derive masses and unravel the companions' nature, which is the aim of
this paper.
Due to the tidal influence of the companion in close binary systems,
the rotation of the primary becomes synchronised to its orbital motion.
In this case it is possible to constrain the mass of the companion, if
the primary mass, its projected rotational velocity as well as its
surface gravity are known. For the first time we measured the projected
rotational velocities of a large sdB binary sample from high resolution
spectra. We analysed a sample of 51 sdB stars in close binaries, 40 of
which have known orbital parameters comprising half of all such systems
known today.
Synchronisation in sdB binaries is discussed both from the
theoretical and the observational point of view. The masses and the nature of the unseen companions could be constrained in 31
cases. We found orbital synchronisation most likely to be established in binaries with orbital
periods shorter than
.
Only in five cases it was impossible to
decide whether the sdB's companion is a white dwarf or an M dwarf. The
companions to seven sdBs could be clearly identified as late M stars.
One binary may have a brown dwarf companion. The unseen companions of
nine sdBs are white dwarfs with typical masses. The mass of one white
dwarf companion is very low. In eight cases (including the well known
system KPD1930+2752) the companion mass exceeds
,
four of which even
exceed the Chandrasekhar limit indicating that they may be neutron
stars. Even stellar mass black holes are possible for the most massive
companions. The distribution of the inclinations of the systems with
low mass companions appears to be consistent with expectations, whereas
a lack of high inclinations becomes obvious for the massive systems.
We show that the formation of such systems can be explained with common
envelope evolution and present an appropriate formation channel
including two phases of unstable mass transfer and one supernova
explosion. The sample also contains a candidate post-RGB star, which
rotates fast despite its long orbital period. The post-RGB stars are
expected to spin-up caused by their ongoing contraction. The age of the
sdB is another important factor. If the EHB star is too young, the
synchronisation process might not be finished yet. Estimating the ages
of the target stars from their positions on the EHB band, we found
PG 2345+318, which is known not to be synchronised, to lie near
the zero-age extreme horizontal branch as are the massive candidates
PG 1232-136, PG 1432+159 and PG 1101+249. These star may
possibly be too young to have reached synchronisation.
The derived large fraction of putative massive sdB binary systems in
low inclination orbits is inconsistent with theoretical predictions.
Even if we dismiss three candidates because they may be too young and
assume
that the other sdB primaries are of low mass, PG 1743+477 and, in
particular, HE 0532-4503 remain as candidates whose companions may
have masses close to or above the Chandrasekhar limit. X-ray
observations and accurate photometry
are suggested to clarify their nature. As high inclination systems must
also exist, an appropriate survey has already been launched to find
such binaries.
Key words: binaries: spectroscopic - subdwarfs - stars: rotation
1 Introduction
Subluminous B stars (sdBs) show
similar colours and spectral characteristics as main sequence stars of
spectral type B, but are much less luminous.
Compared to main sequence B stars the hydrogen Balmer lines in the spectra
of sdBs are stronger while the helium lines are much weaker (if present at
all)
for the colour. The strong line broadening and the early confluence of the
Balmer series is caused by the high surface gravities (
)
of these compact stars
(
).
Subluminous B stars are considered to be helium core burning stars with
very thin hydrogen envelopes and masses of about half a solar mass (Heber 1986)
located at the extreme end of the horizontal branch (EHB).
Subdwarf B stars are found in all Galactic stellar populations and are sufficiently common to account for the UV-upturn of early-type galaxies. Understanding the origin of the UV-upturn phenomenon hence has to await a proper understanding of the origin of the sdB stars themselves.
The discovery of short-period multi-periodic pulsations
in some sdBs provided an excellent opportunity to probe the
interiors of these stars using the tools of asteroseismology.
They were theoretically predicted by
Charpinet et al. (1996) at around the same time as they were
observed by
Kilkenny et al. (1997).
They are
characterised by low-amplitude, multi-periodic, short-period (
)
light variations that are due to pressure (p)-mode
oscillations.
A second family of pulsating sdB stars was discovered by Green et al. (2003),
again showing low-amplitude, multi-periodic pulsations, but periods are longer (
)
and are identified as
gravity (g) modes. An important recent achievement of sdB asteroseismology
is the determination of the most
fundamental parameter of a star,
i.e. its mass (for a review see Fontaine et al. 2008).
The origin of EHB stars, however, is wrapped in mystery (see Heber
2009 for a review).
The problem is how some kind of mass loss mechanism in the
progenitor manages
to remove all but a tiny fraction of the hydrogen envelope at about
the same time as the helium core has attained the mass (0.5
)
required for the helium flash.
This requires enhanced mass loss, e.g. due to helium mixing driven by
internal rotation (Sweigart 1997) or at the helium flash itself.
Mengel et al. (1976) demonstrated that the required strong mass loss can occur in a close-binary system. The progenitor of the sdB star has to fill its Roche lobe near the tip of the red-giant branch (RGB) to lose most of its hydrogen-rich envelope. The merger of binary white dwarfs was investigated by Webbink (1984) who showed that an EHB star can form when two helium core white dwarfs merge and the product is sufficiently massive to ignite helium.
Interest in the binary scenario was revived, when Maxted et al. (2001) determined a very high fraction of radial velocity variable sdB stars, indicating that about two thirds of the sdB stars in the field are in close binaries with periods of less than 30 days (see also Morales-Rueda et al. 2003; Napiwotzki et al. 2004a). The companions, as far as their nature could be clarified, are mostly M dwarfs or white dwarfs. If the white dwarf companion is sufficiently massive, the merger of the binary system might exceed the Chandrasekhar mass and explode as a type Ia supernova. Indeed, Billères et al. (2000) and Maxted et al. (2000a) discovered KPD 1930+2752, a system that might qualify as a type Ia supernova progenitor (see also Geier et al. 2007).
These discoveries triggered new theoretical evolutionary calculations
in the context of binary population-synthesis to identify the
importance of various channels of close-binary evolution (Han
et al. 2002,2003), i.e. two phases of common-envelope ejection, stable Roche-lobe overflow and white dwarf merger.
1.1 Outline of the paper
The purpose of this paper is to clarify the nature of the unseen companions for 40 short-period sdB binaries, which comprises about half of the sdB stars in single-lined close binary systems with known periods and radial velocity amplitudes. We assumed tidally locked rotation and made use of the sdBs' gravities and projected rotational velocities.The paper is structured in two parts. After a short review on close binary sdB stars (Sect. 2), part I (Sects. 3
to 8) describes the analysis of the sample. Besides constraining the
mass of the companions and unravelling the nature of most companions as
M dwarfs or typical white dwarfs, it reports the discovery of a
population of eight unseen compact companions with masses exceeding
(in addition to KPD 1930+2752), some of which even exceed the
Chandrasekhar limit. Accordingly, the latter should be neutron stars
(NS) or black holes (BH). Even if they were massive white dwarfs, it
would be surprising to find such a large fraction, as massive white
dwarfs are rare. As no binary system containing an sdB plus a NS/BH is
known today, we investigate
potential formation scenarios in Sect. 8 and find it indeed possible to create such systems through two phases of common envelope evolution.
Our results rest on the assumption of tidally locked rotation. Therefore, part
II of the paper (Sects. 9 and 11) deals with the synchronisation time
scales of sdB stars in close binaries both from a theoretical point of view
and from the perspective of empirical constraints.
The general result is that systems with periods
shorter than
should be synchronised. Empirical evidence is available that
systems with periods below
are synchronised as is indeed the case for
the systems with massive companions.
Although selection effects would favour the detection of highly inclined systems,
no such system was found among those binaries with massive companions
in our sample. This calls for a careful
inspection of alternative explanations (Sect. 11). There are two aspects to be discussed.
First, the sdB may not burn helium at all and, thus, is spun up due to ongoing contraction.
Alternatively the actual evolutionary age of
individual stars may be smaller than appreciated, i.e. the EHB star may just have formed only
recently and the systems would therefore not be
synchronised. In Sect. 12 we summarise and discuss the results.
2 Hot subdwarf binaries
Several studies aimed at determining the fraction of hot subdwarfs
residing in close binary systems. Samples of hot subdwarfs have been checked for
RV variations. The resulting fractions range from
39% to 78% (Green et al. 1997; Maxted et al. 2001;
Napiwotzki et al. 2004a). Several studies were undertaken to
determine the orbital parameters of subdwarf binaries
(Edelmann et al. 2005; Green et al. 2008;
Morales-Rueda et al. 2003,2004; Karl et al. 2006).
The orbital periods range from


![]() |
Figure 1: Period distributions of the 40 binaries in our sample with known orbital parameters (dashed histogram) and all known 81 sdB binaries in the Ritter & Kolb (2003) catalogue (blank histogram). |
Open with DEXTER |
2.1 Binary evolution
For close binary sdBs common envelope ejection is the most probable formation channel. In this scenario two main sequence stars of different masses evolve in a binary system. The heavier one will reach the red giant phase first and fill its Roche lobe. If the mass transfer to the companion is dynamically unstable, a common envelope (CE) is formed. Due to friction the two stellar cores lose orbital energy, which is deposited within the envelope and leads to a shortening of the binary period. Eventually the common envelope is ejected and a close binary system is formed, which contains a core helium-burning sdB and a main sequence companion. If this star reaches the red giant branch, another common envelope phase is possible and can lead to a close binary with a white dwarf companion and an sdB.
If the mass transfer to the companion is dynamically stable, no common envelope is formed and the primary slowly accretes matter from the secondary. The companion eventually loses most of its envelope and evolves to an sdB. This leads to sdB binaries with much larger separation and therefore much longer orbital periods. Although lots of sdBs have spectroscopically visible main sequence companions, no radial velocity variable system was detected up to now. Therefore the so called stable Roche lobe overflow (RLOF) channel remains without proof.
Binary evolution also provides a possibility to form single sdB stars via the merger of two helium white dwarfs (Webbink 1984; Iben & Tutukov 1984). Close He white dwarf binaries are formed as a result of two CE-phases. Loss of angular momentum through emission of gravitational radiation will cause the system to shrink. Given the initial separation is short enough the two white dwarfs eventually merge and if the mass of the merger is high enough, core helium burning is ignited and an sdB with very thin hydrogen envelope is formed. Recently Politano et al. (2008) proposed a new evolutionary channel. The merger of a red giant and a low mass main-sequence star during a common envelope phase may lead to the formation of a rapidly rotating hot subdwarf star. Soker (1998) proposed similar scenarios with planetary companions. A candidate substellar companion to the sdB star HD 149382 has been discovered recently (Geier et al. 2009c).
2.2 SN Ia progenitors
Double degenerate systems in close orbits are viable candidates for progenitors of type Ia supernovae (SN Ia), which play an important role as standard candles for the study of cosmic evolution (e.g. Riess et al. 1998; Leibundgut 2001; Perlmutter et al. 1999). The nature of their progenitors is still under debate (Livio 2000). The progenitor population provides crucial information for backing the assumption that distant SN Ia can be used as standard candles like the ones in the local universe.
There is general consensus that only the thermonuclear explosion
of a white dwarf (WD) is compatible with the observed features of
SN Ia. For this a white dwarf has to accrete mass from a close
companion to reach the Chandrasekhar limit of
(Hamada & Salpeter 1961). According
to the so-called double degenerate scenario (Iben & Tutukov 1984), the
mass-donating companion is a white dwarf, which eventually merges with the
primary due to orbital shrinkage caused by gravitational wave radiation.
A progenitor candidate for the double degenerate scenario must have a total
mass near or above the Chandrasekhar limit and has to merge in less than a
Hubble time. Systematic radial velocity (RV) searches for double degenerates
have been undertaken (e.g. Napiwotzki 2003 and references therein). The largest of these projects was the ESO SN Ia Progenitor Survey
(SPY, Napiwotzki et al. 2001b). The best known double degenerate
SN Ia progenitor candidate system KPD 1930+2752 has an sdB primary
, which
will become a white dwarf within about
before the merger occurs in about
(Maxted et al. 2000a; Geier et al. 2007). Another sdB+WD binary with massive companion has been found recently (Geier et al. 2010a).
Most recently Mereghetti et al. (2009) showed that in the X-ray binary HD 49798 a very massive (>
)
white dwarf accretes
matter from the wind of its closely orbiting subdwarf O companion.
Iben & Tutukov (1994) predicted that such a system will evolve into a SN Ia when the
primary fills its Roche lobe and transfers mass to the white dwarf to reach the
Chandrasekhar limit. This makes HD 49798 a candidate for SN Ia progenitor
for this so called single degenerate scenario.
2.3 Nature of the companions
An up-to-date compilation of hot subdwarf binaries with known orbital
parameters is presented by Ritter & Kolb (2003) which lists 81 such
systems.
In general it is difficult to put constraints on the nature of the close
companions of sdB stars. Since most of these binaries are single-lined, only
lower limits to the companion masses could be derived from the stellar mass
functions, which are in general compatible with late main sequence stars of
spectral type M or compact objects like white dwarfs. For single-lined binaries
with longer orbital periods the stellar mass function can help to further
constrain the nature of the unseen companion. Assuming the canonical mass
(
;
Han et al. 2002,2003) for the subdwarf, the
minimum mass of the companion may be high enough to exclude main sequence
stars,
because they would contribute significantly to the flux and therefore appear in the spectra. This mass limit lies near
(Lisker et al. 2005).
Twelve sdB binaries have been reported to show eclipses. A combined analysis of the light curves and time resolved spectra of these stars allows to derive the system parameters as well as the companion types. Eight of them have late M companions (see For et al. 2010 for a review), while four show shallow variations caused by the eclipse of a white dwarf (Orosz & Wade 1999; Green et al. 2004; Bloemen et al. 2010).
If close binary stars are double-lined, the mass ratio of the systems can be derived from the RV semi-amplitudes of the two components. Until recently, only one double-lined He-sdB+He-sdB binary could be analysed (Ahmad & Jeffery 2004).
Light variations can help to unravel the nature of the companion by means of the reflection effect and by ellipsoidal
variations, even if there are no eclipses.
In short period sdB binaries with orbital periods up to about half a day and
high inclination the hemisphere of a cool main sequence or substellar
companion directed towards the subdwarf is significantly heated up by the hot
primary. This leads to a characteristic modulation of the light curve with the
orbital period, which is a clear indication for an M-star or substellar
companion. Such light variations are easily measured in short period binaries
with high orbital inclinations. Fourteen sdB+M binaries with
this so-called reflection effect are known so far. Since detailed physical
models of the reflection effect are not available yet, several free parameters
have
to be adjusted to fit the observed light curves. Only very limited constraints
can therefore be put on the companion masses and radii from an observed
reflection effect alone. The absence of a reflection effect can also help to
constrain the nature of the unseen companions (Maxted et al. 2004; Shimanskii et al. 2008). This method works best for binaries with periods of less than
because otherwise the expected reflection effect from an M dwarf
companion is hard to detect (Drechsel, priv. comm.; Napiwotzki
et al., in prep.). The binary JL 82 shows a very strong
reflection, because it is clearly detectable despite the long orbital
period of
.
What causes the strong variation is not yet understood (Koen 2009, see also Sect. 7.1).
A massive white dwarf companion was identified as companion of an sdB (Billères et al. 2000; Maxted et al. 2000a; Geier et al. 2007), which shows a variation in its light curve caused by the tidal distortion of the sdB. Similar signs of ellipsoidal deformation could be detected in five other cases (Orosz & Wade 1999; O'Toole et al. 2006; Geier et al. 2008a; Koen et al. 2010; Bloemen et al. 2010). These stars must have white dwarf companions, because the effect of tidal distortion in the light curve is much weaker than a reflection effect, if present.
From 81 close binary subdwarfs with known orbital parameters (Ritter & Kolb 2003), 13 have bona fide M dwarf companions, while 7 companions have to be white dwarfs. In another 11 binaries compact companions are most likely. One of the binaries has a subdwarf companion. The nature of the unseen companions in the remaining 50 binaries could not be clarified with the methods described so far.
Some hot subluminous stars may not be connected to EHB-evolution at all, as exemplified by HD 188112 (Heber et al. 2003), which was found to be of too low mass to sustain helium burning in the core. Its atmospheric parameters place the star below the EHB. An object like HD 188112 is considered to be a direct progenitor of low-mass white dwarfs (Liebert et al. 2004), which descend from the red giant branch and cool down.
2.4 Rotational properties
While the rotational properties of blue horizontal branch (BHB) stars both in
globular clusters and in the field are thoroughly examined
(see e.g. Behr 2003), there is no systematic study for EHB stars yet. Most of the sdB stars where
-measurements are available, are slow rotators (Heber et al. 2000; Napiwotzki et al. 2001a; Edelmann 2005).
The knowledge of the projected rotational velocity, combined with the gravity determination, allows to derive the mass of single-lined binaries, if the rotation is tidally locked to the orbit. A similar technique has been applied to low-mass X-ray binaries. Kudritzki & Simon (1978) made use of this method for the first time in the field of hot subdwarfs to constrain the parameters of the sdO binary HD 49798. Recently, also a few sdB systems have been studied in this way (e.g. Napiwotzki et al. 2001a; O'Toole et al. 2004; Geier et al. 2007, 2008a, 2010a). Here we apply this technique to a much larger sample.
Part I: Quantitative spectral analysis and binary evolution
Here we present our measurements of projected rotational velocities for a sample of 51 radial velocity variable sdBs stars in total. 40 of them are drawn from the Ritter & Kolb (2003) catalogue (including GD 687, a system published more recently, Geier et al. 2010a) and have well determined orbital parameters. Eleven additional radial velocity variable sdB stars have also been analysed, but orbital parameters have not yet been determined. The main aim is to constrain the masses of the companions under the assumption of tidally locked rotation.
Observations and analysis method are described in Sects. 3 and 4. Surface gravity (Sect. 5) and projected rotational velocities (Sect. 6) will be combined with the mass function to derive companion masses and inclinations. The nature of the companions is discussed Sect. 7. An evolutionary scenario for the formation of neutron star or black hole companions to sdB stars is proposed in Sect. 8.
3 Observations and data reduction
The first set of UVES spectra were obtained in the course of the
ESO Supernovae Ia Progenitor Survey (SPY, Napiwotzki et al. 2001b,2003)
at spectral resolution
covering
with two small gaps at
and
.
Each of the 19 stars were observed at least twice.
The data reduction is described in Lisker et al.
(2005). For some of the systems follow-up
observations with UVES in the same setup were undertaken to derive the orbital
parameters. These were taken through a narrow slit for better accuracy.
For the high priority target PG 1232-136 we obtained 60 short
exposures (
)
with UVES through a very narrow slit (0.4'')
to achieve higher resolution (R=80 000) covering
and
.
High resolution spectra (R=30 000,
)
of 12 known
close binary subdwarfs have been taken with the HRS fiber spectrograph at the
Hobby Eberly Telescope (HET) in the second and third trimester 2007.
The spectra were reduced using standard ESO MIDAS routines.
Another sample of 11 known bright subdwarf binaries was observed with the
FEROS spectrograph (R=48 000,
)
mounted at the ESO/MPG 2.2 m telescope. The spectra were
downloaded from the ESO science archive and reduced with the FEROS-DRS
pipeline under the ESO MIDAS context in optimum extraction mode.
Three spectra of subdwarf binaries were obtained with the FOCES spectrograph (R=30 000,
)
mounted at the CAHA 2.2 m telescope.
Three spectra were taken with the HIRES instrument (R=45 000,
)
at the Keck telescope. Two spectra taken with the echelle spectrograph (R=20 000,
)
at the 1.5 m Palomar telescope were provided by Reid (priv. comm.).
Because a wide slit was used in the SPY survey and the seeing
disc did not always fill the slit, the instrumental profile of some of the UVES spectra was seeing dependent.
This has to be accounted for to estimate the instrumental resolution.
The seeing of all single exposures was measured with the DIMM seeing monitor
at Paranal Observatory and taken from the ESO science archive
(Sarazin & Roddier 1990). As a test the seeing was also estimated from
the width of the echelle orders perpendicular to the direction of dispersion in some cases
and found to be consistent with the DIMM measurements.
The errors are considered to be lower than the change of seeing during the
exposures (up to
).
The resolution of the spectra taken with the fiber spectrographs
FEROS, FOCES and HRS was assumed as constant. Changes in the instrumental
resolution because of temperature variations and for other reasons were
considered as negligible.
The single spectra of all programme stars were RV-corrected and co-added in order to achieve higher signal-to-noise.
4 Analysis method
Since the the programme stars are single-lined spectroscopic binaries,
no information about the orbital motion of the sdBs' companions is
available, and thus only their mass functions can be calculated.
Although the RV semi-amplitude K and the period P are determined by the RV curve, the sdB mass


In the following analysis we adopt the mass range for sdBs in binaries which underwent the common envelope channel given by Han et al. (2002, 2003) if no independent mass determinations are available (see Sect. 7 for details).
In close binary systems, the rotation of the stars becomes synchronised to their
orbital motion by tidal forces (see Sect. 9
for a detailed discussion). In this case their rotational periods equal
the orbital periods of the binaries. If the sdB primary is synchronised
in this way its rotational velocity
can be calculated.
![]() |
(2) |
The stellar radius R is given by the mass-radius relation and can be derived, if the surface gravity g has been determined.
![]() |
(3) |
The measurement of the projected rotational velocities



This method has already been applied to the sdB+WD binaries HE 1047-0436 (Napiwotzki et al. 2001a), Feige 48 (O'Toole et al. 2004), KPD 1930+2752 (Geier et al. 2007), PG 0101+039 (Geier et al. 2008a) and GD 687 (Geier et al. 2010a).
There are no signatures of companions visible in the optical spectra of our
programme stars. Main sequence stars with masses higher than
could therefore be excluded because
otherwise spectral features of the cool secondary (e.g. Mg I lines at
)
would appear in the spectra (Lisker et al. 2005) and a flux excess in the
infrared would become visible in the spectral energy distribution (Stark & Wade
2003; Reed & Stiening 2004).
Table 1: Atmospheric and orbital parameters.
Another possibility to detect M dwarf or brown dwarf companions
are reflection effects in the binary light curves. The detection of a
reflection effect provides solid evidence for the presence of an
M dwarf or brown dwarf companion. The non-detection of such a
modulation can be used to constrain the nature of the companion as
well, since a compact object like a white dwarf would be too small to
contribute significantly to the total flux and cause a detectable
reflection effect. But constraining the companion type in this way is
problematic for several reasons. First of all, the amplitude of the
reflection becomes very small (a few mmag) unless the binary has a
short period (<
,
Drechsel, priv. comm.; Napiwotzki et al., in prep.). Unless the
photometry is excellent, such shallow variations over long timescales
are not detectable from the ground. Furthermore, the amplitude of the
modulation depends on the binary inclination, which is not known in
general. An sdB+M binary seen at very low inclination does not show a
detectable reflection effect. But most importantly the physics behind
the reflection effect itself is poorly understood and one has to use
rather crude approximations to derive its amplitude. The most recent
detection of a surprisingly strong reflection effect in the long period
system JL 82 (Koen 2009) illustrates this.
Some of our programme stars have already been checked for modulations
in their light curves. We consider the lack of a reflection effect as
significant constraint, if the orbital period of the binary is shorter
than
.
In this case the companion should be a compact object. In the case of
binaries with longer periods the non-detection of a reflection effect
is used as consistency check.
The atmospheric parameters effective temperature and surface gravity of most
of our programme stars have been derived from low resolution spectra with
sufficient accuracy and can be taken from literature in most cases. In order
to measure projected rotational velocities of sdB stars however, high spectral
resolution is necessary, because the
are small in most
cases.
5 Determination of the surface gravity and systematic errors
Since the precise determination of the atmospheric parameters,
especially the surface gravity, is of utmost importance for our
analysis, this section is devoted to the systematic uncertainties
dominating the determination of these parameters. Spectra of sdB stars
in the literature were analysed either with metal line-blanketed LTE
model atmospheres or with NLTE model atmospheres neglecting metal line
blanketing altogether. As pointed out by Heber et al. (2000), Heber & Edelmann (2004) and Geier et al.
(2007), systematic differences between these two approaches are
present. Most importantly the gravity scale differs by about
.
Most of the atmospheric parameters of our programme stars are taken from
literature and were derived by fitting LTE or NLTE models (Table 1). The
adopted errors in
range from 0.05 to 0.15. It is important to note that all stars except
PG 1336-018, HW Vir, PG 1432+159 and PG 2345+318
have been analysed with the same grids of LTE and NLTE atmospheres and
the same fitting procedure. The error in surface gravity starts to
dominate the error budget of the derived parameters as soon as the
error in
drops below about
(see Sect. 6).
In cases where no reliable atmospheric parameters could be found in literature, we determined them by fitting LTE models.
Since the accuracy of the parameters is very much dependent on the higher Balmer
lines, a high S/N
in this region is necessary. The quality of high resolution spectra
obtained with FEROS or FOCES declines toward the blue end. This can
cause systematic shifts in the parameter determination (up to
and
). That is why we chose UVES, HIRES or low resolution
spectra to determine the atmospheric parameters if possible. In order to
improve the atmospheric parameter determination of TON S 183,
BPS CS 22169-0001 and [CW83] 1735+22 we obtained additional
medium resolution spectra with WHT/ISIS in August 2009. A medium resolution spectrum of KPD 1946+4340
taken with ISIS (Morales-Rueda et al. 2003) and a low resolution spectrum taken with the B&C spectrograph
mounted at the
Bok telescope on Kitt Peak (Green, priv. comm.) have been fitted with metal-enriched
models.
For the hot stars BPS CS 22169-0001, [CW83] 1735+22 and
KPD 1946+4340 the NLTE models usually applied gave a strong mismatch
for the He II line at
.
Using metal line blanketed LTE models of solar composition did not
improve the fit. A similar problem was found by O'Toole & Heber (2006)
in their analysis of our programme star CD -24 731 (and two
other hot sdBs), which is of similarly high temperature. The problem
was remedied by using metal enhanced models. Later, the same indication
was found for KPD 1930+2752 (Geier et al. 2007) and AA Dor (Müller et al. 2010).
For this reason we used model atmospheres of ten times solar
metallicity. Although the atmospheric parameters did not change much,
the He II line at
was matched well in concert with the He I and hydrogen Balmer lines.
Only in the case of JL 82 we had to rely on FEROS spectra. Since the parameters derived from these spectra (
,
)
turned out to
be very similar to the ones derived from the FEROS spectra of TON S 183 (
,
), the systematic shifts (
,
)
should be similar as well. The parameters of JL 82 have therefore been corrected for
these shifts.
Results are summarised in Table 1 and plotted in
Fig. 2, where they are compared to canonical models for the EHB band.
The programme stars populate the EHB band between the zero-age (ZAEHB)
and the terminal-age EHB (TAEHB). Most of the hottest stars (>
)
are located above the TAEHB and probably have evolved off the
EHB already.
6 Projected rotational velocities
With the gravity at hand, we can derive masses once the projected rotational velocities have been measured. This is not an easy task because the sdB stars are known to be slow rotators. Hence, the broad Balmer and helium lines are ill-suited.
Sharp metal lines are most sensitive to rotational broadening, in particular for low velocities, while they tend to be ironed out for fast rotators. In order to reach the best accuracy it is necessary to make use of as many weak metal lines as possible.
6.1 Projected rotational velocities from metal lines
![]() |
Figure 2:
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In order to derive
,
we compared the observed spectra
with rotationally broadened, synthetic line profiles using a semi-automatic
analysis pipeline. The profiles were computed for the stellar parameters given
in Table 1 using the LINFOR program (developed by Holweger, Steffen
and Steenbock at Kiel university, modified by Lemke 1997).
For a standard set of up to 187 unblended metal lines from 24 different ions and with wavelengths ranging from 3700 to
a model grid with
appropriate atmospheric parameters and different elemental abundances was
automatically generated with LINFOR. The actual number of lines used as input
for an individual star depended on the wavelength coverage. Due to the
insufficient quality of the spectra and the pollution with telluric features in the regions blueward of
and redward of
we excluded them from our analysis. A simultaneous fit of
elemental abundance, projected rotational velocity and radial velocity was
then performed separately for every identified line using the FITSB2
routine (Napiwotzki et al. 2004b). A more detailed description
of the line selection and abundance determination will be published in
Paper III of this series (Geier et al., in prep.).
Ill-suited lines were rejected. This rejection procedure
included several criteria. First the fitted radial velocity had to be
low, because all spectra were corrected to zero RV before. Features
with high RVs (>
)
were considered as misidentifications or noise features. Then the fit quality given by the
had to be comparable to the average. Lines with
-values more than 50% higher than the average were excluded. A spectral
line was also rejected, if the elemental abundance was lower or higher than
the model grid allowed. Equivalent width and depth of the line were measured
and compared to the noise to distinguish between lines and noise features.
Mean value and statistical error were calculated from all measurements
(see Figs. 4, 5). The set of usable lines differs
from star to star due to the different atmospheric parameters and chemical
compositions. In some cases the line list had to be modified and lines were
included or excluded after visual inspection. All outputs of the pipeline
have been checked by visual inspection.
Behr (2003) used a similar method to measure the low
of blue horizontal branch stars from high resolution spectra.
The errors given in that work are of the same order as the ones given here.
6.2 Systematic errors in the determination of the projected rotational velocity from metal lines
Since the velocities measured from the metal lines are low, a thorough
analysis of the errors is crucial. To quantify them, we carried out numerical
simulations. Synthetic spectra with fixed rotational broadening were computed
and convolved with the instrumental profile. The standard list of metal lines and average sdB parameters (
,
)
were adopted. Random noise was added to mimic the observed spectra. The
rotational broadening was measured in the way described above using a
grid of synthetic spectra for various rotational broadenings and noise
levels. As the resolution is seeing dependent for a subset of spectra
we also varied the instrumental profile.
Variations in the instrumental profile changed the measured
by up to
for low S/N and poor
seeing and about
in case of high S/N and good seeing. The noise level caused errors ranging from
per line dependent of S/N. Accounting for the number of lines used the error of the average is
of the order of typically
.
A variation of the atmospheric parameters within the derived error limits gives an error of
and is therefore negligible.
We used a standard limb darkening law for the rotational broadening
independent of wavelength. Berger et al. (2005) estimated
the influence of applying a wavelength dependent limb darkening law on the
measurements of projected rotational velocities in DAZ white dwarf spectra.
In the case of the Ca II K lines they used, a small difference in the line
cores was found. Nevertheless, the systematic deviation in
was smaller than
.
Because systematic errors caused by this effect would lead to higher
real projected rotational velocities than measured, the influence of a
wavelength dependent limb darkening law on our results was tested as
well. We found the effect to be even lower, because the analysed metal
lines are much weaker than the Ca II K lines used by
Berger et al. (2005) and the effect becomes more significant for
stronger lines. A limb darkening law independent of wavelength is therefore appropriate for our analysis.
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Figure 3:
Left hand panels: numerical simulations.
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6.2.1 Individual line fits
Our numerical experiments included typical numbers of spectral lines
(20-50) as have been used in the analysis spread over the entire
wavelength range available (
dependent on the instruments used). Figure 3 shows the results of two numerical simulations. The top panel displays the result for
well above the detection limit and high S/N=100. The fitted
values for individual lines show small dispersion.
The bottom panel of Fig. 3 shows the result for
,
which is closer to the detection
limit, and low S/N =20. Due to the lower S/N individual lines scatter more strongly around the mean. Since negative values of
are not possible, the distribution of the measurements is expected to
be a truncated Gaussian. As can be seen in the lower right hand panel
the distribution doesn't look like a Gaussian, but rather bimodal with
many zero measurements. This distribution can be explained, because the
truncation of the Gaussian occurs at the detection limit rather than
.
This detection limit is different
for each star. It is caused by the thermal broadening of the lines, which
scales with
,
A being the atomic weight. The mix of
spectral lines used ranges from C (A=12) to Fe (A=56). The hotter the
star, the poorer the result as the number of lines decreases with
while the detection limit increases. Other important parameters
affecting the detection limit are spectral resolution and the S/N level of the spectra.
That is why including the zero values of the bimodal distribution in the
calculation of the mean would lead to a systematic shift of
to lower values (see Fig. 3 lower left panel). For this reason all zero values were excluded and the artificial rotational broadening could be
measured properly. As the lower limit for this method we derived about
depending on the resolution of the instrument. If more than two thirds
of the lines were measured to be zero, this value was adopted as upper
limit
for
.
As can be seen in the upper panel of Fig. 3 the measured mean value slightly deviates from the true rotational broadening by
.
Although this deviation is still within the error bars, it turned out that such shifts of up to
can be caused by systematic effects. The most likely explanation is
that for each individual line not only the rotational broadening, but
also the elemental abundance is fitted. This should affect the
-distribution
and cause a deviation from the ideal case of random distribution around
the mean. Instead of changing the rotational broadening a slightly
different elemental abundance may lead to a similar
-value. Due to this systematic effect a minimum
-error of
is adopted even if the statistical error is lower.
Our analysis revealed that the restriction to just a few metal lines in a small wavelength range can lead to even higher systematic deviations and that it is better to use as many lines as possible scattered over an extended wavelength range to measure projected rotational velocities.
There is also an upper limit. With increasing
the lines are getting broader and broader and eventually cannot be detected any more in
spectra with S/N typical for our sample. As soon as
exceeds about
almost no metal lines can be used unless
the S/N is much higher than the average of our sample. To measure higher
projected rotational velocities the Balmer and helium lines must be used as described in Sect. 6.3.
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Figure 4:
Rotational
broadening fit result for HE 1047-0436. The measured
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Figure 5:
Rotational broadening fit result for PG 1232-136
(see Fig. 4). Despite the high quality of the data no
significant
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6.2.2 Fitting several lines simultaneously
The FITSB2 routine also allows to fit a lot of lines simultaneously and
to use different methods of calculating the fitting error (e.g.
bootstrapping). In principle it is possible to measure the rotational
broadening from all lines simultaneously and derive the error. But in
practice this approach is problematic. Fitting up to 25 parameters
(24 abundances and
)
to more than 50 lines simultaneously and derive the
error using a bootstrapping algorithm requires a lot of computer power. In
test calculations we fitted up to nine lines of a synthetic spectrum with
noise, rotational and instrumental broadening added simultaneously. The
bootstrap error was consistent with the error we derived with the method
described above. Furthermore our error estimate turned out to be slightly
higher, which renders our approach more conservative. In the case of very
low
only some lines remain sensitive to changes in line
shape due to rotational broadening. The lower limit that can be reached with
the simultaneous approach is therefore higher than what can be detected with
the single line approach.
6.2.3 Orbital smearing
In the case of binary systems with very short orbital periods
(
)
and high RV amplitudes, the variable Doppler shift of the spectral
lines during the exposure can lead to a smearing effect, which can be
misinterpreted as rotational broadening unless the S/N of the spectra is
very high. Orbital smearing is clearly visible in most FEROS spectra of
PG 1232-136, which has an orbital period of
and an
RV-semiamplitude of
(Edelmann et al. 2005).
The exposure times of these spectra ranged from 6 to 30 min.
Choosing one single FEROS spectrum with sharp lines obtained at the
orbital phase when smearing should be minimal, we derived
(Geier et al. 2009a).
Due to the importance of this object for our conclusions we obtained another
60 spectra of PG 1232-136 with UVES at higher resolution (R=80 000). The exposure time of each spectrum was only 2 min. After co-adding all these spectra
we constrained
(see Fig. 5). Although the difference between these two results
appears to be not very large, it nevertheless illustrates the influence of orbital smearing.
In the case of the short period (<
)
eclipsing sdB+M binary
HS 0705+6700 with an RV-semiamplitude of
the effect
is much stronger. While Drechsel et al. (2001) measure
from medium resolution spectra
with short exposure times (
), we measure
from a high resolution
spectrum taken with HET/HRS and an exposure time of
.
From the high resolution data we can only constrain an upper limit of
.
Two other stars of our sample (PG 1336-018 and PG 1043+460)
may also be affected by orbital smearing, if the spectra we used were
obtained during unfavourable orbital phases. Only upper limits can be
given for their
.
6.2.4 Other systematic errors and their impact on the companion mass determination
Other possible sources of systematic errors are broadening through microturbulence or unresolved pulsations. No significant microturbulence could be measured which is consistent with the analysis of Edelmann et al. (2001). Our sample contains six long-period pulsating sdBs of V 1093 Her type (Green et al. 2003) and four short period pulsators of V 361 Hya type (Kilkenny et al. 1997). It has been shown by Telting et al. (2008) that unresolved high amplitude pulsations with short periods can significantly contribute to or even dominate the line broadening. This is not a problem for our sample stars, because the pulsation periods of the V 1093 Her stars are long compared to our exposures times and the amplitudes are low. No significant pulsational broadening is expected in the case of the short period pulsators Feige 48 and HE 0230-4323 as well, because the amplitudes of the pulsations are low (Reed et al. 2004; Charpinet et al. 2005b; Kilkenny et al. 2010). The line broadening of KPD 1930+2752 and PG 1336-018 is totally dominated by their rotation, because the sdBs are spun up by their close companions (Geier et al. 2007; Vuckovic et al. 2007).
It has to be pointed out that unresolved pulsations, microturbulence and any other unconsidered effect would cause an extra broadening of the lines. The true projected rotational velocity would therefore always be lower than the one we determined. In this case the derived orbital inclination would also be lower and the estimated mass of the unseen companion would be higher (see Sect. 4). Unaccounted systematic effects would therefore lead to higher companion masses. This fact is important for the interpretation of the results (see Sect. 7).
6.3 Projected rotational velocities from hydrogen and helium lines
A few sdBs, which reside in close binary systems, are known to be spun up by
the tidal influence of their companions. The projected rotational velocities of these stars are as high as
(e.g. Drechsel et al.
2001; Geier et al. 2007).
Rotational broadening irons out the weak metal lines unless the spectra are of excellent S/N. However, for higher projected rotational velocities,
Balmer and helium lines remain the only choice
to determine
.
Due to thermal and pressure broadening Balmer and helium lines are less
sensitive to rotational broadening than metal lines. From our
simulations we derive detection limits of
for helium lines and
for the Balmer line cores given an
.
For lower quality data these limits go up significantly. For many of
our spectra the Balmer and helium lines are insensitive unless
exceeds
.
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Figure 6: Rotational broadening fit result for HE 0532-4503 (see Fig. 4). |
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Figure 7: Selected helium lines of KPD 1946+4340 are plotted against the shift relative to rest wavelengths. The spectrum (histogram) is overplotted with the best fitting rotationally broadened model (strong line). A model without rotational broadening (weak line) is overplotted for comparison. |
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To measure the
we calculated LTE model spectra with the
appropriate atmospheric parameters (see Table 1) and
performed a simultaneous fit of rotational broadening and helium abundance to
all usable Balmer line cores and helium lines using the FITSB2 routine
(Napiwotzki et al. 2004b, for an example see Fig. 7). All systematic effects discussed in
the previous section except orbital smearing become negligible in this case. The quoted uncertainties are 1
-
-fit errors.
The helium ionisation problem in hot sdBs (see Sect. 5)
caused by neglected metal opacity can affect the measurement of the
rotational broadening, if helium lines are used. This became apparent
in the analysis of the eclipsing sdOB binary AA Dor. While Rauch
& Werner (2003) used metal-free NLTE models and measured
for the He II line at
,
Fleig et al. (2008) measured
by fitting metal line blanketed NLTE models to FUSE spectra. Rucinski (2009) derived
by an analysis of line profile variations during the eclipse and reported a mismatch between the Mg II line at
and the He II line at
.
Müller et al. (2010) resolved this conundrum and showed that consistent results (
)
can be achieved if the appropriate (metal enriched) model atmospheres are used (see Sect. 5).
To account for this effect we used LTE models with ten times solar
metallicity rather than metal-free NLTE models to measure the
rotational broadening of the Balmer line cores and helium lines in the
two hot sdOBs KPD 1946+4340 (see Fig. 7) and [CW83] 1735+22. While in the case of [CW83] 1735+22 the
-values
derived with the two different model grids were the same, a significant
difference was measured for KPD 1946+4340. The
derived with the metal-free models was
compared to
with metal-enriched models.
Due to the fact that KPD 1946+4340 is eclipsing (Bloemen et al. 2010) it is possible to verify that the
measured with metal enriched models is fully consistent with the assumption of synchronised rotation (see Sect. 10).
6.4 Results
Projected rotational velocities of 46 close binary subdwarfs have been measured and supplemented by five measurements taken from literature (Tables 2 and 3). For 40 systems the orbital parameters are known. In general the projected rotational velocities are small. The other 11 systems are slow rotators, too. These systems can not be analysed further as their mass functions are still unknown.
Table 2: Projected rotational velocities for the binary sdB systems from Table 1.
Table 3: Projected rotational velocities of radial velocity variable sdBs, for which orbital parameters are unavailable or uncertain.
The projected rotational velocities of HE 1047-0436 and Feige 48 have
been measured by Napiwotzki et al. (2001a) and O'Toole et al.
(2004) using a technique similar to the one described here, but
restricted to just a few metal lines. Napiwotzki et al. (2001a)
derived an upper limit of
for
HE 1047-0436. Our measurement of
is just slightly higher
(see Fig. 4). While O'Toole et al. (2004) give an upper
limit of
for Feige 48 we derive
.
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Figure 8:
Shaded histogram showing the distribution of the measured
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Figure 9:
The measured
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Figure 9 shows the measured
plotted against the
orbital periods of the binaries. A trend is clearly visible: The longer the
orbital period of the systems, the lower the measured
.
While the short period systems (
)
were spun up by their
close companions and have high
up to
,
the mean
decrease to
below
as the periods increase to
.
For orbital periods exceeding
,
the
-values scatter around the average
for single sdB stars
(Geier et al. 2009a). We conclude that tidal forces do not
influence the rotation of sdBs for orbital periods considerably longer than one day.
As can be seen in Fig. 8 the
-distribution of the RV variable sdBs (Tables 2, 3)
differs from the uniform distribution of the single stars
(Geier et al. 2009a).
The rotational properties of the full sample of single sdB stars will
be presented in paper II of this series by Geier et al. (in
prep.). A large fraction of binary sdBs exceeds the derived maximum
significantly. The most likely reason for this is tidal interaction with the companions.
7 Constraining masses, inclinations and the nature of the unseen companions
Having determined the projected rotational velocity we are in a position to derive the companion mass as a function of the sdB mass as described in Sect. 4.
From 40 sdB binaries, for which all necessary parameters have been determined, 31 could be solved consistently under the assumption of tidally locked rotation. Two examples are shown in Figs. 10 and 11. Derived inclinations, subdwarf masses and the allowed masses for the companions are given in Table 4.
If the sdB mass could not be constrained with other methods (e.g. from
photometry, see Table 4), the theoretically predicted mass range
was taken from Han et al. (2002, 2003). For the common envelope
ejection channels, which are the only plausible way of forming sdBs in close
binary systems, the possible masses for the sdBs range from
to
.
Since in all simulation sets
of Han et al. (2002, 2003) the mass distribution
shows a very prominent peak at
this mass range is
the most likely one.
The choice of the adopted sdB mass range is backed up by recent mass
determinations via asteroseismology of
short-period pulsating sdBs. Fontaine et al. (2008) showed the
mass distribution of 12 of these objects, which is in good agreement with
the predicted distribution by Han et al. (2002, 2003).
Consistent with theory no star of this small sample has a mass much lower
than
.
The few sdB masses, that could be constrained by
analyses of eclipsing binary systems also range from
to
(see e.g. Sect. 7.1 and For et al.
2010).
Hence we adopt
as the mass range
for the sdBs in the binary systems we studied, if there is no independent
mass determination either from binary light curve analysis or asteroseismology.
If the derived minimum sdB mass assuming a sychronised orbit (see Eq. (4)) exceeds
this reasonable mass range (
)
the sdB primary spins
faster than synchronised and no consistent solution can be found.
This is the case for 9 binaries from our sample.
Most of these systems have orbital periods exceeding
,
where we find that synchronisation is no longer established
(see Sect. 9). It has to be pointed out that only
subdwarfs rotating faster than synchronised can be identified in this way.
If an sdB should rotate slower than synchronised, one would always get an
apparently consistent, but incorrect solution, which overestimates the
companion mass (see Sect. 11.2). For PG 0133+114 there is some doubt whether
the star is synchronised or not as the minimum mass for the sdB is
at the upper end of the predicted mass range for core
helium-burning objects and its period is rather long (
).
The minimum companion mass would be
,
while the statistically
most likely one (
)
,
indicating it is a white dwarf, if the
system is synchronised.
The nature of the companion was deduced unambiguously for most of the remaining stars (except five)
from the masses and additional information. The companions to PG 1248+164,
HE 1421-1206, Feige 48
, and
HE 2135-3749 could be either main sequence stars or white dwarfs
because their
masses are lower than
.
We shall describe the results for three groups of companion stars.
Starting with sdBs orbited by low mass dwarf companions, we proceed to the
systems with white dwarf companions of normal masses. Finally we discuss the
group of binaries that contain massive
compact companions exceeding
,
because such systems
are of particular interest, e.g. as potential SN Ia progenitors.
This includes KPD 1930+2752, the most massive white dwarf companion to an sdB star known so far.
Table 4: Derived inclination angles, companion masses and likely nature of the companions.
7.1 Late main sequence stars and a potential brown dwarf
PG 1017-086 is the sdB binary with the shortest orbital period known
to date. Maxted et al. (2002) reported the detection of a significant
reflection effect, but no eclipses in the light curve. Taking these informations into
account, one can constrain the inclination angle to be lower than
(no eclipses!) and derive a minimum sdB mass of
.
The minimum mass of the companion is constrained to
.
The companion is therefore most likely a brown dwarf (BD) or a very late
M dwarf. Only two other candidate sdB+BD systems are known.
HS 0705+6700 is an eclipsing sdB+M binary with reflection effect.
Drechsel et al. (2001) performed a detailed photometric and
spectroscopic analysis of this system and derived an inclination of
,
an sdB mass of
and a companion mass of
.
Drechsel et al. (2001) also estimated
and
derived the companion mass. Although our result is much less accurate
(
), it comes close to that derived from the light curve.
Much better agreement is reached for HW Vir, the prototype eclipsing
sdB+M binary, where excellent high resolution spectra are available.
Edelmann (2008) recently determined the absolute parameters
of this system spectroscopically using shallow absorption lines of the secondary
to obtain its RV curve for the first time. Edelmann (2008) derives
an sdB mass of
and a companion mass of
.
Adopting this sdB mass our derivation of the companion
mass agrees very well (
). The derived inclination
angle of
is consistent with the more accurate photometric
solution
given by Wood et al.
(1993). Most recently Lee et al. (2009) presented an analysis on HW Vir based on new photometric
data. Their best solution (
,
,
)
is fully consistent with our results.
The eclipsing and pulsating sdBV+M binary PG 1336-018 (NY Vir)
has been analysed by Vuckovic et al. (2008), but no unique
solution could be found. In an asteroseismic study Charpinet et al.
(2008) derived the fundamental parameters of this star by
fitting simultaneously the observed pulsation modes detectable in the
light curve. Adopting the asteroseismic value for the sdB mass
(
)
for our analysis, the companion mass is
>
.
This result is in agreement with the second solution from Vuckovic et al.
(2008):
,
.
Charpinet et al. (2008)
concluded that the binary must be synchronised to account for the observed
rotational splitting of the pulsation modes and predict
a
.
This predicted value is
consistent with the derived upper limit of
.
BPS CS 22169-0001 was proposed to host a BD companion
(Edelmann et al. 2005), but we derived a very low inclination and
therefore a companion mass too high for a BD (
).
In the light curves of the four binaries BPS CS 22169-0001,
HE 0230-4323, JL 82 as well as PG 1329+159 reflection
effects have been detected (see references in Table 4).
The derived companion mass ranges are consistent with the masses of late M dwarfs.
7.2 White dwarfs
Ten stars must have white dwarf companions because no lines from cool companions are visible and the absence of a reflection effect can be used to exclude a main sequence companion in some cases.
Among these binaries KPD 1946+4340 sticks out. Most recently Bloemen et al. (2010)
discovered eclipses and ellipsoidal variations in a spectacular high
precision light curve obtained by the Kepler mission. The eclipses are
clearly caused by a WD companion. We derive a mass range of
for the unseen companion consistent with a WD. Due to the fact that the
binary is eclipsing, the inclination angle has to be close to
.
Assuming the canonical sdB mass of
the companion mass can be constrained to
,
which is the average mass of WDs with C/O core. This result is
perfectly consistent with the indepedent analysis of Bloemen
et al. (2010).
The companion of GD 687 has already been shown to be a white dwarf by Geier et al. (2010a) utilising the same technique as used in this paper and is included for the sake of completeness. Its merging time is
,
which is just a little shorter than the Hubble time
.
A remarkable object which has a high inclination and a very low companion mass
(>
)
is PG 1043+760. Due to its short period of
a reflection effect should be easily detectable.
But Maxted et al. (2004)
report a non-detection of variations in the light curve. The companion
of this star must be a compact object, most likely a helium-core white
dwarf of very low mass.
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Figure 10: Mass of the sdB primary CPD -64 481 plotted against the mass of the unseen companion. The companion mass error is indicated by the dashed lines. The mass range of the CE ejection channel (Han et al. 2002) is marked with dotted vertical lines. |
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In the case of PG 1627+017, a main sequence companion can be excluded
as well. With a mass exceeding
the companion would be
visible in the spectra in this case. The non-detection of a reflection effect
(Maxted et al. 2004; For et al. 2010) is consistent with our result.
The companion of PG 0101+039 is a white dwarf. Despite of the long
orbital period of
a main-sequence companion could be excluded. A light curve was taken with the MOST satellite. Instead of a reflection
effect the shallowest ellipsoidal deformation ever detected could be
verified (Geier et al. 2008a). The white dwarf companion could be
quite massive (
). In this case the total mass
comes close the Chandrasekhar limit, but the merging time would be higher
than the Hubble time. PG 0101-039 does therefore not qualify as SN Ia
progenitor candidate. The companion mass range of PG 0001+275 is
quite similar (
). A main sequence companion
can be most likely excluded and no reflection effect was detected (Maxted et al. 2004; Shimanskii et al. 2008). The orbital period of
is also too long to make PG 0001+275 a SN Ia progenitor candidate.
Edelmann et al. (2005) derived a very low minimum companion mass
for CPD -64 481. At high inclination the companion mass would have
been consistent with a brown dwarf. However, our analysis provides evidence
that this binary has a very low inclination (
to
), actually
the lowest one of the entire sample,
and therefore a companion mass way too
high for a BD (
)
indicating a white dwarf binary.
Due to the low projected rotational
velocity of this star, the fractional error is very high and the companion
mass not very well constrained. For the highest possible companion mass the
system would exceed the Chandrasekhar limit and qualify as SN Ia progenitor
candidate due to its short orbital period. However, the inclination angle must
be lower than
is this case. That is why this extreme scenario is
considered to be very unlikely.
The unseen companions in the binaries HE 1047-0436, and HD 171858 also have masses consistent with white dwarfs.
The mass of the companion to PG 1116+301 is slightly above the limit of
.
Despite the high inclination derived for this binary no reflection effect was detected in its light curve (Maxted et al. 2004; Shimanskii et al. 2008), which is consistent with a WD companion
.
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Figure 11: Mass of the sdB primary HE 0532-4503 plotted against the mass of the unseen companion. The companion mass error is indicated by the dashed lines. The mass range of the CE ejection channel (Han et al. 2002) is marked with dotted vertical lines. The Chandrasekhar mass limit is plotted as solid horizontal line. |
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7.3 Massive compact companions - white dwarfs, neutron stars, black holes
Seven subdwarf binaries (in addition to KPD 1930+2752) have
massive compact companions (see e.g. Figure 11) exceeding
.
For all of
these binaries main sequence companions can be excluded, because they would
significantly contribute to the flux or even outshine the subdwarf primary.
The massive companions therefore have to be compact.
The nature of the unseen companion in the binary KPD 1930+2752 could
be clarified by Geier et al. (2007).
The short period system consists of a synchronously rotating, tidally
distorted sdB and a massive white dwarf. The combined mass of the
systems reaches the Chandrasekhar limit and the stars will most
probably merge in
.
KPD 1930+2752 is the best
double degenerate candidate for SN Ia progenitor so far.
The companion mass of TON S 183 is as high as that of KPD 1930+2752.
However, the error bar is much larger. Hence we can not exclude that it is a
normal white dwarf of
.
On the other hand the total mass of the system may exceed the
Chandrasekhar limit, but TON S 183 does also not qualify as SN Ia progenitor
candidate, because of its long orbital period the merging time exceeds the
Hubble time by orders of magnitude.
For PG 1101+249 and HE 0929-0424 the companion mass is slightly above the Chandrasekhar limit, but we can not exclude a massive white dwarf given the errors. The merging times of HE 0929-0424 and especially PG 1101+249 on the other hand would be near or below Hubble time and the total masses of the systems would most likely exceed the Chandrasekhar limit. If the companions should be massive white dwarfs of C/O composition, these binaries would be SN Ia progenitor candidates.
The companions of PG 1432+159, HE 0532-4503 and
PG 1743+477 may be neutron stars as well as black
holes as their masses exceed the Chandrasekhar limit even when errors
are accounted for. Light curves have been obtained of both
PG 1432+159 and PG 1743+477. The non-detection of reflection
effects is perfectly consistent with compact companions (Maxted
et al. 2004).
In the case of PG 1743+477 only a lower limit for the companion
mass could be derived. Due to their short orbital periods the
companions in PG 1432+159 as well as in HE 0532-4503 will
merge in a few billion years at most. Since the average lifetime on the
EHB is only
the sdBs will evolve to white
dwarfs in the meantime. The outcome of a merger between a white dwarf and a neutron star
or a black hole is unclear. Such systems may be progenitors for gamma-ray
bursts or more exotic astrophysical transients (see discussion in Badenes et al. 2009).
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Figure 12:
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Figure 13:
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In the case of PG 1232-136 only a lower limit can be given for the companion mass
(>
)
which is higher than all theoretical NS masses. The
companion of this sdBs may therefore be a BH.
7.4 Distribution in the T eff-logg-plane
Figure 12 shows the distribution of the 31 solved binaries in the
-
-diagram.
Within their error bars most of the sdB primaries are associated with
the EHB as expected. Only three of them (BPS CS 22169-0001,
KPD 1930+2752, KPD 1946+4340) have evolved beyond the TAEHB.
No trends with companion types can be seen. The location on the EHB is
a function of the thickness of the stars' hydrogen layers. The thinner
this layer is, the higher are
and
at the beginning of EHB-evolution and the more envelope mass has been
lost during the CE-ejection. The efficiency of this process seems to be
not much affected by the companion type. Companions of all types
ranging from low mass M dwarfs or brown dwarfs to massive compact
objects are scattered all over the EHB.
While the fraction of evolved sdBs is only 10% in the solved sample, two out of nine subdwarfs (22%) are found in binaries, which could not be solved under the assumption of synchronisation, are obviously not located on the EHB (see Fig. 13). A possible reason for this discrepancy is discussed in Sect. 11.1.
7.5 Distribution of companion masses
Figure 15 shows the low mass end of the companion mass distribution.
Excluding the massive systems described in Sect. 7.3
the histogram mass distribution (Fig. 15) displays a peak at companion masses ranging from
.
Most of the low mass objects <
have been identified as M dwarfs.
The bona fide white dwarf companions seem to peak at masses ranging from
to
.
Because close binary evolution is involved, there should be deviations
from the normal mass distribution of single white dwarfs, which shows a
characteristic peak at an average mass of
.
We therefore conclude that the mass distribution of the restricted
sample looks reasonable and no obvious systematics can be seen. The
high fraction of massive compact companions (up to 20% of our sample)
on the other hand looks suspicious.
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Figure 14:
Mass ranges for the unseen companions of 31 binaries under the assumption of synchronisation (see Table 4). The companion mass ranges are derived for the most likely sdB mass range of
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As the companion mass depends on the primary mass, the companion masses would be
lower, if the primaries' masses were overestimated.
We have adopted the masses of the sdB primaries to range from
to
as suggested by the models of Han et al.
(2002, 2003) and backed-up by asteroseismology.
However, the minimum mass of a core helium burning
star can be as small as
.
In Fig. 16 the companion mass distribution is plotted under
the extreme assumption that all sdBs have this minimum mass for core helium
burning (or the minimum mass allowed by other constraints). Looking at the
low mass regime and comparing the distribution with
Fig. 15 one immediately notices that this assumption
leads to unphysical results. The distribution of low mass companions peaks
at masses lower than
,
which is very unlikely
especially for white dwarf companions.
Under this extreme assumption only the companion of PG 1232-136 remains
more massive than the Chandrasekhar limit.
Furthermore the companions of PG 1743+477 and HE 0532-4503 still are
more massive than
in this case. With just slightly
higher sdB masses the companion masses would exceed the Chandrasekhar limit.
7.6 The inclination problem
By plotting the companion masses versus inclination angles
(Fig. 18) an anomaly becomes apparent. While the systems with
low mass companions cover all inclination angles with a slight
preference for high inclinations, the systems with massive compact companions
are found at low inclinations between
and
.
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Figure 15: Companion mass distribution of the binaries with low mass companions (Table 4, Fig. 14). The solid histogram shows the fraction of subdwarfs with confirmed white dwarf companions, the dashed histogram the detected M dwarf companions. The dashed vertical line marks the average white dwarf mass. |
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Our sample has been drawn from the catalogue of Ritter & Kolb (2003), which is a compilation extracted from literature and not a systematic survey. Hence selection effects can not be quantified. Most of the low-mass, high-inclination systems have been discovered by photometry (eclipses and reflection effect), while all others stem from radial velocity surveys. The radial velocity technique is biased against low inclinations and low masses. Hence, massive systems at high inclinations should be found most easily. However, except for KPD 1930+2752, there is no high inclination object among the subsample of massive compact companions. One may speculate that such systems may have been overlooked, because their spectra may look peculiar due to orbital smearing and are therefore not classified as sdB stars.
We refrain from further speculations about selection effects and proceed to search for an evolutionary scenario that can explain the formation of sdB binaries with neutron star or black hole companions.
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Figure 16: Mass distribution of the unseen companion stars (see Fig. 15). The lowest possible companion mass is plotted against the total number of binaries under the assumption of the lowest possible sdB mass. |
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8 The formation of sdB+NS/BH binaries
Neutron stars and stellar-mass black holes are the remnants of massive stars ending their lifes in supernova explosions. Detecting these exotic objects is possible when they are in a close orbit with another star. If matter is transferred from the companion star to the compact object, X-rays are emitted. Not many neutron stars or stellar mass black holes could be found up to now. On the other hand evolved, non-interacting binaries containing such objects should exist, since X-ray binaries only represent a relatively short phase of stellar evolution. Without ongoing mass transfer the companion remains invisible, but should be detectable indirectly from the reflex motion of the visible star. Badenes et al. (2009) discovered a massive compact companion to a white dwarf and concluded that this companion is likely to be a neutron star. But Marsh et al. (2010) convincingly showed that the system is a double degenerate system consisting of a low mass and a very high mass WD. Kulkarni & van Kerkwijk (2010) performed an independent analysis with similar results. In this section the question whether sdB stars with hidden neutron star or black hole companions do exist is discussed in detail.
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Figure 17: Schematic diagram of formation scenarios leading to hot subdwarf binaries with neutron-star (left hand panel) or black-hole (right hand panel) companions. |
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The existence of sdB+NS/BH systems requires an appropriate formation channel.
The evolution that leads to such systems requires an initial binary,
consisting of a primary star that is sufficiently massive to produce a
neutron star or black hole, and a companion, the progenitor of the hot
subdwarf, of typically several solar masses. The initial orbital
period has to be quite large (a few to 20 years), so that mass
transfer only starts late in the evolution of the star, and these
systems generally experience two mass-transfer phases and one
supernova explosion (see Fig. 17). The short orbital periods
observed
for our systems imply that the second mass-transfer phase from the red
giant progenitor of the subdwarf to the compact companion had to be
unstable, leading to a common-envelope and spiral-in phase of the
compact object. The condition for unstable mass transfer constrains
the mass of the progenitor to be larger than the mass of the compact
object (otherwise, mass transfer would be stable and lead to a much
wider system, Podsiadlowski et al. 2002).
Figure 17 illustrates the evolution that leads to
systems of this type for two typical examples. While this scenario can
explain most of our systems with high-mass compact components, the
inferred masses of the putative black hole in PG 1232-136 is
larger than we would estimate ()
for a 0.5
sdB star. This may suggest that this system has experienced another
mass-transfer phase after the two common-envelope phases in which mass
was transferred from the sdB star to the compact object. It should
also be noted that, while we assume here that
the mass of the subdwarf is
,
consistent with the
properties of the observed systems, the sdB mass range allowed by this
scenario is
for the neutron-star systems and
for the black-hole systems. Compared with the mass
range of
for the standard evolutionary
channel (Han et al. 2002, 2003), the subdwarf may therefore
be more massive. An independent determination of the sdB mass (e.g. by
obtaining parallaxes) could therefore help to verify this
scenario.
At the beginning of the second mass-transfer phase, these systems are
expected to pass through a short X-ray binary phase, lasting 105 yr, in which a neutron star may accrete up to
and become a moderately recycled millisecond
pulsar (Podsiadlowski et al. 2002). This links these system to the
X-ray binary population
(in a sense, they are failed low-mass X-ray binaries). Population
synthesis estimates (Pfahl et al. 2003) suggest that up to one in
104
stars in the Galaxy experience this evolution, implying that of order
1% of all hot subdwarfs should have neutron-star or black-hole
companions. This means that tens of thousands of these systems could
exist in the Galaxy compared to just about 300 known X-ray
binaries. The binary PSR J1802-2124, which consists of a
millisecond pulsar and a CO white dwarf in close orbit (
,
)
may have evolved in a similar way (Ferdman et al. 2010).
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Figure 18: Companion mass versus inclination. The solid squares mark compact companions (WD/NS/BH), the solid diamond MS or BD companions. The solid circles mark objects where both companion types are possible. |
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Part II: Synchronisation - theory and empirical evidence
9 Orbital synchronisation of sdB binaries
The results presented above are based on the assumption of tidal synchronisation. Since especially the discovery of sdB+NS/BH systems challenges our understanding of stellar evolution, it is necessary to investigate whether this assumption holds in the case of sdBs. A thorough discussion of tidal synchronisation in sdB binaries both from the theoretical and the observational point of view is therefore given.
9.1 Theoretical timescales for synchronisation
Which mechanism is responsible for orbital synchronisation in binaries is still under debate. Theoretical timescales for synchronisation are given by Zahn (1977) and Tassoul & Tassoul (1992), but unfortunately they are not consistent for stars with radiative envelopes and convective cores like hot subdwarfs.
Zahn (1977) was the first to calculate synchronisation and circularisation timescales for main sequence stars in close binary systems. Observations of eclipsing binaries were in good agreement with his theoretical calculations for late type main-sequence stars with radiative cores and convective envelopes. Tidal friction caused by the equilibrium tide, which forms under the tidal influence of the close companion, is very efficient in this case because convection connects the inner regions of the stellar envelope with its surface. For radiative envelopes another mechanism is needed to explain the observed degree of synchronism in early type main-sequence binaries. Dynamical tides, which are excited at the boundary layer between the convective core and the radiative envelope are thought to be radiatively damped at the stellar surface and to transfer angular momentum outwards. This mechanism turns out to be much less efficient and the predicted synchronisation timescales are too long to explain the degree of synchronism in some early type main-sequence stars (e.g. Giuricin et al. 1984).
Tassoul & Tassoul (1992) introduced another, hydrodynamical braking mechanism. Tidally induced meridional currents in the non-synchronous binary components should lead to synchronisation and circularisation of the system. This mechanism is very efficient, but it was debated whether it is valid or not (Rieutord 1992; Tassoul & Tassoul 1997). Claret et al. (1995, 1997) studied both mechanisms and compared them to the available observations. Due to the necessary calibration of many uncertain parameters a definitive answer as to which mechanism is in better agreement with observation could not be given.
Applying the theory of tidal synchronisation to sdB binaries is not an easy
task. One of the key results of both theories is that tidal circularisation of
the orbit is achieved after the companions are synchronised.
This means that
once an orbital solution is found and the orbit turns out to be circular, both
companions can be considered as synchronised without knowing their rotational
properties. This simple law cannot be used in the case of sdBs. The reason is
that close binary sdBs were formed via the CE ejection channel.
The common envelope phase is very efficient in circularising the orbit and
all known close binary sdBs have circular orbits or show only small
eccentricities (
;
Edelmann et al. 2005;
Müller et al. 2010; Napiwotzki et al., in prep.).
Stellar structure plays an important role. The synchronisation timescale of
Zahn (1977) scales with
,
where
is the
radius of the convective core and R the stellar radius. The larger the
convective core of a star, the shorter the time span until synchronisation is
reached.
In order to estimate the synchronisation times of the analysed binaries we
used the formulas of Zahn (1977) and Tassoul & Tassoul
(1992).
Here









In this equation M, R (solar units) and q are defined in the same way as above. P is the orbital period in days. The luminosity




It has to be pointed out that both theories predict the synchronisation timescale
to increase strongly with increasing orbital period and to
decrease with increasing sdB radius as
and
.
In the
theory of Zahn (1977) the exponents are
and
,
while the Tassoul & Tassoul formula gives
and
.
In addition the synchronisation timescale decreases as the mass ratio
increases. Hence it will take lower mass companions longer to synchronise the sdB
star if the other parameters are constant.
9.2 Synchronisation of our sample
The synchronisation time scale depends strongly on orbital period and
radius. Because the radii of the sdBs differ only little we display the
results of our calculations as a function of orbital period in
Fig. 19. The synchronisation timescales are given in units of the average EHB lifetime (
;
Dorman et al. 1993). A binary is thought to be synchronised, if the EHB
lifetime is much longer than the synchronisation time. Due to the larger exponents
and
the slope of the
relations is steeper and the scatter larger for the Zahn (1977) theory compared to the one proposed by Tassoul & Tassoul (1992). What can be seen immediately is that the timescales of Zahn (1977) and Tassoul & Tassoul (1992)
differ by 2-8 orders of magnitude.
Observational evidence is needed to constrain the timescales of tidal
synchronisation in close binary sdBs.
For periods shorter than
both theories predict synchronised
rotation and are consistent with our observations. In the period range
only the synchronisation times of Tassoul are consistent with
observation, while the timescales of Zahn quickly exceed Hubble time.
If the orbital periods exceed
the assumption of synchronisation does not yield consistent results any more, although the
timescales calculated with the prescription of Tassoul & Tassoul
(1992) would still predict synchronised rotation.
According to our results, the period limit where synchronisation breaks down, lies near
.
The binaries HE 2150-0238 (
)
and PG 1512+244 (
)
cannot be solved consistently although their periods
are only slightly longer than that of HE 1047-0436 (
)
and PG 0133+114 (
), which can be solved.
Despite its long period, HD 171858 can be solved
consistently, making it the longest period (
)
object in our sample that is synchronised. Why is this? Besides the
orbital period the size of the star matters: The larger the star, the
shorter the synchronisation time (see Eqs. (5) and (6)).
The gravity of HD 171858 is lower than that of all other stars with periods ranging from
to
by a factor of 2 at least. Hence its radius is larger and
synchronisation can be achieved more quickly than in the other stars of
slightly shorter periods.
[CW 83] 1735+22 stands out among the longer-period binaries, because its projected rotational velocity (
)
is unusually high. Because of its period (
)
it is not necessarily expected to be synchronised. This system is discussed in detail in Sect. 11.1.
We also found that the short period binary PG 2345+318 (
)
rotates slower than synchronised.
This peculiar system is discussed in detail in Sect. 11.2.
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Figure 19:
Observed orbital period is plotted against the
synchronisation times of Zahn (1977, open symbols) and
Tassoul & Tassoul (1992, filled symbols) both in units of the average lifetime on the EHB (
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In general the synchronisation mechanism of Zahn (1977) is not efficient enough to explain the observed level of synchronisation, while the mechanism of Tassoul & Tassoul (1992) on the other hand appears to be much too efficient. Nevertheless, care has to be taken interpreting these results, because both theories give timescales for the synchronisation of entire stars from the core to the surface, while only the rotation at the surface can be measured from line broadening. Goldreich & Nicolson (1989) showed that in stars with radiative envelopes and Zahn's braking mechanism at work, the synchronous rotation proceeds from the surface towards the core of the star. This means that the outer layers are synchronised faster than the rest of the star. This effect would explain the discrepancy between Zahn's theory and our results at least to a certain extent. Unfortunately it was not possible to quantify this effect so far (see e.g. review by Zahn 2005).
Tidal synchronisation does not necessarily lead to an equality of orbital and rotational period. Higher spin resonances are possible and would change the derived parameters significantly (in case of the planet Mercury the ratio of orbital and rotational period is 3/2). To fall into a higher resonance, the binary eccentricity has to be high at some point of its evolution. But close sdB binaries underwent at least one common envelope phase (maybe two in case of compact companions), which led to a circularisation of the orbit. The small eccentricities in some of our programme binaries reported by Edelmann et al. (2005) and Napiwotzki et al. (in prep.) are considered to be still consistent with this scenario. For these reasons, higher resonances are unlikely to occur in this evolutionary channel.
10 Empirical evidence for synchronisation
The timescale of the synchronisation process is highly dependent on the tidal force exerted by the companion. If the companion is very close and the orbital period therefore very short, synchronisation is established much faster than in binaries with longer orbital periods. If an sdB binary with given orbital period is proven to be synchronised, all other sdB binaries with shorter orbital periods should be synchronised as well. Although the timescales also scale with sdB radius and companion mass, the orbital period is the dominating factor because sdB radii differ only little and the dependence on companion mass is not so strong.
10.1 Eclipsing and ellipsoidal variable systems
Eclipsing sdB binaries are of utmost importance to test the synchronisation
hypothesis because the inclinations can be derived directly from their
light curves. It has been shown in Sect. 7.1 that the parameters of the
eclipsing sdB+dM binaries PG 1336-018, HS 0705+6700 and HW Vir are consistent
with synchronised orbits. This essentially means that the calculated
for synchronous rotation, which can be obtained as
described in Sect. 4 given the orbital period, the radius of the
sdB and the inclination angle are known, is consistent with the measured value.
In eclipsing systems, all these parameters can be measured.
This provides clear empirical evidence that at least the upper layers of the
stellar envelopes are synchronised to the orbital motion of the eclipsing sdB
binaries in our sample. We therefore conclude that all sdBs in close binaries with orbital periods up to
should be synchronised as well.
Two well studied sdBs clearly show ellipsoidal variations in their light curves with
periods exactly half the orbital periods (KPD 1930+2752, Billères et al. 2000;
Maxted et al. 2001; Geier et al.
2007, is further discussed in Sect. 7.2;
KPD 0422+5421, Koen et al. 1998; Orosz & Wade 1999, is not part of our sample).
This alone is only an indication for tidal synchronisation, because the
light curve variations have to be present at the proper orbital phases as
well. To really prove synchronisation it is necessary that the stellar
parameters determined independently from the light curve analysis are
consistent with a synchronised orbit. This is the case for KPD 0422+5421 as
well as KPD 1930+2752. Both ellipsoidal variable systems have very short periods of
and high inclination. Otherwise ellipsoidal variations are very hard to detect.
Most compelling evidence for synchronisation in a binary system with a
period considerably longer than that of the above mentioned systems is
provided in the case of the eclipsing sdB+WD binary KPD 1946+4340
(
).
Bloemen et al. (2010) derived most accurate binary parameters from a spectacular high-S/N
light curve obtained by the Kepler mission. These results are fully
consistent with the constraints we put on this system (see Sect. 7.2). We therefore conclude that sdB binaries with periods shorter than
should be synchronised.
Furthermore, the sdB+WD binary PG 0101+039 (
)
shows very weak luminosity
variations at half the
orbital period detected in a 16.9 day long, almost uninterrupted light curve
obtained with the MOST satellite (Randall et al. 2005). Geier
et al. (2008a) showed that the sdB in this binary is most likely
synchronised. The empirical lower limit for tidal synchronisation in close sdB binaries is therefore raised to
.
10.2 Asteroseismology
An independent method to prove orbital synchronisation is provided by
asteroseismology. Van Grootel et al. (2008) were able to
reproduce the main pulsation modes of the short period pulsating sdB in the binary
Feige 48 (
), derived the surface rotation from the
splitting of the modes and concluded that the subdwarf rotates synchronously.
Charpinet et al. (2008) reach a similar conclusion for the short period eclipsing binary PG 1336-018 (
). Furthermore
they probed the internal rotation of the star below the surface layers by
applying a differential rotation law and showed that the sdB rotates as a
rigid body at least down to
.
The remarkable consistency
of the binary parameters derived by asteroseismology (Charpinet et al.
2008), binary light curve synthesis (Vuckovic et al.
2007) and the analysis presented here has to be pointed out
again (see Sect. 7.1). Asteroseismic analyses revealed that sdB binaries up to orbital periods of about
are synchronised.
We therefore conclude that all sdBs in close binaries with shorter periods
should be synchronised as well.
11 Synchronisation challenged
In Sect. 9.2 we have shown that synchronisation in our sample has been established for binaries with periods below
.
This is corrobated by the theory of synchronisation
although different version of the theory give vastly different results. Empirical evidence sets a
limiting period of
.
About half of our sample has periods below that limit
and should therefore be synchronised. These arguments are correct for the sample
but may not hold for individual objects.
We envisage two options: The subdwarf may not be core helium-burning (Sect. 11.1). Or an individual EHB star may be too young to have reached synchronisation (Sect. 11.2).
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Figure 20:
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11.1 [CW 83] 1735+22 and post-RGB evolution
The only sdB star known not to burn helium in the core is the single-lined close binary HD 188112 (Heber et al. 2003). According to its atmospheric parameters it is situated well below the EHB (see Fig. 20). By interpolation of evolutionary tracks from Driebe et al. (1998) a mass of
was derived, which could be verified directly, because an accurate
parallax of this object was obtained by the Hipparcos satellite.
The different evolution of so called post-RGB objects like
HD 188112 compared to EHB stars should affect their rotational
properties. Post-RGB stars constantly shrink during their evolution
towards the WD cooling tracks. Since these stars are not expected to
lose angular momentum during the contraction, they have to spin up. In
contrast to this a core helium-burning sdB star expands by a factor of
about two within
and is expected to spin down. Besides HD 188112 some other objects
are also considered to belong to this class (see Fig. 20).
The post-RGB scenario may explain the unusual properties, especially the fast rotation, of the sdB binary [CW 83] 1735+22 (see Sect. 9.2). The star is among the hottest in our sample and it lies far from the EHB band (see Fig. 20). According to the mass tracks of Driebe et al. (1998) [CW 83] 1735+22 would have a mass of about
(see Fig. 20). Such a star should shrink by a factor of 5.5 within
(Driebe et al. 1998),
which is much shorter than the synchronisation time. Hence we regard
its high projected velocity as strong evidence that
[CW 83] 1735+22 is a post-RGB star just like HD 188112.
Since the lifetime of such an object is predicted to be only a few
million years, such stars should be rare. The predicted low mass of
[CW 83] 1735+22 can be verified in the way described in Heber
et al. (2003) as soon as the GAIA mission will have measured an accurate trigonometric parallax of this star.
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Figure 21:
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One may speculate that the different rotational properties of post-RGB stars may have an influence on the synchronisation process if they are in close binary systems. The spin-up caused by the shrinkage of the star may counteract the spin-down caused by the tidal influence of the companion. Should post-RGB stars have longer synchronisation timescales than EHB stars this may be invoked as a convenient explanation for the putative high fraction of sdB binaries with massive compact companions. If these binaries should have post-RGB primaries and should not be synchronised, the derived companion masses would be wrong.
This scenario is considered to be unlikely. First of all, we would expect post-RGB stars to rotate faster than synchronised. For the putative sdB+NS/BH systems low projected rotational velocities are measured. If the sdBs should rotate even faster than synchronised, the inclination angle would be even lower and the derived companion masses would go up.
Another strong argument against a post-RGB nature of the sdBs in the
candidate systems with massive compact companions is their location in
the
diagram (see Fig. 21).
All these binaries are found on or near the EHB, while the known
post-RGB stars are obviously not concentrated near the EHB (see
Fig. 20). We therefore conclude that the sdBs with putative massive compact companions are post-EHB rather than post-RGB stars.
11.2 The role of the stellar age
Up to now we have assumed that the sdB stars already have spent a
significant part of their total life time on the EHB. In the canonical
picture it might be possible to estimate the age of an
individual star by comparing its position in the (
,
)-diagram to EHB evolutionary tracks (e.g. Dorman et al. 1993),
as the core mass is fixed at the core helium flash. In binary
population models, however, a degeneracy between mass and age arises as
there is a spread of sdB masses (see Zhang et al. 2009).
Because our sample stars nicely populate the canonical EHB band (see Figs. 2, 12, 13), we shall assume that a star is young if it is on or close to the zero-age extreme horizontal branch (ZAEHB) and old if not. Note that the speed of evolution along the EHB tracks is nearly constant.
We shall now explore whether some of our targets might possibly be too young to be synchronised. We shall start with PG 2345+318 and inspect the sample in the light of the lesson to be learnt.
11.3 PG 2345+318
PG 2345+318 is a short period (
)
sdB binary.
We derive a high companion mass of
at an
inclination angle of about
indicating
that the companion is another massive compact object, i.e. a neutron
star or a massive white dwarf. At such a low inclination eclipses are
not expected to occur.
However, Green et al. (2004) presented a preliminary light curve of this star, and detected a shallow eclipse probably by a white dwarf. Without the additional information from the light
curve this object would therefore be identified as another candidate sdB binary with massive
compact companion. The detection of eclipses immediately rules out this
scenario. The inclination angle has to be near
and the
companion a white dwarf with a mass of
according to the constraint set
by the binary mass function. This means that the sdB star in this binary
rotates more slowly than synchronised and proves that such objects exist
among binaries with short orbital periods. The most reasonable explanation for this may be that the
system is very young and the synchronisation process not finished yet.
The atmospheric parameters of this star (see Table 1) place it indeed near the zero-age EHB (Fig. 21),
although they have somewhat larger errors than most other stars due to
the lack of high quality low resolution spectra (Saffer et al. 1994). But the light curve presented by Green et al. (2004) reveals more
information, which corrobate this scenario. An interesting feature is the presence of a
shallow reflection effect and a weak secondary minimum, which provides
evidence that the white dwarf contributes significantly to the optical flux. This in
turn means that the white dwarf must be young (assuming a luminosity of
evolutionary tracks imply an age of the order of
)
and is another piece of evidence that the system is too young to be
synchronised. Since no light curve solution for PG 2345+318 is published
yet, the discussion of this object must remain preliminary.
11.4 Are the systems with massive compact companions too young to be synchronised?
What are the implications for our candidate sample of sdB binaries with
massive compact companions? The orbital periods of these binaries range from
to
where synchronisation should be established
according to the results presented in Sects. 9.2 and 10. Given these short orbital periods, the
binaries in question should be synchronised.
Even if the candidate systems were bona-fide EHB stars, they may just be too young to be synchronised. In Fig. 21 we plot the positions of the candidate systems with compact companions and compare them to the calibrators Feige 48, PG 0101+039 and KPD 1946+4340. It is obvious that the first two of these synchronised sdBs lie closer to the terminal age EHB than to the zero age EHB. KPD 1946+4340 is already evolved from the EHB and most likely burning helium in a shell. These are indications that these binaries are relatively old. We also note that the position of PG 1743+477 nearly coincides with that of PG 0101+039. From this coincidence we would expect it to be synchronised and, hence, the constraint on the companion mass to be reliable.
We also plot the position of the non-synchronised system PG 2345+318 in Fig. 21 which lies near the zero-age EHB. PG 1232-136 and PG 1432+159 are found close to PG 2345+318 and near the zero-age EHB and thus may be rather young as well. The same holds for PG 1101+249 which is considerably hotter but also situated very near the zero-age EHB (ZAEHB).
The remaining candidate sdB binaries with putative massive compact companions are in a similar evolutionary stage as the synchronised systems in the middle of the EHB band. We conclude that some but not all sdBs in the candidate systems could be too young to have reached synchronisation.
12 Summary and outlook
We have analysed a sample of 51 sdB stars in close single-lined binary systems. This included 40 systems for which the orbital parameters have been determined previously. The subsample comprises half of all systems known so far. From high resolution spectra taken with different instruments the projected rotational velocities of these stars have been derived to an unprecedented precision. Accurate measurements of the surface gravities have mostly been taken from literature. Assuming orbital synchronisation and an sdB mass distribution as suggested by binary population synthesis models as well as by asteroseismology, the masses and the nature of the unseen companions could be constrained in 31 cases. Only in five cases we were unable to classify unambiguously. These companions may either be low mass main-sequence stars or white dwarfs. The companions to seven sdBs could be clearly identified as late M stars. One binary may have a brown dwarf companion. The unseen companions of nine sdBs are white dwarfs with typical masses, one WD companion has a very low mass.
In eight cases (including the well known system KPD1930+2752)
the companion mass exceeds
.
Four of the companions even
exceed the Chandrasekhar limit indicating that they may be neutron
stars; even a stellar mass black hole is possible for the most massive
companions.
The basic assumption of orbital synchronisation in close sdB binaries has been
discussed in detail. Our analysis method yielded consistent
results for binaries up to an orbital period of
.
Theoretical timescales for synchronisation were calculated using two different
approaches. The theory of Zahn (1977) was found to be too inefficient
while that of Tassoul & Tassoul (1992) predicts too short timescales.
The predictions from both theories are strongly discrepant, calling for
empirical constraints.
Independent observational evidence for synchronisation in sdB binaries
comes from light curve analyses of eclipsing, ellipsoidal deformed, and pulsating sdBs.
Due to this evidence sdB binaries with periods shorter than
should be synchronised. This includes all of the putative
massive systems.
Hence, an evolutionary model for the origin of sdB stars with neutron star or black hole companions was devised indicating that common envelope evolution is indeed capable of producing such systems, though at a lower rate than observed. An appropriate formation channel includes two phases of unstable mass transfer and one supernova explosion.
The distribution of the inclinations of the systems of normal mass appears to be consistent with expectations, whereas a lack of high inclinations became obvious for the massive systems.
There is one star in the sample which rotates fast despite its rather long orbital period. This as well as its position far from the EHB band hints at a post-RGB nature. The post-RGB stars are expected to be spun-up due to their ongoing contraction.
The larger number of putative massive companions in low
inclination systems is puzzling.
Therefore, we investigated alternative interpretations. The fraction of
massive unseen companions can only be lowered, if the sdBs themselves
have masses much lower than the anticipated range of
for EHB stars. Evolutionary calculations
showed that EHB stars with masses as low as
can be formed if helium ignites under non-degenerate
conditions but should be very rare. Assuming such low sdB masses, only one unseen companion remains
more massive than the Chandrasekhar limit.
This fraction of 3% is roughly
consistent with theoretical predictions.
Whether the sdB mass is small or not can be checked directly as
soon as accurate parallaxes of
these relatively bright stars will become available through the GAIA mission.
The putative massive sdB systems might not be synchronised if their age
is much less than anticipated. That this can happen is witnessed by
PG 2345+318, a short-period sdB binary in our sample, that we would have
classified as a low-inclination massive system as well, if it were not proven
by eclipses to be highly inclined. Hence the system is not synchronised
despite of its short period (
).
Due to a degeneracy between mass and age, it is
difficult to estimate the sdB's age without knowing its mass. Adopting the
canonical mass, we nevertheless estimated the stars' ages from their position
in the EHB band. Indeed, PG 2345+318, is located right on the zero-age EHB
as are the massive candidates PG 1232-136, PG 1432+159 and PG 1101+249.
These stars may possibly be too young to have reached synchronisation. Hence
the companion masses we derived would be spurious.
However, there is no indication that the other massive systems could be young.
Even if we dismiss three candidates because they may be too young and assume that the others are of low mass, PG 1743+477 and, in particular, HE 0532-4503 remain as massive candidates whose companions have masses close to or above the Chandrasekhar mass.
Different approaches may be chosen to directly verify the presence of neutron
star or black hole companions in our candidate systems.
None of the sdBs in our target systems fills its Roche lobe. No mass transfer
by Roche lobe overflow to the unseen companion can occur and
therefore no X-ray emission is expected.
The ROSAT all-sky survey catalogue (RASS, Voges et al. 1999) has been checked and, indeed, no sources have been detected at the positions of any candidate sdB+NS/BH systems.
The detection limit of this survey reaches down to about
.
However, sdB stars are expected to have weak winds. Hence accretion from the
sdB wind might result in faint X-ray emission. This occurs in the bright sdO+WD system HD 49798 (Mereghetti et al. 2009). Although stellar wind mass loss rates in sdBs are predicted to be small (<
,
e.g. Vink & Cassisi 2002; Unglaub 2008), they may be sufficient
to cause detectable X-ray flux powered by wind accretion. X-ray telescopes like Chandra or XMM-Newton may
be sensitive enough to detect such weak sources. Pulsar signatures of rapidly spinning
neutron star companions may be detectable with radio telescopes.
Tidal forces by the companion cause an ellipsoidal deformation of the primary
in close binary systems. This deformation appears as a variation of light at
half the orbital period. Two very close subdwarf binaries with orbital periods of
and high orbital inclination show light variations of
about 1%, which can be detected from the ground. Performing binary
light curve synthesis it was possible to derive the masses of the binary
components (Orosz & Wade 1999; Geier et al. 2007). Signatures
of ellipsoidal deformation in the light curves of binaries with longer orbital
periods and lower inclination are much weaker (
,
Drechsel, priv.
comm.; Napiwotzki et al., in prep.) and therefore not detectable from the ground. The existence of such very
shallow variations has been proven for the subdwarf binary PG 0101+039 with an orbital period of
using a light curve of almost
days duration taken with the MOST satellite. The ellipsoidal variation was found to be 0.025% (Geier et al. 2008a).
The full potential of high precision photometry for the analysis of sdB binaries has most
recently been demonstrated by Bloemen et al. (2010),
who analysed a Kepler light curve of the eclipsing sdB+WD binary
KPD 1946+4340. High precision light curves of the best candidates
in our sample should be measured with HST. The nature of their unseen
companion could then be clarified.
Most of the candidate massive systems have low orbital inclination. High inclination systems must exist as well. In this case a determination of the orbital parameters is sufficient to put a lower limit to the companion mass by calculating the binary mass function. If this lower limit exceeds the Chandrasekhar mass and no sign of a companion is visible in the spectra, the existence of a massive compact companion is proven without making any additional assumptions. The MUCHFUSS project (Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS, Geier et al. 2010b) was launched in 2007. The aim of this project is to search for sdB binaries with massive compact companions at high inclinations in a sample of stars selected from the SDSS data base.
AcknowledgementsWe would like to thank Z. Han for providing us with stellar structure models of sdB stars. We thank E. M. Green, N. Reid and L. Morales-Rueda for sharing their data with us. We are grateful to R. H. Østensen and S. Bloemen, who provided us with informations about new detections or non-detections of indicative features in sdB light curves, as well as H. Drechsel for modelling such light curves for us. S. G. was supported by the Deutsche Forschungsgemeinschaft under grant He 1354/40-3. Travel to La Palma for the observing run at the WHT was funded by DFG through grant He 1356/53-1.
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Footnotes
- ... companions
- Based on observations at the Paranal Observatory of the European Southern Observatory for programmes number 165.H-0588(A), 167.D-0407(A), 068.D-0483(A), 069.D-0534(A), 070.D-0334(A), 071.D-0380(A), 071.D-0383(A) and 382.D-0841(A). Based on observations at the La Silla Observatory of the European Southern Observatory for programmes number 073.D-0495(A), 074.B-0455(A) and 077.D-0515(A). Some of the data used in this work were obtained at the Hobby-Eberly Telescope (HET), which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen, for programmes number UT07-2-004 and UT07-3-005. The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly. Based on observations collected at the Centro Astronómico Hispano Alemán (CAHA) at Calar Alto, operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC). Some of the data presented here were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. Some of the data used in this work were obtained at the Palomar Observatory, owned and operated by the California Institute of Technology. Based on observations with the William Herschel Telescope operated by the Isaac Newton Group at the Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias on the island of La Palma, Spain.
- ... primary
- The more massive component of a binary is usually defined as the primary. But in most close sdB binaries with unseen companions the masses are unknown and it is not possible to decide a priori which component is the most massive one. For this reason we call the visible sdB component of the binaries the primary throughout this paper.
- ... PG 1248+164
- A light curve of this star has been taken by Maxted et al. (2004). No variability could be detected. Although the orbital period is rather long (
) and a reflection effect therefore shallow, the companion may be a low-mass WD rather than an M dwarf.
- ... Feige 48
- The mass of the pulsating subdwarf Feige 48
has been determined in an asteroseismic analysis (van Grootel et al.
2008) to
. The corresponding companion mass is
. Therefore the nature of the unseen companion remains unclear. It may be a low mass white dwarf as well as a late M dwarf. Due to the derived very low inclination and the presence of short period pulsations, a reflection effect or ellipsoidal variations are probably too small to be detectable.
- ... time
- Wood & Saffer (1999) detected these features in low resolution spectra before.
- ... time
- The merging times of all binaries have been calculated using the formula given in Ergma et al. (2001).
- ... companion
- The upper limit to the companion mass of PG 1116+301 is identical with the most likely companion mass (see Table 4, Fig. 14). The system can only be synchronised if the inclination reaches its maximum value of
. In this case the upper limit to the sdB mass is lower than
, but still within the possible range (see Sect. 4).
- ... dwarf
- Besides KPD 0422+5421 (Orosz & Wade 1999), PG 0941+280 (Green et al. 2004) and KPD 1946+4340 (Bloemen et al. 2010) this is just the fourth such system known.
All Tables
Table 1: Atmospheric and orbital parameters.
Table 2: Projected rotational velocities for the binary sdB systems from Table 1.
Table 3: Projected rotational velocities of radial velocity variable sdBs, for which orbital parameters are unavailable or uncertain.
Table 4: Derived inclination angles, companion masses and likely nature of the companions.
All Figures
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Figure 1: Period distributions of the 40 binaries in our sample with known orbital parameters (dashed histogram) and all known 81 sdB binaries in the Ritter & Kolb (2003) catalogue (blank histogram). |
Open with DEXTER | |
In the text |
![]() |
Figure 2:
|
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Left hand panels: numerical simulations.
|
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Rotational
broadening fit result for HE 1047-0436. The measured
|
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Rotational broadening fit result for PG 1232-136
(see Fig. 4). Despite the high quality of the data no
significant
|
Open with DEXTER | |
In the text |
![]() |
Figure 6: Rotational broadening fit result for HE 0532-4503 (see Fig. 4). |
Open with DEXTER | |
In the text |
![]() |
Figure 7: Selected helium lines of KPD 1946+4340 are plotted against the shift relative to rest wavelengths. The spectrum (histogram) is overplotted with the best fitting rotationally broadened model (strong line). A model without rotational broadening (weak line) is overplotted for comparison. |
Open with DEXTER | |
In the text |
![]() |
Figure 8:
Shaded histogram showing the distribution of the measured
|
Open with DEXTER | |
In the text |
![]() |
Figure 9:
The measured
|
Open with DEXTER | |
In the text |
![]() |
Figure 10: Mass of the sdB primary CPD -64 481 plotted against the mass of the unseen companion. The companion mass error is indicated by the dashed lines. The mass range of the CE ejection channel (Han et al. 2002) is marked with dotted vertical lines. |
Open with DEXTER | |
In the text |
![]() |
Figure 11: Mass of the sdB primary HE 0532-4503 plotted against the mass of the unseen companion. The companion mass error is indicated by the dashed lines. The mass range of the CE ejection channel (Han et al. 2002) is marked with dotted vertical lines. The Chandrasekhar mass limit is plotted as solid horizontal line. |
Open with DEXTER | |
In the text |
![]() |
Figure 12:
|
Open with DEXTER | |
In the text |
![]() |
Figure 13:
|
Open with DEXTER | |
In the text |
![]() |
Figure 14:
Mass ranges for the unseen companions of 31 binaries under the assumption of synchronisation (see Table 4). The companion mass ranges are derived for the most likely sdB mass range of
|
Open with DEXTER | |
In the text |
![]() |
Figure 15: Companion mass distribution of the binaries with low mass companions (Table 4, Fig. 14). The solid histogram shows the fraction of subdwarfs with confirmed white dwarf companions, the dashed histogram the detected M dwarf companions. The dashed vertical line marks the average white dwarf mass. |
Open with DEXTER | |
In the text |
![]() |
Figure 16: Mass distribution of the unseen companion stars (see Fig. 15). The lowest possible companion mass is plotted against the total number of binaries under the assumption of the lowest possible sdB mass. |
Open with DEXTER | |
In the text |
![]() |
Figure 17: Schematic diagram of formation scenarios leading to hot subdwarf binaries with neutron-star (left hand panel) or black-hole (right hand panel) companions. |
Open with DEXTER | |
In the text |
![]() |
Figure 18: Companion mass versus inclination. The solid squares mark compact companions (WD/NS/BH), the solid diamond MS or BD companions. The solid circles mark objects where both companion types are possible. |
Open with DEXTER | |
In the text |
![]() |
Figure 19:
Observed orbital period is plotted against the
synchronisation times of Zahn (1977, open symbols) and
Tassoul & Tassoul (1992, filled symbols) both in units of the average lifetime on the EHB (
|
Open with DEXTER | |
In the text |
![]() |
Figure 20:
|
Open with DEXTER | |
In the text |
![]() |
Figure 21:
|
Open with DEXTER | |
In the text |
Copyright ESO 2010
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