Download Exposing the hidden white dwarf binary origin by means of a

Mon. Not. R. Astron. Soc. 420, 2339–2344 (2012)
doi:10.1111/j.1365-2966.2012.20198.x
Exposing the hidden white dwarf binary origin by means of a synthetic
population model for nearby single stars
S. A. Dawson and K.-P. Schröder
Departamento de Astronomia, Universidad de Guanajuato, AP 144, Guanajuato, GTO, CP 36000, Mexico
Accepted 2011 November 14. Received 2011 November 12; in original form 2011 September 18
ABSTRACT
We present a new synthetic population model for local thin-disc (d ≤ 100 pc) single-star white
dwarfs (WDs), including effective temperature and mass distribution. The only two parameters
of the synthetic population model are the initial mass function (IMF) and the star-formation
rate (SFR). Depletion losses through kinematic heating of the stellar ‘gas’ vertical to the
Galactic plane are prescribed empirically using the observed local velocity dispersion as a
function of age. We apply the same SFR and IMF for the WD population model as previously
determined from a study based upon the latest Hipparcos and binary catalogue data to yield a
matching synthetic single-star population.
A striking result of comparing the synthetic WD population with the complete local observed
sample (with d < 13 pc) is the excellent agreement between the absolute number of WDs when
binary stars are not excluded from the empirical basis used to calibrate our synthetic population.
When looking at the total expected WD number after a rigorous accounting for binary stars,
we see that this is significantly lower than the corresponding observed WD number. Hence,
many of these apparently single WDs must have a hidden binary-system history, i.e. some may
be end products of binary mergers or of mass overflows. We suspect that many of the WDs
exist in hidden double-degenerate systems.
There is good agreement between the temperature distribution of our synthetic WD sample
and observations, as well as between our synthetic mass-distribution peak (at 0.67 M ) and
the one recently observed (0.65 M ). Remarkably, both values are about 0.06 M higher than
those stated by earlier studies. In the case of our synthetic sample, older stars of lower mass
experience a greater amount of dynamic depletion and the remaining local WDs within the
sample tend to be slightly more massive. The small, remaining discrepancy may be explained
by the stated contamination by WDs of binary origin.
Key words: binaries: general – stars: evolution – white dwarfs – Galaxy: kinematics and
dynamics – solar neighbourhood – Galaxy: stellar content.
1 I N T RO D U C T I O N
A strong motive for studying the white dwarf (WD) disc population
and interpreting it in terms of synthetic populations is the fact that
it contains a wealth of information about the past stellar content of
the Galactic disc. The star-formation rate history lies buried here,
and the well-known cooling times of WDs allow us to use the
temperature distribution of such a sample as a measure of the age of
the Galactic disc, provided our WD population model is compatible
with the other relevant previously well-determined parameters: star-
E-mail: [email protected]
C 2012 The Authors
C 2012 RAS
Monthly Notices of the Royal Astronomical Society formation rate (SFR), initial mass function (IMF) and depletion by
Galactic kinematics.
The initial motive for this particular study was to apply our improved single-star population model (Dawson & Schröder 2010,
hereafter referred to as DS2010). We determined the required SFR
and IMF of the local stellar disc population by rigorously and consistently subtracting the binary content found among the nearest
stars, as well as employing a stellar depletion description based on
the actual, observed stellar velocity dispersion for different agegroups of stars, to model the young, local single-star population
accurately.
In addition, a significant improvement in the observed local
WD population (d < 20 pc) has been recently presented by Holberg et al. (2008), hereafter referred to as HOS. This catalogue
2340
S. A. Dawson and K.-P. Schröder
provides an excellent opportunity to test WD population models
with a nearly complete, albeit statistically small, sample of observed
WDs.
We have restricted our population models to single stars because
binary-system evolution is a lot more complex in both its physics
and its dependence on a number of additional parameters like the
initial orbital parameters. Currently there is no complete evolution
grid available on which a synthetic binary population could be
generated.
In the past decade there has been a dramatic rise in the estimated
fraction of binary and multiple-star systems within the total stellar
content. Therefore, by using the latest observational evidence, we
derived (DS2010) a binary and multiple star fraction of 71 per cent
among the young local population of stars for stellar masses above
1.1 M . By comparison, in our first study of the single-star population (Schröder & Pagel 2003, hereafter referred to as SP2003) we
only subtracted the binary systems then known from the Hipparcos
catalogue. Their fraction becomes smaller when looking at larger
distances. Over the whole sample, known binary systems made up
only a little more than one third of all objects. Therefore, since
DS2010 we should also expect a much more significant number of
present-day WDs that did not evolve from single stars.
While previously single stars and related WD numbers were
overestimated, earlier observed WD samples such as that of Holberg, Oswalt & Sion (2002) still suffered from significant incompleteness. That led to a by-chance coincidence in the matching
of absolute numbers with the synthetic WD population then obtained (Schröder, Pauli & Napiwotski 2004, hereafter referred to
as SPN2004), as derived from SP2003. The present study will now
show that a rigorous exclusion of binary stars, yielding a precise
single-star population, reveals a lot more apparently single WDs
when compared with the local WD sample of much improved completeness (HOS, d < 13 pc) than there should be when considering
a pure single-star population.
The question of total WD numbers and completeness of any
observed sample is much related to the temperature distribution
of the WDs, since the older, cooler objects are the faintest of the
sample and most likely to be lost at even quite close distance. When
studying this problem in detail there is, within the limited number
statistics, a good coincidence between the temperature distribution
of our synthetic population with a nearly complete observed WD
sample by Holberg et al. (2008). For this matter we use the ratio of
WDs cooler than 6300 K over those hotter, R6300 , already introduced
by SPN2004.
The observed WD mass distribution has also been the subject
of previous studies, using large but consequently very incomplete
samples. The WD mass distribution peaks between about 0.55 M
(Koester et al. 2001) and 0.59 M (Napiwotzki, Green & Saffer 1999). By contrast, previous synthetic WD populations based
on single-star evolution model grids suggested, depending on the
assumptions for IMF, Galactic age and selection effects, values
between 0.57 M (Yuan 1992) and 0.61 M (Wood 1995). In
SPN2004, we found a mass peak of our synthetic WD sample of
0.61 M if complete and of 0.59 M if magnitude-limited. This
systematic difference occurs because the latter sample type misses
out on faint WDs, which on average had been of smaller mass and
therefore larger size, hence cooling faster.
In the present study, we compare the mass distribution of our new
synthetic WD population with the recent observational evidence.
Here, Holberg et al. (2008) found an increased empirical peak mass,
close to 0.67 M . While that value appears to be at odds with
earlier work, we find that our improved population model agrees
very well with the most recent empirical values of Holberg et al.
(2008).
2 M O D E L L I N G T H E L O C A L W D P O P U L AT I O N
2.1 Creation of a synthetic sample of single-star WDs
The solar-neighbourhood WD population, which is formed as the
end product of stellar evolution, is continually being fed by the
‘death rate’ of the local stellar population. For solar-neighbourhood
single stars, within d < 100 pc we have already generated statistically significant models that are a quantitative match (using
the star-count method) for the Hipparcos single-star Hertzsprung–
Russell (HR) diagram, M V ≥ 4. Special consideration was given to
matching the numbers of He-burning giants and red-giant branch
(RGB) stars (SP2003, DS2010), whilst also eliminating any binary
and multiple-star systems, believed to account for 71 per cent of the
total stellar content. We have used the best-fitting parameters (tage =
9 Gyr, IMF = 1.85, SFR = 618 stars/Myr kpc, SFR exponent (γ ) =
−0.03) determined through modelling the larger single-star population alongside well-tested evolutionary grids (Pols et al. 1997,
1998; Schröder, Pols & Eggleton 1997) to generate our older synthetic WD populations.
In addition, the kinetic heating of the local population resulting
in the loss of stars from the column becomes particularly prominent
for more evolved stars such as WDs (Wielen 1977; Holmberg,
Nørdstrom & Anderson 2007). There is much debate about the
heating of the thin disc and some evidence suggests that there may
have been a shallow decrease in heating at approximately 3–5 Gyr
(Binney & Aumer 2009). Any prolonged decrease in the heating of
the stellar content provided by a constant SFR and continued radial
mixing would result in fewer stars leaving the volume and therefore
revealed by an overpopulated synthetic sample.
We model an average heating effect over the lifetime of the thin
disc, with a decreasing (SF Rt∗ = SF Rt0 exp−γ ) resulting in a continual loss of stellar content into the column that is proportional to
stellar age (DS2010). Our age-dependent depletion factor F depl (t∗ )
is inversely proportional to the scaleheight of the stellar spatial
density:
Fdepl (t∗ ) = 195 pc/Hz (t∗ ),
Hz (t∗ ) = 184 pc × (1 + τ/Gyr)0.45 pc,
for stars that are old enough to have reached thermalized kinematics
(t∗ > 7 × 108 yr).
For WD numbers within a spherical radius of 13 pc, as required
for a comparison with HOS, we assume a homogeneous distribution
and apply volume ratios. The 13-pc spherical volume is 5.56 × 10−3
smaller than the thin slab (d < 100 pc, |z| ≤ 25), therefore reducing
the 2338 WDs to 13 WDs. These 13 WDs account for 29 per
cent of the total WD population, with the rest existing in binary
and multiple-star systems; by including these star systems the total
population of WDs within a sphere of radius 13 pc rises to 44 (13
single, 31 multiple). These 44 WDs exist within a sphere of radius
13 pc and form a spatial density of 4.8 × 10−3 star pc−3 .
We have explored and tested the possibility of slightly different
values for the input parameters; IMF, SFR and age of the thin
disc. This has enabled us to generate slightly different synthetic
populations that we also compare with HOS (see Table 1 and Section
2.3). For comparison of synthetic and observed populations, we used
a weighted mean σ of the differences between the observed and
empirical values of well-defined star groups, divided by the square
root of the empirical value (see DS2010).
C 2012 The Authors, MNRAS 420, 2339–2344
C 2012 RAS
Monthly Notices of the Royal Astronomical Society The hidden WD binary origin
2341
Table 1. WD numbers within 13 pc as predicted by different synthetic populations and their deviations from the
observed values (HOS, in 13 pc) in units of the average statistical variation |δ|av . The preferred model results (for
tage = 9 Gyr, IMF = 1.85, SFR = 618 stars/Myr kpc, based on DS2010) are shown in bold. Alternative models with
different parameters show the impact upon the goodness of fit.
Sample/Model
Observed (HOS)
Preferred (DS2010)
Older disc (tage = 10 Gyr)
Younger disc (tage = 8 Gyr)
Constant SFR
Higher SFR (956*/Myr kpc)
Change in IMF at 1.6 M (2.2, 1.7)
Number of white dwarfs
Single
Double Total
34
13
15
11
15
20
12
11
31
36
26
36
48
29
2.2 Modelling white dwarf cooling
In order to use the temperature distribution of the synthetic sample
to match the observed sample better, the most realistic prescription
of cooling has been employed. The basic physics of WD cooling
is well established (Mestel 1952; Mestel & Ruderman 1967). The
principles are well illustrated by a simple model of a WD: a fully degenerate, nearly isothermal core of high thermal conductivity, containing nearly all the mass M WD , surrounded by a non-degenerate,
radiative envelope with Kramers opacity. The WD luminosity L at
−1.4
.
the WD age tWD is then given by L ∝ MWD tWD
This model applies only to DA-type WDs and excludes others
such as DBs, DCs, etc. These other WD types were created without
any significant outer H layer and should cool down much faster than
the more common DA-type WDs, owing to the very low opacity
of He-rich atmospheres (Hansen 1999). Although differences are
present between both sets of evolutionary tracks during all phases
of WD evolution, the faster cooling of He-envelope WDs of typical
mass starts only after 4 Gyr, by which time they have already cooled
down to under 6000 K. Therefore we do not expect a large impact
upon the R6300 value from their small ≈20 per cent of the sample,
unless those He-rich WDs have cooled down to invisibility.
For our synthetic population model, we based our WD luminosities mostly on the detailed WD models of Chabrier et al. (2000),
who also consider in detail the energy locked away in the crystal
lattice structure of the WD core region below the Debye temperature
(Hamada & Salpeter 1961) as well as realistic envelope opacities
(SPN2004). For WDs younger than about 1 Gyr, however, we follow the respective models of Wood (1995), which suggest up to 20
per cent higher luminosities in the range tWD = 1–3 Gyr. Our simple
analytical approximation averages between Wood’s and Chabrier’s
WD luminosities and these luminosities do indeed follow the decline with temperature suggested by Mestel (1952). The reader is
referred to SPN2004 for a more in-depth explanation of the WD
cooling model.
45
44
51
37
51
68
41
Space density
(×10−3 star pc−3 )
M av
(M )
R6300
δ av
4.8
4.8
5.5
4.0
5.5
7.4
4.5
0.665
0.653
0.650
0.657
0.652
0.653
0.647
0.7994
64
0.90
1.06
0.78
1.06
0.91
0.91
–
0.15
0.71
0.80
0.70
2.34
0.45
completeness for a subsample out to a reach of 13 pc. The catalogues
contain three key pieces of information: the total number of WDs
N WD , the average mass of the WD population M WD and a simple,
single parameter to characterize the WD temperature distribution
R6300 , introduced by SPN2004: R6300 = N cool /N warm , the number
ratio of N cool WDs cooler than 6300 K over N warm WDs hotter than
6300 K. Therefore the larger R6300 , the cooler (and older on average)
the WD sample.
Undoubtedly, the observed WD sample has been greatly improved by Holberg et al. (2008), in particular in reducing the incompleteness among old, cool and very faint WDs. Over their full
sample, to 20 pc distance, Holberg et al. (2008) estimate a fair 80
per cent of completeness. For a comparison with our synthetic WD
sample in absolute numbers, we here assume full completeness to
exist in a subsample reaching out to a radius of only 13 pc, which
contains only 44 WDs (of 126 with d < 20 pc) and has a space
density of 4.8 × 10−3 star pc−3 .
For the total sample (within 20 pc), Holberg et al. (2008) find
R6300 = 0.79 (see Fig. 1). Since a 20 per cent incompleteness
should mainly affect the faint, cool side of the WD distribution,
this observed R6300 value must still be seen as a lower limit to
the actual value. Unfortunately, using just the WDs within the
3 C O M PA R I S O N B E T W E E N S Y N T H E T I C
A N D O B S E RV E D W D P O P U L AT I O N
3.1 Completeness limits of the observed WD sample
It is vital that a volume-limited complete WD sample is used for
the verification of the synthetic population, even if that only allows
a severely restricted sample reach. Holberg et al. (2008) present an
updated catalogue of the one published by Holberg et al. (2002),
listing all observed WDs within 20 pc of the Sun and claiming
C 2012 The Authors, MNRAS 420, 2339–2344
C 2012 RAS
Monthly Notices of the Royal Astronomical Society Figure 1. Temperature distribution of the observed, nearly complete sample
of 120 WDs for a volume of 20-pc radius around the Sun, as given by Holberg
et al. (2008). An R6300 of 0.79 ± 0.15 is determined.
2342
S. A. Dawson and K.-P. Schröder
supposedly complete subsample (reach 13 pc) results in such poor
number statistics that we determine the sample inadequate to ascertain R6300 .
3.2 The synthetic white dwarf temperature distribution
In the present work, we have developed the SPN2004 approach further by accounting for a much more empirically based description
of the depletion of stars from the plane (DS2010). This depletion of
stars is most significant for the older, low-mass stars, leaving a relatively larger number of more massive stars in the solar neighbourhood, which create massive, fast-cooling WDs. Our new synthetic
WD population now yields the temperature distribution shown in
Fig. 2. The distribution is constructed from a binning of 2338 stars
over the range 0–30 000 K using a bin size of 500 K. From this we
obtain R6300 = 0.90, which is a little larger than the value found by
SPN2004 but still in good agreement with the empirical value of
0.79 found by Holberg et al. (2008), considering that the latter is
still a lower limit to the real value.
Any overestimation of the depletion of stars would result in a
decrease in the cooler white dwarfs from the sample and therefore
decrease the value of R6300 . Hence, if the age of the thin disc was a
little lower, around 8 Gyr instead of the 9 Gyr assumed for the bestmatching population of DS2010 (on which we base our WD model),
our synthetic WD temperature distribution would yield R6300 = 0.80
(other parameters unchanged, see Table 1). The opposite is true for
an older thin disc (10 Gyr, R6300 = 1.06), which results in too many
cool white dwarfs.
In view of the remaining bias of the observed sample, we are unable to draw further conclusions. The data from GAIA will provide
a much larger statistical basis (complete to nearly 40 pc distance
when limited to B = 19) to determine the age of the thin Galactic
disc through the local WD temperature distribution.
Figure 2. Temperature distribution of a synthetic, complete sample of 2338
single WDs for a volume of 100-pc radius around the Sun, created with the
cooling time-scales of the Chabrier et al. (2000) models and the synthetic
stellar population of DS2010. The R6300 of 0.90 is in good agreement with
the empirical value derived from the Holberg et al. (2008) sample of nearby
WDs (see Fig. 1).
3.3 The synthetic white dwarf mass distribution
Our preferred synthetic WD population yields the mass distribution
shown in Fig. 3. The distribution is constructed from a binning
of 2338 stars over the range 0.55–0.80 M using a bin size of
0.02 M . Similarly to the temperature distribution, it is dependent
upon the IMF, SFR(t), the depletion description plus the relationship
between the intial and final masses (M i − M f ) suggested by the
evolutionary tracks.
In the range 1.0 M ≤ M i ≥ 2.5 M , our evolutionary tracks
suggest final masses close to M f /M = 0.55 × (M i /M )0.29 (see
Schröder & Sedlmayr 2001), which is slightly above the relation derived from non-volume-limited observational studies (Weidemann
1997, 2000; Napiwotski, Green & Saffer 1999) but well aligned to
the most recent, volume-limited study by Holberg et al. (2008), in
particular the mean mass found from their 44 WDs within 13 pc,
0.67 M .
Napiwotski et al. investigated the mass distribution of white
dwarfs from the ROSAT Wide Field Planetary Camera, i.e selected
by their radiation in the far-UV. They determined a peak of 0.59 ±
0.02 M , which is much lower than the 0.67 M determined from
the complete 13-pc sample of Holberg et al. (2008), as given by
Fig. 4.
Our mean WD mass of 0.65 M is very close to that of Holberg
et al. (2008). This synthetic WD mean mass value has increased
by 0.04 M from our previous (SPN2004) value of 0.61 M . This
must be seen as the result of (i) an improved description of depletion,
which strongly favours the loss of older stars of lower mass (which
would have left more lower-mass WDs) and (ii) the consequent
exclusion of binary stars from the empirical sample of nearby stars
used to calibrate the population model. However, the same evolutionary tracks have been applied as were used in work by SP2003
and SPN2004.
It is interesting to note that our synthetic sample generates a much
wider peak than has been determined from observational data (Bergeron, Saffer & Liebert 1992; Liebert, Bergeron & Holberg 2005).
A narrow peak suggests a high proportion of single WDs generated from a restricted range of progenitor main-sequence masses
Figure 3. The distribution of masses in the same, volume-limited synthetic
sample of WDs shown in Fig. 2. The average mass of 0.653 M is in
good agreement with the value of 0.665 M determined from the complete
Holberg et al. (2008) sample (see Fig. 4.)
C 2012 The Authors, MNRAS 420, 2339–2344
C 2012 RAS
Monthly Notices of the Royal Astronomical Society The hidden WD binary origin
2343
This indicates that there are many unresolved binary systems
(most probably double-degenerate) within the observed WD sample and/or that many binary systems evolve into single WDs (see
discusson).
4 DISCUSSION
The impact of empirically modelling the depletion of stars away
from the disc, as well as rigorously and consistently considering the
binary fraction in nearby stars and stellar systems has resulted in
the following.
Figure 4. The distribution of observed WD masses determined from the
Holberg et al. (2008) sample. The average mass of 0.665 M is skewed
towards a higher mass due to the inclusion of three large WDs within the
sample.
and ages. It can therefore be expected that if a complete sample
were modelled, accounting for binary stars, the peak would broaden
slightly. However, part of the apparent discrepancy between the observed and theoretical WD mass distributions may be explained
by observational uncertainties. In particular, the narrow peak determined by Liebert et al. (2005) was based upon a spectroscopic
sample of stars with temperatures greater than 13 000 K. The HOS
does not provide enough stars for a statistically significant comparison of the peaks.
In addition, however, our stellar evolution models may still underestimate the cumulative mass loss, which we prescribed by an
improved Reimers formula for the RGB and earlier asymptotic giant branch (AGB: Schröder & Cuntz 2005) and by the dust-driven
mass-loss rates of Wachter et al. (2002) at the tip of the AGB.
3.4 The white dwarf binary ratio
Holberg et al. (2008) determine a binary fraction of 25 per cent
(31/124) within their 20-pc sample and 24 per cent (11/45) within
the 13-pc subsample. Interestingly, they note that 6 out of the 8
Sirius-like systems consisting of a white dwarf and main-sequence
companion with spectral types A0V to K7V are found within the
13-pc sample. Recent work by Sion et al. (2009) has further increased the number of Sirius-like systems within the 20-pc sample
to 10 (11, unpublished). However, if we consider the next equal volume of space (from 20–25 pc), then only one additional Sirius-like
system is discovered. The inescapable conclusion is that there are
a considerable number of unidentified Sirius-like systems beyond
the 20-pc sample (Holberg 2009) and most probably within it.
Our best-fitting model parameters are based upon a 71 per cent
binary fraction and generate only 13 single WDs, much fewer than
the 34 found within the 13-pc sample. However, when the binary
content is accounted for the synthetic sample WD number increases
by 31 WDs, giving a total of 44 WDs, which is in striking agreement with the observed total of 45 WDs. In fact when comparing
the spatial densities, which have the virtue of containing an error
estimate, our synthetic sample and HOS both determine a value of
4.8 × 10−3 star pc−3 to 1 decimal place.
C 2012 The Authors, MNRAS 420, 2339–2344
C 2012 RAS
Monthly Notices of the Royal Astronomical Society (i) The expectation of an increased ratio of cooler WDs with
a larger average mass when compared with the previous work of
SPN2004. The new synthetic sample now provides a much better fit
to the most recent complete, observed sample, HOS, even though
there may be an unresolved deficiency in the mass-loss prescription
used by our evolution models. Hence, the mass peak of our synthetic
WD population is rather broad and provides more of an upper limit.
(ii) Since our synthetic population of WDs modelled from
single-star origins is now much lower than the observed sample,
a lot of apparently single WDs must have a hidden binary-star origin. These initial binary systems may have merged in the past or are
now hosting an unidentified WD companion. This hypothesis agrees
well with the broader observed WD mass distribution (Fig. 4).
Identifying in exactly what form these unidentified systems exist
is very challenging. However, with the advent of near-IR 2MASS
and Spitzer observations it is relatively clear that unresolved systems cannot be accounted for solely by WDs with very low luminosity companions. These systems are easily recognized by their
red-excess composite spectra and so we can be confident that most of
these systems have been identified within HOS. Double-degenerate
systems are much more difficult to detect; only one such system
exists within HOS, WD 0423+120, and it was revealed through a
mismatch between its absolute luminosity (from parallax) and expected luminosity based on spectroscopy. It is therefore more likely
that the unidentified WDs exist within double-degenerate systems.
Fisher, Schröder & Smith (2005), who studied the spectroscopic
binary star population of the solar neighbourhood considering the
distance-related incompleteness, found that a fraction of at least 8
per cent of all stars and stellar systems are short-period binaries
(P < 10 d, groups III and IV), at least 16 per cent are of medium
period (10 < P < 500 d, group II) and at least 14 per cent have
longer periods. Obviously, due to the small orbital velocities involved in the latter two cases, their real shares should be larger.
This study also considered the astrometric binaries known in the
solar neighbourhood. This and new spectroscopic binary data included an additional 30 per cent of stars and stellar systems that
have a binary nature, mostly of wide orbits. The latter would naturally be expected to reconcile the observed binary WDs mentioned
in the previous section.
There is a large reservoir of binaries with moderately wide orbits, which we may expect to result in unresolved but always wellseparated WD pairs. The light from these pairs may be dominated
by the more recently formed, hence hotter and more luminous of the
two, WDs. One such system WD 1210+533 has been discovered
(Holberg et al. 1995).
In the absence of any interaction or mass exchange, each of the
WDs has been formed by a single-star evolution route. This case
appears to be one source of apparently single WDs, which brings
the HOS well above our expected number of WDs of single star
origin. In fact, the probability of resolving short-period WD systems
2344
S. A. Dawson and K.-P. Schröder
decreases rapidly with decreasing period and they may therefore
be observed as single WDs (Robinson & Shafter 1987). This may
provide an explanation for why non-complete observational samples
of WDs yield a lower value of the average WD mass (Wood 1995).
The 8 per cent of with of short periods provide another source
of contamination, as these systems are expected to merge at some
point in their evolution and most such merged stars would end as
a single WD. Among these, low-mass multiple-star systems form
much tighter orbits and the orbital shrinkage due to the loss of angular momentum and emission of gravitational wave radiation occurs
at a much faster rate than in larger mass binary systems. Research
suggests that WDs with a mass less than 0.6 M should merge
within a Hubble time (Icko Iben 1991). The increased probability
of low-mass binary mergers over higher-mass mergers results in a
reduction of low-mass stars from any complete WD sample such as
HOS. Although most such mergers are far from conservative, losing some of their total mass, the resultant single star, and eventually
its WD, can be expected to have a larger mass than either of the
two initial binary stars. The same would be true in the case of an
interaction with only a partial mass overflow for the receiving WD
in the pair.
Both these effects may explain why our strictly single-star synthetic WD population yields the following results.
(i) A significantly lower total number of WDs than those found
within HOS in the immediate solar neighbourhood, while at the
same time the numbers would compare well if we did not exclude the
binary stars from the empirical stellar sample we used to calibrate
our population. Most of these apparently single WDs from a hidden
binary origin may be remnants of the many systems with moderately
wide orbits.
(ii) The contamination by a total of at least 8 per cent of all
stellar systems and stars, which are doomed to merge at some point
in their evolution, provides a source of WDs that are physically very
different from those formed by the single-star evolution routes but
which are now single WDs. A contamination of the observed WD
sample by these objects clearly has the potential to broaden and
slightly increase the overall peak of the observed mass distribution
(Fig. 4) when compared with our expectation for a WD sample
derived from single-star evolution alone (Fig. 3).
5 OUTLOOK
This study clearly identifies the need for and importance of a larger
observed, volume-limited WD sample, which would be complete
down to the lowest T eff . This would allow a much more critical
analysis of the remaining uncertainties in WD models and synthetic
samples. We are looking forward with great interest to observational
progress in this field. A quantum leap will be provided by the GAIA
data, which are supposed to register all WDs down to B = 19 mag.
AC K N OW L E D G M E N T S
The referee, Jay Holberg, is thanked for his very helpful comments. This research was supported by CONACyT grant no. 57744
(CB-2006).
REFERENCES
Bergeron P., Saffer R. A., Liebert J., 1992, ApJ, 394, 228 (BSL)
Binney J., Aumer M., 2009, MNRAS, 397, 1286
Chabrier G., Brassard P., Fontaine G., Saumon D., 2000, ApJ, 543, 987
Dawson S. A., Schröder K.-P., 2010, MNRAS, 404, 917
Fisher J., Schröder K.-P., Smith R. C., 2005, MNRAS, 361, 495
Hamada T., Salpeter E. E., 1961, ApJ, 134, 683
Hansen B. M. S., 1999, ApJ, 520, 680
Holberg J. B., 2009, J. Phys. Conf. Ser., 172, 012022
Holberg J. B., Saffer R. A., Tweedy R. W., Barstow M. A., 1995, ApJ, 452,
L133
Holberg J. B., Oswalt T. D., Sion E. M., 2002, ApJ, 571, 512
Holberg J. B., Sion E. M., Oswalt T., McCook G. P., Foran S., Subasavage
J. P., 2008, AJ, 135, 1225
Holmberg J., Nørdstrom B., Anderson J., 2007, A&A, 475, 519
Iben I., 1991, ApJS, 76, 114
Koester D. et al., 2001, A&A, 378, 556
Liebert J., Bergeron P., Holberg J. B., 2005, ApJS, 156, 46
Mestel L., 1952, MNRAS, 112, 583
Mestel L., Ruderman M. A., 1967, MNRAS, 136, 27
Napiwotzki R., Green P. J., Saffer R. A., 1999, ApJ, 517, 399
Pols O. R., Tout C. A., Schröder K.-P., Eggleton P. P., Manners J., 1997,
MNRAS, 289, 869
Pols O. R., Schröder K.-P., Hurley J. R., Tout C. A., Eggleton P. P., 1998,
MNRAS, 298, 525
Robinson E. I., Shafter A. W., 1987, ApJ, 322, 296
Schröder K.-P., Cuntz M., 2005, ApJ, 630, L73
Schröder K.-P., Pagel B. E. J., 2003, MNRAS, 343, 1231
Schröder K.-P., Sedlmayr E., 2001, A&A, 366, 91
Schröder K.-P., Pols O. R., Eggleton P. P., 1997, MNRAS, 285, 696
Schröder K.-P., Pauli E.-M., Napiwotski R., 2004, MNRAS, 354, 727
Sion E. M., Holberg J. B., Oswalt T. D., McCook G. P., Wasatonic R., 2009,
AJ, 138, 1681
Wachter A., Schröder K.-P., Winters J.-M., Arndt T., Sedlmayr E., 2002,
A&A, 384, 452
Weidemann V., 1997, in Rood R. T., Renzini A., eds, Advances in Stellar
Evolution. Cambridge Univ. Press, Cambridge, p. 169
Weidemann V., 2000, A&A, 363, 647
Wielen R., 1977, A&A, 60, 263
Wood M. A., 1995, Lecture Notes in Phys., 443, 51
Yuan J. W., 1992, A&A, 261, 105
This paper has been typeset from a TEX/LATEX file prepared by the author.
C 2012 The Authors, MNRAS 420, 2339–2344
C 2012 RAS
Monthly Notices of the Royal Astronomical Society