Download White dwarfmain sequence binaries identified within SDSS DR7 and

Mon. Not. R. Astron. Soc. 424, 1841–1851 (2012)
doi:10.1111/j.1365-2966.2012.21285.x
White dwarf–main sequence binaries identified within SDSS DR7
and UKIDSS DR5
Cheng Liu,1,2,3 Lifang Li,1,3 Fenghui Zhang,1,3 Yu Zhang,1,2,3 Dengkai Jiang1,3
and Jinzhong Liu4
1 National
Astronomical Observatories, Yunnan Observatory, Chinese Academy of Sciences, PO Box 110, Kunming 650011, China
University of Chinese Academy Sciences, Beijing 100039, China
3 Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming 650011, China
4 National Astronomical Observatories/Xinjiang Observatory, Chinese Academy of Sciences, Urumqi 830011, China
2 Graduate
Accepted 2012 May 9. Received 2012 May 3; in original form 2011 August 22
ABSTRACT
We develop optical and near-infrared colour-selection criteria based on the model colours of
binaries consisting of a white dwarf and a main-sequence star. Using our colour-selection
algorithm, we present a catalogue of 523 white dwarf–main sequence (WDMS) binaries
from the spectroscopic Sloan Digital Sky Survey Data Release 7 (SDSS DR7), most of them
previously identified. Among them, we identify 86 objects as new WDMS binaries. 95 WDMS
candidates are also found from the photometric SDSS DR7, cross-matched with the United
Kingdom Infrared Telescope (UKIRT) Infrared Sky Survey Data Release 5 (UKIDSS DR5).
Based on a χ 2 minimization technique, we derive independent stellar parameters such as
the effective temperatures, surface gravities, masses and distances of the white dwarfs and
secondary stars and the metallicities of the secondaries. Meanwhile, we determine the cooling
age via interpolation through evolutionary models for the effective temperature and surface
gravity of each DA white dwarf. Distributions of these stellar parameters have been used
to study both the general properties and the completeness of WDMS binaries. A comparison
between the distances measured to the white dwarfs and the secondary stars shows a clear trend
towards higher distances for the white dwarf component. It is found that the mean cooling age
of the WDMS sample is t cool ∼ 4.2 × 108 yr and our sample contains at least 11 per cent old
systems, which were formed about 1.0 × 109 yr ago. The new and updated WDMS binaries
will improve the completeness of the catalogue of WDMS binaries.
Key words: binaries: close – binaries: spectroscopic – stars: fundamental parameters – white
dwarfs.
1 I N T RO D U C T I O N
Close binaries containing a white dwarf (WD) primary and a mainsequence (MS) companion are formed from main-sequence binaries. White dwarf–main sequence (WDMS) binaries lead to interesting objects such as catalysmic variables (CVs: Warner 1995),
low-mass X-ray binaries (LMXBs) and Type Ia supernovae (SNe
Ia: Han & Podsiadlowski 2004), which are standard candles for
cosmology. The WDMS binaries with mass transfer process are the
potential progenitors of gravitational wave sources in the Galaxy
(Liu 2009). Binary population-synthesis models (Willems & Kolb
2004) indicate that ∼25 per cent of the binary population is believed
to undergo a phase of dynamically unstable mass transfer when the
more massive star leaves the main sequence. As a result, the en-
E-mail: [email protected]
C 2012 The Authors
C 2012 RAS
Monthly Notices of the Royal Astronomical Society velope of the massive star will engulf its core and the companion
and the system will enter a common-envelope (CE) phase (Livio &
Soker 1988; Iben & Livio 1993; Taam & Sandquist 2000; Webbink
2008). In the CE evolution phase, the stars start a spiral-in process,
where friction inside the envelope will cause a rapid decrease of
the binary separation. Consequently orbital energy and angular momentum are extracted from the orbit and lead to the ejection of the
envelope, exposing a post-common-envelope binary (PCEB). The
CE phase is thought to happen very fast (Hjellming & Taam 1991;
Taam & Sandquist 2000; Webbink 2008) so that planetary nebulae
with central binary stars are very rare. PCEBs are driven by angular momentum loss (AML) due to gravitational wave radiation and
magnetic braking and evolve into the semi-detached CV configuration or supersoft X-ray sources. Unfortunately, the efficiency of
magnetic braking is rather uncertain and the outcomes of the two
currently favoured prescriptions for magnetic braking (Verbunt &
Zwaan 1981; Rappaport, Verbunt & Joss 1983; Sills, Pinsonneau
1842
C. Liu et al.
& Terndrup 2000; Andronov, Pinsonneault & Sills 2003) are very
different. The observed gap (2–3 h) in the period distribution of
CVs can be successfully explained by disrupted magnetic braking
(Rappaport et al. 1983; Paczynski & Sienkiewicz 1983; Spruit &
Ritter 1983; King 1988), which has been confirmed by a sharp
change in rotational velocity of single M dwarfs near spectral
types ∼M3.5 (Reiners & Basri 2008; Reiners & Mohanty 2012).
Meanwhile, as predicted by population synthesis, a significant accumulation of CVs occurs near the period minimum so that about
95 per cent of CVs have an orbital period shorter than 2 h. The predicted accumulation of CVs near the period minimum has been observationally confirmed (Gänsicke et al. 2009; Uemura et al. 2010;
Woudt et al. 2012). Although much progress has been made in the
investigation of CVs in the last decade, at least two predictions of
the standard model of CVs are still not confirmed by observations
(Schreiber & Gänsicke 2003): (1) the predicted minimum orbital
period is shorter by 10 per cent than the observed value (Kolb &
Baraffe 1999) and (2) the space density derived from the currently
known sample of CVs (10−6 pc−3 : Downes 1986; Ringwald 1996)
is much lower than that predicted by population-synthesis models
(10−4 pc−3 : de Kool 1992; Politano 1996).
Although theories of the CE phase have made great progress
by using parametrized energy (Webbink 1984; Willems & Kolb
2004; Webbink 2008) or angular momentum equations (Nelemans
& Tout 2005), the detailed physics and outcome are still not well
understood and suffer much uncertainty. Theories of both the CE
phase and magnetic braking are poorly constrained by observations
(Schreiber & Gänsicke 2003). A complete and unbiased population
of observational close binaries that have undergone a CE and subsequent orbital AML can be used to constrain theories of CE evolution
and magnetic braking. Detached PCEBs consisting of a white dwarf
and a main-sequence star are an ideal source for constraining CE
evolution. However, a small number of PCEBs have well-defined
physical parameters and show a trend towards young systems, although about 300 PCEBs and strong PCEB candidates have been
identified (Schreiber & Gänsicke 2003; Rebassa–Mansergas et al.
2007, 2008; Schreiber et al. 2008, 2010; Nebot Gómez-Morán et al.
2009; Pyrzas et al. 2009). A complete and unbiased WDMS binary
sample appears most promising in that respect. WDMS binaries
consisting of a common final stage of stellar evolution, a white
dwarf, and the most frequent type of star, an M dwarf star, are also
very important in the research area (Heller et al. 2009).
Since Raymond et al. (2003) first attempted to study white dwarf–
M dwarf pairs from the Sloan Digital Sky Survey (SDSS: York
et al. 2000; Stoughton et al. 2002), more than a thousand detached
WDMS binaries have been identified (Raymond et al. 2003; Silvestri
et al. 2007; Augusteijn et al. 2008; Heller et al. 2009; Rebassa–
Mansergas et al. 2010; Schreiber et al. 2010). The first catalogue of
1602 WDMS binaries from the spectroscopic SDSS Data Release 6
(DR6) was compiled by Rebassa–Mansergas et al. (2010). However,
the WDMS binary sample is still incomplete. We try to identify
more cold white dwarf binaries from the SDSS and improve our
knowledge of the basic parameters of WDMS binaries.
In this work, we have developed two special colour-cuts for the selection of WDMS systems from SDSS DR7 Abazajian et al. (2009)
and the United Kingdom Infrared Telescope Infrared Deep Sky Survey (UKIDSS) DR5. Using these colour-cuts, 86 new WDMS binaries and 95 candidates are found within SDSS DR7 and UKIDSS
DR5, respectively. In addition, we provide a coherent analysis of the
physical parameters of both stellar components to study the properties of WDMS systems. Analysing the fraction and characteristics
of PCEBs will provide a follow-up study of WDMS binaries, to
provide strong constraints on current theories of magnetic braking
and CE evolution.
The structure of this paper is as follows. In Section 2 we present
our colour-selection algorithms for WDMS binaries and provide the
colour-selection criteria to identify the WDMS systems presented
in Section 3. Using a χ 2 minimization technique (Heller et al. 2009)
to decompose each combined spectrum, we derive independent parameter estimates for the white dwarf and its companion in Section 4
and discuss the stellar parameter distributions, such as effective temperatures, surface gravities, masses, distances and cooling ages of
white dwarfs, in Section 5. Finally, in Section 6 we summarize our
results.
2 W H I T E DWA R F – M A I N S E Q U E N C E B I N A RY
COLOUR SELECTION
2.1 The combined WDMS ugrizJHK colours
Smolčič et al. (2004) identified a WDMS binary bridge that belongs to the second stellar locus in colour–colour diagrams based
on the SDSS DR1 and generated model colours for binary systems,
by assuming SDSS colours for a single M dwarf and white dwarf.
Several attempts were then made to develop colour-selection criteria to select WDMS binaries from the SDSS (Szkody et al. 2002;
Raymond et al. 2003; Smolčič et al. 2004; Eisenstein et al. 2006;
Silvestri et al. 2006, etc.). In this work, we follow their idea and
generate theoretical ugrizJHK colours of WDMS binaries by restricting more component parameter boundaries and present our
colour-selection criteria. The colour criteria are designed to avoid
those selected binary systems that only contain extremely hot white
dwarfs or late spectral-type secondary stars.
Using the fitting formulae for the zero-age main sequence radii
and luminosities of stars as functions of their masses and metallicities (Tout et al. 1996) and the second version of the Basel Stellar Library (BaSeL) synthetic UBVRIJ BB H BB K BB LBB M BB colours
library (Lejeune, Cuisinier & Buser 1996, 1998), we determine
the optical UBVRI magnitudes and near-infrared J BB H BB K BB magnitudes (Bessell & Brett 1988) of K and M dwarfs. Combining
these with UBVRIJHK s magnitudes of white dwarfs (Wood 1995;
Fontaine, Brassard & Bergeron 2001; Holberg & Bergeron 2006),
we obtain the ugriz colours and JHK colours of WDMS binaries
for SDSS and UKIDSS, based on empirical photometric-system
transformation equations (Carpenter 2001; Jordi, Grebel & Ammon 2006). The range of white dwarf effective temperatures and
surface gravities covers T eff = 6000–110 000 K and log g = 7.0–9.5,
respectively. The initial input parameters of main-sequence stars are
[Fe/H] = −2.5–0.5 and M = 0.08–0.8 M .
Fig. 1 shows the location of the combined WDMS binaries in
four different colour–colour diagrams. Each track is formed by a
white dwarf with fixed effective temperature and surface gravity
combined with a K or M dwarf of a certain metallicity. Six effective temperatures (6 000 K, 10 000 K, 15 000 K, 20 000 K, 30 000 K,
110 000 K) of white dwarfs combined with a certain metallicity of
M and K dwarfs are used in our models. The dashed lines show
the results for a white dwarf with log g = 9.0 combined with a
main-sequence star with [Fe/H] = 0.5, and the solid lines show
the results for a white dwarf with log g = 7.0 combined with a
main-sequence star with [Fe/H] = −2.5. This figure implies that
the higher the surface gravity of the WDs and the metallicity of the
main-sequence companions, the redder the colours of the WDMS
binaries.
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Monthly Notices of the Royal Astronomical Society Identifying WDMS binaries
1843
resolution of λ/λ 2200, based on colours and morphology (York
et al. 2000; Stoughton et al. 2002). The SDSS DR7 (Abazajian et al.
2009) achieved a completion of the original goals of the SDSS, including 11 663 deg2 and 9380 deg2 of image and spectroscopy data,
respectively.
Here we develop ugriz colour-cuts to select WDMS systems from
the photometric and spectrospic DR7. Fig. 2 shows the WDMS
selection criteria as black lines. The background main stellar loci
(dark cluster) in the three diagrams are the main-sequence stars from
the SDSS ∩ USNO-B proper motion catalogue (Gould & Kollmeier
2004). The colour-selection criteria are given as the following:
14 < g < 20, g − r > 0.80 × (u − g) − 0.65,
g − r > −0.40, r − i > 0.60 × (g − r) − 0.18,
g − r < 1.70, i − z > 0.46 × (r − i) + 0.24,
r − i < 1.30, i − z < 1.06 × (r − i) + 0.53.
Figure 1. ugrizJHK colour–colour diagrams to illustrate WDMS targetselection criteria. Both six solid and dashed lines represent white dwarfs with
different temperatures (6 000 K, 10 000 K, 15 000 K, 20 000 K, 30 000 K,
110 000 K). Dashed lines show the results for white dwarfs with log g =
9.0 combined with main-sequence stars with [Fe/H] = 0.5, while solid
lines show the results for white dwarfs with log g = 7.0 combined with
main-sequence stars with [Fe/H] = −2.5.
The more luminous star determines the binary system colour
if the luminosities of the two stars are unequal. Binaries containing a very cold white dwarf or an early K star are located near
main-sequence stars and are difficult to identify as WDMS. For binaries with a hot white dwarf or a very late M dwarf or even a brown
dwarf, the colours are close to those of the single white dwarf or
quasi-stellar object (QSO) region (Richards et al. 2002). Therefore,
we parametrize the system colours through the luminosity ratio of
the two components in the r band. The location of binaries in the
colour–colour diagram is dominated by the luminosity ratio of both
components. Although Willems & Kolb (2004) argued that the distribution of the luminosity ratio of the white dwarf to the secondary
star has a peak between 10−5 and 10−3 for the WDMS, the distribution of channel 4 (Case B CE phase with a white dwarf remnant),
which goes through the CE phase, extends up to a higher luminosity
ratio. In addition, the detection of the white dwarf’s spectral signature becomes increasingly difficult with decreasing luminosity ratio
(Willems & Kolb 2004).
As mentioned above, the completeness of a WDMS binary sample is uniquely determined by the range of the r-band luminosity
ratio. The area covered by WDMS binaries in the colour–colour
diagram will quickly increase with increasing ratio in a region between 0.01 and 50. When the luminosity ratio exceeds this region,
the colour region covered by WDMS binaries will increase slowly.
Although some colour tracks cross the main sequence in Fig. 2 if
the luminosity ratio of binaries is smaller than 0.5 or larger than
10 in our models, we choose a ratio of white dwarf luminosity to
main-sequence star luminosity from 0.01–50.
2.2 WDMS colour-selection criteria
2.2.1 WDMS colour-selection criteria for the SDSS
The SDSS provides homogeneous and deep photometry in five
passbands (u, g, r, i and z) that are accurate to 0.02 mag. Objects
are flagged for spectroscopic follow-up using a 640-fibre-fed spectrograph, which gives wavelength coverage from 3800–9200 Å at a
C 2012 The Authors, MNRAS 424, 1841–1851
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Monthly Notices of the Royal Astronomical Society Obviously, our colour criteria cover almost all the region of QSOs
(dark cluster) and some main-sequence stars (background, faint
cluster) in the u − g versus g − r and g − r versus r − i colour–
colour diagrams, but our main cut is the r − i versus i − z diagram;
this is because we try to find a large and unbiased WDMS sample
within the SDSS. Meanwhile, we want to isolate the WDMS binaries
from the main sequence and QSOs as much as possible.
Our colour criteria differ from the colour-cuts used by Silvestri
et al. (2006) and Schreiber et al. (2007). The photometric selection
criteria defined by Silvestri et al. (2006) and Raymond et al. (2003)
are based on the idea that WDMS systems have to be blue (hot
WD) and red (MS) at the same time. These selection criteria lead
to the sample of WDMS-biased hot white dwarfs. Schreiber, Nebot
Gómez-Morán & Schwope (2007) also developed special colourcuts to select old WDMS systems from the Sloan Extension for
Galactic Understanding and Exploration (SEGUE), but they did
not consider the fact that the colours change with different surface
gravities of white dwarfs and metallicities of companion stars.
In the last plot of Fig. 2, our colour-cuts can be divided into two
regions (I and II) at r − i = 0.3. Most objects in region I are QSOs
(Richards et al. 2002) and are observed spectroscopically, but it is
still the main locus of those WDMS binaries for which spectra have
been provided by the SDSS, and most of them have been identified
by former investigators. Our colour selection criteria also cover this
area. In this work, a huge number of photometric candidates are
found; however, the number of candidates selected from photmetric
and spectroscopic catalogues does not exceed 1000. Finally, 523
WDMS binaries are identified from these candidates. Some new
WDMS systems are also found in target selection region I.
Our WDMS binary models contain white dwarfs with temperatures in a very wide region. It is expected that we will find more
cold white dwarf binaries than former authors in region II, where
most binary systems containing a hot white dwarf are excluded
from our colour-cuts. In addition, the detection of WDMS becomes
increasingly difficult with increasing mass of the secondary (M sec >
0.5 M ), as they are so close to the main sequence.
2.2.2 WDMS colour-selection criteria for the UKIDSS
The UKIRT Infrared Deep Sky Survey (UKIDSS: Dye et al. 2006;
Lawrence et al. 2007; Warren et al. 2007) used the Wide Field Camera (WFCAM), which has the largest étendue of any infrared astronomical instrument to date, on the 3.8-m United Kingdom Infrared
Telescope(UKIRT). It is many times deeper than the Two-Micron
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C. Liu et al.
Figure 2. The area formed by black lines shows the colour cuts used to select WDMS within DR7. The background main stellar loci in all colour–colour
diagrams are the main-sequence stars that come from the SDSS ∩ USNO-B proper-motion catalogue (Gould & Kollmeier 2004).
All-Sky Survey (2MASS: Skrutskie et al. 2006) and is considered to
be the near-infrared (near-IR) counterpart of the SDSS. The Large
Area Survey (LAS), providing infrared YJHK magnitudes, aims to
cover the northern sky by approximately 4000 deg2 ; combined with
the SDSS it produces an atlas covering almost an order of magnitude
in wavelength (Lawrence et al. 2007).
Since we designed the ugriz colour criteria, we have found a
small fraction of candidates that were observed spectroscopically
in the SDSS DR7. Many candidates might be WDMS binaries, but
we cannot identify them because there are no spectra provided for
them from the SDSS data base. In particular, a few WDMS binaries
are identified at the top of the colour–colour diagrams in the next
secion because of observational selection effects. Apart from the
optical colour criteria, universal JHK colour-cuts are designed to
select WDMS binaries from UKIDSS DR5 cross-matched with
SDSS DR7. Although no spectral evidence can be obtained for
these candidates from SDSS and UKIDSS, this can improve the
probability of every candidate being a WDMS binary with near-IR
excess emission. There is an overlapping region between candidates
identified in this section and those identified in Section 2.2.1. The
near-IR JHK colour criteria are shown in Fig. 3. These can be
described as follows:
binaries. 20 new WDMS binaries that belong to DR6 are not listed
in the catalogue of Rebassa–Mansergas et al. (2010). Most of them
are DA white dwarf plus M dwarf binaries, and the second largest
category of binaries consists of a DB white dwarf and an M dwarf.
Fig. 4 shows the positions of the identified WDMS binaries and the
candidates in colour–colour space. Black crosses and red diagonal
crosses indicate the published WDMS and WDMS newly identified
by us, respectively. The candidates (green squares) selected from
UKIDSS DR5 cross-matched with SDSS DR7 are also plotted in
colour–colour space. Apparently most of the WDMS binaries overlap the QSO region in the u − g versus g − r and g − r versus
r − i panels, because most of them have been selected from spectra
of QSO candidates. Meanwhile, we also identify many old WDMS
binaries that are far away from QSOs in the r − i versus i − z plot.
Combining our ugriz colour criteria with r − i > 0.3, standard
clean-photometry flag-setting and requesting point spread function (psf) errors to be below 0.1 (Nebot Gómez-Morán 2010),
we find 94 366 candidates in SDSS DR7. Since so many WDMS
binary candidates have been found in the SDSS since universal
JHK colour criteria were designed, we cross-matched our list of
H − K > 0.31 × (J − H ) − 0.01,
H − K < 0.68 × (J − H ) − 0.01,
H − K < −1.29 × (J − H ) + 0.92.
Our results show that 11 published targets with photometric and
spectroscopic data are included from 106 candidates, and many
targets cluster at the top of the colour–colour panels in Fig. 4. The
two WDMS samples and other samples discussed before or during
Section 4 are classified in Table 1.
3 W D M S B I N A RY S A M P L E
In addition to the colour criteria, we require redshift z0 less than 0.01
for the selection of targets from the photometric joining spectroscopic catalogues within DR7. 792 stellar objects that have spectroscopic observations fill the colour–colour spaces. Among them, 523
systems are identified as WDMS ones, including 86 new WDMS
Figure 3. The JHK colour-cuts, combined with ugriz colour criteria, used
to select WDMS systems within UKIDSS DR5 cross-matched with SDSS
DR7.
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Monthly Notices of the Royal Astronomical Society Identifying WDMS binaries
1845
Figure 4. The positions are the identified WDMS binaries and candidates in the colour–colour diagrams. The crosses indicate published WDMS and the
diagonal crosses are the first WDMS identified by us; WDMS candidates are denoted by squares.
Table 1. The numbers of WDMS/candidates identified from SDSS
or UKIDSS.
Types
SDSS
UKIDSS (cross-matched)
Photometric (r − i > 0.3)
Stellar spectroscopic
New WDMS/candidates
WDMS spectra (published)
WDMS photometries
93466
792
86
437
523
106
WDMS sample and 4 candidates have only magnitudes. The remaining 91 photometric-only candidates are listed in Table 2.
Table 2 also provides the coordinates, SDSS and UKIDSS magnitudes of 523 WDMS found from the DR7.
There are identified WDMS binaries in the areas where the photometric candidates exist in colour–colour space (Fig. 4), such as a
WDMS (red diagonal cross) lying at the top right of the u − g versus
g − r panel. It implies that the candidates selected from the SDSS
and UKIDSS are highly potential WDMS binaries. According to
the positions of the candidates, many of them might contain cold
white dwarf binaries if they are WDMS binaries.
95
11
15
candidates with DR5 of UKIDSS. Within 2 arcsec, the nearest
SDSS source to each WFCAM source will be the most likely
match. Fig. 4 also shows the position of 106 candidates (blue)
in ugrizJHK colour space. 15 of these candidates have been published by Augusteijn et al. (2008), Heller et al. (2009), Rebassa–
Mansergas et al. (2010) and Schreiber et al. (2010). Among
them, 11 WDMS candidates with spectra are included in our
4 S T E L L A R PA R A M E T E R S
In our work, we use a χ 2 minimization technique (Heller et al.
2009) to decompose a WDMS binary spectrum into a white dwarf
and a main-sequence star component and derive independent parameter estimates for each component. In the following sections we
Table 2. Coordinates and SDSS–UKIDSS magnitudes for a part of the 523 WDMS binaries and 95 candidates. This is a sample of
the full table, which is available as Supporting Information with the electronic version of the paper. We use ‘...’ to indicate that no
magnitude is available.
SDSS J
001324.33−085021.4
002106.46+151247.1
002620.41+144409.2
005227.58+000553.4
005457.61−002517.0
005624.46−005107.3
010045.94+150659.2
011446.96+132825.3
012259.52+154253.8
012438.94−005309.8
013009.76+131137.4
RA (◦ )
Dec. (◦ )
u
g
r
i
z
Y
J
H
K
3.35139
5.27693
6.58504
13.11491
13.74005
14.10194
15.19143
18.69571
20.74807
21.16224
22.54066
−8.83929
15.21309
14.73589
0.09815
−0.42143
−0.85203
15.11644
13.47370
15.71497
−0.88605
13.19371
19.73
19.82
17.55
19.28
18.88
22.11
19.34
20.19
19.37
22.01
18.27
19.73
17.35
17.34
16.91
18.56
19.77
18.84
19.67
18.98
19.83
17.97
19.66
16.00
17.33
15.46
18.74
18.34
18.97
19.66
18.98
18.44
17.45
19.08
14.82
16.64
14.61
18.48
17.24
18.74
19.11
18.56
17.74
17.22
18.55
13.98
16.02
13.65
18.02
16.38
18.27
18.57
18.04
17.08
20.89
...
13.05
15.13
12.75
17.27
15.52
17.51
...
...
16.29
19.96
...
12.59
14.60
12.24
16.82
14.94
17.03
...
...
15.82
19.80
...
12.11
14.07
11.73
16.45
14.41
16.44
...
...
15.28
19.45
...
11.84
13.80
11.47
16.05
14.18
16.25
...
...
15.06
18.98
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Monthly Notices of the Royal Astronomical Society 1846
C. Liu et al.
describe the models used in the spectral decomposition and fitting, the distance estimates derived for the two components and the
cooling time of white dwarfs in detail.
4.1 Models
We use theoretical spectra based on a model atmosphere to construct
a model spectral grid of the WDMS binary population in which
each binary contains a white dwarf and a main-sequence star, used
to calculate the independent parameters of white dwarfs and mainsequence stars. The grids provide spaces of M-dwarf parameters
WD
M
, log gM , [Fe/H]M and white dwarf parameters Teff
and log gWD ,
Teff
respectively. Since most WDMS binaries contain a DA white dwarf,
the white dwarf spectra are calculated from DA (pure hydrogen atmosphere) white dwarf spectra based on the model atmosphere code
described by Koester (2010), which covers surface gravities of 7 ≤
log gWD ≤ 9 with a step size of 0.5 dex in a temperature range from
6–60 kK. We adopt steps of 1 kK between 6 and 20 kK and steps
of 5 kK between 20 and 60 kK. Low-resolution (R ∼ 300) mainsequence spectra, obtained by interpolation based on the effective
temperature, surface gravity and metallicity in the second version
of BaSeL standard library (Lejeune et al. 1996, 1998), cover temM
≤ 4000 K with a step size of 200 K, surface
perature 2400 ≤ Teff
gravity 3.5 ≤ log gWD ≤ 5.5 every 0.5 dex and metallicity [Fe/H]M ∈
{−2.0, −1.5, −1.0, −0.5, 0.0, 0.1, 0.2, 0.3, 0.4}. Although the resolution of main-sequence theoretical spectra is lower than that of
SDSS observed spectra, the M-dwarf spectrum is dominated by a
continuous spectrum and the theoretical spectrum fitting for an M
dwarf can be taken as the continuous spectrum fitting, which is not
strongly dependent on the resolution of the theoretical spectra. Also,
no distinct systematic error appears when we compare the distribution of WDMS parameters with the results of Rebassa–Mansergas
et al. (2010).
4.2 Spectrum fitting
We use the same χ 2 fitting method as Heller et al. (2009) to fit the
observed spectra of WDMS binaries in a five-dimensional parameter
WD
M
, Teff
, log gM , [Fe/H]M and log gWD . In the
space, spanned by Teff
first step, a binary spectrum with a total number of n observed data
points is reproduced by a combination of white dwarf and secondary
star. They are weighted with scaling factors that depend on the
distances and radii of the stars. As mentioned above, it is apparent
that the resolution of the theoretical spectra of main-sequence stars
is lower than that of SDSS spectra. The same resolution of the
secondary observed spectra is generated by a linear interpolation
based on n points in our fitting code. We then used an evolutionary
strategy based on reduced χ 2 to find the best two single-star models.
This allows us to estimate some important parameters of the white
dwarf and the secondary, such as the mass, radius, distance and
cooling age of the white dwarf. An example of a typical WDMS
spectrum reproduced by the combination of a DA white dwarf and
an M dwarf is shown in Fig. 5. This method is able to avoid a mutual
dependence of scaling factors and the effects of identifying a local
χ 2 minimum, since the system of equations can be solved uniquely
(Heller et al. 2009).
For all of the fitted spectra, Heller et al. (2009) have argued that
the quality of spectra fitting was poor in a mathematical context
and that the standard deviations of measured parameters were quite
weak in terms of physical significance. As a way to estimate the
errors in the measured parameters, we refer to Hügelmeyer et al.
(2006) and assume an uncertainty of half the model step width
for the WDs and MS stars. Because of the low resolution of the
SDSS spectra and the step size of our model grid, the accuracy of
the surface gravities is given as σlog(gWD ) ≈ σlog(gM ) ≈ 0.5 dex. We
also assume an uncertainty of 0.3 dex for metallicity below 0.0. For
[Fe/H]M > 0.0, the absolute value of our accuracy is given by half
of the model step width of 0.1 dex.
4.2.1 Distance estimate of WDMS
With the best-fitting flux scaling factors that scale the model flux
to the observed flux, we can estimate the distances of the two
components of WDMS binaries from the Earth. The distances of
the white dwarf and the secondary can be estimated by the following
equation:
f obs = πFem (R/d)2 ,
(1)
where f obs is the observed flux of the spectral component, F em the
astrophysical flux at the stellar surface given by the model atmosphere, R the radius of the spectral component and d the distance to
the white dwarf or main-sequence star.
Using the empirical effective temperature–spectral type (T eff –
Sp), mass–spectral type (M–Sp) and radius–spectral type (R–Sp) relations (Rebassa–Mansergas et al. 2007) and the flux scaling factor,
we derive a estimate of distance dsec to the secondary. The uncertainties in the distances are given based on the errors in R, where
we used the standard deviation from Table 3 (Rebassa–Mansergas
et al. 2007).
A similar method is applied to deduce the distance dwd of the
white dwarf. We estimate the masses and radii of white dwarfs by
interpolating the cooling tracks (Wood 1995; Fontaine et al. 2001)
for log g and T eff . Combining this with the scaling factor, we obtain
the distance estimate for the white dwarf. Since the error in Rwd
depends mainly on the error in log g and mass in our procedure, the
uncertainties in its distance also depend primarily on the error in
log g and mass. The maximum standard deviation of the WD mass
function at 0.58 M is about 0.1 M (Hu, Wu & Wu 2007). It can
cause about an 8.6 per cent error in the WD distance estimate. As the
uncertainty of the surface gravities is given by σlog(gwd ) ≈ 0.5 dex,
the maximum error in WD distances will be about 12 per cent for
log g = 9.0.
4.2.2 The cooling age of DA white dwarfs
The accurate cooling ages of field white dwarfs have been obtained
from their effective temperatures and masses, since the detailed evolutionary cooling sequence of single white dwarfs has been modelled. Therefore, we determine the cooling ages for the WDMS in
our sample by interpolation from the evolutionary tracks according to the determined effective temperature and surface gravity of
the DA white dwarf (in Table 3). The cooling-age estimates are
also given in Table 3. The white dwarf evolution tracks1 we used
are carbon-core cooling models (Wood 1995) with pure hydrogen
model atmospheres for effective temperature T eff ≥ 30 000 K, while
for T eff < 30 000 K we rely on cooling models similar to those described in Fontaine et al. (2001) but with carbon–oxygen cores.
According to the Mestel model (Mestel 1952), the cooling age
of a white dwarf is related to its core chemical composition, envelope chemical composition, mass and luminosity. However, the
cooling ages are obtained by interpolation from the evolution tracks
1
http://www.astro.umontreal.ca/~bergeron/CoolingModels/
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C 2012 RAS
Monthly Notices of the Royal Astronomical Society Identifying WDMS binaries
1847
Figure 5. Top panel: DA–dM combination (solid line) fits to SDSSJ155040.53+052150.3. The top panel shows the observed WDMS spectrum and the white
dwarf and M-dwarf model spectra (dotted lines). The spectrum close to 5600 Å is an artefact of the SDSS data reduction (Silvestri et al. 2006) and has been
ruled out in our fitting routine. Centre panel: estimate of the fit as defined in equation (9) in Heller et al. (2009). Bottom panel: the residuals to the fit.
based on the effective temperature and surface gravity in our work.
Since the mass and luminosity of a white dwarf are related to the
effective temperatures and surface gravities, the uncertainty of our
cooling age is determined by the uncertainties in the DA white
dwarf’s effective temperature, surface gravity and core composition.
As mentioned above, the uncertainties in white dwarf temperature
and surface gravity are about half the model step size and 0.5 dex,
respectively. In addition, the model mass has uncertainty; the corresponding uncertainties of the derived cooling ages might be up to
the order of ∼2, which is still irrelevant for comparison with binary
evolution time-scales.
The core composition of the white dwarf may be affected by
binary evolution. If CVs have a low-mass primary (M 1 < 0.5 M ),
the primary will be a helium-core white dwarf (de Kool & Ritter
1993; de Kool 1992; Politano 1996; Howell, Nelson & Rappaport
2001). Low-mass white dwarfs in close binary systems have also
been identified by Marsh, Dhillon & Duck (1995). The cooling
models of He white dwarfs (Driebe et al. 1998, 1999) show that the
cooling ages are significantly larger than those gained from model
calculations that neglect hydrogen-shell burning for very low-mass
stars. SG03 proved that the effect of different core compositions for
low-mass (M 1 ≤ 0.4 M ) and cool (T eff ≤ 20 000 K) white dwarfs
should be taken into account. However, the cooling ages are still
C 2012 The Authors, MNRAS 424, 1841–1851
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Monthly Notices of the Royal Astronomical Society derived from CO or C tracks for the low-mass primaries of our
WDMS sample. This would provide an underestimate of ages for
low-mass white dwarfs.
5 R E S U LT S A N D D I S C U S S I O N
In this section, we present distributions of surface gravities, effective
temperatures and masses of DA white dwarfs as well as distributions of the effective temperatures, metallicities and masses of the
companion stars in our sample (Fig. 6). We also provide a distribution of secondary spectral types to facilitate the comparison with
Rebassa–Mansergas et al. (2010). For the distribution of stellar parameters, we only perform a χ 2 test for WDMS systems. This yields
the surface gravity, effective temperature and mass of white dwarfs
of 474 WDMS binaries and the secondary spectral-type distribution
of 509 WDMS binaries, respectively.
5.1 Parameter distributions of white dwarfs
Here, we will give the distributions of white dwarf parameters, including effective temperatures, surface gravities and masses, which
are shown in the upper three panels of Fig. 6. It is found that the
s/r
s/e/h/r
s/e/a/h/r
s/e/a/r
s/e/h/r
s/e/a/h/r
r
s/e/a/h/r
4.76
10.59
5.32
2.65
2.69
2.78
4.11
3.28
...
0.04
−0.04
−0.32
−0.21
−0.27
0.31
−0.12
0.32
0.32
0.32
0.32
0.32
0.32
0.13
0.32
128
38
108
125
124
103
37
102
491
144
412
480
475
393
344
391
...
8.37
7.84
8.48
8.65
8.67
8.29
8.57
...
0.93
0.62
0.61
0.93
0.60
0.61
0.61
...
15
34
27
35
24
48
29
...
152
387
301
349
267
538
330
5.5
5.0
4.5
4.5
5.0
5.0
5.0
4.5
3200
3200
3200
3200
3200
3200
2600
3200
52138
52233
51913
51821
51821
51893
54465
52168
001324.33−085021.4
002620.41+144409.5
005457.61−002517.0
010045.94+150659.2
011446.96+132825.3
012259.52+154253.8
013356.07−091535.1
015132.82−080047.7
WD/M
DA/M
DA/M
DA/M
DA/M
DA/M
DA/M
DA/M
652
753
394
421
423
424
2878
665
321
79
110
463
242
404
636
322
...
19000
20000
13000
15000
11000
15000
12000
...
8.5
8.0
8.0
8.5
8.0
8.0
8.0
0.0
0.0
0.0
0.0
0.0
0.0
0.1
0.0
log gsec
MJD
SDSS J
Type
PLT
FIB
wd
Teff
(K)
log gwd
[Fe/H]sec
sec
Teff
(K)
dwd
(pc)
err
M wd
(M )
log (Age)
(yr)
dsec
(pc)
err
M sec
(M )
C
2
χred,min
Flag
C. Liu et al.
Table 3. Example table of stellar parameters for 523 WDMS binaries. The uncertainties are mentioned in Section 4. Flags e, s, a, h and r for binaries indicate that those binaries have been studied previously by
Eisenstein et al. (2006), Silvestri et al. (2007), Augusteijn et al. (2008), Heller et al. (2009), Rebassa–Mansergas et al. (2007) and Rebassa–Mansergas et al. (2010), respectively. This is a sample of the full table,
which is available as Supporting Information with the electronic version of the paper. Again, we use ‘...’ to indicate that stellar parameters are unavailable.
1848
majority of white dwarf temperatures are between 10 000 and
20 000 K and that white dwarfs with temperatures higher than
40 000 K are very rare. This might suggest that our selection criteria
can be used to select WDMS binaries with cold or old white dwarfs.
The white dwarf surface gravity clusters together around log gwd 8.0. It looks as though there are two peaks for white dwarf mass
distribution. The strong peak is located at about M wd = 0.65 M
and another peak is located around M wd = 1.1 M . On closer inspection, the distribution of white dwarf masses in our sample has
a more pronounced fraction of large-mass white dwarfs compared
with the distribution of Rebassa–Mansergas et al. (2010).
A detailed comparison of white dwarf effective temperature, surface gravity and mass and secondary spectral type with the results
of Rebassa–Mansergas et al. (2010) is shown in Fig. 7. These distributions have been normalized to facilitate this comparison. The
solid lines represent the parameter distributions of our WDMS binary sample, while Rebassa–Mansergas’s parameter distributions
are drawn with dashed lines. Apparently, the distributions of three
white dwarf parameters of our sample are quite similar to those of
Rebassa–Mansergas’s sample. Rebassa–Mansergas’s sample has a
longer tail towards very high temperatures, but this is not found
in our sample. As mentioned in Section 2, those WDMS binaries
containing very hot white dwarfs have probably been excluded by
our colour criteria.
Because of the surface gravity covering log gwd = 7.0–9.0 in steps
of 0.5 dex, the distribution of white dwarf surface gravities in our
sample does not have a tail extending to very low surface gravities.
As the white dwarf mass depends on the effective temperature and
surface gravity, there is not a tail towards lower masses in our white
dwarf mass distribution compared with the distribution in Rebassa–
Mansergas et al. (2010).
5.2 Parameter distribution of the secondaries
As well as the parameter distribution of white dwarfs, we also
give the effective temperature, metallicity and mass distributions
of the secondary stars. Using the empirical Sp–M and Sp–T eff relations given by Rebassa–Mansergas et al. (2007), we obtain the
secondary masses and spectral types from their effective temperatures. This clearly shows that the secondary temperatures have a
peak at 3200 K, which corresponds to a spectral type about M3.5. It
is similar to the companion spectral-type distribution of Rebassa–
Mansergas et al. (2010), which has a peak at M3–M4 and declines
steeply to late spectral types. In comparison with the Rebassa–
Mansergas’s spectral-type distribution, our sample has a smaller
extended spectral type of M dwarfs. The distribution of secondary
star masses is quite similar to that of their effective temperature.
There is a peak around M sec = 0.26 M . Our results as regards
metallicity and mass can also be seen in Fig. 6 (bottom). Almost
all the metallicities of the M stars cluster around [Fe/H]M = 0. All
the characteristics of the secondary parameter distributions might
be caused by the observational selection effects of the SDSS and
our colour-selection criteria.
5.3 Distance distributions of the two components
As outlined in Section 4.2.1, the flux scaling factors obtained from
the fitting of the two spectral components of each WDMS binary provide two independent estimates for their distances from
the Earth. We compare the white dwarf distances with their companion distances in Fig. 8. Both distance estimates should be equal,
within the errors. The masses of the white dwarfs are obtained by
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Monthly Notices of the Royal Astronomical Society Identifying WDMS binaries
1849
Figure 6. The parameter distribution of 474 DA white dwarfs and 509 secondary stars from the SDSS in our WDMS binaries sample.
Figure 7. Comparison of effective temperature (top left), white dwarf mass
(top right), surface gravity (bottom left) and spectral type (bottom right) of
our WDMS sample (solid lines) with the sample from Rebassa–Mansergas
et al. (2010) (dashed lines). The four panels show the cumulative distribution
functions.
Figure 8. Distribution of the obtained distances of the two components in
our sample. The diagonal is the ideal for physical binaries. About 67 per
cent of the 425 systems have dwd dsec within their 1σ errors.
interpolation from the cooling models; therefore the error in the
determination of white dwarf mass might bring a relative error to
the white dwarf distance estimate. However, if we only consider
systems with relative errors from the uncertainty of the surface
gravities, the error of the white dwarf distance estimate would be
less than 12 per cent. Rebassa–Mansergas et al. (2007) argued that
the relative error in dsec is dominated by the scatter in the spectral type–radius relation, which represents an intrinsic uncertainty
rather than a statistical error related to the fitting. We therefore accept all distance estimates for the two spectral components in our
sample.
In Fig. 8, about 67 per cent of the 425 systems, in which discrepancy coefficient C (Heller et al. 2009) between dwd and dsec are
between −0.5 and 0.5 have dwd dsec within a 1σ error. The discrepancy in two distances may be caused by the strong Hα emission of
the WDMS spectra (Heller et al. 2009), because our main-sequence
star models do not consider Hα emission. This also leads to the spike
in the fitting error at the Hα wavelength. At least 126 spectra have
been found with Hα emission, and some of them also exhibit other
types of Balmer emission, such as SDSS J211205.31+101427.9 and
SDSS J111544.56+425822.4. The hydrogen emission is probably
produced by magnetically active M dwarfs with chromospheric
emission or by the fact that M dwarfs might be subject to the
primary irradiation (Silvestri et al. 2006). The fraction of spectra
with Hα emission is 24.0 per cent, which matches the value found
by West et al. (2004) and Heller et al. (2009). Taking into account
all the other error sources mentioned before, this can probably explain most discrepancies of dwd and dsec . There is a trend, which
is similar to Heller’s distance distribution, where there are higher
distance estimates for the white dwarf components for systems with
a distance larger than 500 pc in Fig. 8. This is probably caused by
weak white dwarf and M-dwarf features in the spectrum due to the
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Monthly Notices of the Royal Astronomical Society 1850
C. Liu et al.
Figure 9. Gaussian distributions of the white dwarfs and secondary distances in our sample.
large distance of the system, or to the underestimation of M WD in
magnetic binaries (Heller et al. 2009).
The distance distributions for the white dwarfs and secondary
stars respectively are given in Fig. 9. The Gaussian functions are
used to fit the shape of the white dwarf and secondary distance
distributions. The white dwarf distance distribution has a maximum
at 332.1 pc with σ = 345.5 pc, while the secondary distance distribution has a maximum at 331.6 pc with σ = 356.4 pc. Although
the two distance distributions have different maxima, the difference is smaller than their errors at maximum. This means that most
of the WDMS distance estimates for the two components are the
same. Meanwhile, 67 per cent of systems have dwd dsec within
a 1σ error. However, the distance distribution of the secondary
clusters around maximum is closer than the white dwarf distribution. This might be caused by the uncertainty in the white dwarf
mass.
5.4 The cooling-age distribution of white dwarfs
As described in Section 4.2.2, DA white dwarf cooling ages are determined by interpolation from the cooling models for the WDMS
binaries in our sample. The cooling-age estimates are shown in
Fig. 10, along with cooling tracks. Cooling tracks are plotted for
six different masses (0.2, 0.4, 0.6, 0.8, 1.0 and 1.2 M ) of white
dwarfs in the top panel of Fig. 10. The positions of the newly
identified WDMS binaries are obtained by interpolation from the
cooling tracks for different masses of DA white dwarfs. The bottom
panel of Fig. 10 displays the age distribution of our DA white dwarf
sample. It is found in Fig. 10 that the distribution covers an age
range from ∼106 –1010 yr and most of the DA white dwarfs have
cooling ages in a region tcool ∼ 1.3 × 108 –3.2 × 108 yr. The mean
cooling age of the WDMS sample containing DA white dwarfs is
t cool ∼ 4.2 × 108 yr. It is larger than that of the 18 PCEB sample obtained by Schreiber & Gänsicke (2003). It is also found that
about 11 per cent of WDMS binaries have gone through ∼1.0 ×
109 yr evolution since they formed. Therefore, the fraction of
old systems is higher than 11 per cent within our WDMS binary
sample.
Figure 10. Cooling tracks are plotted for six masses (0.2, 0.4, 0.6, 0.8,
1.0 and 1.2 M ) of white dwarfs in the top panel. The positions of the
newly identified WDMS binaries are obtained by interpolating between the
cooling tracks for different masses of DA white dwarf primary. The bottom
panel shows the age distribution of the WDMS sample in a histogram with
logarithmic bins.
6 CONCLUSIONS
We construct detached binary models that contain a white dwarf
and a main-sequence star and generate model colours for them. We
assume that the two components in these binaries do not interact
directly. Although the binary models are limited by the luminosity
ratio of the two components in the r band, they still cover a broad
range of parameters. According to the model colours, we design
optical and infrared colour-selection criteria for the selection of
WDMS binaries from SDSS DR7 and UKIDSS DR5, respectively.
Using the optical colour criteria, we have presented 523 WDMS
binaries identified from the spectroscopic SDSS DR7. Combining
them with infrared colour criteria, 95 WDMS candidates are found
from SDSS DR7 cross-matched with UKIDSS DR5. We have used a
χ 2 minimization technique to determine the effective temperatures,
surface gravities, masses and distances to the white dwarfs, as well
as the effective temperatures, surface gravities, metallicities, masses
and distances to the companions from the Earth in our sample. We
also derived the cooling ages of white dwarfs by interpolating the
single white dwarf cooling tracks for their effective temperatures
and surface gravities. The distributions obtained from these stellar
parameters have been used to study both the general properties and
the completeness of WDMS binaries. A comparison between the
distances measured to the white dwarfs and the secondary stars
shows a clear trend towards higher distances for the white dwarf
components. We find that the mean cooling age of the WDMS
sample is t cool ∼ 4.2 × 108 yr and our sample contains at least
11 per cent old systems, in which the white dwarfs were formed
1.0 Gyr ago. Our newly updated WDMS binaries might help to
improve the completeness of the catalogue of WDMS binaries.
AC K N OW L E D G M E N T S
We thank the anonymous referee for helpful comments and suggestions that greatly improved the presentation of the paper and
thank Detlev Koester for kindly providing the white dwarf atmosphere models. This work was in part supported by Natural Science
Foundation (Grant Nos 11073049, 10773026 and 11103054), by
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Monthly Notices of the Royal Astronomical Society Identifying WDMS binaries
the Chinese Academy of Sciences under Grant No. KJCX2-YWT24 and also supported by Xingjiang National Science Foundation
(NO.2011211A104), the program of the Light in China’s Western
Region (LCWR) under grant XBBS201022 and Beyond The Horizons under grant 100020101.
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S U P P O RT I N G I N F O R M AT I O N
Additional Supporting Information may be found in the online version of this article:
Table 2. Coordinates and SDSS–UKIDSS magnitudes for a part of
the selection of 523 WDMS binaries and 95 candidates.
Table 3. Example table of stellar parameters for 523 WDMS
binaries.
Please note: Wiley-Blackwell are not responsible for the content or
functionality of any supporting materials supplied by the authors.
Any queries (other than missing material) should be directed to the
corresponding author for the article.
This paper has been typeset from a TEX/LATEX file prepared by the author.