Draft version October 31, 2018
Preprint typeset using LATEX style emulateapj v. 08/22/09
EVIDENCE FOR A MERGER OF BINARY WHITE DWARFS: THE CASE OF GD 362
E. Garćıa–Berro
, P. Lorén–Aguilar
and A.G. Pedemonte
Departament de F́ısica Aplicada, Universitat Politècnica de Catalunya, Av. del Canal Oĺımpic s/n, E-08860 Castelldefels (Barcelona),
Spain
J. Isern
Institut de Ciències de l’Espai (CSIC), Facultat de Ciències, Campus UAB, Torre C5-parell, E-08193 Bellaterra (Barcelona), Spain
P. Bergeron, P. Dufour and P. Brassard
Département de Physique, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Québec, Canada H3C 3J7
Draft version October 31, 2018
ABSTRACT
GD 362 is a massive white dwarf with a spectrum suggesting a H–rich atmosphere which also shows
very high abundances of Ca, Mg, Fe and other metals. However, for pure H–atmospheres the diffusion
timescales are so short that very extreme assumptions have to be made to account for the observed
abundances of metals. The most favored hypothesis is that the metals are accreted from either a
dusty disk or from an asteroid belt. Here we propose that the envelope of GD 362 is dominated
by He, which at these effective temperatures is almost completely invisible in the spectrum. This
assumption strongly alleviates the problem, since the diffusion timescales are much larger for He–
dominated atmospheres. We also propose that the He–dominated atmosphere of GD 362 is likely to
be the result of the merger of a binary white dwarf, a very rare event in our Galaxy, since the expected
galactic rate is ∼ 10−2 yr−1.
Subject headings: stars: white dwarfs — stars: chemically peculiar — stars: individual (GD 362)
1. INTRODUCTION
GD 362 has been interpreted as a massive, rather cool
(Teff ≈ 9740±50 K), white dwarf with a heavy accretion
disk surrounding it (Kilic et al. 2005; Becklin et al.
2005; Gianinas, Dufour, & Bergeron 2004). The dusty
disk around GD 362 produces an excess of infrared ra-
diation which amounts to ∼ 3% of the total stellar lu-
minosity. The chemical composition of GD 362 is also
rather singular, showing a hydrogen rich atmosphere
with very high abundances of Ca, Mg, Fe and other met-
als (Gianinas, Dufour, & Bergeron 2004). Thus, it is
classified as a massive DAZ (hydrogen–rich) white dwarf.
The origin of such particularly high photospheric abun-
dances — log(NCa/NH) = −5.2, log(NMg/NH) = −4.8
and log(NFe/NH) = −4.5 — and of the surrounding
dusty disk around it still remains a mystery. Since the
diffusion timescales for metals in H–rich white dwarfs
are of only a few years (Koester & Wilken 2006) very
extreme assumptions have to be made in order to ex-
plain these abundances. At present the most widely ac-
cepted scenario is disruption and accretion of a plane-
tary body, although for this scenario to be feasible the
planetary system should survive during the advanced
stages of stellar evolution, which by no means is guaran-
teed. Thus, the formation of an asteroid would require
the previous existence of a disk around this white dwarf
(Livio, Pringle, & Saffer 1992; Livio, Pringle, & Wood
2005). Particularly, a recent analysis (Villaver & Livio
Electronic address: garcia@fa.upc.edu, loren@fa.upc.edu, alba@fa.upc.edu
Electronic address: isern@ieec.fcr.es
Electronic address: bergeron@astro.umontreal.ca, dufourpa@astro.umontreal.ca, brassard@astro.umontreal.ca
1 Institut d’Estudis Espacials de Catalunya, Ed. Nexus-201, c/
Gran Capità 2–4, E-08034 Barcelona, Spain
2007) has shown that planets around white dwarfs with
masses MWD > 0.7M⊙ are generally expected to be
found at orbital radii r > 15 AU because they cannot
survive the planetary nebula phase and that if planets
are to be found at smaller orbital radii around mas-
sive white dwarfs, they had to form as the result of
the merger of two white dwarfs. It is also interesting
to note that there have been previous suggestions about
white dwarfs that are merger products — see for instance
Liebert, Bergeron & Holberg (2005) — but these claims
do not have yet any observational support.
2. THE SCENARIO
Another possibility is that some massive white dwarfs
are the result of the merger of a double white dwarf
close binary system. This scenario has been stud-
ied in several papers. However, in most of these pa-
pers either the resulting nucleosynthesis was not ad-
dressed (Segretain, Chabrier, & Mochkovitch 1997), or
the spatial resolution was poor (Benz et al. 1990), or
the calculations were performed using crude approxi-
mations (Mochkovitch & Livio 1990). Very recently,
and using a Smoothed Particle Hydrodynamics code,
a series of simulations with the adequate spatial reso-
lution were performed and the nucleosynthesis of the
merger was studied (Guerrero, Isern, & Garćıa–Berro
2004; Lorén–Aguilar et al. 2005). The main results of
such simulations are that the less massive white dwarf
of the binary system is totally disrupted in a few or-
bital periods. A fraction of the secondary is directly
accreted onto the primary whereas the remnants of the
secondary form a heavy, rotationally–supported accre-
tion disk around the primary and little mass is ejected
http://arxiv.org/abs/0704.1258v1
mailto:garcia@fa.upc.edu, loren@fa.upc.edu, alba@fa.upc.edu
mailto:isern@ieec.fcr.es
mailto:bergeron@astro.umontreal.ca, dufourpa@astro.umontreal.ca, brassard@astro.umontreal.ca
2 Garćıa–Berro et al.
TABLE 1
Main results of the SPH simulations.
Run 0.4+0.8 0.4+1.0 0.4+1.2 0.6+0.6 0.6+0.8
MWD/M⊙ 0.99 1.16 1.30 0.90 1.09
Mdisk/M⊙ 0.21 0.24 0.30 0.30 0.29
Mej/M⊙ 10
−3 10−3 10−3 10−2 10−3
He 0.94 0.93 0.99 0 0
C 3× 10−2 2× 10−2 5× 10−3 0.4 0.4
O 1× 10−2 3× 10−3 3× 10−3 0.6 0.6
Ca 4× 10−5 2× 10−4 9× 10−6 0 0
Mg 3× 10−5 3× 10−5 6× 10−6 0 0
S 8× 10−5 2× 10−4 5× 10−7 0 0
Si 1× 10−4 2× 10−4 3× 10−5 0 0
Fe 9× 10−3 7× 10−3 5× 10−4 0 0
from the system. The resulting temperatures are rather
high (∼ 9× 108 K) during the most violent phases of the
merger, allowing for extensive nuclear processing.
The enhancement of the abundances of the most rele-
vant nuclear isotopes occurs when one of the coalescing
white dwarfs is made of pure He. Table 1 shows the
average chemical composition of the resulting disk and
the main characteristics of some selected simulations. It
should be noted, however, that the distribution of the
different elements in the disk is rather inhomogeneous.
Obviously those parts of the disk in which the mate-
rial of the secondary has been shocked have undergone
major nuclear processing. Hence, these regions are C–
and O–depleted and Si– and Fe–enhanced. In fact, the
innermost regions (R < 0.1R⊙) of the merged object,
which have approximately the shape of an ellipsoid, are
C– and O–rich. It is expected that this region would be
eventually accreted during the the first moments of the
cooling phase of the central object, leading to a more
massive white dwarf. We also find that the abundance
of intermediate–mass and iron–group elements is consid-
erably larger than that of C and O in the remnants of
the accretion stream (Guerrero, Isern, & Garćıa–Berro
2004) which are at larger distances, thus favoring smaller
accretion rates in order to explain the Ca abundance. In
any case, if the photospheric abundances of GD 362 are
to be explained with this scenario the accretion of He–
rich material is required.
Since He is also accreted onto the surface of GD 362,
the photospheric layers may contain significant amounts
of He which, at the effective temperature of GD 362
would be almost spectroscopically invisible. Thus,
GD 362 would still be classified as a DA white dwarf
provided that some H is present in its atmosphere. Con-
sequently, the H/He ratio can be regarded as a free
parameter. However, the presence of He in a cool
hydrogen-rich atmosphere affects the surface gravity de-
termined from spectroscopy, and thus the mass deter-
mination (Bergeron, Wesemael, & Fontaine 1991). In
Fig. 1 we show three almost identical synthetic spec-
tra representative of GD 362 with various assumed He
abundances. If He/H=10 is adopted then log g = 8.25 is
obtained (MWD ∼ 0.8M⊙) whereas if we adopt He/H=1
then the surface gravity turns out to be log g = 8.72.
This corresponds to a mass of the primary of MWD ∼
1.0M⊙, which can be obtained from the coalescence of
a 0.4 + 0.8M⊙ binary system. Additionally, in this case
the largest abundances of the relevant elements are ob-
Fig. 1.— Spectrum of GD 362 for three different helium abun-
dances. The black line shows the spectrum of GD 362 when a
pure hydrogen atmosphere is assumed, leading to a surface grav-
ity of log g = 9.12. For increasing amounts of He — namely
N(He)/N(H)=1, red curve, and N(He)/N(H)=10, blue curve
— the corresponding surface gravities are smaller. The inset
shows an expanded view of the predicted He line at 5876 Å for
N(He)/N(H)=10. High quality spectroscopic observations should
be able to confirm its presence, which has been recently reported
(Jura et al. 2007). See the electronic edition of the Journal for a
color version of this figure.
tained. Thus, we choose the 0.4 + 0.8M⊙ simulation as
our reference model, although reasonable results can be
obtained adopting other masses. In passing, we note that
nevertheless the He abundance is rather uncertain since
equally good fits to the observed spectrum of GD 362 can
be obtained with very different He abundances. Thus,
the mass of GD 362 is also rather uncertain. More im-
portantly, if the mechanism producing the unusual pho-
tospheric abundance pattern of GD 362 were to be ac-
cretion from the inner regions of the disk — which are
C– and O–rich — atomic lines of CI, and C2 molecular
bands should be rather apparent in the spectrum. But
the strength of these spectral features depends very much
on the adopted He abundance, because the atmospheric
pressure and the opacity also depend very much on the
H/He ratio, which is rather uncertain.
In order to know whether the chemical abundances
of GD 362 can be reproduced by direct accretion from
the keplerian disk we proceed as follows. Given the sur-
face gravity and the effective temperature of our model
we compute the luminosity, the radius and the cooling
time of the white dwarf according to a set of cooling
sequences (Salaris et al. 2000). We obtain respectively
log(LWD/L⊙) ≃ −3.283, log(RWD/R⊙) ≃ −2.096, and
tcool ≃ 2.2 Gyr. Hence, in this scenario GD 362 has
had enough time from the moment in which the merger
occurred to cool down, to accrete most of the C– and
O–rich region, settle down the accretion disk, and to
form dust. Additionally, the central white dwarf has had
time enough to accrete (at a rate much smaller than the
Bondi–Hoyle accretion rate) the small amount of hydro-
gen from the ISM to show spectroscopic hydrogen fea-
tures. We further assume that the accretion luminosity:
Lacc =
GṀMWD
Evidence for a merger of binary white dwarfs: the case of GD 362 3
Fig. 2.— Spectral energy distribution of GD 362. The figure
shows the spectral energy distribution of GD 362. The dotted line
shows the spectrum of a white dwarf with and effective temperature
of 9740 K and log g = 8.72, which corresponds to a mass of about
one solar mass, the dashed line shows the spectrum of a passive flat,
opaque dust disk and the solid line depicts the composite spectrum.
The observational data were obtained from Becklin et al. (2005).
is, in the worst of the cases, smaller than the luminosity
of the white dwarf. This provides us with an (extreme)
upper limit to the accretion rate, which turns out to be
1.3 × 10−13M⊙ yr
−1. Next, we assume that the abun-
dance of Ca is the result of the equilibrium between the
accreted material and gravitational diffusion:
ṀXdisk =
MenvXobs
τdiff
where Xdisk is the abundance in the accretion disk,
Xobs is the photospheric abundance, Menv is the mass
of the envelope of GD 362 and τdiff is the diffusion
timescale. The diffusion timescale of Ca for H–rich at-
mospheres is of the order of a few years. However, the
accreted material is He–rich, so the diffusion timescale
is probably more typical of a He–rich envelope, which
is much larger (Paquette et al. 1986), of the order of
τdiff ∼ 1.5 × 10
4 yr. Unfortunately, diffusion timescales
for mixed H/He envelopes do not exist. However, the
diffusion characteristic times scale as τdiff ∝ ρT
−1/2g−2
(Alcock & Illarionov 1980). We have computed detailed
atmosphere models for pure H, He/H=1 and He/H=10
and scaled the diffusion timescale using the values of
the density and the temperature at the base of the
convective zones and the appropriate chemical composi-
tion. For our fiducial composition (He/H=10) we obtain
τdiff ∼ 8.5 × 10
3 yr. From this we obtain the mass of
the region where diffusion occurs, which turns out to be
Menv ∼ 7.2× 10
−9M⊙, which is much smaller than that
obtained by accretion from the interstellar medium at the
Bondi–Hoyle accretion rate (∼ 1.5 × 10−6M⊙). Hence,
the photospheric abundances of GD 362 can be success-
fully explained by direct accretion from the surrounding
disk.
Now we assess whether the flux from the accretion disk
can be fitted by the results of our SPH simulations. In
Fig. 3.— Evolution of the rotational velocity for several field
strengths, the observational upper limit is shown as a horizontal
dashed line.
order to compute the flux radiated away from the system
two contributions must be taken into account. The first
one is the expected photospheric flux from the star, for
which we use the spectral energy distribution (BWD) of
a white dwarf of mass 1M⊙, at Teff ≈ 9740 K:
FWD = π
BWD(Teff), (3)
Given the luminosity of our model and the apparent
magnitude of GD 362 we obtain a distance of DWD =
33 pc. The second contribution to the total flux comes
from the emission of the disk, which for a passive flat,
opaque dust disk is (Chiang & Goldreich 1997; Jura
2003):
Fdisk ≃ 12π
1/3 cos i
2kBTs
∫ xout
ex − 1
dx (4)
where i is the inclination of the disk (which we adopt to
be face–on), xin = hν/kBTin and Tin = 1200 K is the
condensation temperature of silicate dust. The outer ra-
dius is taken from the results of our SPH simulations and
turns out to be Rout ≈ 1R⊙. The result is displayed in
Fig. 2. The dots are the observational data for GD 362.
The proposed scenario has apparently two weak points.
The first one is that infrared observations indicate the
presence of SiO. This requires that O should be more
abundant than C in order to form it. However our simu-
lations show that the ratio of C to O is a function of the
distance to the primary and, in some regions of the disk
the ratio is smaller than 1, allowing for the formation of
SiO in the accretion disk. Furthermore, after 2.2 Gyr of
evolution the resulting disk has had time to form planets
or asteroids with the subsequent chemical differentiation.
The second apparent drawback of the model is that
the central white dwarf rotates very fast. However, an
4 Garćıa–Berro et al.
unobservable magnetic field can brake down the central
star to acceptable velocities. Using the observed spec-
trum of GD 362 it is possible to set an upper limit to
the rotation speed of v sin i . 500 km s−1. We assume
that the central white dwarf has a weak magnetic field,
B. The magnetic torques that lead to spin–down are
caused by the interaction between the white dwarf and
the surrounding disk. The evolution of the angular ve-
locity due to the coupling of the white dwarf magneto-
sphere and the disk is given by (Livio & Pringle 1992;
Armitage & Clark 1996; Benacquista et al. 2003):
2µ2Ω3
sin2 α+
(RcRm)3/2
ṀR2mΩ
where µ = BR3WD, Rm is the magnetospheric radius of
the star, I is the moment of inertia, α is the angle be-
tween the rotation and magnetic axes (which we adopt
to be 30◦) and
is the corotation radius. The first term in this expression
corresponds to the magnetic dipole radiation emission,
the second to the disk–field coupling and the last one
to the angular momentum transferred from the disk to
the white dwarf. The magnetic linkage between the star
and the disk leads to a spin–down torque on the star if
the magnetospheric radius is large enough relative to the
corotation radius:
≥ 2−2/3 (7)
We adopt Rm = Rc. Solving numerically the previous
differential equation with the appropriate parameters for
our case, the evolution of the rotation velocity is shown
in figure 3. As can be seen a weak magnetic field of
about 50 kG is able to brake down the white dwarf to
velocities below the observational limit. This magnetic
field is much smaller than the upper limit of about 0.7
MG obtained from the spectrum of GD 362. Hence, our
scenario also accounts for the low rotational velocity of
GD 362, without adopting extreme assumptions.
3. CONCLUSIONS
We have shown that the anomalous photospheric chem-
ical composition of the DAZ white dwarf GD 362 and of
the infrared excess of surrounding disk can be quite nat-
urally explained assuming that this white dwarf is the
result of the coalescence of a binary white dwarf system.
This scenario provides a natural explanation of both the
observed photospheric abundances of GD 362 and of its
infrared excess without the need to invoke extreme as-
sumptions, like the accretion of a planet or an asteroid,
since direct accretion from the disk surrounding disk pro-
vides a self–consistent way of polluting the envelope of
the white dwarf with the required amounts of Ca, Mg,
Si and Fe. Moreover, this last scenario can be also well
accomodated within the framework of our scenario given
that the formation of planets and other minor bodies is
strongly enhanced in metal–rich disks. Hence, GD 362
could be the relic of a very rare event in our Galaxy: the
coalescence of a double white dwarf binary system.
This work has been partially supported by the MEC
grants AYA05–08013–C03–01 and 02, by the European
Union FEDER funds, by the AGAUR and by the
Barcelona Supercomputing Center (National Supercom-
puter Center). This work was also supported in part by
the NSERC (Canada). P. Bergeron is a Cottrell Scholar
of the Research Corporation.
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http://arXiv.org/abs/astro-ph/0702724
http://arXiv.org/abs/astro-ph/0701469
http://arXiv.org/abs/astro-ph/0702724

  GD 362 is a massive white dwarf with a spectrum suggesting a H-rich
atmosphere which also shows very high abundances of Ca, Mg, Fe and other
metals. However, for pure H-atmospheres the diffusion timescales are so short
that very extreme assumptions have to be made to account for the observed
abundances of metals. The most favored hypothesis is that the metals are
accreted from either a dusty disk or from an asteroid belt. Here we propose
that the envelope of GD 362 is dominated by He, which at these effective
temperatures is almost completely invisible in the spectrum. This assumption
strongly alleviates the problem, since the diffusion timescales are much larger
for He-dominated atmospheres. We also propose that the He-dominated atmosphere
of GD 362 is likely to be the result of the merger of a binary white dwarf.

Draft version October 31, 2018
Preprint typeset using LATEX style emulateapj v. 08/22/09
EVIDENCE FOR A MERGER OF BINARY WHITE DWARFS: THE CASE OF GD 362
E. Garćıa–Berro
, P. Lorén–Aguilar
and A.G. Pedemonte
Departament de F́ısica Aplicada, Universitat Politècnica de Catalunya, Av. del Canal Oĺımpic s/n, E-08860 Castelldefels (Barcelona),
Spain
J. Isern
Institut de Ciències de l’Espai (CSIC), Facultat de Ciències, Campus UAB, Torre C5-parell, E-08193 Bellaterra (Barcelona), Spain
P. Bergeron, P. Dufour and P. Brassard
Département de Physique, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Québec, Canada H3C 3J7
Draft version October 31, 2018
ABSTRACT
GD 362 is a massive white dwarf with a spectrum suggesting a H–rich atmosphere which also shows
very high abundances of Ca, Mg, Fe and other metals. However, for pure H–atmospheres the diffusion
timescales are so short that very extreme assumptions have to be made to account for the observed
abundances of metals. The most favored hypothesis is that the metals are accreted from either a
dusty disk or from an asteroid belt. Here we propose that the envelope of GD 362 is dominated
by He, which at these effective temperatures is almost completely invisible in the spectrum. This
assumption strongly alleviates the problem, since the diffusion timescales are much larger for He–
dominated atmospheres. We also propose that the He–dominated atmosphere of GD 362 is likely to
be the result of the merger of a binary white dwarf, a very rare event in our Galaxy, since the expected
galactic rate is ∼ 10−2 yr−1.
Subject headings: stars: white dwarfs — stars: chemically peculiar — stars: individual (GD 362)
1. INTRODUCTION
GD 362 has been interpreted as a massive, rather cool
(Teff ≈ 9740±50 K), white dwarf with a heavy accretion
disk surrounding it (Kilic et al. 2005; Becklin et al.
2005; Gianinas, Dufour, & Bergeron 2004). The dusty
disk around GD 362 produces an excess of infrared ra-
diation which amounts to ∼ 3% of the total stellar lu-
minosity. The chemical composition of GD 362 is also
rather singular, showing a hydrogen rich atmosphere
with very high abundances of Ca, Mg, Fe and other met-
als (Gianinas, Dufour, & Bergeron 2004). Thus, it is
classified as a massive DAZ (hydrogen–rich) white dwarf.
The origin of such particularly high photospheric abun-
dances — log(NCa/NH) = −5.2, log(NMg/NH) = −4.8
and log(NFe/NH) = −4.5 — and of the surrounding
dusty disk around it still remains a mystery. Since the
diffusion timescales for metals in H–rich white dwarfs
are of only a few years (Koester & Wilken 2006) very
extreme assumptions have to be made in order to ex-
plain these abundances. At present the most widely ac-
cepted scenario is disruption and accretion of a plane-
tary body, although for this scenario to be feasible the
planetary system should survive during the advanced
stages of stellar evolution, which by no means is guaran-
teed. Thus, the formation of an asteroid would require
the previous existence of a disk around this white dwarf
(Livio, Pringle, & Saffer 1992; Livio, Pringle, & Wood
2005). Particularly, a recent analysis (Villaver & Livio
Electronic address: garcia@fa.upc.edu, loren@fa.upc.edu, alba@fa.upc.edu
Electronic address: isern@ieec.fcr.es
Electronic address: bergeron@astro.umontreal.ca, dufourpa@astro.umontreal.ca, brassard@astro.umontreal.ca
1 Institut d’Estudis Espacials de Catalunya, Ed. Nexus-201, c/
Gran Capità 2–4, E-08034 Barcelona, Spain
2007) has shown that planets around white dwarfs with
masses MWD > 0.7M⊙ are generally expected to be
found at orbital radii r > 15 AU because they cannot
survive the planetary nebula phase and that if planets
are to be found at smaller orbital radii around mas-
sive white dwarfs, they had to form as the result of
the merger of two white dwarfs. It is also interesting
to note that there have been previous suggestions about
white dwarfs that are merger products — see for instance
Liebert, Bergeron & Holberg (2005) — but these claims
do not have yet any observational support.
2. THE SCENARIO
Another possibility is that some massive white dwarfs
are the result of the merger of a double white dwarf
close binary system. This scenario has been stud-
ied in several papers. However, in most of these pa-
pers either the resulting nucleosynthesis was not ad-
dressed (Segretain, Chabrier, & Mochkovitch 1997), or
the spatial resolution was poor (Benz et al. 1990), or
the calculations were performed using crude approxi-
mations (Mochkovitch & Livio 1990). Very recently,
and using a Smoothed Particle Hydrodynamics code,
a series of simulations with the adequate spatial reso-
lution were performed and the nucleosynthesis of the
merger was studied (Guerrero, Isern, & Garćıa–Berro
2004; Lorén–Aguilar et al. 2005). The main results of
such simulations are that the less massive white dwarf
of the binary system is totally disrupted in a few or-
bital periods. A fraction of the secondary is directly
accreted onto the primary whereas the remnants of the
secondary form a heavy, rotationally–supported accre-
tion disk around the primary and little mass is ejected
http://arxiv.org/abs/0704.1258v1
mailto:garcia@fa.upc.edu, loren@fa.upc.edu, alba@fa.upc.edu
mailto:isern@ieec.fcr.es
mailto:bergeron@astro.umontreal.ca, dufourpa@astro.umontreal.ca, brassard@astro.umontreal.ca
2 Garćıa–Berro et al.
TABLE 1
Main results of the SPH simulations.
Run 0.4+0.8 0.4+1.0 0.4+1.2 0.6+0.6 0.6+0.8
MWD/M⊙ 0.99 1.16 1.30 0.90 1.09
Mdisk/M⊙ 0.21 0.24 0.30 0.30 0.29
Mej/M⊙ 10
−3 10−3 10−3 10−2 10−3
He 0.94 0.93 0.99 0 0
C 3× 10−2 2× 10−2 5× 10−3 0.4 0.4
O 1× 10−2 3× 10−3 3× 10−3 0.6 0.6
Ca 4× 10−5 2× 10−4 9× 10−6 0 0
Mg 3× 10−5 3× 10−5 6× 10−6 0 0
S 8× 10−5 2× 10−4 5× 10−7 0 0
Si 1× 10−4 2× 10−4 3× 10−5 0 0
Fe 9× 10−3 7× 10−3 5× 10−4 0 0
from the system. The resulting temperatures are rather
high (∼ 9× 108 K) during the most violent phases of the
merger, allowing for extensive nuclear processing.
The enhancement of the abundances of the most rele-
vant nuclear isotopes occurs when one of the coalescing
white dwarfs is made of pure He. Table 1 shows the
average chemical composition of the resulting disk and
the main characteristics of some selected simulations. It
should be noted, however, that the distribution of the
different elements in the disk is rather inhomogeneous.
Obviously those parts of the disk in which the mate-
rial of the secondary has been shocked have undergone
major nuclear processing. Hence, these regions are C–
and O–depleted and Si– and Fe–enhanced. In fact, the
innermost regions (R < 0.1R⊙) of the merged object,
which have approximately the shape of an ellipsoid, are
C– and O–rich. It is expected that this region would be
eventually accreted during the the first moments of the
cooling phase of the central object, leading to a more
massive white dwarf. We also find that the abundance
of intermediate–mass and iron–group elements is consid-
erably larger than that of C and O in the remnants of
the accretion stream (Guerrero, Isern, & Garćıa–Berro
2004) which are at larger distances, thus favoring smaller
accretion rates in order to explain the Ca abundance. In
any case, if the photospheric abundances of GD 362 are
to be explained with this scenario the accretion of He–
rich material is required.
Since He is also accreted onto the surface of GD 362,
the photospheric layers may contain significant amounts
of He which, at the effective temperature of GD 362
would be almost spectroscopically invisible. Thus,
GD 362 would still be classified as a DA white dwarf
provided that some H is present in its atmosphere. Con-
sequently, the H/He ratio can be regarded as a free
parameter. However, the presence of He in a cool
hydrogen-rich atmosphere affects the surface gravity de-
termined from spectroscopy, and thus the mass deter-
mination (Bergeron, Wesemael, & Fontaine 1991). In
Fig. 1 we show three almost identical synthetic spec-
tra representative of GD 362 with various assumed He
abundances. If He/H=10 is adopted then log g = 8.25 is
obtained (MWD ∼ 0.8M⊙) whereas if we adopt He/H=1
then the surface gravity turns out to be log g = 8.72.
This corresponds to a mass of the primary of MWD ∼
1.0M⊙, which can be obtained from the coalescence of
a 0.4 + 0.8M⊙ binary system. Additionally, in this case
the largest abundances of the relevant elements are ob-
Fig. 1.— Spectrum of GD 362 for three different helium abun-
dances. The black line shows the spectrum of GD 362 when a
pure hydrogen atmosphere is assumed, leading to a surface grav-
ity of log g = 9.12. For increasing amounts of He — namely
N(He)/N(H)=1, red curve, and N(He)/N(H)=10, blue curve
— the corresponding surface gravities are smaller. The inset
shows an expanded view of the predicted He line at 5876 Å for
N(He)/N(H)=10. High quality spectroscopic observations should
be able to confirm its presence, which has been recently reported
(Jura et al. 2007). See the electronic edition of the Journal for a
color version of this figure.
tained. Thus, we choose the 0.4 + 0.8M⊙ simulation as
our reference model, although reasonable results can be
obtained adopting other masses. In passing, we note that
nevertheless the He abundance is rather uncertain since
equally good fits to the observed spectrum of GD 362 can
be obtained with very different He abundances. Thus,
the mass of GD 362 is also rather uncertain. More im-
portantly, if the mechanism producing the unusual pho-
tospheric abundance pattern of GD 362 were to be ac-
cretion from the inner regions of the disk — which are
C– and O–rich — atomic lines of CI, and C2 molecular
bands should be rather apparent in the spectrum. But
the strength of these spectral features depends very much
on the adopted He abundance, because the atmospheric
pressure and the opacity also depend very much on the
H/He ratio, which is rather uncertain.
In order to know whether the chemical abundances
of GD 362 can be reproduced by direct accretion from
the keplerian disk we proceed as follows. Given the sur-
face gravity and the effective temperature of our model
we compute the luminosity, the radius and the cooling
time of the white dwarf according to a set of cooling
sequences (Salaris et al. 2000). We obtain respectively
log(LWD/L⊙) ≃ −3.283, log(RWD/R⊙) ≃ −2.096, and
tcool ≃ 2.2 Gyr. Hence, in this scenario GD 362 has
had enough time from the moment in which the merger
occurred to cool down, to accrete most of the C– and
O–rich region, settle down the accretion disk, and to
form dust. Additionally, the central white dwarf has had
time enough to accrete (at a rate much smaller than the
Bondi–Hoyle accretion rate) the small amount of hydro-
gen from the ISM to show spectroscopic hydrogen fea-
tures. We further assume that the accretion luminosity:
Lacc =
GṀMWD
Evidence for a merger of binary white dwarfs: the case of GD 362 3
Fig. 2.— Spectral energy distribution of GD 362. The figure
shows the spectral energy distribution of GD 362. The dotted line
shows the spectrum of a white dwarf with and effective temperature
of 9740 K and log g = 8.72, which corresponds to a mass of about
one solar mass, the dashed line shows the spectrum of a passive flat,
opaque dust disk and the solid line depicts the composite spectrum.
The observational data were obtained from Becklin et al. (2005).
is, in the worst of the cases, smaller than the luminosity
of the white dwarf. This provides us with an (extreme)
upper limit to the accretion rate, which turns out to be
1.3 × 10−13M⊙ yr
−1. Next, we assume that the abun-
dance of Ca is the result of the equilibrium between the
accreted material and gravitational diffusion:
ṀXdisk =
MenvXobs
τdiff
where Xdisk is the abundance in the accretion disk,
Xobs is the photospheric abundance, Menv is the mass
of the envelope of GD 362 and τdiff is the diffusion
timescale. The diffusion timescale of Ca for H–rich at-
mospheres is of the order of a few years. However, the
accreted material is He–rich, so the diffusion timescale
is probably more typical of a He–rich envelope, which
is much larger (Paquette et al. 1986), of the order of
τdiff ∼ 1.5 × 10
4 yr. Unfortunately, diffusion timescales
for mixed H/He envelopes do not exist. However, the
diffusion characteristic times scale as τdiff ∝ ρT
−1/2g−2
(Alcock & Illarionov 1980). We have computed detailed
atmosphere models for pure H, He/H=1 and He/H=10
and scaled the diffusion timescale using the values of
the density and the temperature at the base of the
convective zones and the appropriate chemical composi-
tion. For our fiducial composition (He/H=10) we obtain
τdiff ∼ 8.5 × 10
3 yr. From this we obtain the mass of
the region where diffusion occurs, which turns out to be
Menv ∼ 7.2× 10
−9M⊙, which is much smaller than that
obtained by accretion from the interstellar medium at the
Bondi–Hoyle accretion rate (∼ 1.5 × 10−6M⊙). Hence,
the photospheric abundances of GD 362 can be success-
fully explained by direct accretion from the surrounding
disk.
Now we assess whether the flux from the accretion disk
can be fitted by the results of our SPH simulations. In
Fig. 3.— Evolution of the rotational velocity for several field
strengths, the observational upper limit is shown as a horizontal
dashed line.
order to compute the flux radiated away from the system
two contributions must be taken into account. The first
one is the expected photospheric flux from the star, for
which we use the spectral energy distribution (BWD) of
a white dwarf of mass 1M⊙, at Teff ≈ 9740 K:
FWD = π
BWD(Teff), (3)
Given the luminosity of our model and the apparent
magnitude of GD 362 we obtain a distance of DWD =
33 pc. The second contribution to the total flux comes
from the emission of the disk, which for a passive flat,
opaque dust disk is (Chiang & Goldreich 1997; Jura
2003):
Fdisk ≃ 12π
1/3 cos i
2kBTs
∫ xout
ex − 1
dx (4)
where i is the inclination of the disk (which we adopt to
be face–on), xin = hν/kBTin and Tin = 1200 K is the
condensation temperature of silicate dust. The outer ra-
dius is taken from the results of our SPH simulations and
turns out to be Rout ≈ 1R⊙. The result is displayed in
Fig. 2. The dots are the observational data for GD 362.
The proposed scenario has apparently two weak points.
The first one is that infrared observations indicate the
presence of SiO. This requires that O should be more
abundant than C in order to form it. However our simu-
lations show that the ratio of C to O is a function of the
distance to the primary and, in some regions of the disk
the ratio is smaller than 1, allowing for the formation of
SiO in the accretion disk. Furthermore, after 2.2 Gyr of
evolution the resulting disk has had time to form planets
or asteroids with the subsequent chemical differentiation.
The second apparent drawback of the model is that
the central white dwarf rotates very fast. However, an
4 Garćıa–Berro et al.
unobservable magnetic field can brake down the central
star to acceptable velocities. Using the observed spec-
trum of GD 362 it is possible to set an upper limit to
the rotation speed of v sin i . 500 km s−1. We assume
that the central white dwarf has a weak magnetic field,
B. The magnetic torques that lead to spin–down are
caused by the interaction between the white dwarf and
the surrounding disk. The evolution of the angular ve-
locity due to the coupling of the white dwarf magneto-
sphere and the disk is given by (Livio & Pringle 1992;
Armitage & Clark 1996; Benacquista et al. 2003):
2µ2Ω3
sin2 α+
(RcRm)3/2
ṀR2mΩ
where µ = BR3WD, Rm is the magnetospheric radius of
the star, I is the moment of inertia, α is the angle be-
tween the rotation and magnetic axes (which we adopt
to be 30◦) and
is the corotation radius. The first term in this expression
corresponds to the magnetic dipole radiation emission,
the second to the disk–field coupling and the last one
to the angular momentum transferred from the disk to
the white dwarf. The magnetic linkage between the star
and the disk leads to a spin–down torque on the star if
the magnetospheric radius is large enough relative to the
corotation radius:
≥ 2−2/3 (7)
We adopt Rm = Rc. Solving numerically the previous
differential equation with the appropriate parameters for
our case, the evolution of the rotation velocity is shown
in figure 3. As can be seen a weak magnetic field of
about 50 kG is able to brake down the white dwarf to
velocities below the observational limit. This magnetic
field is much smaller than the upper limit of about 0.7
MG obtained from the spectrum of GD 362. Hence, our
scenario also accounts for the low rotational velocity of
GD 362, without adopting extreme assumptions.
3. CONCLUSIONS
We have shown that the anomalous photospheric chem-
ical composition of the DAZ white dwarf GD 362 and of
the infrared excess of surrounding disk can be quite nat-
urally explained assuming that this white dwarf is the
result of the coalescence of a binary white dwarf system.
This scenario provides a natural explanation of both the
observed photospheric abundances of GD 362 and of its
infrared excess without the need to invoke extreme as-
sumptions, like the accretion of a planet or an asteroid,
since direct accretion from the disk surrounding disk pro-
vides a self–consistent way of polluting the envelope of
the white dwarf with the required amounts of Ca, Mg,
Si and Fe. Moreover, this last scenario can be also well
accomodated within the framework of our scenario given
that the formation of planets and other minor bodies is
strongly enhanced in metal–rich disks. Hence, GD 362
could be the relic of a very rare event in our Galaxy: the
coalescence of a double white dwarf binary system.
This work has been partially supported by the MEC
grants AYA05–08013–C03–01 and 02, by the European
Union FEDER funds, by the AGAUR and by the
Barcelona Supercomputing Center (National Supercom-
puter Center). This work was also supported in part by
the NSERC (Canada). P. Bergeron is a Cottrell Scholar
of the Research Corporation.
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