Evidence for a merger of binary white dwarfs: the case of GD 362

TL;DR

This paper suggests that GD 362's metal-rich atmosphere is likely He-dominated due to a white dwarf merger, explaining observed abundances with longer diffusion timescales and supporting a merger origin.

Contribution

It introduces the hypothesis that GD 362's He-dominated atmosphere results from a binary white dwarf merger, providing a new explanation for its metal abundances.

Findings

He-dominated atmosphere explains metal abundances better.

Merger of binary white dwarfs likely caused the atmosphere composition.

Diffusion timescales are longer in He atmospheres, supporting the hypothesis.

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.

Figures

Tables

Table 1. 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
$M_{\mathrm{WD}}/M_{☉}$	0.99	1.16	1.30	0.90	1.09
$M_{\mathrm{disk}}/M_{☉}$	0.21	0.24	0.30	0.30	0.29
$M_{\mathrm{ej}}/M_{☉}$	${10}^{-3}$	${10}^{-3}$	${10}^{-3}$	${10}^{-2}$	${10}^{-3}$
He	0.94	0.93	0.99	0	0
C	$3\times {10}^{-2}$	$2\times {10}^{-2}$	$5\times {10}^{-3}$	0.4	0.4
O	$1\times {10}^{-2}$	$3\times {10}^{-3}$	$3\times {10}^{-3}$	0.6	0.6
Ca	$4\times {10}^{-5}$	$2\times {10}^{-4}$	$9\times {10}^{-6}$	0	0
Mg	$3\times {10}^{-5}$	$3\times {10}^{-5}$	$6\times {10}^{-6}$	0	0
S	$8\times {10}^{-5}$	$2\times {10}^{-4}$	$5\times {10}^{-7}$	0	0
Si	$1\times {10}^{-4}$	$2\times {10}^{-4}$	$3\times {10}^{-5}$	0	0
Fe	$9\times {10}^{-3}$	$7\times {10}^{-3}$	$5\times {10}^{-4}$	0	0

Equations

$$L_{\mathrm{acc}}=\frac{G\dot{M}{M}_{\mathrm{WD}}}{R_{\mathrm{WD}}}$$

$$\dot{M}{X}_{\mathrm{disk}}=\frac{M_{\mathrm{env}}{X}_{\mathrm{obs}}}{{\tau }_{\mathrm{diff}}}$$

$$F_{\mathrm{WD}}=\pi {\left(\frac{R_{\mathrm{WD}}}{D_{\mathrm{WD}}}\right)}^2{B}_{\mathrm{WD}}(T_{\mathrm{eff}}),$$

$$F_{\mathrm{disk}}\simeq$$

$$\dot{\Omega }$$

$$R_{\mathrm{c}}={\left(\frac{G{M}_{\mathrm{WD}}}{{\Omega }^2}\right)}^{1/3}$$

$$\left(\frac{R_{\mathrm{m}}}{R_{\mathrm{c}}}\right)\ge 2^{-2/3}$$

Full text

1. Introduction

GD 362 has been interpreted as a massive, rather cool ($T_{\rm eff}\approx 9740\pm 50$ 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 radiation which amounts to $\sim 3\%$ of the total stellar luminosity. 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 metals (Gianinas, Dufour, & Bergeron, 2004). Thus, it is classified as a massive DAZ (hydrogen–rich) white dwarf. The origin of such particularly high photospheric abundances — $\log(N_{\rm Ca}/N_{\rm H})=-5.2$, $\log(N_{\rm Mg}/N_{\rm H})=-4.8$ and $\log(N_{\rm Fe}/N_{\rm H})=-4.5$ — 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 explain these abundances. At present the most widely accepted scenario is disruption and accretion of a planetary 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 guaranteed. 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, 2007) has shown that planets around white dwarfs with masses $M_{\rm WD}>0.7\,M_{\sun}$ 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 massive 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 studied in several papers. However, in most of these papers either the resulting nucleosynthesis was not addressed (Segretain, Chabrier, & Mochkovitch, 1997), or the spatial resolution was poor (Benz et al., 1990), or the calculations were performed using crude approximations (Mochkovitch & Livio, 1990). Very recently, and using a Smoothed Particle Hydrodynamics code, a series of simulations with the adequate spatial resolution were performed and the nucleosynthesis of the merger was studied (Guerrero, Isern, & García–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 orbital periods. A fraction of the secondary is directly accreted onto the primary whereas the remnants of the secondary form a heavy, rotationally–supported accretion disk around the primary and little mass is ejected from the system. The resulting temperatures are rather high ($\sim 9\times 10^{8}$ K) during the most violent phases of the merger, allowing for extensive nuclear processing.

The enhancement of the abundances of the most relevant 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 material 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 ($R<0.1\,R_{\sun}$) 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 considerably larger than that of C and O in the remnants of the accretion stream (Guerrero, Isern, & García–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. Consequently, 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 determined from spectroscopy, and thus the mass determination (Bergeron, Wesemael, & Fontaine, 1991). In Fig. 1 we show three almost identical synthetic spectra representative of GD 362 with various assumed He abundances. If He/H=10 is adopted then $\log g=8.25$ is obtained ($M_{\rm WD}\sim 0.8\,M_{\sun}$) 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 $M_{\rm WD}\sim 1.0\,M_{\sun}$, which can be obtained from the coalescence of a $0.4+0.8\,M_{\sun}$ binary system. Additionally, in this case the largest abundances of the relevant elements are obtained. Thus, we choose the $0.4+0.8\,M_{\sun}$ 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 importantly, if the mechanism producing the unusual photospheric abundance pattern of GD 362 were to be accretion 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 surface 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 $\log(L_{\rm WD}/L_{\sun})\simeq-3.283$, $\log(R_{\rm WD}/R_{\sun})\simeq-2.096$, and $t_{\rm cool}\simeq 2.2$ 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 hydrogen from the ISM to show spectroscopic hydrogen features. We further assume that the accretion luminosity:

[TABLE]

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 $1.3\times 10^{-13}\,M_{\sun}\,{\rm yr}^{-1}$. Next, we assume that the abundance of Ca is the result of the equilibrium between the accreted material and gravitational diffusion:

[TABLE]

where $X_{\rm disk}$ is the abundance in the accretion disk, $X_{\rm obs}$ is the photospheric abundance, $M_{\rm env}$ is the mass of the envelope of GD 362 and $\tau_{\rm diff}$ is the diffusion timescale. The diffusion timescale of Ca for H–rich atmospheres 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 $\tau_{\rm diff}\sim 1.5\times 10^{4}$ yr. Unfortunately, diffusion timescales for mixed H/He envelopes do not exist. However, the diffusion characteristic times scale as $\tau_{\rm diff}\propto\rho T^{-1/2}g^{-2}$ (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 composition. For our fiducial composition (He/H=10) we obtain $\tau_{\rm diff}\sim 8.5\times 10^{3}$ yr. From this we obtain the mass of the region where diffusion occurs, which turns out to be $M_{\rm env}\sim 7.2\times 10^{-9}\,M_{\sun}$, which is much smaller than that obtained by accretion from the interstellar medium at the Bondi–Hoyle accretion rate $(\sim 1.5\times 10^{-6}M_{\sun}$). Hence, the photospheric abundances of GD 362 can be successfully 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 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 ($B_{\rm WD}$) of a white dwarf of mass $1\,M_{\sun}$, at $T_{\rm eff}\approx 9740$ K:

[TABLE]

Given the luminosity of our model and the apparent magnitude of GD 362 we obtain a distance of $D_{\rm WD}=33$ 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):

[TABLE]

where $i$ is the inclination of the disk (which we adopt to be face–on), $x_{\rm in}=h\nu/k_{\rm B}T_{\rm in}$ and $T_{\rm in}=1200$ K is the condensation temperature of silicate dust. The outer radius is taken from the results of our SPH simulations and turns out to be $R_{\rm out}\approx 1\,R_{\sun}$. 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 simulations 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 unobservable magnetic field can brake down the central star to acceptable velocities. Using the observed spectrum of GD 362 it is possible to set an upper limit to the rotation speed of $v\sin i\lesssim 500$ 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 velocity due to the coupling of the white dwarf magnetosphere and the disk is given by (Livio & Pringle, 1992; Armitage & Clark, 1996; Benacquista et al., 2003):

[TABLE]

where $\mu=BR^{3}_{\rm WD}$, $R_{\rm m}$ is the magnetospheric radius of the star, $I$ is the moment of inertia, $\alpha$ is the angle between the rotation and magnetic axes (which we adopt to be $30^{\circ}$) and

[TABLE]

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:

[TABLE]

We adopt $R_{\rm m}=R_{\rm c}$. 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 chemical composition of the DAZ white dwarf GD 362 and of the infrared excess of surrounding disk can be quite naturally 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 assumptions, like the accretion of a planet or an asteroid, since direct accretion from the disk surrounding disk provides 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 Supercomputer Center). This work was also supported in part by the NSERC (Canada). P. Bergeron is a Cottrell Scholar of the Research Corporation.