REMNANTS OF BINARY WHITE DWARF MERGERS

Type Ia supernovae (SNeIa) are commonly accepted to be the observed transient produced after a thermonuclear detonation inside a white dwarf star. While the preferred mechanism for producing SNeIa involves accretion from an evolved main-sequence star onto a white dwarf (Whelan & Iben 1973; Nomoto 1982a, 1982b; Hillebrandt & Niemeyer 2000; Yoon & Langer 2004), the observed SNeIa rate is incompatible with the narrow range of helium accretion rates that initiate a carbon detonation as opposed to accretion-induced collapse or classical novae (Nomoto & Kondo 1991; Hardin et al. 2000; Pain et al. 2002; Ruiter et al. 2009). Moreover, many recent observations of abnormally luminous SNeIa have been interpreted as having derived from double-degenerate systems involving two white dwarfs.

For example, photometric observations of SN 2007if suggest 1.6 ± 0.1$\thinspace M_{\odot }$ of ⁵⁶Ni was formed, implying a progenitor mass of 2.4 ± 0.2$\thinspace M_{\odot }$ (Scalzo et al. 2010), which is well above the Chandrasekhar limit (Chandrasekhar 1931). Spectroscopic observations of SN 2009dc suggest ≳ 1.2$\thinspace M_{\odot }$ of ⁵⁶Ni (Tanaka et al. 2010), depending on the assumed dust absorption. Since 0.92$\thinspace M_{\odot }$ of ⁵⁶Ni is the greatest yield a Chandrasekhar mass can produce (Khokhlov et al. 1993), this yield also implies a super-Chandrasekhar progenitor mass. And observations of SN 2003fg by Howell et al. (2006) and of SN 2006gz by Hicken et al. (2007) infer ∼1.3$\thinspace M_{\odot }$ of ⁵⁶Ni each.

Generally, for the purposes of cosmological measurements, obvious double-degenerate candidates are excluded from SNeIa surveys. The Phillips relation, or the width–luminosity relation (WLR), which established SNeIa as standard candles (Phillips 1993), relates the peak luminosity of an SNIa to the change in magnitude after 15 days. The WLR for standard SNeIa indicates that SNeIa with bright peak magnitudes also decay at a slower rate than dimmer SNeIa. This is often thought to be the result of a relationship between the ⁵⁶Ni yield and the opacity of the ejecta material, assuming a total mass not exceeding the Chandrasekhar mass. However, a double-degenerate system may have up to twice the Chandrasekhar mass, and so the relationship between the ⁵⁶Ni yield and the ejecta opacity need not be similar to single-degenerate scenarios, and the WLR may not be applicable to these SNeIa. In fact, it is more likely that for a given ⁵⁶Ni production and energy deposition history, an increased ejecta mass results in an increased opacity, reducing the peak magnitude and broadening the light curve in a fashion that is the inverse of the standard WLR (Pinto & Eastman 2000; Mazzali et al. 2001; Mazzali & Podsiadlowski 2006; Kasen et al. 2009).

Complicating matters is the possibility that SNeIa deriving from double-degenerate progenitors can have ordinary ⁵⁶Ni yields, depending on the progenitor mechanism (see, e.g., collisional mechanisms in Raskin et al. 2009, 2010 and Rosswog et al. 2009) and the final, central densities of the degenerate material before ignition. Thus, double-degenerate SNeIa may be masquerading as typical SNeIa. If they do not conform to the WLR, they may introduce systematic errors into cosmological surveys. In order to reduce the scatter in the Hubble diagram, we must first establish whether double-degenerate SNeIa are standardizable, and if not, we must identify the telltale signatures of a double-degenerate progenitor mechanism.

The most probable double-degenerate progenitor scenario involves two white dwarfs in a tight binary, though other progenitor systems have been considered (Benz et al. 1989; Raskin et al. 2009; Rosswog et al. 2009). Binary white dwarf systems were first seriously explored as plausible SNIa progenitors by Iben & Tutukov (1984) and Webbink (1984). In such a system, tidal dissipation and gravitational radiation drive the binary pair into an ever closer orbit. Eventually, the least massive white dwarf, being physically larger as R∝M^−1/3, overflows its Roche lobe and begins to accrete material onto the primary or more massive companion star. For many mass combinations, this is a fundamentally unstable process in which the loss of mass from the secondary causes it to outgrow its Roche lobe faster than its orbit widens due to conservation of angular momentum (see, e.g., Marsh et al. 2004).

Benz et al. (1990) performed one of the first simulations of double-degenerate mergers, examining a binary system consisting of a 1.2$\thinspace M_{\odot }$ white dwarf primary and a 0.9$\thinspace M_{\odot }$ white dwarf secondary. They used a smooth particle hydrodynamics code with 3000 particles per star and found that the merger remnant consisted of a 1.7$\thinspace M_{\odot }$ core surrounded by a rotationally supported disk. This is more massive than the Chandrasekhar limit, but they concluded that the central object was not entirely degenerate, having been considerably heated, and thus, much of the object's support against gravitational collapse came simply from thermal pressure.

Since this pioneering work, others have revisited the white dwarf merger scenario with up-to-date simulation codes and higher resolutions than were possible in the past (see, e.g., Yoon et al. 2007; Lorén-Aguilar et al. 2009). In this paper, we revisit white dwarf merger simulations, examining a wide range of possible mass combinations with high resolution, more accurate initial conditions, and up-to-date physics for the equation of state (EOS) and nuclear reaction network. The structure of this paper is as follows. In Section 2, we outline our methods and initial conditions. We discuss the results of our simulations in Section 3, and compare our work to previous studies of white dwarf mergers in Section 4. Finally, in Section 5, we summarize our results and conclusions and discuss possible avenues for advancing remnant evolution in future studies.

As in our previous work on white dwarf collisions (Raskin et al. 2010), we employ the three-dimensional smooth particle hydrodynamics code SNSPH (Fryer et al. 2006). Particle codes are ideally suited to simulating binary systems as they excel at conserving angular momentum, which is crucial for properly simulating accretion flows in binary systems. We include a Helmholtz free energy EOS (Timmes & Arnett 1999; Timmes & Swesty 2000) that spans a range of possible thermodynamic conditions, from cold, electron-degenerate gas, to hot, non-degenerate gas, and includes Coulomb corrections and photon pressures. For nucleosynthesis, we use a 13-isotope, α-chain nuclear network with a hybrid photodisintegration capture scheme as described in Raskin et al. (2010), which utilizes a similar method for sub-cycling the reaction rates to what is implemented in MAESTRO (Nonaka et al. 2010). We limit our hydrodynamic time step to that which results in at most a 30% change in internal energy (u) due to nuclear reactions as this was found in Raskin et al. (2010) to strike the right balance between accuracy of the result and efficiency of the calculation. If nuclear reactions are not important, the time step is not allowed to grow larger than what is derived from the Courant–Friedrichs–Lewey condition.

For our constant mass particle arrangements, we use Weighted Voronoi Tessellations (WVT; Diehl & Statler 2006), which ensures the lowest energy particle configuration for our stars. We initiate each of our carbon–oxygen white dwarfs with 5 × 10⁵ particles per star and a uniform composition of 50% ¹²C and 50% ¹⁶O plus a thin atmosphere (no greater than q(He) = M_He/M < 0.025) of pure ⁴He that approximates atmospheric mass estimates from stellar evolution models (Iben & Tutukov 1985; Salaris et al. 2000). The ⁴He masses for each star are given in Table 1. Each of our stars is relaxed to an isothermal temperature of roughly 10⁷ K. The noise in the temperatures of the isothermal stars due to the particle nature of our simulations is of order ∼10⁶ K.

There is some debate over whether white dwarfs in tight binaries will be tidally locked. The timescales for inspiral and for spinning up the white dwarfs are roughly commensurate. Yoon et al. (2007) initialized their binary systems with tidally locked white dwarfs, while Lorén-Aguilar et al. (2009) assumed they were not tidally locked. Since many close white dwarf binaries are expected to be tidally locked (Claret & Cunha 1997; Marsh et al. 2004; Geier et al. 2008), we make a conscious choice to simulate our binaries in a tidally locked configuration.

We initially allow our stars to fall from rest toward each other until there is noticeable tidal distortion in the least massive star. This is done via an iterative process whereby the stars free-fall, and at intervals of 5 s each, all particles have their velocities reset to zero and free-fall begins again. This ensures that the binary system is in a metastable configuration and that the stars are still in hydrostatic equilibrium after tidal distortions have first appeared.

This method avoids stellar oscillations and unnaturally high accretion rates that result from the secondary white dwarf overflowing its Roche lobe immediately upon the start of the simulation. Figure 1 shows the effective potential at t = 0 in the rotating frame of the 0.64$\thinspace M_{\odot }$ + 0.81$\thinspace M_{\odot }$ merger simulation, where Φ_eff = Φ_g − 1/2Ω²r² normalized to 1.79 × 10¹⁷ erg g⁻¹ with Ω being the orbital velocity. As is evident, none of the particles in the 0.64$\thinspace M_{\odot }$ star lie outside of the Roche lobe, and no particle has a higher potential than the potential wall between the two stars. Dan et al. (2011) discuss how previous efforts in this area have overestimated the accretion rates due to inappropriate initial conditions, and this can have implications for the final arrangement of the system and on the long-term evolution prospects.

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Our iterative method for creating the initial conditions of the mergers avoids immediate and rapid mass-transfer while also placing the stars very near the stage where mass transfer would naturally begin. At this stage, the stars are set into their tidally locked orbits about their common center of mass with the initial periods given in Table 2 for each of our chosen mass combinations. Over several orbits, the tidal distortions grow and material from the secondary star overflows its Roche lobe and mass transfer begins. Our mass combinations all lie safely in the regime of unstable mass transfer (Marsh et al. 2004), and so resolving a steady accretion stream that could possibly lead to stable accretion using a discretized method like SPH is not important.

Pakmor et al. (2010) also explored a double-degenerate merger of two 0.9$\thinspace M_{\odot }$ white dwarfs in a hybrid SPH/grid-code simulation study that was the first of its kind to track a merger from the initial inspiral to the final detonation and subsequent homologous expansion phase. They found that if such a merger features a prompt detonation before settling into a metastable core–disk configuration, the resultant supernova would be exceptionally dim, appearing much like 1991bg. However, the detonation in their simulations was inserted by hand at the location at which the large-scale conditions matched those found in offline calculations to produce microphysical conditions necessary for detonation.

At first glance, this is a reasonable approach since initiations of detonations are often difficult to resolve in large hydrodynamical simulations. While the conditions across a single SPH particle may not be sufficient to initiate a detonation on their own, it is reasonable to suspect that temperature fluctuations that are unresolved in SPH could lead to a detonation that would not be captured in a simulation like this. However, Seitenzahl et al. (2009) have demonstrated that spontaneous detonations of ¹²C/¹⁶O material depend very sensitively on both the local thermodynamic conditions and the conditions of the surrounding medium. They find that unless the surrounding medium is also >10⁹ K, thermodynamic conditions that would otherwise lead to a detonation (e.g., 2.9 × 10⁹ K and 3.8 × 10⁶ g cm⁻³ as was used in Pakmor et al. 2010) would require pre-detonation hotspots to be of order 10⁷ cm in extent. In fact, many of our simulations produced similar detonation preconditions in local hotspots at the surface of the accretor star as in Pakmor et al. (2010), but these hotspots were isolated in a medium of relatively colder material. Moreover, they were not gravitationally confined as they were part of an orbiting flow. Instead, they merely expanded outward hydrodynamically and floated away from the surface, cooling rapidly. This rapid cooling quenched any significant carbon burning and staved off spontaneous carbon detonations arising naturally in the simulations. More importantly, the initial conditions used in Pakmor et al. (2010) vastly overestimate the accretion flow, and thus the accretion shock and shock heating of the disk material. For these reasons, we choose not to insert detonations into those hotspots.

In our simulations of equal-mass binaries, such as simulation 5 with $0.8\hbox{$\thinspace M_{\odot }$}\times 2$, depicted in Figure 2, there is first a protracted accretion phase that persists for several orbits. During this time, both stars lose material, and thus angular momentum, through the L2 and L3 points. This brings the stars closer together, hastening their mass loss. The helium atmospheres that the stars were initially given also burn fairly rapidly to carbon and oxygen during this phase. Finally, one of the stars is disrupted entirely, owing primarily to slight inhomogeneities in the constituent stars. At this stage, ≈2% of the carbon is burned into heavier, silicon-group elements, but the iron-group yield from the merger is negligible.

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After many orbital periods, the system settles into a metastable configuration with a dense core, a shock-heated, sub-Keplerian disk, and a semi-degenerate interface between them. As Figure 3 indicates, much of the core has been heated slightly to ≈2 × 10⁸ K, while the interface reaches temperatures near 10⁹ K. The core and interface also exhibit solid-body rotation out to ≈1.05$\thinspace M_{\odot }$.

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While the disk is large in spatial extent with an outer radius of ≈0.8 R_☉, it represents ≈35% of the total system mass or ≈0.57$\thinspace M_{\odot }$. Moreover, most of the mass of the disk lies much nearer to the core, with the half-mass radius at ≈0.02 R_☉, as compared to the radius of the core, ≈0.008 R_☉. This disk is optically thick, and while the timescale for molecular diffusion is of order Myr, radiation at the surface of the disk will drive convection. With convection turning over much of the gas in the disk and acting as a viscosity, angular momentum will be lost from the inner parts of the disk and it will accrete onto the core. We can estimate the timescale for accretion using an α-disk prescription for the viscosity (Shakura & Sunyaev 1973) as

$$\begin{equation} \tau _{{\rm acc}}\simeq \alpha ^{-1} \left(\frac{r_d}{2h}\right)^2\Omega ^{-1}, \end{equation} \tag{ 1 }$$

where α is a free parameter that relates the viscosity to the speed of sound times the scale height h, r_d is the half-mass radius of the disk, and Ω is the angular speed. As Figure 4 shows for an edge-on view of the disk in simulation 5 with the core removed, there remains considerable dense material at high latitudes, with h/r_d ≈ 0.1. For an assumed α ≈ 0.1, we find that the accretion time for these disks is of order ∼100 orbital times. This is similar to the timescale derived by van Kerkwijk et al. (2010) for the results of simulations carried out in Lorén-Aguilar et al. (2009).

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Simulation 8 ($0.96\hbox{$\thinspace M_{\odot }$}\times 2$, depicted in Figure 5) exhibited very much the same behavior as simulation 5 ($0.81\hbox{$\thinspace M_{\odot }$}\times 2$) with both featuring Mach >2 accretion shocks. Here, the larger densities of the constituent stars and faster orbital velocity resulted in greater shock heating, with some of the material reaching temperatures of ≈2 × 10⁹ K in a very similar fashion to the simulation studied in Pakmor et al. (2010). However, as evidenced by subsequent snapshots, this shock-heated gas simply expands and cools, joining the flow of material into the disk.

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As Figure 6 demonstrates, the remnant core is slightly colder and the core–disk interface is slightly hotter than the remnant in simulation 5. This implies that while the shock heating of the disk and interface was stronger, the shock was less able to penetrate through the primary star. In fact, the core of the primary remains essentially unchanged from its original state.

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For simulation 1, $0.64\hbox{$\thinspace M_{\odot }$}\times 2$, the common-envelope phase is foreshortened, and unlike the more massive pairs of equal-mass white dwarfs, the cores of both stars merge at the center of mass, as depicted in Figure 7. This is most likely due to the stars being less massive and, thus, more susceptible to tidal disruption.

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The merged core of the remnant in simulation 1 has a temperature of ∼2 × 10⁸ K and exhibits solid-body rotation out to ≈0.84$\thinspace M_{\odot }$. Roughly 2% of the initial helium is burned to carbon and oxygen in this simulation, and with ≈0.03$\thinspace M_{\odot }$ of helium still remaining in the disk, sub-Chandrasekhar detonation mechanisms that require helium atmospheres may still be viable for this system.

For unequal-mass simulations, the least massive star is always disrupted entirely, forming an accretion disk around the primary. This is not unlike the equal-mass simulations with the more massive constituent stars. However, for mass pairs that involved a 1.06$\thinspace M_{\odot }$ primary, the accretion stream shock on the surface of the primary was sufficiently strong to sustain a helium detonation. This is most clearly evident in simulation 9, 0.96$\thinspace M_{\odot }$ + 1.06$\thinspace M_{\odot }$, depicted in Figure 8.

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This detonation burns ≈60% of the helium on the surface of the 1.06$\thinspace M_{\odot }$ primary and propagates a shock through its core, raising its core temperature slightly and expanding its outer layers on the opposite side of the accretion shock. The detonation shock joins the accretion shock in the accretion stream and stalls as the material there is moving at near the sound speed onto the primary. The energy released from the initial detonation is ∼10⁴⁹ erg, however, the detonation was not sufficiently energetic to burn carbon in considerable quantities or to unbind the primary star.

Surface helium detonations in white dwarf binary mergers were also observed in grid-based simulations by Guillochon et al. (2010). They found that Kelvin–Helmholtz instabilities were the culprit mechanism for initiating a surface detonation on a 0.9$\thinspace M_{\odot }$ primary, and that the likelihood of a detonation depended very sensitively on the stream geometry and spatial resolution. SPH methods are not well suited for resolving instabilities of this type, and so, given that all of our 1.06$\thinspace M_{\odot }$ primary simulations featured helium detonations, it is likely that for massive primaries, helium detonations are a robustly replicated result.

This has significant implications for double-detonation progenitor models (e.g., Nomoto 1982a, 1982b; Woosley & Weaver 1994; Fink et al. 2010) wherein a helium detonation initiates a shock that ignites a carbon detonation in the core of a sub-Chandrasekhar white dwarf. Fink et al. (2007) found that caustics were responsible for igniting the carbon–oxygen cores in their simulations of 1.0$\thinspace M_{\odot }$ white dwarfs. Our simulations and those of Guillochon et al. (2010) did not result in double detonations, and in our case, we cannot capture caustics at our resolution limit and with the SPH method. Instead, we observed only a single shock propagating through the carbon–oxygen core, launched by the initial helium detonation. However, it is likely that for larger primary masses, the single shock we observed would be sufficient to ignite a carbon detonation as the higher central densities of more massive white dwarfs reduce the length scales required for spontaneous detonation of ¹²C/¹⁶O.

Except for the helium detonation, simulation 9 proceeds in a very similar fashion to the equal-mass simulations already discussed. While the 0.96$\thinspace M_{\odot }$ secondary is entirely disrupted into an accretion disk, the core of the 1.06$\thinspace M_{\odot }$ primary is largely unchanged, though slightly heated by the detonation shock. As shown in Figure 9, the core–disk interface is much hotter than previous simulations, reaching a maximum temperature of 1.25 × 10⁹ K. The core exhibits solid-body rotation out to ≈1.23$\thinspace M_{\odot }$.

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Simulations 4 and 7, 0.64$\thinspace M_{\odot }$ + 1.06$\thinspace M_{\odot }$ and 0.81$\thinspace M_{\odot }$ + 1.06$\thinspace M_{\odot }$, both featured these helium detonations as well. The detonation for simulation 4 is illustrated in Figure 10. As in simulation 9, 0.96$\thinspace M_{\odot }$ + 1.06$\thinspace M_{\odot }$, the detonation propagated a shock through the primary, expanding its outer layers, but it did not significantly affect the remnant properties or the formation of a disk. The properties of the disk in this simulation and of the disks in each of our simulations are given in Table 3.

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In each of the simulation remnants that featured a cold core with a hot disk, a non-negligible fraction of the inner parts of the disks were supported mainly by thermal pressure, as their orbital velocities were sub-Keplerian. Moreover, much of the inner portions of the disks had orbital energies below that which would sustain an orbit at the surface of the core. It follows then, that as these disks cool, their inner parts will accrete onto their cores, irrespective of angular momentum transfer, and may do so on rapid timescales.

The disks of simulations 8–10 retain considerable material (≳0.2$\thinspace M_{\odot }$) held aloft only by thermal pressures, suggesting that the cores in those scenarios may grow to super-Chandrasekhar masses from cooling alone, before the disk becomes appreciably thin. If this proves to be the case in future simulations that include radiative cooling, any supernovae that result from these scenarios would appear very much unlike standard SNeIa as they would be enshrouded by thick disk material.

3.1. Convergence

To test convergence of our results, we ran simulation 5, $0.81\hbox{$\thinspace M_{\odot }$}\times 2$, at various particle resolutions including 10⁵, 2 × 10⁵, 5 × 10⁵, 10⁶, and 2 × 10⁶ particles per star, as this simulation contained equal and representative white dwarf masses, and thus provides the best opportunity to examine resolution effects. In all of our trials, the values for M_disk, r_d, and Ω differed by about 2%, as seen in Figure 11. From this and the fact that these values did not exhibit a trend in any particular direction, we conclude that the results of our other simulations at 5 × 10⁵ particles per star are indeed converged.

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At very high particle counts, such as our simulation with 4 × 10⁶ particles total, the asymmetry of the stars stemming naturally from a particle-based method is not sufficient to disrupt one of the stars onto the other. Instead, the system settled into a stable equilibrium with a matter bridge extending between the two stars. Since this configuration is highly unlikely in nature, we reduced the mass of one of the stars by 2% in the initial condition state to restore an asymmetry. Even in this scenario, the three variables tested for convergence, M_c, r_d, and Ω are nearly identical to the previous trials, only reduced slightly due to the reduced total system mass. From this, we conclude that when there is an asymmetry either from numerical noise or enforced by mass constraints, the physics that leads to the final configuration is robust at our resolutions.

Other groups have simulated white dwarf mergers of various mass pairs and at varying resolutions in the past. Table 4, while not meant to be exhaustive, summarizes many of the past works on this topic and provides a comparison to the work outlined in this paper.

Table 4. Tabular Summary of Simulation Studies of White Dwarf Mergers

No.	Reference	EOS	Network	Masses	Particles
				($\thinspace M_{\odot }$)
1	Benz et al. 1990	Chandraa	⋅⋅⋅	0.9+1.2	3 × 103
2	Rasio & Shapiro 1995	Polytrope	⋅⋅⋅	⋅⋅⋅	4 × 104
3	Segretain & Chabrier 1997	Chandra	⋅⋅⋅	0.6+0.9	5.83 × 104
4	Guerrero et al. 2004	3 press.b	14 isotope	0.6+0.8, 0.6+1.0,	4 × 104
				0.8+1.0
5	Yoon et al. 2007	Helmholtzc	QSE+α-chain	0.6+0.9	2 × 105
6	Lorén-Aguilar et al. 2009	3 press.	14 isotope	0.3+0.5, 0.4+0.8,	4 × 105
				0.6+0.6, 0.6+0.8,
				0.6+1.2
7	Pakmor et al. 2010, 2011	Helmholtz	13 isotope	0.89+0.89, 0.7+0.9,	106
				0.76+0.9, 0.81+0.9,
				0.89+0.9
8	Dan et al. 2011	Helmholtz	7 isotope	Manyd	4 × 104–2 × 105
9	This work	Helmholtz	13 isotope	See Table 2	106

Notes. ^aChandrasekhar 1939. ^bIdeal gas + Fermi pressure + radiation. ^cTimmes & Arnett 1999. ^d0.2 + 0.8, 0.3 + 1.1, 0.5 + 1.2, 0.3 + 0.6, 0.6 + 0.9, 0.2 + 0.3, 0.3 + 0.4, 0.9 + 1.2, 0.45 + 0.9, 0.45 + 0.67.

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Groups 1–3 completed pioneering work, modeling white dwarf mergers in smooth-particle hydrodynamics codes. Their particle resolutions were quite low compared to what is possible with current computing resources, and their EOSs were mainly analytical approximations for degenerate matter. They also did not include any nuclear reaction networks in their calculations. Rasio & Shapiro (1995) consider the hydrodynamics of binary coalescence between two polytropic stars using a rotating-frame potential. Accounting for tidal distortions on the separation distance for Roche overflow, and thus capturing more realistic accretion rates, they find merger times on the order of minutes, rather than tens of seconds as other groups had found. Rasio & Shapiro (1995) did not explicitly list the masses of their binary configurations since the hydrodynamical response using a polytropic EOS should depend only on mass ratio.

With improved computing power, merger calculations began to incorporate more accurate EOSs and to include nuclear reaction networks such as those used by groups 4–6. Resolutions were also moderately improved, and more mass combinations were explored such as those of Lorén-Aguilar et al. (2009). And while Lorén-Aguilar et al. (2009) simulated what was, up to then, the largest sample of mass combinations, each of the groups numbered 4–6 used approximate initial conditions that started the stars much closer than in Rasio & Shapiro (1995), which had the result of overestimating the accretion stream and underestimated the breakup time of the secondary star. Lorén-Aguilar et al. (2009) also did not attempt mass combinations where both stars had $M>0.6\hbox{$\thinspace M_{\odot }$}$. Moreover, in their conclusions, Yoon et al. (2007) singled out three important factors that would be important for subsequent calculations: (1) the effects of tidal forces on the heating of the stars and disk, (2) the presence of hydrogen/helium atmospheres, and (3) a larger range of mass combinations that can lead to varying final remnant configurations. All of these are taken into account in the present work.

More recently, Pakmor et al. (2010, 2011) simulated a wide variety of almost exclusively high-mass pairs with the aim of studying the outcomes of early detonations in white dwarf mergers. However, as stated previously, their initial conditions were approximate and prone to overestimating the accretion rate of the disk material.

The work of Rasio & Shapiro (1995) and of Dan et al. (2011) motivated our choice of initial conditions. This group also studied a wide range of mass combinations, but as their primary focus was on Roche overflow and accretion rates, their resolutions were comparably low and their nuclear network was minimal. In the work outlined in this paper, we have attempted to combine the best features of all of these previous works including high resolutions, a wide range of mass combinations (and high-mass pairs), a robust EOS and nuclear network, and accurate initial conditions that properly model accretion rates. We have also included helium atmospheres in order to gauge how robust helium detonations are on the surfaces of the primary stars, and to what extent those detonations affect the final merger remnants.

Double-degenerate progenitor scenarios are drawing new interest among the supernova community. They have the potential to explain some of the confounding mysteries that remain about SNeIa, and to enhance their usefulness as cosmological probes. Here, we have conducted a large survey of white dwarf binary merger models in order to begin to understand how these systems evolve, and to piece together some of the observational signatures of double-degenerate SNeIa.

In each of our simulations, the merger remnant consisted of a cold, degenerate core surrounded by a hot accretion disk, with h/r_d ≈ 0.1. The only exception to this remnant configuration was the simulation of two 0.64$\thinspace M_{\odot }$ white dwarfs, where the cores of both stars merged at the center of mass, heating the remnant core considerably and lifting most of its degeneracy. Since it is unlikely that two identical-mass white dwarfs would form in a binary in nature, this scenario might seem of trivial importance, but the merging of the cores was less the result of their masses being identical than it was of the stars being highly susceptible to tidal disruption. Our other equal-mass simulations with more massive constituent stars featured merger scenarios wherein one of the stars was completely disrupted into an accretion disk around the core of the other, provided there was a non-trivial asymmetry between the two. Therefore, it is likely that merger scenarios involving slightly unequal but low-mass white dwarfs might also exhibit core merging, though more simulations are certainly needed to confirm this conjecture.

Evolving these metastable remnants further will require the implementation of new physics beyond hydrodynamics and nuclear burning. Since the disks are optically thick, radiative losses from the surface are the dominant evolutionary mechanism, and efforts are underway to incorporate this process. As the surface layers lose energy through radiation, the material will sink to lower latitudes, driving convective currents that will increase the disk viscosity. We expect this viscosity will mimic an α-disk prescription, and thus the accretion times will be of order 100 orbital times. However, the three most massive combinations simulated have disk configurations that suggest the cores might grow to become super-Chandrasekhar masses on shorter timescales, after cooling has removed some of the thermal support for the inner portions of the disks.

While none of our simulations exhibited prompt carbon detonations, all of the simulations that included a 1.06$\thinspace M_{\odot }$ primary did exhibit prompt helium detonations on the surface of the primary. These helium detonations were not sufficiently energetic to significantly burn much of the carbon or to unbind either of the constituent stars, but the detonation shocks they produced did alter the structure of the primary before complete merger. Moreover, at ∼10⁴⁹ erg, the energy these detonations released is likely sufficient to be observable by many of the upcoming transient surveys, such as the Large Synoptic Survey Telescope mission.

Whether white dwarf mergers produce SNeIa is still an open question. Our simulations and others' represent only the beginnings of our exploration of this progenitor mechanism. Preliminary results look very promising, and it is doubtless that the viability of mergers as SNeIa progenitors will be established in the near term. Meanwhile, it remains an exciting time to be exploring these dynamical scenarios that continue to surprise us.

This work was supported by the National Science Foundation under grant AST 08-06720, by the National Aeronautics and Space Administration under NESSF grant PVS0401, and by a grant from the Arizona State University chapter of the GPSA. All simulations were conducted at the Advanced Computing Center at Arizona State University. We also thank Peter Hoeflich, Philip Chang, Marten van Kerkwijk, Dan Kasen, Stephan Rosswog, James Guillochon, Enrico Ramirez-Ruiz, Ken Shen, Andy Nonaka, and Ann Almgren for insightful discussions during the creation of this manuscript.