ABSTRACT
We present the results of a systematic numerical study of an alternative progenitor scenario to produce Type Ia supernova explosions, which is not restricted to the ignition of a CO white dwarf (WD) near the Chandrasekhar mass. In this scenario, a shock-triggered thermonuclear explosion ensues from the collision of two WDs. Consistent modeling of the gas dynamics together with nuclear reactions using both a smoothed particle and a grid-based hydrodynamics code are performed to study the viability of this alternative progenitor channel. We find that shock-triggered ignition and the synthesis of Ni are in fact a natural outcome for moderately massive WD pairs colliding close to head-on. We use a multi-dimensional radiative transfer code to calculate the emergent broadband light curves and spectral time series of these events. The synthetic spectra and light curves compare well to those of normal Type Ia supernovae over a similar B-band decline rate and are broadly consistent with the Phillips relation, although a mild dependence on viewing angle is observed due to the asymmetry of the ejected debris. While event rates within galactic centers and globular clusters are found to be much too low to explain the bulk of the Type Ia supernovae population, they may be frequent enough to make as much as a one percent contribution to the overall rate. Although these rate estimates are still subject to substantial uncertainties, they do suggest that dense stellar systems should provide upcoming supernova surveys with hundreds of such collision-induced thermonuclear explosions per year.
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1. INTRODUCTION
Type Ia supernovae (SNe Ia) are of major astrophysical relevance. They have acquired particular cosmological significance as a probe of the scale and geometry of the universe, providing the first evidence for its acceleration (Riess et al. 1998; Perlmutter et al. 1999; Astier et al. 2006). These results depend crucially on the assumption that SNe Ia are standard candles. This assumption could be tested if the origins of SNe Ia are recognized. Knowledge of their nature is also of importance for understanding the metallicity evolution and star formation history of galaxies. Yet, despite their relevance, no consensus on the nature of their progenitor systems has been reached.
While there is broad agreement that the disintegration of a white dwarf (WD) in a thermonuclear explosion constitutes the supernova event itself, there are two main classes of competing models for the events that lead to the explosion. In the single-degenerate scenario, the exploding WD accretes from a non-degenerate stellar companion (Whelan & Iben 1973; Nomoto 1982), which is expected to survive and be potentially identifiable. In the double-degenerate scenario, the donor star is also a WD. The most commonly discussed progenitor system involves the coalescence of two CO WDs (Iben & Tutukov 1984; Webbink 1984), which after explosion should leave no remnant. There has been no conclusive proof to date that either scenario can lead to normal SNe Ia, nor has the evidence that the SN Ia rate is different for different stellar populations led to any firm conclusions. Therefore, any new observational or theoretical constraint on the progenitor systems is of great value.
Here we present an alternative evolutionary scenario to produce an SN Ia, which is not restricted to mass transfer in gravitationally bound double stellar systems. This new paradigm considers WDs that reside within dense stellar systems where the stars are sufficiently close to each other to make collisions quite likely. The resultant shock compression could then lead to densities which exceed the threshold for pycnonuclear reactions so that thermonuclear runaway ensues. Understanding the feasibility of this channel for producing successful thermonuclear explosions as well as exploring the observational manifestations of such phenomena are the main purpose of this Letter. The layout is as follows. A concise summary of the numerical methods and the initial models is given in Section 2. We describe the detailed hydrodynamic simulations in Section 3, while the resulting broadband light curves and spectra together with a discussion of the relevance of this new progenitor channel to upcoming supernova surveys are presented in Section 4.
2. NUMERICAL SCHEMES AND INITIAL MODELS
As two stars approach each other to within a few stellar radii, their mutual gravitational interactions lead to the development of large-scale tidal distortions that substantially alter their global structures. If the trajectories of the stars bring them so close to each other that they experience a collision, the response of the stellar material to the impact is critical in understanding the future evolution of the system. As such, it is no longer appropriate to treat the stars as point masses, and a hydrodynamical description of the encounter becomes necessary. The outcome of a collision between two WDs depends in an essential way on several factors: their masses and nuclear compositions; their relative speed; and the distance of closest approach.
To study this problem, we use two complementary approaches: the Eulerian, adaptive-mesh hydrodynamics code FLASH (Fryxell et al. 2000), and a Lagrangian hydrodynamics code (Rosswog et al. 2008, 2009) based on the smoothed particle hydrodynamics (SPH) method (Benz 1990; Monaghan 2005; Rosswog 2009). Both codes incorporate the Helmholtz equation of state (Timmes & Swesty 2000) and similar, small nuclear reaction networks tuned to correctly reproduce nuclear energy release (Hix et al. 1998; Timmes 1999; Timmes et al. 2000), but they differ in their treatment of hydrodynamics and gravity. Using the same stellar models and impact conditions, this approach not only provides a classic code verification, but also in particular allows us to gain unique insight into the physics of WD encounters.
Some of the questions at the forefront of our attention are the effects of the initial nuclear composition and masses of the WDs as well as the impact conditions. We have performed a large set of three-dimensional calculations. A detailed account of all models will be given elsewhere, here our focus is on central collisions. A summary of the performed calculations is given in Table 1. The stars with 0.4 M☉ are instantiated as pure He, those with larger masses as a homogeneous mixture of 50% C and 50% O. All stars are initially cold (104 K), placed at a mutual distance of three times their combined unperturbed stellar radii and with the relative free-fall velocities of the corresponding point mass values.
Table 1. Masses in M☉, Initial Separation a0 in R1 + R2, Densities and Energies in cgs units, "Res." Refers to the Particle Number for SPH Calculations, and to Maximum Linear Resolution in cm for FLASH
| Run | Masses | a0 | Res. | log(ρmax) | Tmax,9 | log(Enuc) | mesc | Remnant | ||
|---|---|---|---|---|---|---|---|---|---|---|
| SPH | ||||||||||
| A | 0.2, 0.2 | 5 | 2.0 × 105 | 5.97 | 2.5 | 48.53 | 0.044 | Hot, He-WD | ||
| B | 0.4, 0.4 | 3 | 2.0 × 106 | 7.16 | 4.0 | 51.19 | 0.80 | None | ||
| C | 0.5, 0.5 | 3 | 1.0 × 106 | 7.20 | 4.8 | 50.00 | 0.21 | CO-WD in Ne-Mg-Si cloud | ||
| D | 0.6, 0.6 | 3 | 2.0 × 106 | 7.92 | 8.9 | 51.21 | 1.20 | None | ||
| E | 0.4, 0.9 | 3 | 2.5 × 106 | 7.56 | 3.4 | 50.75 | 0.40 | CO-WD in He-Si cloud | ||
| F | 0.6, 0.9 | 3 | 2.0 × 106 | 8.40 | 7.9 | 50.61 | 0.30 | CO-WD in C-O-Si-Fe cloud | ||
| G | 0.9, 0.9 | 3 | 1.0 × 106 | 7.55 | 6.3 | 51.41 | 1.80 | None | ||
| FLASH | ||||||||||
| H | 0.6, 0.6 | 3 | 4.9 × 106 | 7.47 | 5.5 | 51.11 | 1.20 | None |
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3. SHOCK-TRIGGERED THERMONUCLEAR EXPLOSIONS FROM WHITE DWARF IMPACTS
The relative velocity at contact is entirely dominated by the mutual gravitational attraction, i.e., it is much larger than typical globular cluster (GC) velocity dispersions, σGC ≈ 10 km s−1, vrel = 4000 km s−1(Mtot/1.2 M☉)1/2(2 × 109 cm/(R1 + R2))1/2 > cs. The sound velocity cs in the core of a 0.6 M☉ WD is about 2600 km s−1, and thus shocks are a natural result of a WD collision. Figure 1 shows the thermodynamic evolution of the most common combination of masses, 2 × 0.6 M☉. The snapshots of density and temperature in the upper two rows were obtained with SPH, the lower two are the result of FLASH (19-isotope network, minimum linear resolution 5 × 106 cm). The details of the collision differ slightly in the two simulation environments, which is evident in the shock geometries. However, the overall behavior is similar: shortly after contact, a discus-shaped, shock-heated region forms in which nuclear processing occurs. Since the ignition site is not coincident with the original central density peak of either WD, the shocks more quickly propagate through the shallow density gradient that is perpendicular to the direction of infall. As a result, the hot processed material first breaks out through a ring which lies in a plane that is parallel to the collisional plane. It is only when the rear of the stars have passed through the shock fronts that a significant overall expansion can set in. Apart from hydrodynamics and gravity, the codes also differ in the used reaction networks, the SPH code is coupled to a seven-species network (Hix et al. 1998), while the FLASH run uses a 19-isotope network (Timmes 1999). As a test of the energy generation accuracy, we have used both networks along 1000 thermodynamic trajectories extracted from the SPH simulation. Maximum deviations in the resulting energy generation were 15%, while 95% of the trajectories agreed to better than 5%. The mass fractions reported in this Letter are all post-processed or direct results of the 19-isotope network. While the networks could be partly responsible for the shock structure differences the latter may also be influenced by the local resolution and details how burning directly in the shock is suppressed in both codes. A further difference between both runs is the spike-like feature at the rear side of the star in the FLASH simulation, this is an artifact of the rapid advection across the grid. Despite these differences our main conclusions are robust: the shocks trigger an explosion producing a substantial amount of 56Ni (0.32 M☉ for SPH, 0.16 M☉ for FLASH).
Figure 1. Comparison of density and temperature evolution of the central collision of two 0.6 M☉ CO WDs. The upper two rows are the SPH results, the lower two are produced by FLASH. The shown box length is 3 × 109 cm, limiting values color bar (left to right): log(ρ)max = [7.12, 7.05, 6.91, 6.84, 6.70, 6.64], T9,max = [1.49, 4.79, 3.99, 3.65, 3.39, 3.24], log(ρ)min = 2, and T9,min = 0 everywhere.
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Standard image High-resolution imageMass-segregated environments may favor encounters of more massive WDs, though. We therefore show in Figure 2 the outcome of a 2 × 0.9 M☉ collision (run G; left: density and temperature, right: mass fractions). This event yields 0.66 M☉ of 56Ni, comparable to a typical SN Ia.
Figure 2. Collision between two 0.9 M☉ WDs: density and temperature (left) and nuclear mass fractions (right). Note the different scales in both panels.
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Standard image High-resolution imageThe topic of WD collisions has been pioneered by Benz et al. (1989), in which they modeled the WDs with an equation of state containing contributions from degenerate, relativistic electrons, from a Boltzmann gas of nuclei and from photons. Moreover, they coupled their SPH code to a 14-isotope network. At that time, their calculations were restricted to 5000 SPH particles resulting in a moderate numerical resolution. Although in some cases substantial nuclear burning took place, none of their models resulted in a complete disintegration of the WD pairs. For comparison, we performed a test run of a head-on collision between two 0.6 M☉ WDs using 5000 SPH particles in total, similar to their run 1. Consistent with their work, we find a surviving remnant and only 0.30 M☉ of expelled material (0.09 M☉ in their work). The degraded numerical resolution results in a 1 order of magnitude reduction of the released nuclear energy compared with our run D. The remaining differences between our test run and the results of Benz et al. are mainly due to the different equations of state, but they may to some extent also reflect the differences in the networks and the advances in the SPH method. Our overall results are similar to those of Raskin et al. (2009) which were submitted while our Letter was under review.
4. DISCUSSION
4.1. Light Curves and Spectra
Some WD collisions should produce luminous light curves powered by the decay of radioactive 56Ni synthesized in the explosion. To predict the observable emission, we post-processed select models using the radiative transfer code SEDONA (Kasen et al. 2006). This code is three-dimensional, time-dependent, multi-wavelength, and includes a detailed treatment of the physics of 56Ni decay and bound–bound line opacity. As initial conditions, we used the SPH results with post-processed abundances for the 2 × 0.6 M☉ (run D) and 2 × 0.9 M☉ (run G) collisions, at a simulation time late enough that the ejected material had reached the free, homologous phase of expansion. Given the axial symmetry of head-on encounters, the results where azimuthally averaged onto a cylindrical grid.
In Figure 3 (right panel), we show synthetic spectra of the models, computed at the peak of the light curve (∼20 days after collision). The model spectra closely resemble those of normal SNe Ia, with broad P-Cygni line features due to Si ii, S ii, and Ca ii. This outcome is not surprising given that the ejecta compositional stratification (Figure 1) is very similar to that of standard SNe Ia models, with an outer layer of intermediate-mass elements and an inner core of iron group elements. The asymmetry of the ejected debris introduces some variation of the spectrum with viewing angle, most prominently in the ultraviolet where the radiation transport is most sensitive to line blanketing opacity. The velocity of the supernova photosphere, as measured form the Doppler shift of the line absorption minima, is 13,000–16,000 km s−1, similar to, though slightly higher than that observed in average SNe Ia.
Figure 3. Radiative transfer calculations of the light curves and spectra resulting from central collisions of 2 × 0.6 M☉ (run D) and 2 × 0.9 M☉ (run G) WD pairs. The synthetic B-band light curves (central panel) closely resemble those of normal Type Ia supernovae. The peak brightness and decline rate of the light curves vary somewhat with the viewing angle (left panel), but are broadly consistent with the slope and spread of the observed Phillips relation (gray shaded band). The maximum light spectra (right panel) closely resemble that of the normal Type Ia supernova SN 1981B.
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The light curves of the WD collisions (Figure 3, center panel) also resemble those of SNe Ia. As expected, the models which produced more 56Ni have brighter light curves which decline more slowly. The calculated peak magnitudes and B-band decline rates lie within the range of typical SNe Ia, and are consistent with the slope and normalization of the observed Phillips relation (Figure 3, left panel). This result is not totally unexpected, given that the principle parameter underlying the Phillips relation is the 56Ni mass, which influences both the supernova luminosity and the ejecta opacity (Kasen & Woosley 2007, and references therein). On the other hand, the light curve width is also sensitive to the total ejected mass. In collision models, unlike most standard SN Ia scenarios, this value is not constrained to be the Chandrasekhar mass. Thus, although the particular models studied here roughly obey the Phillips relation, in detail WD collisions could show small but systematic deviations.
4.2. Diversity
The explosion mechanism reported here is not tied to a particular mass scale and therefore allows for considerably more diversity. As mentioned above, collisions between WDs provide a pathway to ignite CO WDs that completely disintegrate the WD pair. In contrast, for low-mass collisions (run A) or for collisions between a CO and a He WD a remnant remains, which, in the latter case, produces an identifiable outcome: a hot, high-speed (∼1000 km s−1) CO WD engulfed by a cloud of intermediate-mass elements.
The mechanism discussed here is found to work for the collision of two 0.4 M☉ He WDs, but does not lead to an explosion in the case of 2 × 0.5 M☉. This is mainly the result of the different available fuel–helium burning releases more energy on the way to iron group elements (
He→Fe = 1.73 MeV nucleon−1, CO→Fe = 0.98 MeV nucleon−1). Due to the WD mass function, collisions between 0.6 M☉ WDs are expected to dominate unless they occur in a strongly mass-segregated environments where more massive WDs would then be preferred. On average, however, this SN Ia channel will preferably ignite lighter WDs than standard channels (Hillebrandt & Niemeyer 2000; Podsiadlowski et al. 2008) and, as a result, the nucleosynthetic yields should be less neutron-rich due to the slower Ye-evolution via electron captures.
4.3. Detection Prospects
In order to critically evaluate the outcome of these ideas, the frequency of such encounters must be addressed. For a core-collapsed GC, the high densities in the core completely dominate the collision rate. We assume the WDs to be distributed homogeneously within a spherical core of radius rc. We further assume that the total number density nwd and stellar velocity dispersion σc are constant within rc. Together with the dominating gravitational focusing, this means we can approximate the total collision rate as νcol = 20 Gyr−1 f1 f2(nc/3 × 106 pc−3)2(rc/0.1 pc)3(σc/10 km s−1)−1([m1 + m2]/1 M☉)(rcol/5 × 103 km), where fi ⩽ 1 is the fractional number of stars of type i within rc and we use the properties of the well-studied, prototypical core-collapsed GC M15 (van den Bosch et al. 2006). Fokker–Planck model fits to M15 predict the presence of a significant population of WDs with M > 0.7 M☉, so that fi > 0.5. By setting the distance of closest approach to the sum of the radii of the two WDs, rcol = r1 + r2, an estimate of the collision rate Rcol ≈ 102fccf1 f2 yr−1 Gpc −3 can be obtained by multiplying νcol (per GC) with the average GC space density of ngc = 4.2 Mpc-3 (Brodie & Strader 2006). Here, ngc is derived by combining the number of GCs per galaxy with the galaxy luminosity density distribution, and fcc is the fraction of core-collapsed clusters. This is most likely an underestimation since, for example, the effect of binaries in GCs can increase νcol by a moderate factor (∼2; J. Fregeau 2009, private communication). Moreover, if M 15 formed at higher initial concentration, it might have been in (or around) deepest core collapse for a longer time, significantly increasing the (average) νcol. Numerical experiments for the dominant 2 × 0.6 M☉ case indicate that about 20% of the collisions may result in explosions.
Although these rates are still subject to significant uncertainties such as whether other GCs follow a similar core-collapse evolution, they indicate that WD collisions in their dense cores are not unlikely and can contribute with a modest fraction to the SNe Ia population, whose event rates are estimated to be of order a few 104 yr−1 Gpc−3 (Cappellaro et al. 1999). In addition, a number of collisions are also expected from ultra-compact dwarf galaxies (Hilker et al. 1999; Drinkwater et al. 2000, 2003), the hypercompact stellar systems that form when supermassive black holes are ejected from galactic centers by the action gravitational wave recoil (Merritt et al. 2009) and from more "typical" galactic centers.
The transient sky at faint magnitudes is poorly known, but there are major efforts under way that would increase the discovery rate for SNe Ia from a few thousands to about hundreds of thousands per year. While the estimates given above are much too low to explain the bulk of the SNe Ia population, they may be frequent enough to provide upcoming supernova surveys with hundreds of collision-induced SNe Ia per year.
We thank Holger Baumgardt, Lars Bildsten, John Fregeau, Ken Shen, and Glenn van de Ven for very useful discussions. The simulations presented in this Letter were performed on the JUMP computer of the Höchstleistungsrechenzentrum Jülich and the Pleiades computer of UCSC. We acknowledge support from DFG grant RO 3399 (S.R.), the DOE Program for SciDAC DE-FC02-01ER41176 (D.K. and E.R.), and The David and Lucile Packard Foundation (J.G. and E.R.). Support for D.K. was provided by NASA through Hubble fellowship grant HST-HF-01208.01-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555.