Neutrino and gravitational wave signal of a delayed-detonation model of Type Ia supernovae
The progenitor system(s) and the explosion mechanism(s) of Type Ia supernovae (SNe Ia) are still under debate. Non-electromagnetic observables, in particular gravitational waves and neutrino emission, of thermonuclear supernovae are a complementary window to light curves and spectra for studying these enigmatic objects. A leading model for SNe Ia is the thermonuclear incineration of a near-Chandrasekhar mass carbon-oxygen white dwarf star in a “delayed-detonation”. We calculate a three-dimensional hydrodynamic explosion for the N100 delayed-detonation model extensively discussed in the literature, taking the dynamical effects of neutrino emission from all important contributing source terms into account. Although neutrinos carry away of energy, we confirm the common view that neutrino energy losses are dynamically not very important, resulting in only a modest reduction of final kinetic energy by two per cent. We then calculate the gravitational wave signal from the time evolution of the quadrupole moment. Our model radiates in gravitational waves and the spectrum has a pronounced peak around . Depending on viewing angle and polarization, we find that the future space-based gravitational wave missions DECIGO and BBO would be able to detect our source to a distance of . We predict a clear signature of the deflagration-to-detonation transition in the neutrino and the gravitational wave signals. If observed, such a feature would be a strong indicator of the realization of delayed-detonations in near-Chandrasekhar mass white dwarfs.
pacs:PACS numbers: 04.30.Db, 04.30.Tv, 26.50.+x, 97.60.Bw
The nature of the progenitor system(s) and the explosion mechanism(s) of Type Ia supernovae (SNe Ia) are still under debate. Although synthetic observables such as time dependent spectra or light curves have been calculated for numerous explosion models (e.g. Kasen et al., 2009; Kromer et al., 2010; Pakmor et al., 2012; Kromer et al., 2013; Sim et al., 2013), efforts aimed at unambiguously identifying the explosion scenario based on a comparison of the model spectral evolution to observations remain inconclusive (Röpke et al., 2012). The same holds for the reverse process of inferring the composition profile of the supernova using the techique of abundance tomography (Stehle et al., 2005; Mazzali et al., 2008; Hachinger et al., 2009, 2013). Complementary approaches aimed at distinguishing the nature of the progenitor systems include the search for the contribution to the early-time light curve from a possible companion (Kasen, 2010; Bloom et al., 2012; Brown et al., 2012), Na I D line absorption features interpreted as evidence for circumstellar material (Patat et al., 2007; Sternberg et al., 2011; Dilday et al., 2012), late-time bolometric light curves (Seitenzahl et al., 2009a; Röpke et al., 2012; Kerzendorf et al., 2014), gamma-ray emission (Sim and Mazzali, 2008; Maeda et al., 2012; Summa et al., 2013), setting upper limits on the single degenerate scenario in old stellar populations from the lack of X-ray flux associated with the accretion (Gilfanov and Bogdán, 2010), comparing predictions of SN Ia progenitor models with the properties of observed SN remnants (Badenes et al., 2007; Yamaguchi et al., 2015), searching for the companion stars around young supernova remnants (Ruiz-Lapuente et al., 2004; Kerzendorf et al., 2009; Schaefer and Pagnotta, 2012), or constraining the circumstellar medium and hence the evolutionary channel from radio observations (Horesh et al., 2012; Chomiuk et al., 2012). Another approach aims at constraining the scenarios via rates and delay times, either by comparing prediction of binary population synthesis to observations (Yungelson and Livio, 2000; Ruiter et al., 2009, 2011; Toonen et al., 2012; Ruiter et al., 2013; Mennekens et al., 2010; Wang et al., 2012) or by inferring e.g. merger rates from the statistics of observed WD binary systems (Badenes and Maoz, 2012).
In this work, we determine and discuss the neutrino- and the gravitational wave signal of the N100 explosion model of Seitenzahl et al. (2013a). N100 is a recent, state-of-the-art, three-dimensional hydrodynamic explosion model of a delayed-detonation in a near Chandrasekhar-mass () carbon-oxygen (CO) white dwarf (WD). Such delayed-detonation models are among the most promising candidates to explain a substantial fraction of the SN Ia population (e.g. Hillebrandt and Niemeyer, 2000).
We have chosen the N100 model for our study since its synthetic light curves and spectra make it a rather promising candidate for a “normal” SN Ia (Sim et al., 2013). Furthermore, the nucleosynthetic yields and electromagnetic emission of the N100 model have already been used as representative of near- delayed-detonations in the single degenerate scenario in several recent publications (Röpke et al., 2012; Summa et al., 2013; Liu et al., 2013; Seitenzahl et al., 2013b; Seitenzahl et al., 2015). We emphasize that we actually re-calculate the N100 model from Seitenzahl et al. (2013a), this time also taking internal energy losses due to neutrino escape from all contributing source terms dynamically into account. For completeness, we therefore refer to this model hereafter as N100.
Ii Neutrino signal
The maximum central density of WDs is (see e.g. Timmes and Woosley, 1992). Neutrino trapping starts only at densities of to (Bethe, 1990), WD matter is therefore always transparent to neutrinos; in good approximation, they leave the star without any interaction. This simplifies the neutrino physics greatly, because we can assume that the energy that the neutrinos get when they are created is immediately lost to the star. Nevertheless, in the hot ashes of burnt CO matter, the thermodynamic conditions are such that copious amounts of neutrinos can be emitted. Calculations of the neutrino signal for a few SN Ia explosion models have been presented in the literature. Nomoto et al. (1984) and Kunugise and Iwamoto (2007) calculated the neutrino signal for the W7 model (Nomoto et al., 1984), a one-dimensional fast deflagration of a CO WD. Odrzywolek and Plewa (2011) calculated the neutrino signal for the n7d1r10t15c model (Plewa, 2007), a two-dimensional pure deflagration of a CO WD and the Y12 model (Plewa, 2007), a two-dimensional “detonating-failed-deflagration” (gravitationally confined detonation) model of the same 1.36 CO WD. Although Odrzywolek and Plewa (2011) refer to the Y12 model as a delayed-detonation, this term is usually reserved for SNe Ia that undergo a deflagration-to-detonation transition (DDT) when the deflagration flame front reaches lower densities where it gets shredded by turbulence and the mixing of cold fuel and hot ash triggers a detonation (Khokhlov, 1991). The explosion mechanism in the Y12 model is fundamentally different in that the detonation is triggered not during the rising phase of the deflagration, but rather at a much later time when deflagration ashes that are gravitationally bound to the surface of the WD collide, see Plewa et al. (e.g. 2004); Seitenzahl et al. (e.g. 2009b).
Previously considered multi-dimensional SN Ia models represent only peculiar events, i.e. pure turbulent deflagration and gravitationally confined detonation models. Here, we present neutrino luminosities for a three-dimensional delayed-detonation model of a CO WD that underwent a DDT. These explosion models have been extensively studied in the literature, and may be able to explain “normal” SNe Ia (e.g. Sim et al., 2013; Hillebrandt et al., 2013). For details about our implementation of the DDT model see Ciaraldi-Schoolmann et al. (2013). We distinguish between weak neutrinos produced in nuclear reactions and thermal neutrinos produced by thermal plasma processes. In the following two sections, we introduce the physical processes that generate the neutrinos during thermonuclear burning in WDs.
ii.1 Weak neutrinos
Weak neutrinos are emitted in nuclear reactions involving the
positron capture processes
All reactions, which can also occur inside nuclei, change the electron fraction (defined as the number of electrons per baryon) of the matter.
Neutrinos from electron captures (1) are abundantly produced in the neutronization processes that take place during and immediately after thermonuclear burning. As we will see, the energy released in reactions (1–4) dominates the energy released in all other neutrino generating processes in the physical environment of thermonuclear supernovae.
In particular, electron capture reactions (1) play an important role during the thermonuclear burning of WD matter. They lead to neutronization, expressed as decreasing , lowering the electron degeneracy pressure and thereby affecting the dynamics of the fluid.
Electron captures on the constituent parts of CO WDs, and , would occur via the following reactions (Shapiro and Teukolsky, 1983):
The threshold energy for the first reaction chain is , for the second reaction chain . The Fermi energies of the electrons match these values at densities of and , respectively (Shapiro and Teukolsky, 1983).
As mentioned above, central densities of accreting CO WDs are not expected to exceed (Timmes and Woosley, 1992; Woosley, 1997), well below and , before thermonuclear burning starts in the central region. Therefore, for densities appropriate for CO WDs, no electron captures on the most abundant unburnt nuclei occur. They are only possible after the start of thermonuclear burning, in particular on the hot “ashes”.
Using the weak interaction rates of Langanke and Martínez-Pinedo (2001), Seitenzahl et al. (2009c) calculated extensive tables of the time rate of change of the specific energy and the time rate of change of the electron fraction in these ashes for a three dimensional grid in density, temperature, and . We have extended their tables to determine the mean electron neutrino and electron antineutrino energies by implementing equation 17 of Langanke and Martínez-Pinedo (2001) into the nuclear statistical equilibrium code of Seitenzahl et al. (2009c). We interpolate in the tables to determine the amount of energy carried away by weak neutrinos for each grid cell and simply subtract it from the internal energy of the cell in every time step. The mean neutrino energies are determined by post-processing the output of the hydrodynamics simulations, once again interpolating in the tables, utilizing the NSE mass fraction, electron fraction, temperature, and density stored for each cell.
ii.2 Thermal neutrinos
In the hot plasmas of stellar interiors, neutrinos are also emitted due to processes that are independent of nuclear reactions; the amount of emitted energy depends only on the density and temperature of the matter. Most important are neutrinos originating from electron-positron pair annihilation, photoemission, plasmon decay, bremsstrahlung, and recombination processes (for a brief description and summary of the individual contributions of these processes see (Itoh et al., 1996)). Neutrinos from these processes are often combined as thermal neutrinos, they comprise neutrinos and antineutrinos of all flavors, whereas in reactions (1–4) only electron and anti-electron neutrinos are produced.
We calculate the energy that is released from the WD due to
the emission of thermal neutrinos using a
ii.3 Results and Discussion
The weak- and thermal neutrino luminosities for N100 are shown as a function of time in Fig. 1. The weak neutrino luminosity reaches a maximum of at and the integrated total weak neutrino energy loss amounts to . The weak neutrino luminosity is overwhelmingly dominated by electron neutrinos from electron captures and decay. In comparison, the electron antineutrino luminosity from positron capture and decay is more than six orders of magnitude smaller (see Fig. 1). At the time of maximum luminosity, the mean weak electron neutrino energy is 4.0 MeV and the mean weak electron antineutrino energy is 2.2 MeV (see Fig. 2). The thermal neutrino luminosity reaches a maximum of at and the integrated total thermal neutrino energy loss amounts to . The energy drained from the explosion by neutrinos is therefore small compared to e.g. the nuclear energy released in the explosion, the initial gravitational binding energy, or the final kinetic energy.
Owing to the stochastic nature of our implementation of the deflagration-to-detonation transition (cf. (Ciaraldi-Schoolmann et al., 2013)), even a small additional energy loss could, in principle, lead to very different final explosion. This is, however, not the case here as the time at which the first DDT occurs is only slightly delayed ( vs. ). As a result, there is only a small reduction in kinetic energy between N100 () and N100 (). Although dynamically not very important, it is interesting to note that the energy carried away by neutrinos in is still on the same order of magnitude as the total energy radiated in photons by the SN during its entire duration.
The secondary peak around in both the weak and thermal component of the neutrino signal is a signature of the deflagration-to-detonation transition. The secondary maximum occurs with a time delay with respect to since the increased neutrino emission occurs only when the detonation (which was launched at low density) overruns the highest density fuel in the center that was left unburned by the deflagration. Odrzywolek and Plewa (2011) also find a secondary maximum for the Y12 model and call it a “smoking gun” of delayed-detonation SNe. Their secondary maximum, however, occurs with a relatively long time delay () after the primary maximum. This difference of the occurrence time of the secondary maximum is a reflection of the fundamentally different mechanisms that lead to the initiation of the detonation in the Y12 and N100 models. For a similar reason, these two models also differ by a factor of in their maximum neutrino luminosities, vs. . Although both Y12 and N100 contain both a deflagration and a subsequent detonation, the fact that N100 burns significantly more mass than Y12 during the (for neutrino emission dominant) deflagration phase leads to the fact that the N100 neutrino signal is more like that of pure deflagration models ( (Odrzywolek and Plewa, 2011), (Nomoto et al., 1984)), which, however, lack the characteristic secondary maximum of our simulations.
Iii Gravitational wave signal
Research on gravitational wave signals of SNe Ia is
a largely unexplored field. A large number () Galactic binary
systems – mostly double white dwarfs – are expected to be resolved with
future space-based gravitational wave observatories such as eLISA
(Consortium et al., 2013). Both Nelemans et al. (2001) and Ruiter et al. (2010) predicted
there are about 500 Galactic double degenerate SNe Ia progenitors
Based on their earlier results, (Falta and Fisher, 2011) analyzed the stochastic gravitational wave background originating from thermonuclear supernovae arising from the gravitational confined detonation explosion mechanism. They found that it might pose a considerable source of noise – in the frequency range between and – for future gravitational wave detectors such as DECIGO and BBO (Kawamura et al., 2011; Yagi and Seto, 2011) that are designed to detect the gravitational wave signal of cosmological inflation.
iii.1 Numerical implementation
Our numerical approach for the computation of the gravitational wave signal follows Blanchet et al. (1990) and Müller and Janka (1997). We calculate only the approximate quadrupole radiation because of the Newtonian nature of our simulations.
The most straightforward way to determine the amplitude of gravitational quadrupole waves is by calculating the second derivative of the quadrupole moment . The gravitational quadrupole radiation field in the transverse-traceless gauge is
is the transverse-traceless projection operator
with the normalized position vector and the distance to the source . However, the calculation of the second time derivative gives rise to numerical instabilities, the resulting signal is quite noisy. Therefore, to avoid this unfavorable method, Nakamura and Oohara (1989) and Blanchet et al. (1990) introduced a different way to compute the amplitude. With this new method, which was applied successfully to core-collapse supernovae by Moenchmeyer et al. (1991) and Müller and Janka (1997), the gravitational quadrupole radiation field is calculated by
Here is the velocity and is the usual Newtonian gravitational potential or an effective relativistic gravitational potential. Blanchet et al. (1990) showed that equation (III.1) is equivalent to equation (7), while Moenchmeyer et al. (1991) demonstrated the numerical superiority of the method that implements equation (III.1).
Since gravitational waves have two polarization states (“+” and “”), the amplitude can be written in terms of the two unit linear-polarization tensors and (Misner et al., 1973) as
In the case of a plane wave propagating in -direction, the unit linear-polarization tensors are
where and are the unit vectors parallel to the - and -axis, respectively. We calculate the amplitudes and considering two different lines of sight, as was suggested in Müller and Janka (1997). Since they use preferentially spherical coordinates, they speak of the polar (, ) and equatorial (, ) direction. In our case, as we use exclusively Cartesian coordinates, it is more appropriate to call it the -direction and -direction, which we do from now on. With the definition
the amplitudes and in the -direction can be expressed as
while in the -direction one obtains
We implemented the calculation of these amplitudes according to equation (13) in the simulation code. Next we show results of the calculated gravitational wave signal, beginning with a discussion of the four amplitudes (14–17).
iii.2 Gravitational wave amplitudes
In Fig. 3 we plot four different gravitational wave amplitudes that arise from two different lines of sight (- and -direction), each with two polarization states ( and ), see Sec. III.1 for a detailed explanation. In the first after the ignition of the deflagration, no signal is visible; after that the absolute values of all amplitudes rise in a steady, monotonic way. The initiation of the first detonation at and the time when the detonation reaches the center of the WD leave visible imprints on the signal. For , the signal reaches a maximum value of at , about a factor of less than the maximum amplitude obtained by (Falta et al., 2011) in their GCD model. The smaller maximum amplitude of the N100 delayed-detonation model is naturally explained by the greater compactness of the GCD model when the detonation is triggered. The homologous expansion of the supernova ejecta after generates a signal that is constant in time up to , when the simulation was stopped.
iii.3 Gravitational wave luminosity and spectrum
Beyond the amplitudes, another quantity of interest is the total amount of energy radiated away by gravitational waves, . It can be expressed as (Müller and Janka, 1997)
All values of stated in this work are calculated by means of equation (III.3).
The total gravitational wave energy of N100 amounts to , about an order of magnitude less than the total energy of the GCD model of Falta et al. (2011) – this is again consistent with the results shown in Sec. III.2, because the calculated amplitudes differ by a factor of and the energy is proportional to the square of the amplitudes. These results demonstrate that the gravitational wave energy is dynamically unimportant since it is smaller than the internal-, kinetic-, nuclear-, and even neutrino loss energies. Hence, the error caused by the fact that we did not couple the gravitational waves part of the code to the hydrodynamics part is negligible.
The gravitational wave luminosity as a function of time is plotted in Fig. 4. Clearly visible is a two-peaked structure; the first peak corresponds to the deflagration phase and features a maximum luminosity of at , while the second, considerably higher peak can be attributed to the detonation phase, peaking at the time when the detonation reaches the center of the WD and converts the last remaining high density fuel to iron group elements. Here the maximum luminosity is . In contrast, the GCD model of Falta et al. (2011) predicts a much greater difference in maximum power radiated in the deflagration and detonation phases. This difference is due to the more weakly ignited deflagration, which leads to a smaller degree of expansion and correspondingly a detonation in a more compact WD.
The frequency of a gravitational wave signal is an important quantity to determine, because detectors are only sensitive in a confined frequency range; see (Moore et al., 2015) for a discussion on quantifying gravitational wave source amplitude and sensitivity curves. We adopt the approach of Müller (1982) and Müller et al. (2012) and conduct Fourier analyses of the calculated gravitational wave amplitudes and determine the energy spectrum . The Fourier transforms of the are
Following Müller et al. (2012), we obtain the energy spectrum by
Fig. 5 shows the energy spectrum of the gravitational wave signal, calculated by means of equation (III.3) by evaluating the Fourier integrals (19). The spectrum has a pronounced maximum of at and a secondary local maximum of at .
The energy spectrum calculated by (Falta et al., 2011) for the GCD model peaked at . It is worth noting that Falta et al. (2011) stated that an explosion model with more “pre-expansion” prior to detonation, such as the N100 model presented here, would exhibit a characteristic gravitational wave frequency shifted downward by a factor of , a prediction that we essentially confirm.
Our results show that the detection of gravitational wave signals of SNe Ia provides a way to differentiate between different explosion models with future gravitational wave observatories, if data analysis techniques are developed to extract those signals. The signal of our explosion model bears the mark of the deflagration-to-detonation transition. Gravitational waves generated by mergers of two WDs would feature the characteristic signature of the ringdown phase – according to Dan et al. (2011), the gravitational wave signal in the ringdown phase is of the same magnitude as the signal of the supernova in the above discussed scenarios: to , depending on the WD masses. Finally, GCD models show a sharp single peak in the time evolution of the amplitude (figure 2 in Falta et al. 2011). However, the low frequency range of the signals prevents a detection by second-generation instruments comparable to advanced LIGO; but third-generation space-based detectors like BBO or DECIGO that cover a lower frequency range should be able to detect the gravitational wave signal of at least all Galactic Type Ia supernovae.
The gravitational wave frequencies that we obtain are consistent with the results of Falta et al. (2011) and Falta and Fisher (2011). Our results show that also thermonuclear supernovae modeled as delayed detonations contribute to the stochastic gravitational wave background in the frequency range between and and thus pose a source of noise that might obscure the gravitational wave signal originating from the era of inflation shortly after the Big Bang; the measurement of this signal is a central goal of the planned detectors BBO and DECIGO.
Finally, we estimate the detectability of our N100 delayed-detonation model. Depending on viewing angle and polarization, our gravitational wave amplitudes fall in the range between approximately 1 to (see Fig. 3). At , both BBO and DECIGO have a planned strain sensitivity limit of (Moore et al., 2015). Setting we find that our model’s signal would be detectable out to a distance of 320 kpc and 1.3 Mpc for and , respectively. Thus, a delayed-detonation SN Ia going off in our Milky Way or one of its satellite galaxies would be well within the sensitivity limits of BBO or DECIGO. For fortuitous alignment (i.e. ), even the Triangulum and Andromeda galaxies ( and , respectively) would be within reach.
We conducted a three-dimensional hydrodynamic simulation of a delayed-detonation explosion of a thermonuclear supernova and computed the neutrino and gravitational wave signals. By taking the energetics of neutrino losses on the hydrodynamic evolution into account, we find a reduction in kinetic energy of about two per cent and we conclude that the effects of neutrino emission on the explosion dynamics are indeed small. Nevertheless, our model emits in neutrinos, comparable to the total energy radiated by photons. We present the amplitudes, luminosity as a function of time, and the energy spectrum of the gravitational wave signal of our SN Ia supernova explosion simulation. The energy spectrum of the gravitational wave emission peaks where the proposed space-based gravitational wave missions DECIGO and BBO have the highest design sensitivity and we find that the signal is potentially observable out to a distance of 1.3 Mpc. In both the neutrino and gravitational wave signals we find a distinct signature of the deflagration-to-detonation transition, which, in principle, makes it possible to constrain the explosion model of SNe Ia by observations of their non-electromagnetic neutrino and/gravitational wave radiation.
Acknowledgements.We thank Chistopher Moore for his insightful comments on sensitivity curves of gravitational wave detectors and Rüdiger Pakmor for their discussions on power spectra and Fourier transforms. IRS was funded by the Australian Research Council Laureate Grant FL0992131 and the Deutsche Forschungsgemeinschaft (DFG) through the graduate school on “Theoretical Astrophysics and Particle Physics” (GRK 1147), MH by CompStar, a Research Networking Programme of the European Science Foundation, and FKR by the DFG via the Emmy Noether Program (RO 3676/1-1) and by the ARCHES prize of the German Federal Ministry of Education and Research (BMBF). AJR acknowledges funding support from the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO) through project number CE110001020. STO acknowledges support from the Studienstiftung des Deutschen Volkes. Funding for collaboration was provided by the DAAD/Go8 German-Australian exchange program. This research was supported by the Partner Time Allocation (Australian National University) and the National Computational Merit Allocation Schemes of the NCI National Facility at the Australian National University. Part of the simulations were carried out on the JUGENE supercomputer at the Forschungszentrum Jülich within the Partnership for Advanced Computing in Europe (PRA042).
- Of course, also “thermal” neutrinos are created due to the weak interaction, but their production does not involve nuclear reactions.
- These double CO white dwarf systems are assumed to be SNe Ia progenitors because their combined mass exceeds the Chandrasekhar mass limit and they are expected to merge within a Hubble time.
- D. Kasen, F. K. Röpke, and S. E. Woosley, Nature 460, 869 (2009), eprint 0907.0708.
- M. Kromer, S. A. Sim, M. Fink, F. K. Röpke, I. R. Seitenzahl, and W. Hillebrandt, ApJ 719, 1067 (2010), eprint 1006.4489.
- R. Pakmor, M. Kromer, S. Taubenberger, S. A. Sim, F. K. Röpke, and W. Hillebrandt, ApJ 747, L10 (2012), eprint 1201.5123.
- M. Kromer, M. Fink, V. Stanishev, S. Taubenberger, F. Ciaraldi-Schoolman, R. Pakmor, F. K. Röpke, A. J. Ruiter, I. R. Seitenzahl, S. A. Sim, et al., MNRAS 429, 2287 (2013), eprint 1210.5243.
- S. A. Sim, I. R. Seitenzahl, M. Kromer, F. Ciaraldi-Schoolmann, F. K. Röpke, M. Fink, W. Hillebrandt, R. Pakmor, A. J. Ruiter, and S. Taubenberger, MNRAS 436, 333 (2013), eprint 1308.4833.
- F. K. Röpke, M. Kromer, I. R. Seitenzahl, R. Pakmor, S. A. Sim, S. Taubenberger, F. Ciaraldi-Schoolmann, W. Hillebrandt, G. Aldering, P. Antilogus, et al., ApJ 750, L19 (2012), eprint 1203.4839.
- M. Stehle, P. A. Mazzali, S. Benetti, and W. Hillebrandt, MNRAS 360, 1231 (2005), eprint arXiv:astro-ph/0409342.
- P. A. Mazzali, K. Nomoto, K. Maeda, J. Deng, S. Benetti, F. Röpke, and W. Hillebrandt, 391, 347 (2008).
- S. Hachinger, P. A. Mazzali, S. Taubenberger, R. Pakmor, and W. Hillebrandt, MNRAS 399, 1238 (2009), eprint 0907.2542.
- S. Hachinger, P. A. Mazzali, M. Sullivan, R. S. Ellis, K. Maguire, A. Gal-Yam, D. A. Howell, P. E. Nugent, E. Baron, J. Cooke, et al., MNRAS 429, 2228 (2013), eprint 1208.1267.
- D. Kasen, ApJ 708, 1025 (2010), eprint 0909.0275.
- J. S. Bloom, D. Kasen, K. J. Shen, P. E. Nugent, N. R. Butler, M. L. Graham, D. A. Howell, U. Kolb, S. Holmes, C. A. Haswell, et al., ApJ 744, L17 (2012), eprint 1111.0966.
- P. J. Brown, K. S. Dawson, M. de Pasquale, C. Gronwall, S. Holland, S. Immler, P. Kuin, P. Mazzali, P. Milne, S. Oates, et al., ApJ 753, 22 (2012), eprint 1110.2538.
- F. Patat, P. Chandra, R. Chevalier, S. Justham, P. Podsiadlowski, C. Wolf, A. Gal-Yam, L. Pasquini, I. A. Crawford, P. A. Mazzali, et al., Science 317, 924 (2007), eprint arXiv:0707.2793.
- A. Sternberg, A. Gal-Yam, J. D. Simon, D. C. Leonard, R. M. Quimby, M. M. Phillips, N. Morrell, I. B. Thompson, I. Ivans, J. L. Marshall, et al., Science 333, 856 (2011), eprint 1108.3664.
- B. Dilday, D. A. Howell, S. B. Cenko, J. M. Silverman, P. E. Nugent, M. Sullivan, S. Ben-Ami, L. Bildsten, M. Bolte, M. Endl, et al., Science 337, 942 (2012), eprint 1207.1306.
- I. R. Seitenzahl, S. Taubenberger, and S. A. Sim, MNRAS 400, 531 (2009a), eprint 0908.0247.
- W. E. Kerzendorf, S. Taubenberger, I. R. Seitenzahl, and A. J. Ruiter, ApJ 796, L26 (2014), eprint 1406.6050.
- S. A. Sim and P. A. Mazzali, MNRAS 385, 1681 (2008), eprint 0710.3313.
- K. Maeda, Y. Terada, D. Kasen, F. K. Röpke, A. Bamba, R. Diehl, K. Nomoto, M. Kromer, I. R. Seitenzahl, H. Yamaguchi, et al., ApJ 760, 54 (2012), eprint 1208.2094.
- A. Summa, A. Ulyanov, M. Kromer, S. Boyer, F. K. Röpke, S. A. Sim, I. R. Seitenzahl, M. Fink, K. Mannheim, R. Pakmor, et al., A&A 554, A67 (2013), eprint 1304.2777.
- M. Gilfanov and Á. Bogdán, Nature 463, 924 (2010), eprint 1002.3359.
- C. Badenes, J. P. Hughes, E. Bravo, and N. Langer, ApJ 662, 472 (2007), eprint arXiv:astro-ph/0703321.
- H. Yamaguchi, C. Badenes, A. R. Foster, E. Bravo, B. J. Williams, K. Maeda, M. Nobukawa, K. A. Eriksen, N. S. Brickhouse, R. Petre, et al., ApJ 801, L31 (2015), eprint 1502.04255.
- P. Ruiz-Lapuente, F. Comeron, J. Méndez, R. Canal, S. J. Smartt, A. V. Filippenko, R. L. Kurucz, R. Chornock, R. J. Foley, V. Stanishev, et al., Nature 431, 1069 (2004), eprint arXiv:astro-ph/0410673.
- W. E. Kerzendorf, B. P. Schmidt, M. Asplund, K. Nomoto, P. Podsiadlowski, A. Frebel, R. A. Fesen, and D. Yong, ApJ 701, 1665 (2009), eprint 0906.0982.
- B. E. Schaefer and A. Pagnotta, Nature 481, 164 (2012).
- A. Horesh, S. R. Kulkarni, D. B. Fox, J. Carpenter, M. M. Kasliwal, E. O. Ofek, R. Quimby, A. Gal-Yam, S. B. Cenko, A. G. de Bruyn, et al., ApJ 746, 21 (2012), eprint 1109.2912.
- L. Chomiuk, A. M. Soderberg, M. Moe, R. A. Chevalier, M. P. Rupen, C. Badenes, R. Margutti, C. Fransson, W.-f. Fong, and J. A. Dittmann, ApJ 750, 164 (2012), eprint 1201.0994.
- L. R. Yungelson and M. Livio, ApJ 528, 108 (2000), eprint arXiv:astro-ph/9907359.
- A. J. Ruiter, K. Belczynski, and C. Fryer, ApJ 699, 2026 (2009), eprint 0904.3108.
- A. J. Ruiter, K. Belczynski, S. A. Sim, W. Hillebrandt, C. L. Fryer, M. Fink, and M. Kromer, MNRAS 417, 408 (2011), eprint 1011.1407.
- S. Toonen, G. Nelemans, and S. Portegies Zwart, A&A 546, A70 (2012), eprint 1208.6446.
- A. J. Ruiter, S. A. Sim, R. Pakmor, M. Kromer, I. R. Seitenzahl, K. Belczynski, M. Fink, M. Herzog, W. Hillebrandt, F. K. Röpke, et al., MNRAS 429, 1425 (2013), eprint 1209.0645.
- N. Mennekens, D. Vanbeveren, J. P. De Greve, and E. De Donder, A&A 515, A89 (2010), eprint 1003.2491.
- X. Wang, L. Wang, A. V. Filippenko, G. Aldering, P. Antilogus, D. Arnett, D. Baade, E. Baron, B. J. Barris, S. Benetti, et al., ApJ 749, 126 (2012), eprint 1110.5809, URL http://adsabs.harvard.edu/abs/2012ApJ...749..126W.
- C. Badenes and D. Maoz, ApJ 749, L11 (2012), eprint 1202.5472.
- I. R. Seitenzahl, F. Ciaraldi-Schoolmann, F. K. Röpke, M. Fink, W. Hillebrandt, M. Kromer, R. Pakmor, A. J. Ruiter, S. A. Sim, and S. Taubenberger, MNRAS 429, 1156 (2013a), eprint 1211.3015.
- W. Hillebrandt and J. C. Niemeyer, ARA&A 38, 191 (2000), eprint arXiv:astro-ph/0006305.
- Z.-W. Liu, R. Pakmor, I. R. Seitenzahl, W. Hillebrandt, M. Kromer, F. K. Röpke, P. Edelmann, S. Taubenberger, K. Maeda, B. Wang, et al., ApJ 774, 37 (2013), eprint 1307.5579.
- I. R. Seitenzahl, G. Cescutti, F. K. Röpke, A. J. Ruiter, and R. Pakmor, A&A 559, L5 (2013b), eprint 1309.2397.
- I. R. Seitenzahl, A. Summa, F. Krauß, S. A. Sim, R. Diehl, D. Elsässer, M. Fink, W. Hillebrandt, M. Kromer, K. Maeda, et al., MNRAS 447, 1484 (2015), eprint 1412.0835.
- F. X. Timmes and S. E. Woosley, ApJ 396, 649 (1992).
- H. A. Bethe, Reviews of Modern Physics 62, 801 (1990).
- K. Nomoto, F.-K. Thielemann, and K. Yokoi, ApJ 286, 644 (1984).
- T. Kunugise and K. Iwamoto, PASJ 59, L57+ (2007).
- A. Odrzywolek and T. Plewa, A&A 529, A156 (2011), eprint 1006.0490.
- T. Plewa, ApJ 657, 942 (2007), eprint arXiv:astro-ph/0611776.
- A. M. Khokhlov, A&A 245, 114 (1991).
- T. Plewa, A. C. Calder, and D. Q. Lamb, ApJ 612, L37 (2004), eprint arXiv:astro-ph/0405163.
- I. R. Seitenzahl, C. A. Meakin, D. Q. Lamb, and J. W. Truran, ApJ 700, 642 (2009b), eprint 0905.3104.
- W. Hillebrandt, M. Kromer, F. K. Röpke, and A. J. Ruiter, Frontiers of Physics 8, 116 (2013), eprint 1302.6420.
- F. Ciaraldi-Schoolmann, I. R. Seitenzahl, and F. K. Röpke, A&A 559, A117 (2013), eprint 1307.8146.
- S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars (John Wiley & Sons, New York, 1983).
- S. E. Woosley, ApJ 476, 801 (1997).
- K. Langanke and G. Martínez-Pinedo, Atomic Data and Nuclear Data Tables 79, 1 (2001).
- I. R. Seitenzahl, D. M. Townsley, F. Peng, and J. W. Truran, Atomic Data and Nuclear Data Tables 95, 96 (2009c).
- N. Itoh, H. Hayashi, A. Nishikawa, and Y. Kohyama, ApJS 102, 411 (1996).
- T. e. Consortium, :, P. A. Seoane, S. Aoudia, H. Audley, G. Auger, S. Babak, J. Baker, E. Barausse, S. Barke, et al., ArXiv e-prints (2013), eprint 1305.5720.
- G. Nelemans, L. R. Yungelson, and S. F. Portegies Zwart, A&A 375, 890 (2001), eprint astro-ph/0105221.
- A. J. Ruiter, K. Belczynski, S. A. Sim, W. Hillebrandt, C. L. Fryer, M. Fink, and M. Kromer (2010), eprint 1011.1407.
- M. Dan, S. Rosswog, J. Guillochon, and E. Ramirez-Ruiz, ApJ 737, 89 (2011), eprint 1101.5132.
- D. Falta, R. Fisher, and G. Khanna, Physical Review Letters 106, 201103 (2011), eprint 1011.6387.
- D. Falta and R. Fisher, Phys. Rev. D 84, 124062 (2011), eprint 1112.2782.
- S. Kawamura, M. Ando, N. Seto, S. Sato, T. Nakamura, K. Tsubono, N. Kanda, T. Tanaka, J. Yokoyama, I. Funaki, et al., Classical and Quantum Gravity 28, 094011 (2011).
- K. Yagi and N. Seto, Phys. Rev. D 83, 044011 (2011), eprint 1101.3940.
- L. Blanchet, T. Damour, and G. Schaefer, MNRAS 242, 289 (1990).
- E. Müller and H.-T. Janka, A&A 317, 140 (1997).
- T. Nakamura and K.-I. Oohara, Methods in 3 D numerical relativity. (1989), pp. 254–280.
- R. Moenchmeyer, G. Schaefer, E. Müller, and R. E. Kates, A&A 246, 417 (1991).
- C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (1973).
- C. J. Moore, R. H. Cole, and C. P. L. Berry, Classical and Quantum Gravity 32, 015014 (2015), eprint 1408.0740.
- E. Müller, A&A 114, 53 (1982).
- E. Müller, H.-T. Janka, and A. Wongwathanarat, A&A 537, A63 (2012), eprint 1106.6301.