© ESO, 2013

1. Introduction

While there is general agreement that SNe Ia are the result of the thermonuclear explosions of carbon-oxygen WDs, many questions concerning the progenitor and explosion scenarios still remain open (cf. Hillebrandt & Niemeyer 2000). This lack of knowledge contradicts the relevance of SNe Ia for measuring cosmological distances, as well as their influence on the chemical evolution of the universe, and it emphasizes the need for a more thorough understanding of the underlying physics. To constrain current explosion models as tightly as possible, a multiwavelength approach extending to the gamma-ray regime (MeV energies) is desirable.

The gamma-ray spectra of SNe Ia are dominated by the lines of the ⁵⁶Ni → ⁵⁶Co → ⁵⁶Fe decay chain that powers the observable display of SNe Ia. In contrast to studies in the optical or infrared wavelength regime, where the emissivity strongly depends on the complex opacity structure, which in turn depends on the atomic level populations and chemical composition, the emissivities in the gamma-ray regime are determined from their branching ratios and radioactive half-lives and a few rather simple interaction processes like pair production, Compton scattering, and photo-electrical absorption. This makes the gamma-ray regime an ideal tool for getting a more direct handle on the mass-velocity distribution of the explosion product (Milne et al. 2004). These very promising prospects have led to numerous theoretical efforts (mostly one-dimensional) in investigating the gamma-ray emission of SNe Ia in the past (see for instance Clayton et al. 1969; Clayton 1974; Ambwani & Sutherland 1988; Chan & Lingenfelter 1988, 1990, 1991; Burrows & The 1990; Müller et al. 1991; Höflich et al. 1992; Kumagai & Nomoto 1997; Gómez-Gomar et al. 1998; Höflich et al. 1998; Sim & Mazzali 2008; Isern et al. 2008; Kromer et al. 2010; Maeda et al. 2012). Although there have been first attempts at taking three-dimensional effects into account (e.g. Höflich 2002), a fully three-dimensional treatment of the explosion hydrodynamics, as well as the radiation transfer calculations, has not been carried out in previous SN Ia gamma-ray emission studies. We determine, to our knowledge for the first time, the predicted gamma-ray emission for completely three-dimensional SN Ia explosion models. The three-dimensional approach is important for a realistic description of the distribution of the radioactive isotopes and the surrounding ejecta material – both factors that the gamma-ray emission of SNe Ia is sensitive to as shown in the following. Furthermore, a thorough investigation of the line-of-sight effects of different viewing angles relies on a three-dimensional treatment of the explosion scenario.

However, as of now the detection of SNe Ia at MeV energies has not been feasible owing to the low sensitivities or nonexistence of detection instruments in this energy range. In this paper, we explore the additional benefits from analyzing gamma-ray spectra towards a more sound theoretical understanding of SNe Ia and discuss the detection limits of proposed next-generation gamma-ray observatories. For this aim to be achieved, we ran full detector simulations of the proposed MeV satellite GRIPS (Greiner et al. 2012).

In this paper, we focus on two main branches of suggested SN Ia progenitor models: the explosion of a carbon-oxygen Chandrasekhar-mass WD and the super-Chandrasekhar-mass violent merger of two carbon-oxygen WDs. While the first scenario marks the end of a WD close to the Chandrasekhar limit that accretes mass from a companion star through Roche-lobe overflow or strong stellar winds, the second is considered to be the result of two closely orbiting WDs losing energy due to the emission of gravitational waves and merging finally. The latter scenario has attracted renewed interest in the past years since, in contrast to previous thoughts, the publications by Pakmor et al. (2010, 2011, 2012a) have demonstrated that violent mergers of two carbon-oxygen WDs can directly lead to a thermonuclear explosion while the merger is still going on. As an extension to previous gamma-ray studies of SNe Ia, we discuss the gamma-ray emission of a violent merger for the first time.

Both scenarios generate optical observables that are similar to those of normal SNe Ia (Mazzali et al. 2007; Kasen et al. 2009; Blondin et al. 2011; Pakmor et al. 2012b; Röpke et al. 2012), in spite of significant differences in the total mass and the ejecta structure. Further observable distinctions through SNe Ia gamma-ray spectra would therefore provide an additional handle on the progenitor channel question.

The outline of the paper is as follows. In Sect. 2 we describe the applied explosion models and the radiative transfer scheme. After a discussion of the resulting gamma-ray spectra and a study of the applicability of different diagnostic tools in Sect. 3, we investigate the chances of detecting gamma-ray line emission from SNe Ia in the near future in Sect. 4 and conclude with a short summary of the main findings.

2. Simulation framework

2.1. Explosion models

In the first simulation, we calculated the gamma-ray emission for the explosion of a near Chandrasekhar-mass (M_Ch) WD as a delayed detonation (e.g. Khokhlov 1991). After an initial subsonic deflagration phase of nuclear burning that mainly produces iron group elements, the explosion turns into a supersonic detonation. The remaining fuel is mostly burned to intermediate-mass elements due to the prevailing lower densities caused by the energy release of the deflagration mode and the subsequent expansion of the star. We used the N100 model from the set of three-dimensional delayed detonation simulations carried out by Seitenzahl et al. (2013) with the thermonuclear supernova code Leafs. For a detailed description of the applied techniques we refer the reader to Reinecke et al. (1999), Röpke & Hillebrandt (2005), Schmidt et al. (2006), Röpke & Niemeyer (2007), and to references therein.

We chose the N100 model since it produces optical observables that closely resemble those of “normal” SNe Ia (Röpke et al. 2012). The model is based on an isothermal nonrotating WD in hydrostatic equilibrium with a central density of ρ_c = 2.9 × 10⁹  g   cm^-3. During the explosion, 10⁶ tracer particles reproducing the underlying density profile of the WD record the thermodynamic conditions. We then used the information provided by the tracer particles to calculate the detailed isotopic composition in a post-processing step with a reaction network of 384 nuclides (Travaglio et al. 2004; Röpke et al. 2006; Seitenzahl et al. 2010). The initial chemical composition is assumed to be 47.5% ¹²C, 50.0% ¹⁶O, and 2.5% ²²Ne by mass, resulting in an electron fraction of Y_e = 0.498864, which corresponds to a zero-age main sequence metallicity comparable to that of the Sun. With a kinetic energy of 1.45 × 10⁵¹  erg and a total mass of 1.40 M_⊙ of the ejecta, N100 produced 0.604 M_⊙ of ⁵⁶Ni. Roughly half of the ⁵⁶Ni is located in the inner 0.3 M_⊙ at velocities below 4000  km   s^-1, while the other half is more or less isotropically but inhomogeneously distributed within the remainder of the inner ~ 1.2 M_⊙, up to to velocities of 12   000  km   s^-1.

The second simulation is the violent merger of a 1.1  M_⊙ and a 0.9  M_⊙ WD of Pakmor et al. (2012b). Again, this model reproduces the features of “normal” SNe Ia at optical wavelengths (Röpke et al. 2012). To model the inspiral and the merger, Pakmor et al. (2012a) use a modified version of the SPH code Gadget (Springel 2005). Both WDs are constructed from a total of 1.8 × 10⁶ particles of equal mass. After a relaxation phase, the distance between the WDs is slowly decreased according to the method of Dan et al. (2011) until the first particle of the less massive (secondary) WD reaches the Lagrangian point between the two objects. This triggers the actual simulation to start. During its progress, more and more material from the secondary WD is accreted and heated up on the surface of the primary, giving rise to the formation of hot spots and the ignition of carbon burning. Following the guidelines of microscopic detonation simulations (Seitenzahl et al. 2009), a detonation is initiated in a hot spot that reaches a temperature of more than 2.5 × 10⁹   K and a density of about 2 × 10⁶   g   cm^-3. The mapping of the actual simulation to a uniform Cartesian grid with 768 × 768 × 768 cells and a total box size of 4 × 10⁹   cm is then used as initial state for a simulation of the detonation flame with the Leafs code, where the detonation is ignited at the cell with the highest temperature. For more information about the simulation, see Pakmor et al. (2012a,b). The detailed composition of the material is again calculated with the tracer particle method and a post-processing step using a large nuclear reaction network (see above). The merger model yields are based on the same initial chemical composition as the delayed-detonation model (47.5% ¹²C, 50.0% ¹⁶O, and 2.5% ²²Ne by mass). With an asymptotic kinetic explosion energy of 1.7 × 10⁵¹erg, the merger model produced 0.616 M_⊙ of ⁵⁶Ni out of the combined initial mass of 2.0 M_⊙. In contrast to the delayed-detonation model N100, the ⁵⁶Ni is mainly found at velocities below ~ 10   000   km   s^-1, and it is much more asymmetrically distributed in the ejecta. This is primarily due to the delayed explosion of the secondary into the already burned remains of the primary, which excavates a region virtually free of iron group elements at low velocity (see Fig. 2 of Pakmor et al. 2012a).

2.2. Radiative transfer

Using detailed abundance distributions obtained from the tracer particle method, we mapped the explosion ejecta to a 50 × 50 × 50 Cartesian grid and follow the emission, propagation, and interaction of the gamma-ray photons with the Monte Carlo radiative transfer code Artis (Sim 2007; Kromer & Sim 2009). The main principles of the radiative transport code can be summarized as follows. In contrast to Nature’s way of quantization, the radiation field is divided into Monte Carlo quanta representing indivisible parcels of energy, providing several advantages concerning the simulation technique (Lucy 1999). Initially, the quanta begin as so-called pellets of radioactive material representing ⁵⁶Ni, , , and . Other radionuclei are neglected in Artis since they are typically not important at early times. Upon decay, the pellets are converted to monochromatic gamma-ray packets with frequencies sampled randomly according to the respective branching ratios. These gamma-ray packets are emitted into randomly chosen directions under the assumption of isotropic emission in the comoving frame. Then, their propagation is followed in frequency, three-dimensional space, and time, until they leave the ejecta or are removed from the gamma-ray regime due to interaction processes.

The basic interaction processes of gamma-ray photons are pair production, photoelectrical absorption, and Compton scattering, with the last the most dominant in the encountered energy ranges (Milne et al. 2004). In accordance with the ratios of the cross sections of individual interaction processes to the total cross section, the occurrence of a certain interaction type is sampled randomly. Throughout the simulation, a positronium fraction of zero is assumed, meaning that positrons, e.g. from pair production or nuclear decays, annihilate in situ and directly lead to the production of two gamma-ray photons at 0.511   MeV (cf. Milne et al. 2004). The escaping gamma-ray packets are binned in frequency, time and direction, contributing to the spectral evolution of the gamma-ray emission from the explosion event. Light-travel time effects are taken into consideration. A thorough description of the employed Monte Carlo radiative transfer scheme and additional references can be found in Lucy (2005), Sim (2007), Sim & Mazzali (2008), and Kromer & Sim (2009).

3. Results and discussion

Even though the Chandrasekhar-mass delayed detonation and the violent merger model show distinct differences in total mass and ejecta structure, both models produce nearly the same amount of ⁵⁶Ni (roughly 0.6 M_⊙). In spite of their differences, a straightforward preference for one of the models cannot be given by comparing the simulated optical spectra to the measured for the test case of SN 2011fe (Röpke et al. 2012). In this section, we investigate whether additional distinguishing features can be identified from a study of the gamma-ray emission of the two models.

3.1. Gamma-ray spectra

Figure 1 shows the spectral evolution of the angle-averaged gamma-ray emission arising from the delayed detonation and the violent merger model. Photon fluxes are always normalized to a distance of 1   Mpc. For a discussion of the importance of viewing-angle effects, the reader is referred to the end of this section.

The spectra are dominated by lines of the decay chain ⁵⁶Ni → ⁵⁶Co → ⁵⁶Fe. Owing to the different half-lives of ⁵⁶Ni (6.1   d) and ⁵⁶Co (77.2   d), ⁵⁶Ni lines that dominate at early epochs (e.g. at 0.812   MeV or 1.562   MeV) vanish in the spectra at later times, according to the decreasing amounts of ⁵⁶Ni. Then, the spectra are mainly formed by strong emission lines of ⁵⁶Co and a continuum contribution due to Compton scattering of line photons. The optical depth to Compton scattering mainly depends on the column density of target electrons. Since the energies of gamma-ray photons of ~ 1   MeV are much higher than the corresponding binding energies of electrons in atoms, nearly all electrons, regardless of whether bound or unbound, are accessible as targets of Compton scattering processes. As the ejecta expand with time, optical depths are reduced, leading to an enhancement of the lines with respect to the continuum.

Besides these common properties of both explosion models, there are also some pronounced differences. The gamma-ray emission in the delayed detonation scenario evolves faster than in the WD-WD merger, a fact that is also visible in a comparison of the bolometric gamma-ray light curves (energy range from 0.05   MeV to 4.0   MeV) of the two models (see Fig. 2, upper panel). The delayed detonation produces a peak photon flux of 1.82 × 10^-2   cm²   s^-1 at 54.3   days, whereas the merger yields a maximum flux of 1.43 × 10^-2   cm²   s^-1 at 75.7   days after the explosion. Since the masses of produced radioactive ⁵⁶Ni are nearly equal in both models, this is purely a consequence of the transport of gamma rays only being, to first order, sensitive to the column density of the material above the emission region; i.e., the higher total mass of the WD-WD merger delays the gamma-ray emission and gives rise to a lower (angle-averaged) peak flux compared to the delayed detonation model. The convergence of the two light curves at late times in Fig. 2 reflects the similarity of the ⁵⁶Ni mass in both models. In the optically thin limit, the gamma-ray luminosity is given by (1)where t_Co is the lifetime of ⁵⁶Co (Sim & Mazzali 2008). Thus, if the distance to the object is known, late-time measurements of gamma-ray luminosities can be used to unambiguously determine the explosion yield of ⁵⁶Ni.

Fig. 1 Spectral evolution of the gamma-ray emission from the delayed detonation (red) and the violent merger model (dashed black) for different epochs after the explosion (indicated in the upper left of each panel). The spectral spread due to different viewing angles is shown for the maximum-light epochs of the two models in gamma rays (indicated in light red for the delayed detonation model in the third panel and in gray for the merger model in the fourth panel). Part of the effect is obscured by Monte Carlo noise in particular in the continuum. This problem is largely removed by using hardness ratios and broadband light curves. The 56Ni and 56Co emission lines are indicated in the first panel, and the flux bands C1, L1, and L2 discussed in Sect. 3.2 are depicted in the second panel.

Another distinguishing feature can be seen in the early-time spectra of the delayed detonation model at 20.1 and 34.9   days after the explosion: While two prominent lines of ⁵⁶Ni can be identified at 0.158   MeV and 0.270   MeV, these two lines are nearly totally degraded in the merger model and vanish in the background of continuum emission. This effect can be explained by the energy sensitivity of the Compton cross section. Since the cross section decreases with increasing photon energy, especially lines at low energies suffer from effective Compton down-scattering and the additional contamination of likewise down-scattered higher energy photons. Therefore, the two lines can only build up if a significant amount of ⁵⁶Ni is located at small optical depths (cf. Gómez-Gomar et al. 1998), which directly connects the occurrence of low-energy ⁵⁶Ni lines to the distribution of the radioactive material. These different distributions of ⁵⁶Ni can be seen in Figs. 1 and 2 of Röpke et al. (2012), where it is shown that there is much more ⁵⁶Ni at higher velocities in the delayed detonation model than in the merger model. Furthermore, there is less material surrounding the ⁵⁶Ni regions in the delayed detonation model, and the corresponding column densities are therefore lower than in the merger scenario. This property is clearly mirrored in the evolution of the gamma-ray emission, but cannot be inferred easily from measurements in other wavelength ranges (see e.g. Fig. 3 in Röpke et al. 2012). The greater optical depths outside the ⁵⁶Ni region lead to more efficient Compton down-scattering and thus a softer spectrum of the merger model. This is further enhanced by iron-group elements being confined to lower velocities in the merger, leading to less photoelectric absorption than in the delayed detonation.

Fig. 2 Bolometric gamma-ray light curve (upper panel) and bolometric UVOIR light curve (lower panel) for the delayed detonation (red) and the violent merger model (dashed black). The light curve spread due to different viewing angles is indicated in light red and gray. The photon fluxes and the luminosities are normalized to a distance of 1   Mpc.

Fig. 3 Peak line flux ratios of the gamma-ray emission from the delayed detonation (red) and the violent merger model (dashed black). The graph on the left depicts the line ratio R1 = F(0.847   MeV)/F(2.598   MeV) of two 56Co lines, the graph on the right illustrates the line ratio R2 = F(0.158   MeV)/F(0.847   MeV) of a 56Ni and a 56Co line. The flux ratios are normalized to the optically thin limit.

The influence of different viewing angles on the gamma-ray spectra is illustrated in Fig. 1 for the maximum-light epochs of the two models in gamma rays. While the strongest lines of the delayed detonation model do not show much variation, the asymmetric structure of the ejecta in the merger model leads to spectral features of varying magnitude. For certain viewing angles, a distinction between the spectra of the two models can be very difficult. The low-energy range of the spectra is still the most suitable for distinguishing the two models. In the merger model, the higher column densities due to the higher total mass result in more effective Compton down-scattering of the gamma-ray photons in this energy range than in the delayed detonation model. This hinders the formation of prominent low-energy ⁵⁶Ni lines. The effects of observing the two explosion models at different lines of sight are also illustrated for the bolometric gamma-ray light curves in Fig. 2. As before, the asymmetric distribution of ejecta in the merger model results in a much wider spread of photon fluxes compared to the delayed detonation model. Nevertheless, the different times of maximum flux, as well as the differing early time evolutions of the light curves, provide clear distinctive features that can be used to differentiate the underlying explosion models. These differences are again due to the different total masses involved in the two explosion scenarios. The higher mass of the merger model leads to more efficient photon trapping at earlier times, delays the rise of the photon flux, and results in a flux peak occurring at later times.

As a comparison, we show the bolometric UVOIR light curves of the two models in the lower panel of Fig. 2. For many viewing angles, a distinction between the delayed detonation and the merger model is nearly impossible. This is contrasted by the behavior of the bolometric gamma-ray light curves. Here, in spite of viewing-angle effects, especially early time measurements and the determination of the maximum fluxes are very promising. This again underlines the advantages of gamma-ray emission studies of SNe Ia.

In the following, we discuss further possibilities for distinguishing the two explosion models on the basis of angle-averaged spectra and present the fundamental distinguishing characteristics. As described in the previous paragraph, viewing-angle effects can considerably complicate the process of drawing inferences about certain explosion scenarios, but distinctions are still possible.

3.2. Line and hardness ratios

In addition to the analysis of line fluxes and light curves, line and hardness ratios represent further diagnostic tools that can be utilized to study the gamma-ray emission of SNe Ia (cf. Höflich et al. 1998; Gómez-Gomar et al. 1998; Sim & Mazzali 2008). While the information inferred from absolute flux values is always restricted by how well the distance to the source is known, flux ratios do not depend on distance. In Fig. 3, two characteristic peak-intensity line ratios of the WD-WD merger and the delayed detonation model are illustrated. Following Sim & Mazzali (2008), we define R₁ = F(0.847   MeV)/F(2.598   MeV) as the ratio of two ⁵⁶Co lines and R₂ = F(0.158   MeV)/F(0.847   MeV) as the ratio of a ⁵⁶Ni and a ⁵⁶Co line.

Fig. 4 Hardness ratios of the gamma-ray emission from the delayed detonation (red) and the violent merger model (dashed black). The ratio H1 = C1/L1 is shown on the left, the ratio H2 = L1/L2 is displayed on the right. To illustrate the sensitivity to viewing-angle effects, H1 is shown for different lines of sight in the left panel.

Flux ratios are affected by similar processes to those discussed in the previous paragraph. Owing to the energy sensitivity of Compton cross sections, line ratios are, at early times before the optically thin limit, dependent on the column density of electrons and therefore on the material above the region containing the radioactive species. The ratio of two lines of the same radioactive isotope is therefore determined by the opacity ratios at the respective line energies. This is shown in the left plot of Fig. 3 for the case of R₁. Since the radioactive isotopes in the merger model are surrounded by much more ejecta material, the line ratio shortly after the explosion is much lower. This is different in the delayed detonation model. Here, more ⁵⁶Ni, hence more ⁵⁶Co, at lower optical depths increases the line ratio significantly. It is therefore not crucial to choose two specific ⁵⁶Co lines for the examination of such an effect, but the extent of the diagnostic validity relies on a sufficient spread between the energy of the two selected lines because of the energy dependence of the Compton cross section (cf. Sim & Mazzali 2008).

In contrast to R₁, R₂ is a function that decreases with time. Since R₂ is a ratio of two lines from different isotopes, this behavior reflects the difference between the half-lives of ⁵⁶Ni and ⁵⁶Co: While the ⁵⁶Co line at 0.847   MeV strengthens, the 0.158   MeV line of ⁵⁶Ni fades away at later times, leading to lower peak flux ratios. The information value of R₂ is based on the following aspect. As discussed before, the ⁵⁶Ni present in the outer shells at small optical depths is the main source of the emerging 0.158   MeV line, whereas the emission of the 0.847   MeV line comes from the total abundance of ⁵⁶Co in the ejected material, especially at later times. Therefore, a higher value of R₂ indicates a larger deposit of ⁵⁶Ni in the outer layers of the ejecta, and the different distributions of this isotope in the two models are clearly reflected in the evolution of the line ratios shown in Fig. 3. As stated before (Gómez-Gomar et al. 1998; Sim & Mazzali 2008), the relatively low energy of the 0.158   MeV line makes it also very sensitive to photoelectric absorption processes. Since photoelectric opacities depend on the compositional structure of the ejecta above the radioactive material, appropriate ratios of low-energy ⁵⁶Ni lines to ⁵⁶Co lines at higher energies are well suited to studying the composition of SNe Ia. The success in finding distinct abundance features of course relies on the quality of the measured gamma-ray data and, for this reason, also on the distance to the explosion site (see also the remarks in the next section).

A way to partially circumvent the need for highest quality gamma-ray data for detailed SNe Ia studies is provided by the application of hardness ratios. Instead of discrete line intensities, the fluxes of broader energy bands are compared to each other. On the one hand, in this coarser method, some information is necessarily lost. But on the other hand, in contrast to other wavelength ranges, the relative simplicity of gamma-ray spectra and the rather small number of factors that influence gamma-ray emission processes make hardness ratios an important diagnostic tool. Following Sim & Mazzali (2008), Fig. 4 shows two hardness ratios, H₁ = C₁/L₁ and H₂ = L₁/L₂, as examples for the delayed detonation and the merger model. Here, C₁ denotes the energy band from 0.1   MeV to 0.3   MeV, where the main contribution comes from continuum emission by Compton down-scattering and photo-absorption processes. The energy bands L₁ (from 0.7   MeV to 2.0   MeV) and L₂ (from 2.0   MeV to 4.0   MeV) are characterized by pronounced lines of ⁵⁶Co, while the importance of continuum emission decreases with higher photon energies.

Similar to line ratios, hardness ratios are mainly affected by the energy dependence of the Compton cross section. Since H₁ directly mirrors the strength of the continuum emission relative to that of the lines, the violent merger produces higher H₁ values than the delayed detonation – a direct consequence of the radioactive material’s location at higher optical depths. Similar to the line ratio R₂, H₁ is an indicator of different column densities of target electrons. Since photoabsorption processes can be significant in the energy band C₁, H₁ also serves to a certain degree as an indicator of different compositions. H₂ represents the flux ratio of two line-dominated energy bands and is analogous to the line ratio R₁. It depends mainly on the ratio of the Compton cross sections in the two corresponding energy bands and is also suitable to distinguish our explosion models. As a result, hardness ratios offer an alternative opportunity to extract information from the gamma-ray emission of SNe Ia – particularly for more distant explosion events.

The results in Figs. 3 and 4 show that line and hardness ratios can be used as additional diagnostic tools to distinguish the delayed detonation from the merger model on the basis of their gamma-ray emission. These ratios are directly linked to the distribution of ⁵⁶Ni in the ejecta and their dependence on the column density of target electrons above the radioactive material makes them sensitive to different compositions and masses of the outer ejecta layers. Even in light of possible viewing-angle effects (see left panel of Fig. 4 as an example), hardness ratios have proven to be quite robust in distinguishing our two models. Together with broadband light curve measurements, they provide the best chances for conclusions on certain model features, especially for further SNe Ia.

However, besides the changes in the gamma-ray emission due to different viewing angles, other variations within a certain explosion scenario (e.g. additional rotation and mixing effects, modifications of details in the explosion mechanism) can lead to a spread in gamma-ray fluxes that certainly makes it very difficult to distinguish between different realizations of SN Ia explosions. But concerning our two very different models representing two different progenitor classes, we are confident that the delayed detonation and the violent merger described above will leave a unique imprint on the gamma-ray emission. In the case of the same ⁵⁶Ni mass in both models, a higher total ejecta mass surrounding the radioactive material in the applied violent merger is unavoidable. Corresponding to our results, which we have discussed before, this has a systematic effect on the gamma-ray observables. As we show in the next section, the prospects for differentiating our two models in case of a nearby SN Ia are very promising, but they rely on the development of new MeV satellite missions in the near future.

4. Detection prospects

Despite the importance of the MeV energy range for the study of different astrophysical objects and processes (cf. Greiner et al. 2012; Summa et al. 2011), the mission with the highest sensitivities at these energies was the COMPTEL instrument aboard the CGRO satellite in the mid-nineties. One possible successor with an enhanced sensitivity of a factor 40 is the proposed GRIPS (Gamma-Ray Imaging, Polarimetry and Spectroscopy) mission (Greiner et al. 2009, 2012). The focus of this section is on the progress that could be made in the future concerning the detection of gamma-ray emission from SNe Ia, using the GRIPS instrument as an example.

Because it is able to detect photons with energies from 0.2   MeV to 80   MeV, GRIPS is specifically designed to search for gamma-ray bursts and blazars, to look at particle acceleration and radiation processes in a variety of cosmic sources, and to study supernova explosion and nucleosynthesis mechanisms. The main instrument of GRIPS is the Gamma-Ray Monitor (GRM), a combined Compton scattering and pair creation telescope consisting of two separate detectors with an effective area of 195   cm² and an energy resolution of 17   keV at 1.8   MeV. The so-called tracker, made of silicon strips, is the first detector where the initial interaction of the incoming gamma-ray photons takes place. Except for the entrance surface, it is surrounded by the second detector, a calorimeter composed of LaBr₃ scintillator material that allows for the energy determination of the secondary particles. In the case of a Compton scattering event in the tracker, the incident gamma-ray photon interacts with an electron, whose energy and position can be measured. The scattered photon is recorded in the calorimeter where its energy and interaction point can be reconstructed. With these data, it is possible to calculate the direction and the energy of the incident photon. In the case of a pair creation event, the incident gamma-ray photon is converted into an electron-positron pair within the first detector. The original direction of the incident photon can be determined from the tracked directions of these two particles. The energy of the two secondaries, and therefore the energy of the incident photon, is measured with the help of both the tracker and the calorimeter.

GRIPS measurements of gamma-ray emission from SNe Ia were simulated using the MEGAlib software package (Zoglauer et al. 2006). This package uses the GEANT4 toolkit (Agostinelli et al. 2003) to simulate the passage of gamma rays and other particles through the detector, taking possible particle interactions and decays into account. The detector response to an incident gamma photon was calculated from the energies deposited by the particles in sensitive elements (silicon strips and scintillator crystals), taking instrumental effects into consideration such as the energy resolution and noise suppression thresholds. MEGAlib includes a dedicated event reconstruction algorithm, which was applied to the events that pass the trigger criteria (coincident hits in the silicon strip detector and the calorimeter). This algorithm either reconstructs the event as a valid Compton scattering or pair creation event or rejects it. In the case of a Compton event, the incident photon direction is constrained to a circle around the direction of the scattered photon. To select the events compatible with the source position of the photons, we required the minimum distance between the circle and the source position to be less than 2°. In addition, if the recoil electron left a track in the silicon detector, the Compton scattering plane could be reconstructed and its rotation angle around the direction of the scattered photon was required to be within 30° from the source position. The model of the GRM detector used in this study corresponds to the setup described in Greiner et al. (2012).

Measurements of gamma-ray emission from most sources are strongly affected by the presence of radiation backgrounds. In our simulations we include the background from diffuse cosmic photons based on Gruber et al. (1999) and the background from albedo photons produced in the Earth’s atmosphere (Mizuno et al. 2004; Ajello et al. 2008). In Boggs (2006) these two components were found to be the dominating background for a Compton telescope at a low-inclination low Earth orbit. The generated background photons were processed through the same simulation and selection procedure described above, and then the reconstructed background events were added to the source events.

Fig. 5 Simulated detector response for the GRM instrument aboard GRIPS using an exposure time of 105   s. Shown is a comparison of the simulated angle-averaged gamma-ray spectra of the delayed detonation model (red) and the merger model (dashed black) at 25   days after the explosion for different distances to the source (indicated in the upper right).

Fig. 6 Simulation results for hardness ratio measurements with the GRM instrument (exposure time 105   s) for our two explosion models. On the left, a source distance of 1   Mpc is assumed, and the right figure shows the results for a source distance of 5   Mpc. Taking the sensitivity limits of GRIPS into account, here denotes the energy band from 0.2   MeV to 0.4   MeV. The solid lines show the results of ideal measurements without background fluctuations and statistical errors.

Fig. 7 Simulation results for light curve measurements (energy range from 0.4   MeV to 4.0   MeV) with the GRM instrument (exposure time 105   s) for our two explosion models. On the left, a source distance of 1   Mpc is assumed, and the right figure shows the results for a source distance of 10   Mpc. The solid lines show the results of ideal measurements without background fluctuations and statistical errors.

To account for the specific sensitivity range of GRIPS, we define here the hardness ratio analogous to H₁ as the quotient , where denotes the energy band from 0.2   MeV to 0.4   MeV. In Fig. 5, the simulation results for the measured gamma-ray spectra are shown for the two models at 25   days after the explosion. The exposure time of 10⁵   s corresponds to roughly five days in the all-sky scanning mode of GRM, a time interval that allows for reasonable studies of the time evolution. Accurate measurements of the line and hardness ratios become difficult for large source distances due to background fluctuations and limited event statistics in the high-energy part of the spectrum. For the GRIPS mission, nearly the best discrimination between the two explosion models is provided by measurements of the hardness ratio. The simulation outcomes of the measurement of are depicted in Fig. 6. This ratio can be used to distinguish the models up to a source distance of 5   Mpc to 7   Mpc. Our simulation results for light curve measurements are shown in Fig. 7. For a supernova event at a distance of 1   Mpc, a very detailed and accurate light curve can be measured and constraints on certain explosion models are possible. According to our analysis of light curve measurements, GRIPS should be able to easily distinguish the two explosion scenarios for a source distance up to 10   Mpc.

Using the gamma-ray spectrum of the delayed detonation model at 60   days after the explosion as input, we additionally carried out detector response simulations for different source distances and a longer exposure time of 10⁶   s (roughly 12   days in on-axis pointing mode). The detection capabilities of GRIPS concerning the gamma-ray emission of SNe Ia are illustrated in Fig. 8, where the simulated measurements after background subtraction are depicted. While the strongest lines at medium and higher energies can still be resolved even for sources at 20   Mpc and more, the low-energy range of the measured spectra from sources at greater distances is dominated by background fluctuations. Although GRIPS will provide a spectral resolution of all details in the energy range from 0.2   MeV to 80   MeV only for SNe Ia at distances up to a few Mpc, the application of line and hardness ratios enables valuable spectral studies for even greater distances. For an exposure time of 10⁶   s, our simulations show that the hardness ratio can be used to distinguish the two models up to 10   Mpc. With this longer exposure time, GRIPS light curve measurements can serve as distinctive marks of our models up to distances of 15   Mpc to 16   Mpc. Even explosion events in the Virgo cluster will be accessible for gamma-ray studies with such an instrument.

The success of such investigations of course depends on the accuracy of the applied background models (see above). According to Ajello et al. (2008), an uncertainty of a factor of three seems to be quite reasonable. Although the chances for a clear distinction between certain explosion models decrease considerably for greater source distances, the ability of GRIPS to prove the gamma-ray emission of SNe Ia at distances beyond 20   Mpc will lead to a significant improvement of SNe Ia detection statistics in the gamma-ray energy range. Owing to the low sensitivities of previous gamma-ray observatories, only one SN Ia has been detected up to now (cf. Milne et al. 2004).

Fig. 8 Simulated detector response for the GRM instrument aboard GRIPS for an exposure time of 106   s. Shown is the simulated angle-averaged gamma-ray spectrum of the delayed detonation model at 60   days after the explosion for different source distances (indicated in the upper right).

In cases of events comparable to SN 2011fe, the detection of gamma-ray emission should be easily possible with an instrument like GRIPS. Our simulation results show that important constraints on three-dimensional explosion models can be drawn immediately. Since the limited sensitivity of GRIPS below 300   keV hinders a thorough examination of this energy range for sources at greater distances, the ⁵⁶Ni lines at 0.158   MeV and 0.270   MeV, which can serve as important diagnostic tools (see also Sect. 3.1), are not so easily accessible. This problem can be cured by combining the gamma-ray data of GRIPS with the data of the likewise proposed ASTRO-H mission (cf. Takahashi et al. 2010) that covers the respective energy range with sufficient sensitivity. A recent study concerning the detection capabilities of ASTRO-H shows that distance limits comparable to those of the GRIPS mission can be reached (Maeda et al. 2012). The realization of two missions in the near future with sensitivities and photon energy coverages such as for GRIPS and ASTRO-H would therefore offer unprecedented detection prospects for the gamma-ray emission of SNe Ia and equally support the efforts in reducing the parameter space of current three-dimensional model concepts. Especially the degeneracy concerning optical observables of different explosion models for the recent explosion event SN 2011fe (cf. Röpke et al. 2012) could certainly be removed by a study of the corresponding gamma-ray emission, as shown in the previous paragraphs.

5. Conclusions

Using three-dimensional simulations of a delayed detonation of a Chandrasekhar-mass WD and a violent merger of two WDs as test cases, we showed that the calculated gamma-ray spectra are very useful for drawing conclusions on the different ejecta structures of the two models, but the viewing-angle effects always have to be taken into account. The direct link of gamma-ray spectra to the abundance of ⁵⁶Ni – the radioactive isotope that powers the radiation in all other wavelength bands – and their reduced complexity due to their straightforward connection to fundamental physical processes make them a promising utility that can complement other measurements. Since it is mainly sensitive to the column density of the material above the emission region, the gamma-ray emission of SNe Ia is well suited to studying the composition, as well as the total mass, of the ejecta. Our analysis of different diagnostic tools, such as line and hardness ratios, demonstrates that hardness ratios especially offer the best prospects to distinguish the two models at greater distances. We also underline the value of following the evolution of gamma-ray emission over an extended period of time. Even low-resolution spectra of distant explosion events lead to characteristic light curve shapes that allow a differentiation of the two models. If the flux maximum can be obtained to a precision of about five days, bolometric measurements are sufficient to distinguish the two models. The prospects of success of course depend on the future development in the sector of detection instruments. Concerning the sensitivities in the hard X-ray, as well as in the soft gamma-ray range, a major step forward will occur with the planned ASTRO-H satellite and the proposed GRIPS mission, allowing for observations of gamma-ray emission from SNe Ia up to 20   Mpc according to conservative estimates. Although a spectral resolution of all line features will only be provided for nearby explosion events, our simulated GRIPS observations show that hardness ratio and light curve measurements can distinguish our models up to source distances of 10   Mpc to 16   Mpc, depending on the applied exposure time. This enhances the number of target candidates in the MeV energy range significantly and will allow for more meaningful gamma-ray emission studies of SNe Ia than to now, including potentially unique opportunities for model discrimination.

Acknowledgments

This work was supported by the Helmholtz Association (HGF) through the Nuclear Astrophysics Virtual Institute (VH-VI-417). This work was in part funded by the Deutsche Forschungsgemeinschaft (DFG) through the graduate school on “Theoretical Astrophysics and Particle Physics” (GRK 1147). The work of F. K. Röpke and M. Fink was supported by the Deutsche Forschungsgemeinschaft via the Emmy Noether Program (RO 3676/1-1) and by the ARCHES prize of the German Federal Ministry of Education and Research (BMBF). Funding for collaboration was provided by the DAAD/Go8 German-Australian exchange program. The work of A. Ulyanov was supported under ESA’s Strategic Initiative AO/1-6418/10/NL/Cbi. K. Maeda received support from the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. The simulations presented in this work were carried out at the Jülich Supercomputing Center (Germany) as part of the projects HMU14 and PRA026 within the Partnership for Advanced Computing in Europe (PRACE). The GRIPS/GRM model used in this work was developed by A. Zoglauer. The GRIPS simulations were performed using the UCD Pascal cluster funded through the SFI Equipment Grant for High-Performance Computing Cluster. This work was supported by the NCI National Facility at the Australian National University.

References

All Figures

Fig. 1 Spectral evolution of the gamma-ray emission from the delayed detonation (red) and the violent merger model (dashed black) for different epochs after the explosion (indicated in the upper left of each panel). The spectral spread due to different viewing angles is shown for the maximum-light epochs of the two models in gamma rays (indicated in light red for the delayed detonation model in the third panel and in gray for the merger model in the fourth panel). Part of the effect is obscured by Monte Carlo noise in particular in the continuum. This problem is largely removed by using hardness ratios and broadband light curves. The 56Ni and 56Co emission lines are indicated in the first panel, and the flux bands C1, L1, and L2 discussed in Sect. 3.2 are depicted in the second panel.

In the text

	Fig. 2 Bolometric gamma-ray light curve (upper panel) and bolometric UVOIR light curve (lower panel) for the delayed detonation (red) and the violent merger model (dashed black). The light curve spread due to different viewing angles is indicated in light red and gray. The photon fluxes and the luminosities are normalized to a distance of 1   Mpc.
In the text

Fig. 3 Peak line flux ratios of the gamma-ray emission from the delayed detonation (red) and the violent merger model (dashed black). The graph on the left depicts the line ratio R1 = F(0.847   MeV)/F(2.598   MeV) of two 56Co lines, the graph on the right illustrates the line ratio R2 = F(0.158   MeV)/F(0.847   MeV) of a 56Ni and a 56Co line. The flux ratios are normalized to the optically thin limit.

In the text

	Fig. 4 Hardness ratios of the gamma-ray emission from the delayed detonation (red) and the violent merger model (dashed black). The ratio H1 = C1/L1 is shown on the left, the ratio H2 = L1/L2 is displayed on the right. To illustrate the sensitivity to viewing-angle effects, H1 is shown for different lines of sight in the left panel.
In the text

	Fig. 5 Simulated detector response for the GRM instrument aboard GRIPS using an exposure time of 105   s. Shown is a comparison of the simulated angle-averaged gamma-ray spectra of the delayed detonation model (red) and the merger model (dashed black) at 25   days after the explosion for different distances to the source (indicated in the upper right).
In the text

Fig. 6 Simulation results for hardness ratio measurements with the GRM instrument (exposure time 105   s) for our two explosion models. On the left, a source distance of 1   Mpc is assumed, and the right figure shows the results for a source distance of 5   Mpc. Taking the sensitivity limits of GRIPS into account, here denotes the energy band from 0.2   MeV to 0.4   MeV. The solid lines show the results of ideal measurements without background fluctuations and statistical errors.

In the text

Fig. 7 Simulation results for light curve measurements (energy range from 0.4   MeV to 4.0   MeV) with the GRM instrument (exposure time 105   s) for our two explosion models. On the left, a source distance of 1   Mpc is assumed, and the right figure shows the results for a source distance of 10   Mpc. The solid lines show the results of ideal measurements without background fluctuations and statistical errors.

In the text

	Fig. 8 Simulated detector response for the GRM instrument aboard GRIPS for an exposure time of 106   s. Shown is the simulated angle-averaged gamma-ray spectrum of the delayed detonation model at 60   days after the explosion for different source distances (indicated in the upper right).
In the text