Three-Dimensional Simulation of Double-Detonations in the Double-Degenerate Model for Type Ia Supernovae and Interaction of Ejecta with a Surviving White Dwarf Companion

Three-Dimensional Simulation of Double-Detonations in the Double-Degenerate Model for Type Ia Supernovae and Interaction of Ejecta with a Surviving White Dwarf Companion

Ataru Tanikawa    Ken’ichi Nomoto    Naohito Nakasato
Abstract
333Submitted to the Astrophysical Journal, July 21st 2018

We study the hydrodynamics and nucleosynthesis in the double-detonation model of Type Ia supernovae (SNe Ia) and the interaction between the ejecta and a surviving white dwarf (WD) companion in the double-degenerate scenario. We perform smoothed particle hydrodynamics (SPH) simulation coupled with nuclear reaction networks. We set up a binary star system with and carbon-oxygen (CO) WDs, where the primary WD consists of a CO core and helium (He) shell with and , respectively. We follow the evolution of the binary star system from the initiation of a He detonation, ignition and propagation of a CO detonation, and the interaction of SN ejecta with the companion WD. The companion (or surviving) WD gets a flung-away velocity of  km s, and captures Ni of , and He of . Such Ni and its decay products may not be observed due to sedimentation, while such He can be detected on the surface of surviving WDs. The SN ejecta contains a “companion-origin stream”, and unburned materials stripped from the companion WD (). The ejecta has also a velocity shift of  km s due to the binary motion of the exploding primary WD. These features would be prominent in nebular-phase spectra of oxygen emission lines from the unburned materials like SN 2010lp and iPTF14atg, and of blue- or red-shifted Fe-group emission lines from the velocity shift like a part of sub-luminous SNe Ia. We expect SN Ia counterparts to the D model would leave these fingerprints for SN Ia observations.

binaries: close — galaxies: evolution — hydrodynamics — supernovae: general – white dwarfs
Corresponding author: Ataru Tanikawatanikawa@ea.c.u-tokyo.ac.jp\move@AU\move@AF\@affiliation

Department of Earth Science and Astronomy, College of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan; tanikawa@ea.c.u-tokyo.ac.jp \move@AU\move@AF\@affiliationRIKEN Advanced Institute for Computational Science, 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan

\move@AU\move@AF\@affiliation

Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, 5–1–5, Kashiwanoha, Kashiwa, 277–8583, Japan

\move@AU\move@AF\@affiliation

Department of Computer Science and Engineering, University of Aizu, Tsuruga Ikki-machi Aizu-Wakamatsu, Fukushima, 965-8580, Japan

1 Introduction

The progenitor system of Type Ia supernovae (SNe Ia) is one of the biggest mysteries in astronomy and astrophysics. It is generally thought that an SN Ia is powered by thermonuclear explosion of a carbon-oxygen (CO) white dwarf (WD). However, the progenitor system is yet to be confirmed. Since a single CO WD never starts exploding spontaneously, an exploding CO WD must have a companion star. The stellar type of the companion star has been under debate. There is a famous and long-standing dichotomy between single degenerate (SD; e.g. Nomoto & Leung, 2018) and double degenerate (DD Iben & Tutukov, 1984; Webbink, 1984) scenarios, where the companion star is a main-sequence or red-giant star in the SD scenario, or is an another WD in the DD scenario. Other scenarios are also suggested, such as the core degenerate scenario (Kashi & Soker, 2011).

Recent observations have revealed some significant constraints on the SD scenario. Red-giant stars are absent in the pre-explosion images of SN 2011fe and SN 2014J (Li et al., 2011; Kelly et al., 2014, respectively), which are the closest SNe Ia in these decades. No main-sequence star has been detected in a supernova remnant LMC SNR 0509-67.5 (Schaefer & Pagnotta, 2012; Litke et al., 2017), although spin-up/spin-down models can explain the non-detection (Justham, 2011; Di Stefano et al., 2011; Hachisu et al., 2012; Benvenuto et al., 2015). However, we should note some SNe Ia indicate signals supporting the SD scenario. For example, PTF11kx has given a signature of the interaction of supernova (SN) ejecta and circumstellar matter (Dilday et al., 2012), and iPTF14atg and SN 2012cg exhibit the interaction of supernova ejecta and non-degenerate companion stars (Cao et al., 2015; Marion et al., 2016, respectively). SNe Ia may have several types of progenitor systems, although they may be dominated by a single type of a progenitor system.

The DD scenario suffers from the following problem, if one assumes the DD systems are dominant progenitor systems for SNe Ia. Super-Chandrasekhar DD systems, whose total mass is more than Chandrasekhar mass, merge at a fewer rate than the SN Ia event rate (e.g. Maoz et al., 2014). In the violent merger model (Pakmor et al., 2010), the primary CO WD in a DD system is ignited by hydrodynamical effects, and hence super-Chandrasekhar DD systems is not necessarily needed. However, Sato et al. (2015, 2016) have shown that the violent merger model works well only when DD systems have the companion mass of ; the DD systems are super-Chandrasekhar DD systems. Although Kashyap et al. (2015, 2017) have suggested spiral instability after DD mergers drives thermonuclear explosions, Sato et al’s results have indicated the spiral instability can apply only to super-Chandrasekhar DD systems. Fenn et al. (2016) have numerically demonstrated thermonuclear explosion of the primary WDs in detached DD systems, and found that the successful DD systems are super-Chandrasekhar DD systems. Another solution could be collisional DD models (Raskin et al., 2009; Rosswog et al., 2009; Lorén-Aguilar et al., 2010; Dong et al., 2015). Katz & Dong (2012) have argued DD collisions in triple systems can account most of SNe Ia, but it has been controversial (Maoz et al., 2014).

If we take into account sub-Chandrasekhar DD systems, whose total mass is less than the Chandrasekhar mass, the total merger rate of super- and sub-Chandrasekhar DD systems would be comparable to the SN Ia event rate. Such DD systems may explode as SNe Ia with the aid of helium (He) ignition – the double detonation model.

Originally, the double detonation model has been suggested as a derivative of the SD scenario, since the companion star is a non-degenerate star, such as a He star (Nomoto, 1982; Woosley et al., 1986; Livne, 1990; Livne & Glasner, 1990). Guillochon et al. (2010) and Pakmor et al. (2013) have shown that the primary CO WD in a DD system can possibly experience CO detonation driven by He detonation. In particular, a DD system in Guillochon et al. (2010) is a sub-Chandrasekhar DD system. The double detonation model in DD systems requires only a small amount of He, , since the He detonation is triggered by hydrodynamical effects of shock compression. This model is called “Dynamically Driven Double-Degenerate Double-detonation (D) model” by Shen et al. (2018), or “helium-ignited violent merger model” by Pakmor et al. (2013). Hereafter, we refer to this model as D model fore simplicity. The D model is more advantageous than the double detonation model in SD systems in the following reason. Since the double detonation model in SD systems requires such a large amount of He as (Nomoto, 1982), this model is predicted to leave behind signature of the He detonation (Woosley & Weaver, 1994; Woosley & Kasen, 2011); actually the signature has been found (Jiang et al., 2017; Maeda et al., 2018), although the observations of such signature has been rare.

The distinct point of the D model from other DD models is that the companion WD can survive thermonuclear explosion of the primary WD (Pakmor et al., 2013). The DD system is so close that the surviving WD gets hypervelocity (HV)  km after the primary WD explodes. Recently, Shen et al. (2018) have found out three HV WDs from Gaia DR2. If the D model can explain all the SNe Ia in the Milky Way Galaxy, one should find HV WDs in the current and future Gaia data. The number of HV WDs are fewer than expected. However, if more HV WDs would be found in near future, it would support the D model.

If the D model would be the case for a significant fraction of SNe Ia, it is important to study supernova ejecta and surviving WD of the D model. Guillochon et al. (2010) and Pakmor et al. (2013) have not followed WD explosion although they have investigated the merging process of DD systems, and He detonation. Papish et al. (2015) have focused only on ejecta-companion interaction, manually setting up the blast wave of SN Ia explosion. There are several studies for the interaction of SN ejecta with non-degenerate companions (e.g. Pakmor et al., 2008; Liu et al., 2012, 2013).

Therefore, we numerically follow the following sequence of events: the He detonation, CO detonation, WD explosion, and ejecta-companion interaction by means of Smoothed Particle Hydrodynamics (SPH) simulation coupled with nuclear reactions. Although we treat super-Chandrasekhar DD system, we believe super- and sub-Chandrasekhar DD systems have common features in the D explosion.

Our paper is structured as follows. In section 2, we present our SPH simulation method and initial conditions. In section 3, we show simulation results. In section 4, we compare our results with observations of SNe Ia and HV WDs. In section 5, we summarize this paper.

2 Method

Our SPH code is the same as used in Tanikawa et al. (2017) (see also Kawana et al., 2018; Tanikawa, 2018a, b). We thus briefly describe our code. For equation of state (EoS), we use Helmholtz EoS without Coulomb corrections (Timmes & Swesty, 2000). We couple our SPH code with nuclear reaction networks Aprox13 (Timmes et al., 2000). We optimize our code on massively parallel computing environments utilizing FDPS (Iwasawa et al., 2016; Namekata et al., 2018), and accelerate calculations of particle-particle interactions with AVX/AVX2/AVX512 instructions (e.g. Tanikawa et al., 2012, 2013).

Our initial condition is a binary star system consisting of and WDs. The primary one has a CO core and a He shell, and the companion one has only a CO core. We set up the initial condition as follows. We make a single CO WD in the same way as Tanikawa et al. (2015) (see also Sato et al., 2015, 2016). We map SPH particles consistently with the 1D profile of a fully degenerate CO WD with  K, where the CO composition is  % of carbon and  % of oxygen. Subsequently, we relax a configuration of SPH particles by evolving these SPH particles by our SPH code. For the primary WD, we change the CO composition of SPH particles in the outermost shell with to a composition with  % of helium,  % of carbon, and  % of oxygen. Thus, the He shell contains of helium. Note that He and C+O can be mixed in the merging process of two WDs due to Kelvin-Helmholtz instability (Pakmor et al., 2013).

We put these two WDs so that they orbit around each other on a circular orbit with a semi-major axis of  km, where the Roche-lobe radius of the companion WD is the same as its radius according to an approximate formula of Eggleton (1983). We assign star ID 1 and 2 to SPH particles initially belonging to the primary and companion WDs, respectively. We put a hotspot with a size of  km in the He shell of the primary WD. The hotspot is located at the orbital plane of the binary star system in the propagating direction of the primary WD. We set such a large hotspot in order to initiate a He detonation easily.

The total number of SPH particles is . All the particles have equal mass. This means the mass resolution is .

In section 3, we treat two coordinate systems: Cartesian and spherical coordinate systems. In the Cartesian coordinate system, the barycenter of the binary star system is at the coordinate origin, and the barycenteric velocity is zero. The orbital plane of the binary star system is set to the plane. At the initial time, the centers of the primary and companion WDs sit on the - and -axes, respectively. The angular momentum vector of the binary star system points in the same direction of the -axis. To coordinate transformation between the Cartesian and spherical coordinate systems, , , and , where , and and are the polar and azimuthal angles, respectively.

3 Results

We first overview our simulation results in section 3.1. We investigate the SN ejecta and surviving WD (or companion WD) in detail in sections 3.2 and 3.3, respectively.

3.1 Overview

Figure 3.1 shows the time evolution of the density distribution in the binary star system. He detonation starts in the He shell of the primary WD at the time  s, and propagates in the He shell, not into the CO core of the primary WD. The He detonation converges on the back side of the primary WD from its beginning point at  s. A shock wave separates from the He detonation, invades into the CO core, and converges at an off-centered point in the CO core just before  s. Subsequently, a CO detonation occurs at the converging point of the shock wave. Eventually, the primary WD experiences thermonuclear explosion, and the SN ejecta interacts with the companion WD, or to-be surviving WD.

Two high-density, mushroom-shaped, regions are seen in the panels at  s. These regions have unburned CO materials. Such unburned pockets might be formed due to low mass resolution, although the mass resolution is quite high, . In this paper, we conservatively suppose that these unburned materials could be numerical artifacts, and do not include in our discussion.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefDensity distribution at , , , , , , , and  s.

The interaction between the SN ejecta and the companion WD forms an ejecta shadow behind the companion WD (see the panels at  s). The interaction also strips materials of the companion WD, which can be seen as a stream (or streams) denser than its surroundings in the ejecta shadow at and  s. Hereafter, we call this stream “companion-origin stream”. The companion-origin stream flows out after a shock wave, formed by collision between the SN ejecta and companion WD, passes through the companion WD at  s. Note that the shock wave is not formed by collision between the unburned materials and companion WD. The shock wave can be seen as density discontinuity inside the companion WD in the panel at  s, and as pressure discontinuity, pointed by white arrows, inside the companion WD in Figure 3.1.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefPressure distribution at and  s. White arrows point to the pressure discontinuity.

Figure 3.1 shows the distribution of density, star ID, and mass fractions of chemical elements at  s. Note that they are zoomed out times compared to the panels of Figure 3.1. In the density distribution, we can see the ejecta shadow, circular section-shaped. The surviving (or companion) WD is located at the vertex of the circular section. In the star ID distribution, the surviving WD can be also found at the root of the companion-origin stream. The stream consists of C+O. The solid angles of the ejecta shadow and stream are and steradians, respectively. The ejecta shadow is much wider than the stream.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefDistribution of density, star ID, and mass fractions of chemical elements at  s. Note that, if there is no material, the star IDs “0” are assigned.

Aside from the ejecta shadow and stream, the SN ejecta has a spherically symmetric shape. Chemical elements in the SN ejecta are dominated by Fe-group elements (Cr, Fe, and Ni), the lighter Si-group elements (Si and S), O, C, the heavier Si-group elements (Ar, Ca, and Ti), and He in order from the inside. The heavier silicon-group elements are the products of the He detonation in the He shell mixed with CO compositions. Such chemical structure is typical of the double detonation model.

As seen in Figure 3.1, the surviving WD is located far from the coordinate origin by several  km, despite that the binary system is present at the coordinate origin at  s. This is because the surviving WD flies away free from the gravity of the exploding primary WD. We find the surviving WD has HV of  km s, consistent with the velocity of the binary motion  km s.

3.2 Supernova ejecta

3.2.1 Ni mass

In Figure 3.2.2, we show the mass of chemical elements in the SN ejecta, companion-origin stream, and surviving companion WD. The SN ejecta includes the companion-origin stream. The SN ejecta has Ni, most of which are synthesized by the CO detonation in the primary WD. The He detonation yields little Ni () because the He shell is small in mass and contains  % (in mass fraction) of C+O which are mixed initially. The CO detonation also produces the lighter Si-group elements (Si and S) of through incomplete Si burning. The unburned materials are oxygen and carbon. The He detonation synthesizes the heavier Si-group element (Ar, Ca, and Ti) of , especially dominated by Ca.

We compare our nucleosynthesis yields with those in models 2 of Fink et al. (2010), which has the CO core of and the He shell of , being similar to our primary WD. We focus only on the products of CO detonation, since their He shell consists of pure He. Our Ni mass () is larger than theirs (), while our Si-group mass () is smaller than theirs (). We also compare our products of CO detonation with those of Woosley & Kasen (2011). In their models with the primary WD of , Ni masses are . Our nucleosynthesis yields are roughly consistent with those in previous studies. However, further detailed nucleosynthesis studies are necessary to reach a better agreement.

3.2.2 Nucleosynthesis yields in the velocity space

The total mass of the companion-origin stream is . It consists of mostly  % carbon and  % oxygen in mass, being almost the same as the original compositions, but includes a small amount of Ne, Mg, and Si, for each. They are synthesized by shock heating when the SN ejecta collides with the companion WD.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefMasses of chemical elements in the SN ejecta (red), companion-origin stream (blue) and surviving WD (black) at  s. The SN ejecta includes the companion-origin stream. Materials of the SN ejecta and surviving WD are gravitationally unbound and bound to the surviving WD, respectively.

Figure 3.2.2 shows the chemical elements in mass as a function of the radial velocity. We average the mass fractions over all the angle, and find that the abundance structure is similar to the typical double detonation model. The first high-velocity components ( km s) consist of Ca and Ti, synthesized by the He detonation. The second high-velocity components ( km s) are composed of C+O, unburned materials located at the outer region in the CO core of the primary WD. Behind the unburned materials, the third high-velocity components ( km s) includes Si and S, products of incomplete silicon burning. Low-velocity components ( km s) are composed of Ni. The low-velocity components contain a slight amount of C+O at the velocity of  km s, described below in detail.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefChemical elements in mass fraction as a function of radial velocity.

The low-velocity C+O come from the companion-origin stream. The features show up from the view into which the stream comes, and . Interestingly, the chemical structure from these views is the same as the averaging structure at the velocity of  km s. Therefore, C+O have bimodality in the velocity distribution. One component has a higher velocity than Si and S ( km s), and the other has a lower velocity ( km s). Moreover, the low-velocity C+O have a velocity dependent on the viewing angle,  km s from the view of , and  km s from the view of .

We emphasize that the low-velocity C+O originate from the companion-origin stream, not from the unburned materials of the primary WD. As seen in the star-ID panel of Figure 3.1, the companion-origin stream comes into sight from the viewing angles and .

The distribution of C+O in our SN ejecta is different from the delayed detonation model (Seitenzahl et al., 2013; Leung & Nomoto, 2018), although both models have low-velocity C+O. In the delayed detonation model, C+O are extended from the high-velocity to low-velocity components. On the other hand, C+O in our SN ejecta have two peaks in the velocity space.

No low-velocity C+O can be seen from other views and , and , , and , since the stream does not come into these sights. The velocity distributions of chemical elements from these viewing angles are the same as those in the double detonation model, such that materials are dominated by the He-detonation products (Ca and Ti), unburned materials (CO compositions), incomplete silicon burning products (Si and S), and Ni in the descending order of the velocity.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefMass fractions of oxygen, silicon, and nickel as a function of the radial velocity.

The surviving WD moves at a speed of  km s in the bottom-right direction (closely to ) in Figure 3.1, not only at  s but also at the explosion time of the primary WD. Hence, the primary WD also propagates at a speed of  km s in the opposite direction (closely to ) at the explosion time. Therefore, the SN ejecta should be shifted in the propagating direction of the exploding primary WD.

Figure 3.2.2 shows the velocity distribution of O, Si, and Ni observed from various viewing angles. All chemical elements have higher velocities for the viewing angles closer to the direction of the bulk velocity of the SN ejecta. The velocity difference is  km s between and . The velocity of these elements observed from the other viewing angles is intermediate between the velocity observed from the two viewing angles. This is consistent with the velocity of the binary motion of the exploding primary WD,  km s.

The velocity difference does not come from the asymmetric explosion of the double detonation model. In the asymmetric explosion, when the velocity of O and Si from a viewing angle is larger than from another viewing angle, the velocity of Ni from the former is smaller than from the latter (see Fig. 6 in Fink et al., 2010). Note that the bulk motion of the exploding primary WD (or SN ejecta) systematically increases all the velocity of O, Si, and Ni observed from the viewing angle in the propagating direction.

3.3 Surviving white dwarf

The surviving WD has the total mass of , roughly equal to the initial mass. However, it captures a small amount of materials originally from the exploding primary WD. The total mass of the captured materials is , dominated by Ni of . The captured materials contain slight amount of helium (). The captured materials consist of Ni and He in the following reason. They are captured due to their low velocity. Hence, they are located at the center of the explosion, i.e. in a high-density region. In general, when CO detonation passes a high-density region, it mostly synthesizes Ni owing to the rapid nuclear reactions, and leaves a small amount of He as residuals of He produced by photo-dissociation. The surviving WD also captures unburned materials of , mushroom-shaped, seen in Figure 3.1. We should bear in mind that they could be burnt materials (Ni and He). Shen & Schwab (2017) have estimated that a WD captures Ni, which is consistent with our results.

We investigate 1D profiles of the surviving WD at  s shown in Figure 3.3, where we count only gravitationally bound materials to the surviving WD. We find its internal structure (at  km) is virtually undamaged, comparing its density, temperature, and entropy profiles at and  s. Moreover, the surviving WD keeps its C+O.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHref1D profiles of density, temperature, and entropy of the companion WD at  s (red) and  s (black), and of chemical elements of the companion WD at  s.

On the other hand, its external structure is changed by the interaction with the SN ejecta. The surviving WD captures a part of the SN ejecta, and gets an envelope consisting of Ni, C, O, and He in descending order in mass. These Ni and He result from nucleosynthesis in the primary WD, while C and O come from both the primary and surviving WDs. The C and O originally from the primary WD are the unburned materials seen in Figure 3.1, and those originally from the surviving WD are modestly stripped from the surviving WD by the SN ejecta. The envelope has high temperature ( K) and entropy ( erg g K) due to nuclear reactions in the primary WD, and due to the shock heating arising from the collision between the SN ejecta and surviving WD. The entropy of the captured materials is slightly higher than estimated by Shen & Schwab (2017),  erg g K. Hence, the captured materials are slightly less bound than their estimate.

4 Discussion

4.1 Exploding primary white dwarf

First, we discuss SN Ia counterparts to the D model, based on the results shown in section 3. Here, we ignore products yielded by the He detonation, which are the heavy Si-group elements (Ar, Ca, and Ti) with such high velocities,  km s. This reason is as follows. We set the He shell of the primary WD to be so thick () that the He and CO detonation easily occurs in our simulation. However, the D model would succeed when the He shell is (Guillochon et al., 2010; Pakmor et al., 2013), and would indicate smaller signal of these products than our simulation results.

The most prominent feature in our SN ejecta is the companion-origin stream (see Figure 3.1). Owing to the presence of the stream, the abundance of unburned materials has two peaks in velocity space from specific viewing angles, as seen in Figure 3.2.2. The lower velocity component of the unburned materials (a few  km s) can be observed as oxygen emission lines in nebular-phase spectra. Such oxygen emission lines have been observed in SN 2002cx-likes (Jha et al., 2006; Phillips et al., 2007), and a part of SN 2002es-like SN 2010lp (Taubenberger et al., 2013; Kromer et al., 2013) and iPTF14atg (Kromer et al., 2016). In SN 2002cx-likes, possibly explained by pure-deflagration explosion (Kozma et al., 2005), Ni prevails from the inner to outer ejecta, while our SN ejecta confines Ni to the inner parts with  km s. Hence, we rule out SN 2002cx-likes as D explosion candidates.

SN 2010lp and iPTF14atg could be promising counterparts to D model, since their light curves and spectral evolutions are consistent with the explosion of sub-Chandrasekhar mass WDs (Kromer et al., 2013, 2016, respectively). Although iPTF14atg have ultraviolet (UV) pulse due to collision of the SN ejecta with the non-degenerate companion (Cao et al., 2015), the UV pulse could be explained by surface radio activity of Ni produced by the He detonation (Kromer et al., 2016). However, our SN ejecta may be inconsistent with SN 2010lp. SN 2010lp has both blue- and red-shifted oxygen emissions in its nebular spectra. On the other hand, our SN ejecta would have either of blue- or red-shifted oxygen emissions, since the companion-origin ejecta stream propagates in one direction from the explosion center. Note that it may be difficult to identify these oxygen emissions, since the companion-origin stream has small mass (). We need to study nebular-phase spectra of the D model by performing radiative transfer calculations (e.g. Maeda et al., 2010; Botyánszki & Kasen, 2017).

Another feature is the velocity shift of SN ejecta due to the binary motion of the primary WD,  km s. Maeda et al. (2011) have shown iron and nickel emission lines can be tracers of such a velocity shift. Dong et al. (2018) have compiled cobalt emissions in nebular spectra of various SNe Ia, and have found the cobalt emissions are both blue- and red-shifted in SNe Ia with (SN 2007on, SN 2003hv, and SN 2003gs), and either blue- or red-shifted in those with (SN 2016brx, SN 2005ke, SN 1999by, and SN 1991bg). Although they have attributed these blue- and red-shifted features to the collisional DD model (Benz et al., 1989; Lorén-Aguilar et al., 2010; Raskin et al., 2009, 2010; Rosswog et al., 2009; Hawley et al., 2012; Dong et al., 2015), SNe Ia with either of blue- or red-shifted Fe-group emissions can be also explained by the D model.

4.2 Surviving white dwarf companion

Hereafter, we describe issues related to the surviving WD. Shen & Schwab (2017) have discussed post-supernova winds blown by radioactive Ni on the surfaces of surviving WDs. We can compare our results with their surviving CO WD model with . They have modeled the surface of the surviving CO WD, such that the mass of radioactive Ni is , and the entropy of its surface is  erg g K. As we obtain the Ni mass and entropy on the surface of the surviving WD to be , and  erg g K, our simulation results are consistent with their modeling, although materials on the surface in our results are slightly less bound than those in their models. Thus, SN 2011fe could not be explained by the D model, which is the same conclusion as theirs. This is because SN 2011fe would be more luminous than observed if it contained a surviving WD.

We discuss the surface abundance of the surviving WD. First, we consider the surface pollution by interstellar medium (ISM) and interstellar objects (ISOs). The surviving WD could accrete ISM through the Bondi-Hoyle-Lyttleton accretion. The accreting mass is estimated as

(1)

where is the mass accretion rate through Bondi-Hoyle-Lyttleton accretion, is time the surviving WD spending in the Galactic disk, , , and are, respectively, ISM mass density, number density, and sound speed, is the scale height of the Galactic disk, and and are the mass and velocity of the surviving WD. Moreover, we estimate a collision rate of the surviving WD with ISOs like 1l/‘Oumuamua (Meech et al., 2017). The estimate method is the same as in Tanikawa et al. (2018). Then, the surviving WD collides with ISOs at most once, and accrete the ISO mass of  g at most. Eventually, the surviving WD accretes ISM and ISO mass much less than materials captured from the SN ejecta by several orders of magnitude. Hence, ISM and ISOs cannot pollute the surface of the surviving WD.

As shown in section 3.3, the surviving WD captures Ni of , and He of , an additionally unburned materials of , although the unburned materials could be numerical artifacts. Even if the unburned materials are not numerical artifacts, they cannot be regarded as anomaly, since the surviving WD also has similar unburned materials. The Ni will undergo radioactive decay. The Ni decay products could be identified as anomalous abundances. However, the decay products do not necessarily stay on the surface of the surviving WD, since they will receive sedimentation (Paquette et al., 1986; Dupuis et al., 1992). Note that they can keep their position due to radiative levitation (Chayer et al., 1995a, b). It must be necessary to perform sophisticated numerical calculation to follow the time evolution of the surviving WD if we know whether the decay products stay on the surface of the surviving WD. Here, we do not perform such calculations.

The surviving WD certainly has He on its surface, since He does not experience sedimentation. Shen et al. (2018) did not found He on the surface of their HV WDs, although they suggested He cannot be seen due to the low temperature of the HV WD surfaces even if they are present. LP 40–365 (or GD 492), a WD candidate surviving against the Type Iax explosion (Vennes et al., 2017; Raddi et al., 2018b, a), has He-dominated atmosphere. LP 40–365 may get the He-dominated atmosphere in a similar way to our surviving WD. The He in LP 40–365 originates from residuals of He produced by photo-dissociation involved by the Type Iax explosion of LP 40–365 itself, while He in our surviving WD comes from residuals of He produced by photo-dissociation involved by the double detonation explosion of the primary WD. However, we should note that the presence of He on a HV WD cannot be the smoking-gun evidence that the HV WD is a surviving WD against the D explosion. Since WDs generally have He on its surface, a HV WD gets its HV through mechanism other than the D explosion.

5 Summary

In order to study features of SN ejecta and surviving WD in the D model, we perform SPH simulation of a binary star system with and CO WDs, where the primary WD has a He shell with mixed with C+O. The primary WD undergoes thermonuclear explosion following the He detonation on the shell and the CO detonation in the core. The SN ejecta collides with the companion WD, and the interaction of the SN ejecta with the companion WD form the ejecta shadow and companion-origin stream. The companion WD survives the explosion of the primary WD, and flies away at velocity of  km s as the surviving WD.

The SN ejecta has typical features of the double detonation explosion on average. However, there are two different features from the double detonation explosion. (1) First, the SN ejecta strips materials of the companion WD, and contains the companion-origin ejecta consisting of C+O. The companion-origin ejecta can make oxygen emission lines in nebular-phase spectra. Therefore, SN Ia counterparts to the D model can be a part of SN 2002es-likes, such as SN 2010lp and iPTF14atg which have oxygen emission lines in their nebular-phase spectra. (2) Second, the SN ejecta has velocity shift of  km s due to the binary motion of the exploding primary WD. This velocity shift can result in blue- or red-shifted Fe-group emission lines in nebular-phase spectra seen in sub-luminous SNe Ia, such as SN 2016brx, SN 2005ke, SN 1999by, and SN 1991bg.

The surviving WD certainly has He on its surface. The He originates from residuals of He produced by photo-dissociation at the center of the primary WD. However, since WDs generally have He on their surfaces, the presence of He could not be the smoking-gun evidence of surviving WDs against the D explosion. The surviving WD also has Ni decay products on its surface just after it survives the explosion of the primary WD. However, the decay products would experience sedimentation and radiative levitation. In order to determine the surface abundance of the surviving WD, we should follow the long-term evolution of the surviving WD.

Finally, we summarize observational features of SNe Ia under the D explosion. At an early time, its light curve may show a UV pulse due to radioactive nuclei yielded by the He detonation. At the maximum-light time, its spectra indicate Si absorption lines similarly to ordinary SNe Ia. At late times, in the nebular-phase, oxygen emission lines can be observed, where the oxygen originates from the companion-origin stream stripped by the SN ejecta. From specific viewing angles, blue- or red-shifted Fe-group emission lines can be also seen due to the binary motion of the exploding primary WD.


Numerical computations were carried out on Oakforest-PACS at Joint Center for Advanced High Performance Computing, and on Cray XC50 at Center for Computational Astrophysics, National Astronomical Observatory of Japan. The software used in this work was in part developed by the DOE NNSA-ASC OASCR Flash Center at the University of Chicago. This research has been supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, by the Endowed Research Unit (Dark side of the Universe) by Hamamatsu Photonics K.K., by MEXT program for the Development and Improvement for the Next Generation Ultra High-Speed Computer System under its Subsidies for Operating the Specific Advanced Large Research Facilities, by “Joint Usage/Research Center for Interdisciplinary Large-scale Information Infrastructures” and “High Performance Computing Infrastructure” in Japan (Project ID: jh180021-NAJ), and by Grants-in-Aid for Scientific Research (16K17656, 17K05382, 17H06360) from the Japan Society for the Promotion of Science.

Software: FLASH (Fryxell et al., 2000, 2010)

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