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Issue
A&A
Volume 635, March 2020
Article Number A179
Number of page(s) 7
Section Stellar atmospheres
DOI https://doi.org/10.1051/0004-6361/201937245
Published online 31 March 2020

© ESO 2020

1 Introduction

Type Ia supernovae (SNe Ia) are widely believed to stem from thermonuclear explosions of carbon–oxygen white dwarfs in binary systems, but the exact conditions leading to the runaway are debated (see e.g. Livio & Mazzali 2018 for a recent review). Available scenarios differ depending on whether the white dwarf explodes near or below the Chandrasekhar mass (Mch), and on whether the binary companion star is a non-degenerate star in a “single-degenerate” system (Whelan & Iben 1973) or another white dwarf in a “double-degenerate” system (Iben & Tutukov 1984; Webbink 1984). From observables around peak luminosity alone, it is difficult to distinguish between the scenarios (e.g. Röpke et al. 2012), but nuclear physics effects lead to imprints on the chemical structure of the ejecta (e.g. Seitenzahl et al. 2013; Yamaguchi et al. 2015; Flörs et al. 2018, 2020).

A striking difference between the single-degenerate progenitor scenario and white dwarf mergers is the presence of a close companion in the former. The SN ejecta significantly interact with this companion star after the explosion, stripping some hydrogen/helium-rich material from the companion surface and creating a cavity in the SN ejecta, but the companion survives as a bound stellar object (e.g. Wheeler et al. 1973; Marietta et al. 2000; Pakmor et al. 2008; Liu et al. 2012; Pan et al. 2012; Bauer et al. 2019). This has a number of implications. If SNe Ia result from single-degenerate progenitors, it should be possible to detect the surviving companions in their remnants1 (see Ruiz-Lapuente 2019 for a recent review and Li et al. 2019 for a recent search). Although for the Tycho remnant such a detection has been claimed (Ruiz-Lapuente et al. 2004, but see Kerzendorf et al. 2018) other campaigns could not identify suitable candidates (e.g. Schaefer & Pagnotta 2012; Shappee et al. 2013a). Another implication is the enrichment of the SN ejecta with material stripped off from the companion by the SN blast wave. Corresponding hydrogen/helium lines are expected to be present in late-time spectra of SNe Ia (e.g. Mattila et al. 2005; Lundqvist et al. 2013; Botyánszki et al. 2018), but no hydrogen/helium line has been detected yet in late-time observations (e.g. Leonard 2007; Shappee et al. 2013b; Lundqvist et al. 2015; Maguire et al. 2016; Tucker et al. 2019a,b) except in two fast-declining, sub-luminous events (Kollmeier et al. 2019; Prieto et al. 2020).

The presence of a cavity during the ejecta–companion interaction introduces a large-scale asymmetry in the SN ejecta, thus leading to a polarisation signal for favourable viewing angles. Polarisation predictions were computed by Kasen et al. (2004) for a simplified structure and composition of the SN ejecta. No continuum polarisation was found when looking down the cavity (viewing angle 0 degrees) because the ejecta are symmetric in projection, while non-zero signals were predicted for views away from the cavity with a maximum at 90 degrees.

In this pilot study, we derive the observational imprints of the SN interaction with a companion star in a Mch explosion model. Pure deflagrations in Mch carbon–oxygen white dwarfs have been shown to reproduce key properties of so-called “2002cx-like” SNe (Phillips et al. 2007; Jordan et al. 2012; Kromer et al. 2013; Fink et al. 2014) and perhaps of the more extended class of Type Iax SNe (SNe Iax, see Jha 2017, for a recent review). One event of this class, SN 2012Z, represents the only case in which a progenitor system of a thermonuclear SN has beenidentified in pre-explosion images (McCully et al. 2014), suggesting a possible connection between SNe Iax and Mch white dwarfs exploding in single-degenerate systems. Although the progenitor in SN 2012Z was identified as a He star, in this paper we model the interaction with a main-sequence (MS) star and address the impact of this choice on our conclusions.

We note that SNe Iax show large diversity and it is yet not clear whether they result from one single progenitor channel. In particular, alayered ejecta structure has been suggested to explain SNe Iax (Stritzinger et al. 2015; Barna et al. 2017, 2018), a stratification that is hard to reconcile with the highly mixed ejecta produced in pure deflagration models. The layered structure inferred for SN 2012Z, together with the lack of oxygen and intermediate-mass elements (IME) in the inner regions of the ejecta, has been interpreted by Stritzinger et al. (2015) as evidence for a transition from a deflagration to a detonation phase in the pulsational-delayed-detonation (PDD) scenario (Höflich 1995). While a deflagration phase of burning is likely required to explain SNe Iax, whether this is followed by a detonation is still debated as neither pure-deflagration nor delayed-detonation models are able to uniquely reproduce all SN Iax observables.

2 Simulations

In this study, we focus on the previously well-studied model N5def of Fink et al. (2014), which matches the observational properties of the “02cx-like” SN 2005hk well (Kromer et al. 2013). A comprehensive discussion of the explosion model is provided in Fink et al. (2014) and Kromer et al. (2013).

The explosion was initiated by placing five flame kernels near the centre of the white dwarf in a stochastic way. The small number of ignition sparks induces a strong asymmetry of this ignition configuration causing the ashes to rise buoyantly towards the surface of the white dwarf and to wrap around a core that stays gravitationally bound. About 0.37 M⊙ of material are ejected (Kromer et al. 2013; Fink et al. 2014). The evolution is followed up to 100 s in the hydrodynamic simulation. A subsequent nucleosynthetic post-processing step determines the chemical composition of the ejected material. It is based on one million tracer particles that record representative thermodynamic trajectories in the explosion simulation and employs a 384 isotope nuclear network (Travaglio et al. 2004; Seitenzahl et al. 2010).

As described in detail by Liu et al. (2013), hydrodynamical simulations of the ejecta–companion interaction for the MS donor Mch scenario are performed by using the SPH code stellar gadget (Pakmor et al. 2012; Springel 2005). The MS companion structures at the moment of SN explosion are constructed with 1D detailed binary evolution calculations (Han & Podsiadlowski 2004) and then mapped into the SPH code with the HEALPix (Górski et al. 2005) method (Pakmor et al. 2012). The angle-averaged 1D ejecta structure of the N5def model is adopted to represent a SN Iax explosion.

The impact is then simulated in 3D for several hours until the SN ejecta–companion star interaction is finished (i.e. when quantities like stripped masses and kick velocities have reached stable values). This interaction creates a conical hole in the supernova debris with an opening angle of about 50°, leaving an asymmetric ejecta structure. Model_A in Table 1 of Liu et al. (2013) is used to study the observational imprints of SN ejecta–companion interaction.

We predict synthetic observables for three different models: the 3D N5def model (N5def3D), the angle-averaged 1D N5def model (N5def1D), and the companion-interaction (CI) model. All models are re-mapped to a 503 Cartesian grid. Using the Monte Carlo radiative transfer code ARTIS (Kromer & Sim 2009; Bulla et al. 2015), flux and polarisation spectra are calculated for the N5def3D model to study asymmetries in the explosion, and for the CI model to characterise the signal introduced by the interaction with the companion star. For the N5def3D model, we calculate observables for eight different viewing angles, which are chosen to be representative of each octant in the model: n i =1/ 3  (±1,±1,±1) $\vec{n}_{i}=1/\sqrt{3}\,(\pm 1,\pm 1,\pm 1)$. For the CI model, we restrict the viewing direction to the x–y merger plane2 and calculate spectra for five different viewing angles with increasing angular distance ΔΘ from the cavity carved out by the companion: ΔΘ= (0,30,45,90,180) ° $\Delta\Theta=(0,30,45,90,180)^{\circ}$. This corresponds to the following observer orientations: m1 = (−1, 0, 0), m 2 =(−1/2, 3 /2,0) $\vec{m}_2=(-1/2,\sqrt{3}/2,0)$, m 3 =(−1/ 2 ,1/ 2 ,0) $\vec{m}_3=(-1/\sqrt{2},1/\sqrt{2},0)$, m4 = (0, 1, 0), and m5 = (1, 0, 0).

Synthetic observables are extracted using the Event-Based Technique (EBT; Bulla et al. 2015) in the wavelength range [3500, 10 000] Å and between 5 and 16 days after explosion. This time interval covers the B-band maximum-light phase t B max $t_B^{\mathrm{max}}$, occurring 11 days after explosion (Kromer et al. 2013). Given that redder regions of the polarisation spectra have typically larger Monte Carlo noise due to lower fluxes, we follow Bulla et al. (2015) and employ a different number of Monte Carlo packets below (Nq = 4.5 × 108) and above (Nq = 7.5 × 108) 5700 Å. The computed spectra are re-binned in wavelength to achieve a Monte Carlo noise in the polarisation levels of the same order of that in the spectropolarimetric data of SN 2005hk (σP ~ 0.06 per cent).

3 Results

In the following, we present flux and polarisation spectra predicted for the N5def3D explosion model (Sect. 3.1) and CI model (Sect. 3.2) and provide comparisons to spectropolarimetric data of SN 2005hk. We focus our discussion on the two epochs with available polarisation spectra, that is, four days before t B max $t_B^{\mathrm{max}}$ (Chornock et al. 2006) and at t B max $t_B^{\mathrm{max}}$ (Maund et al. 2010). Data are corrected for interstellar polarisation using values reported in Chornock et al. (2006) and Maund et al. (2010).

thumbnail Fig. 1

Top panels: ejecta composition for the N5def3D model. Density ρ (left) and mass fraction Xi of IMEs (middle) and IGEs (right) are shown in the x–y plane. The x–y projected direction of the 8 viewing angles is shown in the density panel. Bottom panels: flux, Q, U and polarisation spectra (from top to bottom) of the N5def3D models are shown 4 days before (left) and at maximum light (right) for the 8 different orientations (n1 −n8) highlighted in the top left panel. Flux and polarisation P of SN 2005hk is shown in black for comparison, with polarimetric data from Maund et al. (2010, bottom right panel) re-binned of a factor of two to have a similar wavelength resolution (Δλ ~ 50 Å) and polarisation uncertainties (σP ~ 0.06 per cent, error bars inbottom panels) as those from Chornock et al. (2006, bottom left panel). Both observed and modelled fluxes are normalised at 6000 Å for presentation purposes.

3.1 Signatures from the explosion

Figure 1 shows flux and polarisation spectra calculated for the N5def3D model at four days before maximum light (left panels) and at maximum light (right panels). The relatively spherical ejecta distribution of the N5def3D model (see top panels of Fig. 1) is reflected in the synthesised spectra. First, the viewing-angle dependence in the flux spectra is modest. In particular, spectra along different orientations are nearly identical redward ~5000 Å, while a relatively small difference is predicted between the brightest and faintest orientation at shorter wavelengths (a factor of ~1.5 in flux). These blue wavelengths are dominated by line blanketing from iron-group elements (IGEs, defined as elements from scandium to zinc), thus suggesting that the viewing angle-dependence in this region is caused by small asymmetries in the distribution of IGEs (see top right panel). Second, the predicted Q and U polarisation signals are rather small; the overall levels are ≲0.2 per cent at both epochs and across the wavelength range investigated. Polarisation across individual spectral features is larger but still relatively modest; the strongest signals are seen four days before peak across the Si II λ6355 line at ~6200 Å (P ~ 0.4 per cent along n1, red line) and the O I λ7774 line at ~7500 Å (P ~ 0.6 per cent along n3, blue line, and n5, orange line). As shown in Fig. 2, distinctive loops are seen across these lines in the QU plane, which is suggestive of small-scale asymmetries in the distribution of silicon and oxygen within the ejecta (see e.g. Wang & Wheeler 2008 and Bulla 2017 for detailed reviews of loops in the QU planes of SNe). The presence of loops provides evidence for departures from a simple bi-axial (e.g. ellipsoidal; see Stevance et al. 2019) configuration of the ejecta and is a natural consequence of mixing in a deflagration phase of burning, which is common to our model and the PDD models invoked by Stritzinger et al. (2015).

Observed flux and polarisation spectra of SN 2005hk are shown in black in Fig. 1. As already reported by Kromer et al. (2013), we find a good agreement at both epochs between the predicted flux spectra and those observed in SN 2005hk. A reasonable agreement is also seen in the polarisation signal, and both modelled and observed spectra are characterised by an overall low polarisation level and the absence of strong polarisation features. Nevertheless, we note some differences. In particular, the polarisation signal shortward of ~5000 Å increases from the first to second epoch in SN 2005hk, while no significant change is predicted in the N5def3D model. As a consequence, the N5def3D model predicts somewhat smaller signals at peak brightness compared to those observed. We come back to this discrepancy in Sect. 3.2.

thumbnail Fig. 2

QU plane for the N5def3D model as viewed 4 days before peak from the n1 (left), (left), n3 (middle) and n5 (right) orientations. These correspond to the 3 the left panel of Fig. 1 (red, blue, and orange lines, respectively). Loops seen across the Si II λ6355 (left) and the O I λ7774 (middle andright) lines reflect small-scale asymmetries in the distribution of these elements.

3.2 Signatures from the ejecta–companion interaction

Figure 3 shows synthetic observables predicted for the CI model four days before peak (left panels) and at peak (right panel). The green dashed lines in the top panels show spectra for the N5def1D model, which are plotted to gauge the impact of the ejecta–companion interaction on the spectra. This comparison highlights how the interaction affects the spectra only below ~5000 Å, and there are no clear signatures at longer wavelengths.

Similar to the N5def3D model, the viewing-angle dependence in the CI model is confined to IGE-dominated regions below ~5000 Å, while almost identical spectra are predicted at longer wavelengths for different observer orientations. The angular dependence can be understood as a direct consequence of the location of the different observers with respect to the cavity carved out by the companion star. As shown in the top left panel of Fig. 3, photons can more easily escape the system along m1 compared to orientations away from the cavity (m2 to m5). The brightest spectrum is therefore associated with the m1 orientation (red line). An increase in optical depth is found when moving the observer away from the cavity, thus leading to increasingly fainter spectra from m2 (ΔΘ = 30°) to m4 (ΔΘ = 90°). Finally, the optical depth in the m5 direction (ΔΘ = 180°) is relatively similar to that in the m4 direction, and thus the corresponding spectra are rather similar.

The viewing-angle dependence of the polarisation spectra follows the ejecta distribution of the CI model. In particular, the ejecta are relatively symmetric in projection when viewed from m1, that is when looking directly down the cavity (ΔΘ = 0°). The corresponding polarisation signal is therefore very close to zero. Similarly low polarisation levels are predicted along m4 and m5. In contrast, the presence of the cavity breaks the projected symmetry in the m2 and m3 directions, thus producing stronger polarisation signals along these two viewing angles. In particular, the interaction with the companion star produces a maximum-light polarisation signal of P ~ 0.2 per cent below ~5000 Å, a distinctive feature that is not seen in the N5def3D explosion model. This reflects the break of symmetry introduced by the cavity, whose effect is stronger at bluer wavelengths where the IGEs are dominant.

Polarisation predicted for the CI model is in reasonable agreement with that observed for SN 2005hk at both epochs. Similar to the N5def3D, the overall low polarisation signals and absence of strong polarisation features are consistent with spectropolarimetric data of SN 2005hk. We note, however, a significant difference. While the N5def3D model was not polarised enough to explain the polarisation signal of P ~ 0.2 per cent detected for SN 2005hk at maximum light and below ~5000 Å, a better match to data is found for the CI model seen from m2 and m3. This suggests that the polarisation signal observed at blue wavelengths in SN 2005hk might stem from the interaction between theSN ejecta and the companion star. More polarimetric data of SNe Iax is needed to confirm this interpretation.

thumbnail Fig. 3

Same as Fig. 1 but for the CI model viewed from the 5 different orientations (m1 −m5) highlightedin the top left panel. The green dashed lines in the top panels are spectra calculated for the N5def1D model, thus referring to the case with no interaction. The N5def1D model is spherically symmetric by construction and thus no polarisation is expected by definition (see horizontal dashed lines inbottom panels).

4 Discussion and conclusions

In this paper, we carry out radiative transfer calculations and predict signatures from the deflagration of a Mch white dwarf and the subsequent interaction of the ejecta with a companion star. To investigate signatures arising from the explosion, we first study the 3D deflagration model N5def3D (Kromer et al. 2013; Fink et al. 2014) and predict flux and polarisation spectra for eight different orientations. The viewing-angle dependence of the flux spectra and the overall polarisation signals are rather small, owing to the relatively spherical ejecta distribution of the N5def3D model and to the dominant contribution of IGEs that tend to depolarise the escaping radiation.

To estimate the impact of the ejecta–companion interaction, we use simulations from Liu et al. (2013), where an angle-averaged 1D ejecta of the N5def3D model (N5def1D) collides witha MS companion star, and predict synthetic observables for five different viewing angles. We note that a He star is more compact but closer to the white dwarf compared to a MS star, thus creating a cavity with a similar opening angle. We therefore expect similar results in the He star case, a possibility that we plan to address in a future study. Overall, the imprint of the ejecta–companion interaction on both flux and polarisation spectra is only modest and restricted to wavelengths below ~5000 Å. The brightest orientation is found when looking down the cavity carved out by the interaction, while increasingly fainter orientations are predicted when moving away from the cavity. This trend is in qualitative agreement with predictions from Kasen et al. (2004, see their Fig. 3).

The polarisation level in the ejecta–companion interaction model is maximum for orientations 30° and 45° away from the cavity; negligible signals are predicted when the system is viewed down the cavity or 90° and 180° away from it. This is in contrast with predictions from Kasen et al. (2004), who found the continuum polarisation level to peak around 90° (see their Figs. 7 and 10). Given that the choice of the cavity opening angle is similar to that found in our simulations, we interpret the discrepancy as due to the different composition structures and particularly IGE distributions. Kasen et al. (2004) assumed a layered structure adopting the so-called W7 model for normal SNe Ia (Nomoto et al. 1984), where IGEs are confined to the inner regions. In contrast, our interaction model that is based on a 3D explosion simulation is characterised by IGEs that extend throughout the whole ejecta including the cavity created by the interaction. Strong line opacities from IGEs tend to destroy most of the polarisation signal created by electron scattering, thus likely explaining the smaller polarisation signals in our compared to the Kasen et al. (2004) simulations.

Guided by the increasing evidence suggesting that SNe Iax result from deflagrations of Mch white dwarfs in binary systems, we compare our simulations to the only spectropolarimetric data available for a SN Iax, namely SN 2005hk (Chornock et al. 2006; Maund et al. 2010). The observed low polarisation signals and lack of strong polarisation features in SN 2005hk are well reproduced by our models. Interestingly, the ejecta–companion interaction model provides a better agreement to data at maximum light and at blue (≲5000 Å) wavelengths, where the predicted level of P ~ 0.2 per cent matches that observed in SN 2005hk. This level is hard to achieve from the explosion itself given the overall spherical symmetry of the N5def3D model and most importantly the strong depolarising line blanketing at these short wavelengths (although we anticipate exploring more aspherical deflagration models in a future work). We note that a rise in polarisation from shorter to longer optical wavelengths is not a unique prediction of our deflagration model, with the same effect observed for two sub-luminous SNe Ia (SN 1998by; Howell et al. 2001, and SN 2005ke, Patat et al. 2012) and interpreted as a line blanketing effect in the framework of fast-rotating white dwarfs or white dwarf mergers (Patat et al. 2012).

Given that our comparison is limited to one object, it is hard to assess whether or not our results can be generalised to the whole SN Iax class. We thus encourage further polarimetric observations of SNe Iax covering short optical wavelengths, for which an ejecta–companion interaction signature should be detectable in ~6% of the cases (assuming orientations with 30° ≲ ΔΘ ≲ 60° from the cavity).

In this pilot study, we chose to disentangle the asymmetries introduced by the explosion with those originated by the ejecta–companion interaction. In the future, we will combine these two effects and carry out self-consistent calculations in which the full 3D ejecta structure predicted by deflagration models collides with the companion star. We also plan to make predictions for different scenarios, including different companion stars (e.g. He star) and/or using different explosion models more tailored to normal SNe Ia.

Acknowledgements

We thank the anonymous reviewer for his/her valuable comments. We are grateful to Ryan Chornock and Justyn Maund for sharing the spectropolarimetric data of SN 2005hk. This work used the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the National E-Infrastructure. This research was supported by the Partner Time Allocation (Australian National University), the National Computational Merit Allocation and the Flagship Allocation Schemes of the NCI National Facility at the Australian National University. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. The authors gratefully acknowledge the Gauss Centre for Supercomputing (GCS) for providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS share of the supercomputer JUQUEEN (Stephan & Docter 2015) at Jülich Supercomputing Centre (JSC). GCS is the alliance of the three national supercomputing centres HLRS (Universität Stuttgart), JSC (Forschungszentrum Jülich), and LRZ (Bayerische Akademie der Wissenschaften), funded by the German Federal Ministry of Education and Research (BMBF) and the German State Ministries for Research of Baden-Württemberg (MWK), Bayern (StMWFK) and Nordrhein-Westfalen (MIWF). ZWL is supported by the National Natural Science Foundation of China (NSFC, No. 11873016) and the 100 Talents Programme of the Chinese Academy of Sciences. The work of F.K.R. is supported by the Klaus Tschira Foundation and through the Sonderforschungsbereich SFB 881 “The Milky Way System” of the German Research Foundation (DFG). SAS acknowledges support from STFC through grant ST/P000312/1. I.R.S. was supported by the Australian Research Council through grant No. FT160100028.

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1

We note that also for the double-degenerate progenitor model in the so-called D6 scenario, surviving white dwarf companions are expected. Shen et al. (2018) propose candidates in the Gaia sample.

2

This choice is justified by the fact that the CI model is very close to being axially symmetric about the x axis. This symmetry was verified by predicting spectra for additional viewing angles.

All Figures

thumbnail Fig. 1

Top panels: ejecta composition for the N5def3D model. Density ρ (left) and mass fraction Xi of IMEs (middle) and IGEs (right) are shown in the x–y plane. The x–y projected direction of the 8 viewing angles is shown in the density panel. Bottom panels: flux, Q, U and polarisation spectra (from top to bottom) of the N5def3D models are shown 4 days before (left) and at maximum light (right) for the 8 different orientations (n1 −n8) highlighted in the top left panel. Flux and polarisation P of SN 2005hk is shown in black for comparison, with polarimetric data from Maund et al. (2010, bottom right panel) re-binned of a factor of two to have a similar wavelength resolution (Δλ ~ 50 Å) and polarisation uncertainties (σP ~ 0.06 per cent, error bars inbottom panels) as those from Chornock et al. (2006, bottom left panel). Both observed and modelled fluxes are normalised at 6000 Å for presentation purposes.
In the text
thumbnail Fig. 2

QU plane for the N5def3D model as viewed 4 days before peak from the n1 (left), (left), n3 (middle) and n5 (right) orientations. These correspond to the 3 the left panel of Fig. 1 (red, blue, and orange lines, respectively). Loops seen across the Si II λ6355 (left) and the O I λ7774 (middle andright) lines reflect small-scale asymmetries in the distribution of these elements.
In the text
thumbnail Fig. 3

Same as Fig. 1 but for the CI model viewed from the 5 different orientations (m1 −m5) highlightedin the top left panel. The green dashed lines in the top panels are spectra calculated for the N5def1D model, thus referring to the case with no interaction. The N5def1D model is spherically symmetric by construction and thus no polarisation is expected by definition (see horizontal dashed lines inbottom panels).
In the text

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