Long-term evolution of surviving companion stars of Type Iax supernovae

Type Ia supernovae (SNe Ia) are thought to be resulted from thermonuclear explosions of white dwarfs (WDs) in binary systems (Hoyle & Fowler, 1960). Although SNe Ia play a fundamental role in astrophysics, the nature of their progenitor systems and the explosion mechanism remain an unsolved mystery (e.g. Hillebrandt & Niemeyer, 2000; Maoz et al., 2014; Livio & Mazzali, 2018). To explain observational features of SNe Ia, a set of progenitor models which cover different explosion mechanism have been proposed for SNe Ia, including the single-degenerate (SD; Whelan & Iben 1973; Han & Podsiadlowski 2004), the double-degenerate (DD; Iben & Tutukov 1984; Webbink 1984; Dan et al. 2011, 2012), the sub-Chandrasekhar mass (e.g. Nomoto, 1982; Woosley et al., 1986; Fink et al., 2007; Shen & Bildsten, 2007; Sim et al., 2010; Gronow et al., 2020), the violent merger (Pakmor et al., 2010, 2012b), the core-degenerate (e.g. Livio & Riess, 2003; Kashi & Soker, 2011; Ilkov & Soker, 2012), and the WD-WD head-on collisions model (e.g. Benz et al., 1989; Rosswog et al., 2009; Kushnir et al., 2013).

In the SD scenario, the WDs accrete matter from a non-degenerate companion which could be a main-sequence (MS), a subgiant, a red giant, and/or a helium star to trigger thermonuclear explosions when they grow in mass to approach the Chandrasekhar-mass limit (Whelan & Iben, 1973). The companion stars are expected to survive the explosion in this scenario. Therefore, searching for the surviving companion star in galactic SN remnants (SNRs) has been proposed to be a promising approach to test the progenitors of SNe Ia (e.g. Pan et al., 2014; Ruiz-Lapuente, 2019). To explore the impact of SN Ia explosion on its companion, the interaction of SN Ia ejecta with a stellar companion star has been studied in detail by the analytical method, two-dimensional (2D) and/or three-dimensional (3D) hydrodynamical simulations (e.g. Wheeler et al., 1975; Marietta et al., 2000; Pakmor et al., 2008; Liu et al., 2012; Liu et al., 2013a; Liu et al., 2013c; Pan et al., 2012a; Boehner et al., 2017; Bauer et al., 2019; Zeng et al., 2020). There are several ways by which the SN blast wave modifies the properties of the companion star. First, some matters are removed from the surface of the companion star and a significant amount of thermal energy is injected into star during the interaction with SN ejecta. This causes that the surviving companion star dramatically puffs up and becomes overluminous. For instance, By tracing long-term evolution of surviving MS companions produced from 3D hydrodynamical impact simulations, Pan et al. (2012b) found that they dramatically expands and become overluminous (up to about $100\,{L_{\sun}}$) within a few thousand years, depending on the progenitor model (see also Podsiadlowski, 2003; Shappee et al., 2013a). Secondly, the companion star’s surface could be enriched with heavy elements (e.g. $\mathrm{Ni}$, $\mathrm{Fe}$) which come from the inner part of the SN ejecta (e.g. González Hernández et al., 2009; Liu et al., 2012; Liu et al., 2013a; Pan et al., 2013). This is expected to present some features of these heavy elements in spectra of a surviving companion star. In addition, the binary system is destroyed while the SN explodes, the companion star releases and moves in a peculiar velocity compared to other stars in the vicinity, becoming a hypervelocity (or runaway) star (e.g. Geier et al., 2015).

On the observational side, many studies have been focused on searching for the surviving companion star predicted by the SD scenario in SNRs (for a recent review, see Ruiz-Lapuente, 2019). But unfortunately, to date, no promising surviving companion star has been identified yet in SNRs (e.g. Kerzendorf et al., 2009; Schaefer & Pagnotta, 2012; González Hernández et al., 2012; Ruiz-Lapuente, 2019). Although it has been suggested that Tycho G is a possible candidate because of some peculiar features such as its lower surface gravity than a MS star, a peculiar velocity in radial and proper motion (Ruiz-Lapuente et al., 2004; Bedin et al., 2014), and an overabundance of $\mathrm{Ni}$ relative to normal metal-rich stars (González Hernández et al., 2009), some other studies casts some doubts on this identification. For instance, Howell (2011) concluded that Tycho G is apparently not out of thermal equilibrium. In addition, Kerzendorf et al. (2013) showed that the measured $\mathrm{[Ni/Fe]}$ ratio of Tycho G seems to be not so unusual with respect to field stars with the same metallicity.

Type Iax supernovae (SNe Iax) are proposed as one new subclass since they present sufficiently distinct observational properties from the bulk of SNe Ia (e.g. Li et al., 2003; Foley et al., 2013). It has been found that they contribute about 1/3 of total SNe Ia (e.g. Li et al., 2001; Foley et al., 2013). SNe Iax are fainter compared to normal SNe Ia and highly skewed to late-type galaxies (e.g. Foley et al., 2013; Liu et al., 2015a). Their explosion ejecta are characterized by low expansion velocities and show strong mixing features. In addition, strong He lines are identified in spectra of two events, i.e., SN 2004cs and SN 2007J, and late-time spectra of SNe Iax are dominated by narrow permitted Fe II (Jha et al., 2006). We refer to Foley et al. (2013) and Jha (2017) for a detailed introduction of observational features of SNe Iax.

Although the progenitors and explosion mechanism of SNe Iax remain a mystery, it has been suggested that incomplete pure deflagration explosions of near-Chandrasekhar-mass WDs within the SD scenario are able to reproduce the characteristic observational features of SNe Iax (e.g. Jordan et al., 2012; Kromer et al., 2013, 2015; Fink et al., 2014; Liu et al., 2015b; Bulla et al., 2020). Recently, using the smoothed-particle hydrodynamics (SPH) code Stellar Gadget (Springel et al., 2001; Pakmor et al., 2012a), Liu et al. (2013c) have performed 3D hydrodynamical simulations of SN ejecta-companion interaction by assuming that SNe Iax are generally generated from pure deflagration explosions of near-Chandrasekhar-mass WDs in WD + MS progenitor systems. In that work, they concentrated on calculating the amount of stripped H mass from companion surface by SN Iax explosion. They found that H mass stripping in SNe Iax is in inefficient ($\lesssim 0.01\,M_{\sun}$) due to the low kinetic energy of the adopted explosion model, i.e., the N5def model of Kromer et al. (2013)¹¹1In the N5def model, only a part of the Chandrasekhar-mass WD is ejected, leading to a ejecta mass of about $0.37\,M_{\sun}$ and a kinetic energy of $1.34\times 10^{50}\,\mathrm{erg}$. It has been found that this model is able to reproduce the characteristic observational features of a prototypical 2002cx-like event, SN 2005hk (Kromer et al., 2013), suggesting that H lines caused by stripped material from a MS companion star may be hidden in late-time spectra of SNe Iax (Tucker et al., 2020; Jacobson-Galán et al., 2019). However, the long-term evolution of surviving MS companions was not addressed in detail in their work.

In the present work, we map MS companion models obtained from 3D impact hydrodynamical simulations of Liu et al. (2013c) into the 1D stellar evolution code MESA (Paxton et al., 2011; Paxton et al., 2018) to trace their long-term post-impact evolution. Although long-term post-impact evolution of surviving MS companions of normal SNe Ia within the SD progenitor scenario has been done by different previous studies (e.g., Podsiadlowski, 2003; Pan et al., 2012b, 2013, 2014; Shappee et al., 2013b; Bauer et al., 2019), it has never been addressed in the context of SNe Iax. The aim of the present work is to explore the post-explosion observational features of surviving MS companions of SNe Iax by combining the outcome of 3D SPH impact simulations into the 1D stellar evolution code. It is expected to be helpful for searching for the surviving companions and therefore examining the valid of the SD binary systems as progenitors of SNe Iax. The method and companion models used in the present work are described in Section 2. Long-term evolution and appearance of four different MS companion models such as the luminosity and evolutionary tracks are presented in Section 3 before we make discussions in Section 4. Finally, the important results and conclusions of this work are summarized in Section 5.

In this work, we assume that SNe Iax are generally produced from the WD + MS progenitor systems. To investigate long-term post-impact observational properties of surviving MS companion stars, we have performed 3D SPH simulations of SN ejecta-companion interaction in Liu et al. (2013c). Fig. 1 shows density distribution of bound companion material in the orbital plane (i.e. $x-y$ plane) as a function of time from the 3D impact simulation of Liu et al. (2013c) for the Model_A (see their table 1). At the beginning, the companion star is in a hydrostatic equilibrium state. The SN ejecta-companion happens about a few minutes after the SN Iax explosion, removing some H-rich material from the right-hand side of companion surface. As the shock passes through the whole star, more H-rich material is removed from another side of the companion surface. At the end of simulation, the MS companion loses about $\lesssim 1\%$ of its mass due to the stripping and ablation by the SN ejecta, which depends on the progenitor model Liu et al. (2013c, see their table 1). On the one hand, the MS companion star is significantly shocked and heated during the ejecta-companion interaction, leading to that the companion star puffs up dramatically at the end of simulations (about $t=5000\,\mathrm{s}$ after the explosion). On the other hand, the post-impact companion stars are not yet in hydrostatic and thermal equilibrium although it is being spherically symmetric at the end of 3D SPH simulations.

To provide post-impact observational properties of surviving companion stars for their identifications in historical SNRs, it is important to simulate and trace the detailed evolution of surviving companion stars for a long time up to the age of historical SNRs, i.e., a few 10–1000 yr. However, it is really difficult to run 3D hydrodynamical impact simulations for that long time because such simulations have a small time-step which is determined by the dynamical time-scale of the MS companion that is on the order of hundreds of seconds. Therefore, in the present work, 3D SPH post-impact companion models directly taken from 3D impact simulations of Liu et al. (2013c) are mapped into the 1D stellar evolution code MESA (Paxton et al., 2011; Paxton et al., 2018) to trace their subsequent long-term evolution (see also Pan et al., 2012b, 2013).

The first step is to convert 3D post-impact companion models into angle-averaged 1D radial profiles. Therefore, we divide the final 3D companion models of SPH impact simulations (see the bottom right panel of Fig. 1) into 100–200 spherical shells. The parameters such as the internal energy ($\mathcal{E}_{\mathrm{int}}$), composition, density ($\rho$) of SPH particles in each shell are averaged to give a value for that shell. Fig. 2 presents an example of the comparison between 3D density distributions and the angle-averaged 1D radial profile of a surviving companion model, Model_D. However, these 1D angle-averaged MS companion models cannot be used directly by MESA because they are still out of the hydrostatic equilibrium at the end of SPH impact simulations. Therefore, the second step is to import suitable starting models for the MESA based on the obtained 1D angle-averaged radial profiles of SPH models. In this work, by following the method described in Paxton et al. (2018, see their appendix B), we directly used the relaxation routines provided in MESA to compute suitable starting models for MESA. These relaxation routines were developed to construct a starting model in hydrostatic equilibrium based on the specified profiles for entropy, composition, and angular momentum. It has been shown that these relaxation routines can be successfully used for tracing long-term evolution of the outcome of a stellar merger from SPH simulations (Paxton et al., 2018, see appendix B). The comparison between pre-relaxation 1D density profile (green dashed line) and post-relaxation one (red solid line) for Model_D is shown in Fig. 2.

In this work, four different post-impact MS companion models (i.e. the so-called Model_A, Model_B, Model_C, and Model_D) are directly taken from 3D SPH impact simulations of Liu et al. (2013c, see their table 1). The detailed properties of these four models at the moment of SN explosion (i.e. before ejecta-companion interaction) can be found from Liu et al. (2012, see their table 1 and Fig. 8) and Liu et al. (2013c). The spherical averaged 1D profiles of the composition, $\mathcal{E}_{\mathrm{int}}$, and $\rho$ of these post-impact models are put into the relaxation routines of MESA to compute the starting models for their subsequent long-term post-impact calculations. Fig. 3 shows the angle-averaged 1D profiles (left-hand panel) of $\mathcal{E}_{\mathrm{int}}$, helium abundance $Y$, and $\rho$ of four post-impact MS models at the end of SPH simulations of Liu et al. (2013c). The corresponding profiles of the post-relaxed models in MESA are also given in right-hand panel of Fig. 3. Note that a zero angular momentum is set when constructing the starting model for MESA because the orbital motion of the binary system and rotation of a star were not included into SPH impact simulations of Liu et al. (2013c). The effect of orbital motion of the binary and rotation of a star on the results will be investigated by a forthcoming study.

By using the method described in Section 2, post-impact 1D averaged profiles in left-hand panel of Fig. 3 have been put into the relaxation routines of MESA to compute the relaxed starting models (right-hand panel of Fig. 3). We then trace long-term evolution of these models to make predictions on the post-impact observational properties such as temperature, luminosity, radius, and surface abundances. This is will be helpful for current and/or future observations to identify surviving companion stars of SNe Iax and therefore favor (or disfavour) the SD progenitor origin of SNe Iax.

In this work, assuming that SNe Iax are generated from the incomplete deflagration explosions of near-Chandrasekhar mass WDs in WD + MS binary progenitor systems, we have explored long-term post-impact evolution and appearance of surviving MS companion stars by mapping the output model of 3D hydrodynamical simulations of ejecta-companion interaction by Liu et al. (2013b) into the 1D stellar evolution code MESA (Paxton et al., 2011; Paxton et al., 2013, 2015, 2018). Our main results and conclusions can be summarized as follows:

• •

  Depending on different MS companion models, the total amount of injected energy and the depth of energy deposition by SN impact are different. In our models, it is found that about $26$–$40\%$ of the total incident energy is injected into MS companion stars during the ejecta-companion interaction.

• •

  As a result, the surviving MS companion stars continue to expand on a time-scale of $10$–$10^{4}$ yr before they start to contract, leading to that they become significantly more luminous (i.e. about $5$–$500\,L_{\sun}$ from Model_A to Model_D, see right-hand panel of Fig. 4) in their post-impact evolution.

• •

  Comparing our results with the late-time light curve of a prototypical SN Iax, SN 2005hk, it is found that the predicted luminosities of surviving companion stars start to exceed that of SN ejecta in $B$-band about 1000 days after the explosion. Under an assumption that SNe Iax are generally generated from the incomplete deflagration explosions of near-Chandrasekhar-mass WDs in WD + MS progenitor systems, it is therefore suggested that their surviving companion stars would begin to be visible when SN itself has faded about 3 yr after the explosion.

We would like to thank the anonymous referee for reviewing our manuscript. This work is supported by the National Natural Science Foundation of China (NSFC, No. 11873016), the Chinese Academy of Sciences and the Natural Science Foundation of Yunnan Province of China (No. 202001AW070007). The authors gratefully acknowledge the “PHOENIX Supercomputing Platform” jointly operated by the Binary Population Synthesis Group and the Stellar Astrophysics Group at Yunnan Observatories, Chinese Academy of Sciences.

The data underlying this article will be shared on reasonable request to the corresponding author.