Binary Interaction Can Yield a Diversity of Circumstellar Media around Type II Supernova Progenitors

We use stellar evolution code MESA in revision 15140 (Paxton et al. 2011, 2013, 2015, 2018, 2019) to solve stellar evolutions of both stars in the binary from the zero-age main sequence (ZAMS). The computational setup and input parameters in MESA are mainly based on Ouchi & Maeda (2017), with some references to Yoon et al. (2010, 2017) and Laplace et al. (2020, 2021). We describe below the notable parts of this study.

We start the stellar evolutionary simulations with a nonrotating star for all the models. The initial ZAMS mass of the primary star is set to M₁ = 12M_⊙, which is a typical mass of the progenitor of a Type II SN (e.g., Smartt 2009). The secondary-star mass is fixed to M₂ = 10.8M_⊙, corresponding to the initial mass ratio of 0.9. We treat this mass ratio because, as pointed out in Hurley et al. (2002), small mass ratios (q < 0.5) cause unstable mass transfer, which makes computations difficult ³ (see also Ouchi & Maeda 2017). The initial orbital period is parameterized among P_orb = 1100, 1300, 1500, and 1700 days. We adopt these values as the period for reproducing the progenitor of a Type II SN affected by the binary interaction (Ouchi & Maeda 2017). We stop our simulation at the moment of the central carbon depletion t_end = t_C,dep. Here the central carbon depletion is defined as the moment when the mass fraction of carbon in the core falls below 10⁻⁶ (see also Section 2.1.3 and Appendix A). This definition is enough for our purposes because it takes only ∼10 yr from the moment of the central carbon depletion to the core collapse t_cc (see Appendix A and Figure A1 for details), which is shorter than the stellar behaviors under consideration.

In order to construct robust stellar models in terms of spatial resolution, we fix a MESA parameter max_dq = 5 × 10⁻⁴. This parameter choice resolves the mass coordinates in a star at least ∼0.006 M_⊙, satisfying the requirement of Farmer et al. (2016) that the mass resolution of ∼0.01 M_⊙ is desirable for the convergence of the evolution of the star during the main-sequence phase. Hereafter we describe the detailed setups for physical processes directly relevant to our stellar evolutionary simulations. We also refer readers interested in the detailed settings to our inlists uploaded in Zenodo. ⁴

2.1.1. Metallicity and Opacities

2.1.2. Atmosphere

2.1.3. Nuclear Reaction Network

2.1.4. Mixing

2.1.5. Wind

2.1.6. Binary System

In binary systems, we consider only nonconservative mass transfer. Our calculations include the loss of angular momentum due to the binary motion, such as mass loss. We assume that all of the angular momentum loss in the binary system occurs from the vicinity of the accretor star (see Soberman et al. 1997; Paxton et al. 2015). This causes the period of the binary system to evolve in time from the initial period, but these detailed dependencies are beyond the scope of this paper. The Roche lobe radius of the primary star is calculated following the Eggleton (1983) method,

$$\begin{eqnarray}&&{R}_{\mathrm{RL},1}=\displaystyle \frac{0.49{q}^{2/3}}{0.6{q}^{2/3}+\mathrm{ln}(1+{q}^{1/3})}\,a\,,\end{eqnarray} \tag{ 1 }$$

where q = M₁/M₂ is the mass ratio and a is the binary separation expressed as

$$\begin{eqnarray}&&a={\left(\displaystyle \frac{G({M}_{1}+{M}_{2}){P}_{\mathrm{orb}}^{2}}{4{\pi }^{2}}\right)}^{1/3}\,,\end{eqnarray} \tag{ 2 }$$

where G is the gravitational constant. When one of the stars in the binary system initiates Roche lobe overflow, we implicitly compute the mass transfer rate using the prescription described in Kolb & Ritter (1990). Here we introduce the accretion efficiency parameter β (Tauris & van den Heuvel 2006), which prescribes the fraction of the gas accreting onto the secondary star relative to the gas lost from the primary star owing to the binary stripping. In other words, we have the following relationship between the total mass-loss rate of the primary star ${\dot{M}}_{1}$, the mass transfer rate between the binary system ${\dot{M}}_{\mathrm{tr}}$, and the mass outflow rate into the CSM ${\dot{M}}_{\mathrm{CSM}}$:

$$\begin{eqnarray}&&{\dot{M}}_{1}={\dot{M}}_{\mathrm{wind},1}+{\dot{M}}_{\mathrm{tr}},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{CSM}}={\dot{M}}_{\mathrm{wind},1}+(1-\beta ){\dot{M}}_{\mathrm{tr}},\end{eqnarray} \tag{ 4 }$$

where ${\dot{M}}_{\mathrm{wind},1}$ is the mass-loss rate due to the stellar wind of the primary star. In this study we assume β=0.5. We neglect the contribution of the stellar wind from the secondary star. This is because it remains in the main sequence during the simulations so that the mass and momentum budgets belonging to the stellar wind from the secondary star are smaller than those from the primary star itself and the gas under the transfer.

We adopt the code PLUTO (Mignone et al. 2007, 2012) to solve the equations of hydrodynamics in one-dimensional spherical coordinates. We prepare the simulation domain from the inner boundary radius r_in = V_w (t_cc − t_end) ≃ 3 × 10¹³ cm (V_w /10 km s⁻¹) to r_out = 10 pc (≃3 × 10¹⁹ cm) and divide the domain into 256 meshes in the logarithmic scale, where V_w is the value of the velocity of the gas flowing from the binary system. Here we assume t_cc − t_end = 10 yr (see also Section 2.1). As an initial profile we consider the thermodynamic quantities ρ = 1.6 × 10⁻²⁴ g cm⁻³ (corresponding to the number density of n = 1 cm⁻³) and T = 10⁴ K to mimic warm interstellar medium (Draine 2011). The outflow condition is applied to the outer boundary in the simulation domain.

By injecting the gas from the inner boundary following the model for the mass-loss history obtained in Section 2.1, we can construct the hydrodynamical structure of the CSM. We need to assume the value of V_w ; there is uncertainty as to what the realistic values of the velocity of the gas escaping from the binary system should be. The reasonable choice would be the velocity comparable to the escape velocity of the central object $({V}_{w}\sim {V}_{\mathrm{esc}}\propto {R}_{* }^{-1/2}$, where R_* is the stellar radius). ${V}_{w}\sim { \mathcal O }(10)\mathrm{km}\,{{\rm{s}}}^{-1}$ would be expected if the escape velocity of the inflated primary star gives a main contribution, while V_w ∼ 1000 km s⁻¹ might be possible in a case where the gas is coming from the compact secondary star. We examine the values of V_w = 10, 100, and 1000 km s⁻¹ and apply these parameters for the simulation of the CSM formation in the binary models in Section 2.1. The CSM density at the inner boundary radius r_in is given as

$$\begin{eqnarray}&&\begin{array}{l}{\rho }_{\mathrm{inj}}=\displaystyle \frac{{\dot{M}}_{1}}{4\pi {r}_{\mathrm{in}}^{2}{V}_{w}}.\end{array}\end{eqnarray} \tag{ 5 }$$

The structure within the inner boundary would be determined by the progenitor activity after t ∼ t_end, which we do not investigate in detail.

It is also possible to examine the CSM formation by making use of the analytic treatment on the time-dependent wind dynamics as presented in Piro & Lu (2020). This is applicable as long as the ram pressure of the wind surpasses the thermal pressure of the ambient medium swept by the wind. Once these two pressures become comparable to each other, the ambient medium will suppress the expansion of the wind and the shocked wind gas begins to accumulate at the contact discontinuity between the wind and the medium, deviating from the analytical solution (Weaver et al. 1977; Matsuoka et al. 2022). To investigate the large-scale structure of the CSM in the framework of binary interaction, we rely on numerical hydrodynamical simulations in this study. A similar method is employed in the context of numerical simulations of SN remnants (Tenorio-Tagle et al. 1990, 1991; Dwarkadas 2005, 2007; Yasuda et al. 2021; Matsuoka et al. 2022; Yasuda et al. 2022). In addition, the choice of the large outer radius of the simulation domain r_out = 10 pc allows us to find out the difference between numerical and analytical treatments, which is discussed in Appendix B.

Table 1 shows the summary of the total stellar mass and the hydrogen envelope mass of the primary star, as well as the CSM mass in our binary models at the end of the simulations. We can observe a tendency for the total mass of the star and the hydrogen envelope to become smaller as the orbital period is shortened, because a tighter binary suffers more strong binary interaction. We can estimate the ejecta mass of the subsequent SNe at several solar masses for all of the models by subtracting the mass of a newborn neutron star from the final stellar mass. This could be smaller than the median value of Type IIP SNe containing a large amount of the hydrogen envelope (Martinez et al. 2022) but is typical for the SNe II that got rid of some fractions of the hydrogen envelope, such as Type IIL and IIb SNe (Bersten et al. 2012; Moriya et al. 2016).

Figure 1 shows the time evolution of the mass-loss rate $({\dot{M}}_{1})$ and Roche lobe radius (R_Rl,1) of the primary star in the binary models with orbital period P_orb = 1100, 1300, 1500, and 1700 days. The time evolution of the mass-loss rate can be interpreted in the basic framework of the binary evolution (e.g., Ouchi & Maeda 2017). We can see that the models with P_orb = 1100, 1300, and 1500 days experience a drastic increase in the mass-loss rate. The timings of the increase in ${\dot{M}}_{1}$ coincide with the moment when the primary star fills the Roche lobe radius. Our simulations suggest that even without introducing the single star's activity such as eruptions (e.g., Shiode & Quataert 2014; Fuller 2017; Wu & Fuller 2021; Ko et al. 2022), an SN progenitor involved in a binary can boost the mass-loss rate from the system at the moment of the expansion of the stellar radius.

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First, we start the detailed discussion in the model with P_orb = 1300 days as an example. The left panel of Figure 1 shows the time evolution of characteristic mass-loss rates and the radii in the primary star. They show that the primary star experiences a mass loss by the stellar wind in the hydrogen-burning phase (t_lb ≳ 10⁶ yr). Then, due to the increase in the stellar luminosity in addition to the decrease in the effective temperature after the core hydrogen burning, the stellar wind mass-loss rate increases by 30 times around t_lb ∼ 10⁶ yr, while the Roche lobe overflow does not occur at the time in this model. At t_lb ∼ 2 × 10⁴ yr the helium burning in the stellar core ends, and the primary star expands again (see the bottom left panel of Figure 1). At this timing, the stellar radius reaches the Roche lobe radius and the binary mass transfer begins. The mass transfer rate then rapidly increases up to 10⁻² M_⊙ yr⁻¹, and the mass of the primary star reduces down to M₁ ∼ 6 M_⊙. The second bump in the mass transfer history can be seen at t_lb ∼ 5000 yr. This could be associated with the single stellar activity of the primary star, since the evolution of the single star with the same initial mass (black dashed line in the bottom left panel of Figure 1) also shows the slight expansion of the stellar radius at t_lb ∼ 5000 yr (see also Section 4). After that, the Roche lobe overflow continues until the core collapse, while the mass transfer rate is regulated down to ∼10⁻⁵ M_⊙yr⁻¹.

We note that the primary star in the binary model is inflating more than the single star. This is caused by the mass reduction through the Roche lobe overflow after the full growth of the stellar core. We can understand the behavior of the stellar radius on the basis of the energy balance between the gravitational energy and the internal energy of the star, as explained by the Virial theorem (Kippenhahn & Weigert 1990, or see Appendix C for the quantitative interpretation). The internal energy of the star is mainly determined by the thermodynamical state of the stellar core (Laplace et al. 2021). When the Roche lobe overflow initiates in our binary models, the primary star settles in the helium-burning stage, implying sufficient growth of the stellar core. Thus, both the primary star in the binary model and the single star should have similar internal energies at t_lb ≲ 10⁵ yr. In contrast, the reduction of the stellar mass through mass transfer in the binary results in an increase in the gravitational energy of the star. Consequently, the primary star in the binary can easily expand the radius larger than the star without the companion star.

Comparing the evolutions of a single star with the star in a binary can be a clue to understanding the critical physical processes in a binary system. The radius of the primary star in the binary follows the same path as that evolving as a single star until it first fills the Roche lobe radius. This implies that the timing when a star first fills the Roche lobe radius can be roughly understood through the comparison between the Roche lobe radius and the radial evolution in the single stellar evolution (see later).

The right panel of Figure 1 shows the dependence of mass-loss properties on the orbital period P_orb. In all binary models, the primary star will eventually become a Type II SN progenitor because the primary star retains the hydrogen envelope until the core collapse (see Table 1). We can see the trend that the longer the initial orbital period P_orb, the further the timing of the Roche lobe overflow is delayed. When the initial orbital period is too long (P_orb ≳ 1700 days), the mass-loss rate is roughly the same as that in the single stellar evolution model, since the binary does not experience Roche lobe overflow (see dashed black line and solid cyan line in the right panel of Figure 1).

It is possible to compare the binary models with P_orb = 1100, 1300, and 1500 days to the single stellar evolution. All binary models follow the same evolutionary path as the single stellar model until t_lb ∼ 10⁶ yr. The model of P_orb = 1500 days follows almost similar evolution to the model of P_orb = 1300 days discussed above, except that the Roche lobe overflow starts slightly later owing to the larger Roche lobe radius. The model with P_orb = 1100 days undergoes a Roche lobe overflow after the end of the core hydrogen burning at t_lb ∼ 10⁶ yr, which leads to the release of about ∼7 M_⊙ of the hydrogen outer layer. It then experiences another Roche lobe overflow at t_lb ∼ 3 × 10⁴ yr, following a path different from that in single stellar evolution. However, we should emphasize that it is no coincidence that the P_orb = 1100 day model exhibits the mass-loss enhancement at t_lb ∼ 10⁴ yr similarly to the other binary models (P_orb = 1300 and 1500 days). Normally, helium burning in the stellar core ends at ∼10⁴ yr before the core collapses (e.g., Woosley et al. 2002). At this time, the primary star expands again, and thus we can see an enhancement of mass loss.

We note that the model of P_orb = 1700 days follows the same mass-loss history as the single stellar model since the primary star radius remains sufficiently smaller than its Roche lobe radius in the whole of the lifetime of the star. Therefore, while we conducted the CSM reconstruction even for the binary model with P_orb = 1700 days, we do not discuss the result of the model in the next section.

Figure 2 shows the density structures of the CSM for the binary models assuming V_w = 10 km s⁻¹. We can see that the shell-like distribution is standing out at $\sim { \mathcal O }({10}^{17})\mathrm{cm}$ in the models with P_orb = 1300 and 1500 days. The corresponding look-back time is around t_lb ∼ 10⁴ yr, and it is easily found that at that time the mass-loss rate is enhanced by orders of magnitude, compared to that expected for the steady wind of an RSG. As for the model with P_orb = 1100 days, not shell-like but cliff-like structures in the CSM are appearing at the radii of 2 × 10¹⁷ cm and 10¹⁸ cm. These features are associated with the mass-loss enhancements at t_lb ∼ 5000 yr and 3 × 10⁴ yr, respectively. We suggest that binary interaction can give rise to the formation of the shell-like and cliff-like CSM structures.

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We confirm that there is no mixing of heavy elements into the hydrogen envelope of the primary stars within the parameter range of this study. Also as can be seen from Table 1, the mass release from the primary star happens only from the hydrogen layer, not from the helium core. Therefore, the CSM composition is expected to be similar to that of the Sun.

The dependence of the CSM structure on the wind velocity is also worth investigating, which is shown in Figure 3. We can see that higher wind velocity leads to the widely distributed and thin-density structure of the CSM. As V_w becomes faster, the wind can reach the length scale farther from the SN progenitor, while its density becomes smaller (see Equation (5)). We note that the shell-like component in the model with slower wind velocity lies in the smaller length scale.

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The variety of hydrodynamical structures of the CSM would give rise to observational characteristics of subsequent SNe, such as the excess in the optical emission and the rebrightening of radio emission in the late phase of SN−CSM interaction (e.g., Weil et al. 2020; Kilpatrick et al. 2022; Maeda et al. 2023). Here we discuss the possibility that our results can give explanations for characteristics of SNe indicated by late-phase observations. If the wind velocity is as slow as orders of ∼10 km s⁻¹, then the location of the mass shell observed in the model with P_orb = 1300 and 1500 days falls at ∼10¹⁷ cm. This could be an origin for the observational signature of late-time SN−CSM interaction seen in several Type II SNe because the SN shock begins interacting with the shell at a radius of ∼10¹⁷ cm a few years after the explosion. To quantitatively discuss the variation of the CSM density in the radial direction, the mass-loss rate of the SN progenitor can serve as an indicator of the density variation of the CSM. Maeda et al. (2021) argue that the variation in the mass-loss rate only by a factor can emerge as an observational peculiarity in radio light curves of SNe. Maeda et al. (2023) also suggest that the elevation of the mass-loss rate by an order of magnitude could be an explanation for the radio rebrightening of SNe. Other cases are that Weil et al. (2020) and Kilpatrick et al. (2022) ascribe the origin of the excess in the optical light curves as the existence of the CSM with their mass-loss rates not so much higher ($\dot{M}\sim {10}^{-7}\mbox{--}{10}^{-6}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$), but these densities are enough for the appearance of the observable CSM interaction features. As for our binary models reproducing shell-like CSM structures, their density variations range from factors to an order of magnitude, and we expect these variations are significant enough to be ascribed as the origin for the CSM interaction features observed in late-phase SNe.

The cliff-like structure seen in the model of P_orb = 1100 days can also be intriguing since the cliff-like structure may lead to the attenuation of the CSM interaction signature in the late phase of SNe. Indeed, Weiler et al. (2007) reported a steep dimming in the radio emission from SN 1993J ∼10 yr after the explosion. They further suggested that the mass-loss rate increased up to at least 3 times ∼8000 yr before the explosion, corresponding to a length scale of the CSM of 2 × 10¹⁷ cm. Our model with P_orb = 1100 days exhibits a density variation comparable to or even higher than the above implications, supporting that our binary models can be likely to give rise to CSM interaction features sufficiently prominent to be traced by observations. We also note that the binary interaction scenario is consistent with the fact that SN 1993J is a Type IIb SN originating from a massive star that probably suffered from the stripping of the envelope by a companion star (e.g., Maund et al. 2004).

In addition to implications from SN observations, we also note that direct observations of late-type stars in our Galaxy indicated the existence of the multiple-shell structure in the circumstellar environment due to the binarity (Mauron 1997; Mauron & Huggins 1999). This supports that binary interaction can be a feasible origin of the emergence of the shell-like structure in the circumstellar environment of stars (Mauron 1997; Mauron & Huggins 1999).

In this study, we fixed the value of the initial primary mass to clarify the physics of the CSM formation. Our results show that the CSM properties depend on the evolution of the primary star radius R₁, as well as several physical parameters such as P_orb and V_w . Obviously, the radial evolution of the primary star depends on the choice of the initial primary mass, and the variation of the primary mass expands the diversity of stellar evolution itself. Here we present a series of models in which the initial primary mass is parameterized and discuss the effect of the variation of the primary mass on the behavior of the mass-loss history and the resultant CSM structure qualitatively.

Here we note the purpose of this section. We will show how different primary masses, i.e., different stellar evolutions of the primary stars, give rise to different mass-loss activities and CSM structures. This is because the evolution of mass loss due to binary interaction strongly reflects the stellar evolution of the primary star peculiar to itself, as studied for the case of the primary-star mass of M₁ = 12M_⊙ in Section 3. Detailed analysis of the results in this section would necessitate individual stellar evolution calculations, which are beyond the scope of this paper. Hence, we just limit our discussion to showcasing an example of the diversity resulting from different primary-star masses.

Figure 4 shows the time evolution of the mass-loss rate $({\dot{M}}_{1})$ adopted for the primary-star masses M₁ = 14.4, 15, and 16.2 M_⊙. Other physical/binary parameters are fixed: the orbital period P_orb = 1900 days, and the secondary mass M₂ = 13.5 M_⊙. We have confirmed that in all of these models the primary star will eventually become a Type II SN progenitor encompassed by a hydrogen envelope. We can see that the models with M₁ = 15 M_⊙ experience a drastic increase in the mass-loss rate at t_lb ∼ a few × 10³ yr. In addition, the models with M₁ = 16.2 M_⊙ show the multiple episodes in the mass-loss history around t_lb ∼ 3 × 10⁴, 10⁴, and 10² yr. On the other hand, in the models with M₁ = 14.4 M_⊙, no mass-loss gain is observed even though the same orbital period and secondary mass are employed.

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We suppose that the differences among the three models are attributed to the behaviors of the primary star. In the evolutionary stage after the carbon burning, the stellar radius can be variable owing to single stellar activity, such as shell flashes and core convection. When the star is evolving as a single star, these activities would not be reflected in the mass-loss history unless they induce mass loss from the surface of the star (e.g., Quataert & Shiode 2012; Shiode & Quataert 2014). This is true even when the primary star is in a binary but its Roche lobe radius is sufficiently larger than the stellar radius (the case of M₁ = 14.4 M_⊙). However, when the Roche lobe radius becomes comparable to the stellar radius of the primary star, the radial variation of the star would be reflected in the mass loss due to Roche lobe overflow, and thus the complicated evolution of the mass-loss rate would be realized. In other words, binary interaction plays a role in enhancing the stellar behavior of the primary star as a form of mass transfer history. We expect that the difference in the evolution of the stellar radius between M₁ = 15 and 16.2M_⊙ results in the difference in the mass transfer history. We propose that single stellar activities that involve the expansion of the stellar radius but do not induce mass eruptions may also contribute to mass loss if the star is in a binary system. Thus, understanding the massive star's evolution after the carbon-burning phase would be important even for seeking the origin of the dense-CSM structure around SN progenitors.

The mass-loss histories drawn in Figure 4 are informative even for the formation of the resultant CSM structure. As examples, we take up the models with M₁ = 15.0 M_⊙ and M₁ = 16.2 M_⊙. First, we propose that binary interaction can be one of the origins producing dense CSM inferred in Type IIn SNe. We can see that the mass-loss rate seen in the model with M₁ = 15.0 M_⊙ is elevated to ∼10⁻³ M_⊙ yr⁻¹ from a few thousand years before the explosion. This is comparable to those previously inferred for Type IIn SNe (e.g., Kiewe et al. 2012; Moriya et al. 2014) and in good agreement with the discussion in Ouchi & Maeda (2017). If we consider the slow velocity of the CSM (V_w = 10 km s⁻¹), the CSM in this model is expected to have a cliff-like structure: a steep density drop at the radius of ∼10¹⁷ cm. This length scale may be consistent within a factor with the implication of Katsuda et al. (2016), where some Type IIn SNe are suggested to be encompassed by a torus-like CSM truncated at around several times 10¹⁶ cm.

Another suggestion is that binary interaction in the final evolutionary phase can be a possible explanation of the signature of the CSM interaction observed in infant SNe. Figure 5 shows the synthesized CSM structure for the model with M₁ = 16.2 M_⊙. The mass-loss history of this model is characterized by multiple enhancements of the mass-loss rate. The last mass-loss episode happens at t_lb ∼ 50 yr, and the gas expelling from the binary system at that episode would reach out to ∼10¹⁵ cm. We remark that this length scale may be compatible with that inferred for the confined CSM seen in some infant Type II SNe (see, e.g., Yaron et al. 2017 for SN 2013fs, Jacobson-Galán et al. 2022 for SN 2020tlf, and Zimmerman et al. 2023 for SN 2023ixf). We note a caveat that our model is not quantitatively tuned to the observational implication represented by SN 2013fs, and the discussion should be limited qualitatively. Nevertheless, we advocate that the binary interaction episode arising ≲100 yr before the explosion can leave an inhomogeneous structure in the vicinity of the SN progenitor, and it may contribute to the unique observational features of infant Type II SNe such as flash spectroscopy and early excess of optical light curve (Moriya et al. 2017; Morozova et al. 2017; Yaron et al. 2017; Jacobson-Galán et al. 2022).

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A stripped-envelope SN is indicated to originate from a binary system (e.g., Lyman et al. 2016; Fang et al. 2019). There are also suggestions that some stripped-envelope SNe produce a sign of the interaction with the massive shell-like CSM a few years after the explosion (Margutti et al. 2017; Mauerhan et al. 2018; Balasubramanian et al. 2021), and this implication looks consistent with our results. In fact, some binary evolutionary simulations with short orbital periods of P_orb ≲ 10 days through Case A or Case BB mass transfers have been successful in reproducing models for stripped-envelope SN progenitors (Ouchi & Maeda 2017; Gilkis et al. 2019; Laplace et al. 2020), although there has been less attention to mass transfer histories.

We attempted binary evolutionary simulations of such a short-period system with the same stellar masses of the stars by using the mass transfer prescription following Hurley et al. (2002). We found that the mass transfer rate is intensely fluctuating by orders of magnitude within short timescales. This fluctuation has been observed in the previous works (see Figure 8 in Paxton et al. 2015), and it prevents us from understanding the features of the mass transfer history in a tight binary, which we will postpone in future work. However, it may be notable that Wu & Fuller (2022) conducted the stellar evolutionary simulations of low-mass He stars accompanied by a neutron star, and the obtained mass-loss rates therein are not fluctuated.

This study aims to construct CSM models originating from binary interaction, but there are several assumptions and other possible physical processes that could affect our result. This section discusses their roles in characterizing CSM properties and assesses their importance.

• 1.  
  The timing of the termination of stellar evolutionary simulations. We assume that the primary star experiences core collapse t_end − t_cc = 10 yr after entering the central carbon depletion stage. Notice that our definition of the central carbon depletion stage is the phase when the mass fraction of carbon in the core falls below 10⁻⁶. Based on this definition, we believe that the time span from the central carbon depletion stage to the core collapse would not be largely modified depending on stellar quantities by orders of magnitude. Actually, our definition of the central carbon depletion stage corresponds to the epoch just before the ignition of oxygen burning in the core (Tur et al. 2010). Even if there are variations in t_end − tcc by factors, it should affect the neighborhood circumstellar environment of SN progenitors with the length scale of V_w (t_end − tcc) ∼ 3 × 10¹⁴ cm on the assumption of V_w = 10 km s⁻¹. This is sufficiently shorter than the characteristic CSM length scales discussed in Section 3.2.
• 2.  
  Thermodynamical state of external interstellar medium. This study assumes warm interstellar medium (ρ = 1.6 × 10⁻²⁴ g cm⁻³, T = 10⁴ K) as an initial condition of simulations of CSM formation, whereas it is known that the interstellar medium can take various phases including a dense or dilute environment (Draine 2011). However, if we focus on the observational timescale of SNe and the length scale of the CSM (t ≲ a few years or r ≲ 10¹⁷ cm), it does not matter because the characteristics of the CSM are predominantly determined by the bulk properties of the outflow from the Roche lobe overflow. If anything, the difference of the interstellar medium state affects the large-scale structure of the CSM that may influence the evolution of SN remnants (Yasuda et al. 2021; Matsuoka et al. 2022; Yasuda et al. 2022). We also investigate CSM formation properties with the different initial conditions, such as cold (ρ = 1.6 × 10⁻²² g cm⁻³, T = 10² K) and hot (ρ = 1.6 × 10⁻²⁶ g cm⁻³, T = 10⁶ K) interstellar medium. We confirm that the choice of the thermodynamical state of the interstellar medium does not have an influence on the resultant CSM configuration in the region in which we are interested (r ≲ 10¹⁸ cm). Basically, the existence of the interstellar medium affects the location of the contact discontinuity with the CSM, which is determined by the balance between the thermal pressure of the shocked interstellar medium and the ram pressure of the wind (see, e.g., Weaver et al. 1977; Matsuoka et al. 2022). When we consider a cool and dense interstellar medium, the contact discontinuity should be located in the inner region owing to the high thermal pressure of the shocked interstellar medium. If the interstellar medium is hot and more dilute, then the CSM would extend farther in the outer region.
• 3.  
  Asphericity of the outflow. In this study, the outflows (stellar wind and the outflow from the Roche lobe) are assumed to be spherically symmetric, but nonspherical structures of the CSM can be realized. However, some studies suggested that if the outflow is via the Lagrangian point of the binary system, the CSM may be distributed along the equatorial plane with the spiral structure (Lubow & Shu 1975; Shu et al. 1979; Pejcha et al. 2016). Discussing the ejection mechanism and the resultant morphology of the outflow from the Roche lobe overflow would require multidimensional hydrodynamical models, which is beyond the scope of this paper. Nevertheless, we note that if the aspherical structure of the CSM is realized in SNe, they may leave unique signatures on radiative properties of SNe (e.g., Suzuki et al. 2019). We also mention that the circumstellar environment around RSGs can be variable and even clumpy (e.g., VY Canis Majoris; Smith et al. 2009). This implies that if the stellar wind from the primary has dense clumpy components, it can affect the multidimensional configuration of the CSM.