Wave-driven Mass Loss of Stripped Envelope Massive Stars: Progenitor-dependence, Mass Ejection, and Supernovae

Type Ib/c supernovae are caused by the explosion of a massive star in which the surface H envelope has previously been lost through winds or mass transfer in a binary system (see, e.g., Yoon 2015, for a recent review). The launch of Zwicky Transient Factory has led to more detections of supernovae at hours to days after explosion. High-cadence monitoring also allows for detections of pre-supernova outbursts, e.g., in SN 2018gep at about 2 weeks before its final explosion (Ho et al. 2019). Similar outbursts have been observed in both Type II, Type Ib/c, and Type Ibn supernovae such as SN 2007bg (Milisavljevic et al. 2013), SN 2008D (Modjaz et al. 2009; Svirski & Nakar 2014), SN 2010mc (Ofek et al. 2013), PTF13efv (Ofek et al. 2016), SN 2015bh (Elias-Rosa et al. 2016), SN 2015U (Shivvers et al. 2016), and SN 2015G (Shivvers et al. 2017). SN 2009ip (Mauerhan et al. 2013; Ofek et al. 2013) provides evidence of a star resembling a Luminous Blue Variable going supernova, with a clear mass outburst 3 yr before the real explosion. These outbursts have demonstrated the possibility that a massive star can lose mass dynamically, besides its stellar wind mass loss.

Pre-supernova outbursts also connect to the formation of circumstellar medium (CSM) around the exploding star, which has been a challenge in stellar evolution theory. For very massive stars (zero-age main-sequence mass M_ZAMS =80–140 M_⊙), the electron-positron pair instability drives explosive O burning and mass ejection, which accounts for an outburst of ∼0.1 to tens of M_⊙ (Leung et al. 2019; Woosley 2019; Renzo et al. 2020). However, for lower-mass stars, the mechanisms at play are not clear.

The observed transients with a rapid rise time (from a few days to ∼10 days) are usually associated with the existence of some shock interaction between the ejecta and the CSM. The interaction picture has been suggested to explain many bright and rapid transients, such as SN 2006gy (Woosley et al. 2007; Blinnikov 2010), iPTF14hls (Woosley 2018), AT2018cow (Leung et al. 2020), and SN 2018gep (Leung et al. 2021).

Late-phase nuclear burning of massive stars is rapid and strong, which can drive vigorous convective flow within the C- and O-burning regions. The convection triggers wave generation outside the convection zone, and some of these waves leak through the evanescent zones inside the star and propagate outward (Quataert & Shiode 2012). Escaped waves with sufficient energy can form shocks or dissipate via radiative diffusion when they approach the stellar surface, where they deposit their energy as an extra thermal energy source (Shiode & Quataert 2014). Even though the relative amount of energy which can successfully leak is small compared to the whole stellar energy budget, in some cases it may be sufficient to eject the outermost matter from the H and He envelope in a H-rich (Fuller 2017) or H-poor (Fuller & Ro 2018) star. The exact amount of mass ejection depends on the energy budget.

The energy injection can also change the near-surface structure of the star (Owocki et al. 2019; Kuriyama & Shigeyama 2020; Leung & Fuller 2020) and hence its observable optical appearance (Kuriyama & Shigeyama 2021). Additionally, the circumstellar medium can greatly affect the light curve of the subsequent supernova (Suzuki et al. 2019). The outburst mass and energy expected from wave heating are approximately capable of matching some well-observed transients such as SN 2000kf (Ouchi & Maeda 2021) and SN 2018gep (Leung et al. 2021).

In Leung et al. (2021) we used a parameterized wave model to study how the stellar envelope of a H-poor star responds to the wave energy deposition. Depending on the energy deposition and duration, we estimated that the typical mass loss can reach ∼10⁻⁵–10⁻² M_⊙. In this work, we examine the energy deposition computed from realistic stellar models that self-consistently compute the wave flux escaping from the stellar core.

In Section 2, we describe the numerical methods for computing the wave heating rate from stellar models, the following hydrodynamical evolution, and radiative transfer simulations. In Section 3, we describe the wave heating rates from our suite of stellar models, and how it depends on stellar parameters such as mass and metallicity. Section 4 presents hydrodynamical simulations of the stellar response to wave heating, while Section 5 shows light curve models of the subsequent supernova. In Section 6, we discuss implications for transients and comparisons with recent work in the literature, and we conclude in Section 7.

We first examine how the wave energy transport occurs in a typical H-poor model. To illustrate this, we take an example of M_ZAMS = 60 M_⊙, with Z = 0.02. This model evolves to form a 27.2 M_⊙ He core, and later wind-driven mass loss during core helium burning leads to a final mass of ${M}_{\mathrm{pre} \mbox{-} \mathrm{SN}}=17.5\,{M}_{\odot }$.

In Figure 1 we plot the wave energy transport history of this model. We plot the wave energy deposition rate in the envelope (top left panel), cumulative deposited energy (top right panel), nonlinearity (bottom left panel), and the energy escape fraction (bottom right panel). In all the four panels, we mark the data points by color to specify which burning zone contributes the most amount of energy, with He, C, O, Ne, and Si represented by red, orange, green, blue, and purple, respectively.

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From the energy deposition rate, we observe that wave heating first becomes significant during core O burning, about 0.05 yr pre-explosion. C-shell burning and O-shell burning provide additional peaks in the escaped energy at ∼(2–4) × 10⁻³ yr before collapse. After that, the energy escape rate sharply decreases. Si burning is almost insignificant to the energy budget up to 10⁻³ yr before collapse. All told, roughly 10⁴⁶ erg of wave energy escapes to the envelope before core collapse.

The escape fraction measures how much energy can reach the envelope after energy losses in the core and tunneling through evanescent regions. In this particular model, the escape fraction during core O burning (∼2 × 10⁻² yr before core collapse) is much lower than that during subsequent shell C and O burning. Hence, most of the energy from core O burning is damped out via neutrino damping before being able to tunnel into the envelope. The energy escape rate is also greatly decreased by the nonlinearity attenuation factor (Equation (2) squared). In this model, the core O-burning phase experiences a nonlinear attenuation of about 100, while that during C-shell and O-shell burning is about an order of magnitude lower. Hence, the wave heating rate jumps from ∼10³⁹ erg during core O burning to ∼10⁴¹ erg during C- and O-shell burning, demonstrating the importance of nonlinear suppression of wave energy transport.

To understand the features in the H-poor model, it is necessary to discuss the wave transport feature in a H-rich model. To do so, we consider a H-rich model with M_ZAMS = 36 M_⊙, which evolves to have a pre-explosion He-core mass of 17.0 M_⊙. This model has a similar pre-explosion He-core mass as the H-poor model in the previous section, so its core evolves similarly during late stage burning. This model transmits about 2 × 10⁴⁷ erg of wave energy to the surface, about an order of magnitude higher than the corresponding H-poor model with a similar He-core mass.

The energy escape rate is much higher in the H-rich model during O burning with a value ∼10⁴¹ erg s⁻¹, which is about two orders of magnitude higher than that of the H-poor model. The later C-shell and Ne-shell burning deposit energy with the same order of magnitude (see Figure 2). The primary reason for the larger heating is that the H-rich star has a larger escape fraction and much lower wave nonlinearity compared to the H-poor model with the same ${M}_{\mathrm{pre} \mbox{-} \mathrm{SN}}$. In H-rich stars, the convective C-burning shell is usually narrower, such that the g-mode cavity overlying the O-burning core is wider, and the evanescent region separating it from the envelope is smaller. Hence, a larger fraction of the waves escape the core, and a smaller fraction of the wave energy is lost to photon, neutrino, or nonlinear damping.

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To illustrate this idea, we examine in Figures 3 and 4 the wave propagation diagrams for two models when core O burning takes place. The models are chosen to have M_ZAMS = 40 M_⊙ and Z = 0.02. Most of the qualitative features in both H-rich and H-poor models are similar, in terms of the density and temperature profiles, and the luminosity profile. The main difference is the extensive H envelope that appears in the H-rich model that extends to ∼1000 R_⊙. The convective energy transport peaks at ∼10⁻³–10⁻¹ R_⊙, and in both models the O-shell convective frequency is comparable, about 2 × 10⁻³ s⁻¹. The major difference comes the Brunt–Väisälä frequency profiles. In the H-poor model, the convective C-burning shell is thicker, trapping more of the waves generated by the O-burning core beneath it. In the H-rich model, this convective shell is thinner, allowing the waves to more easily tunnel into the overlying radiative region between the C-burning and He-burning shells. Hence, in the H-rich models, more of the wave energy escapes from the core before it is damped.

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We carry out an extensive survey of stellar models by varying two model parameters, initial ZAMS mass and metallicity. We choose a wide range of mass and metallicity to explore the potential mass loss driven by wave energy deposition. For lower metallicity models, we also lower the maximum mass simulated so that other major mass-loss mechanisms, such as the mass loss driven by the pulsational pair instability, are avoided.

In Figure 5 we plot the time-integrated escaped energy of each stellar model against its pre-explosion He-core mass ${M}_{\mathrm{pre} \mbox{-} \mathrm{SN}}$. We choose ${M}_{\mathrm{pre} \mbox{-} \mathrm{SN}}$ as it is more closely related to the final evolution than M_ZAMS. The total escaped energy is integrated from after He-core burning, up to ∼10⁻³ yr before stellar collapse. We have included models with a metallicity from 0.002–0.02. A subset of H-rich models are also included for comparison. We list in Table 1 the outliers of our models and their physical origins.

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The clustering of the data points demonstrates multiple features of stellar evolution at different phases. The H-rich models have the highest escaped energy E_esc. The energy range is consistent with previous work (Wu & Fuller 2021) showing that H-rich stars often release about 10⁴⁷ erg before explosion for a wide range of masses. An outlier is the M = 45 M_⊙ model. This model has an extraordinarily high E_esc ∼ 10⁴⁸ erg. The origin of the high escaped energy is the convective shell merger phenomenon, as reported in previous work (Wu & Fuller 2021). During the C-shell burning, the growing C-burning shell merges with the overlying He-burning shell, dredging He-rich matter down into the actively burning C-shell. The influx of extra He can rapidly increase the nuclear reaction luminosity due to α-capture reactions. As a result, the burning drives vigorous convection and wave generation.

On the other hand, H-poor models in general have a lower E_esc by an order of magnitude (∼10⁴⁶ erg). Regardless of their initial metallicity, most of the data points cluster in a band that starts from about 10⁴⁶ erg at ${M}_{\exp }\sim 5\,{M}_{\odot }$ and then gradually decreases down to 10⁴⁵ erg at ${M}_{\exp }\sim 12.5\,{M}_{\odot }$. The band gradually increases and reaches an asymptotic energy ∼ 10⁴⁶ erg again at ${M}_{\mathrm{pre} \mbox{-} \mathrm{SN}}\sim 17.5\,{M}_{\odot }$.

A few outlying H-poor models have larger total escaped energies, such as the M_ZAMS = 38 M_⊙ model, which has E_esc ∼ 10⁴⁷ erg. The differences come from a number of physical processes which will be discussed in later sections.

In Figure 6 we plot the total escaped energy against deposition time t_dep for each model. We define the deposition time by the time before core collapse at which 50% of the total wave energy has escaped from the core. This corresponds approximately to the time before explosion of any pre-supernova mass ejection that occurs. However, whether or not the star ejects mass must be determined by hydrodynamic simulations of the envelope's response to wave heating (e.g., Section 4 in this article and Leung et al. 2021).

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Regardless of the star being H-rich or H-poor, the majority of models have deposition timescales from 10⁻³–10⁻¹ yr. Stars with higher pre-explosion helium core masses tend to have shorter deposition timescales, but there is large scatter and the value of t_dep is not correlated with the escaped energy. For example, models with M_ZAMS = 25 M_⊙ have an outburst time as early as 0.09 yr before explosion for the model with Z = 0.007, but it is as low as 0.01 yr for Z = 0.02 and 0.001 yr for Z = 0.002. Each represents a distinctive energy deposition history, and hence we expect there corresponding circumstellar environment can be very different.

We also examine how each of the burning channels contributes to the total deposited energy in each model. In Figure 7 we plot the energy deposited by waves generated from convective burning of He (top left panel), C (top right panel), O (bottom left panel) and Ne (bottom right panel). The Si channel in general contributes an insignificant amount of energy except just before core collapse.

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During He burning, the majority of models scatters between 10⁴³ and 10⁴⁵ erg, which is at most about ∼10% of the deposited energy. The extremely high value for one H-rich model corresponds to the shell merger model described in the previous section. For the C burning, the total escaped energy ranges from 10⁴⁴–10⁴⁶ erg. There is no significant trend between the pre-explosion mass and the total escaped energy.

O burning often provides the most energy and has a narrower range between ∼10⁴⁵ and 10⁴⁷ erg, but other types of burning are most important in a significant fraction of models. We observe a narrow band for the H-rich models, which is consistent with previous work (Wu & Fuller 2021) that O burning provides the majority of wave energy to the envelope. Ne burning has a similar scatter as the C-shell with a range from 10⁴³–10⁴⁶. H-rich models have significantly higher energy from Ne burning than H-poor models.

We next focus on a specific group of models with M_ZAMS =25 M_⊙ and Z = 0.002, 0.07, and 0.02. These models have a comparable total deposited energy, but each has a distinctive deposition duration. In Figure 8 we plot the cumulative energy as a function of pre-collapse time for the three models. It is evident that the timing of the wave heating episodes varies significantly between the models, even though they each end up with ∼10⁴⁶ erg of wave heat. Moreover, the burning phase (e.g., helium, carbon, or oxygen burning) responsible for the majority of the heat is different in each model. Clearly, models with similar He-core masses can differ greatly in both net wave energy and the deposition timescale.

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In Figure 5 and Table 1 we show that there are outliers with more escaped wave energy than most models. Here, we study them in detail. We compare two distinctive models: a H-poor model with M_ZAMS = 20 M_⊙ and Z = 0.007 (high-energy model), and a H-poor model with M_ZAMS = 35 M_⊙ and Z = 0.007 (low energy model). In Figure 9 we plot the wave heating rate of each model. The two models demonstrate qualitative similarities, but the wave heating rate is typically 2 orders of magnitude larger in the high-energy model.

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How most of the energy is released at ∼0.01 yr before collapse is different in the two models. Even though there is a sudden burst of wave energy from O- (He-) shell burning in the high (low) energy model, the corresponding escape fraction and nonlinearity during that period is very different. The high-energy model maintains a large escape fraction and a low nonlinearity (∼1) for about 0.003 yr, while the low energy model has a small escape fraction and large nonlinearity (∼8). This drastically impacts the energy that can successfully reach the envelope.

To further diagnose the origin of the different wave energy deposition rates of the models above, we plot in Figure 10 the density and temperature profiles (top left panel), wave propagation diagram (top right panel), the luminosity profile (bottom left panel), and the chemical abundance profile (bottom right panel) of the 20 M_⊙ model at ∼ 9 × 10⁻³ yr from its onset of gravitational collapse. The choice of the model age overlaps with the time where its wave deposition energy is at its maximum. In this model, most of the wave energy arises from the energetic convective shell at r ∼ 10⁻² R_⊙, which burns carbon, oxygen, and neon and carbon at this snapshot. A recent ingestion of carbon from above has increased the burning luminosity and wave frequency. The Brunt–Väisälä frequency and the Lamb frequency profiles indicate the source of the high wave transmission. The outgoing wave frequency is about 10⁻² s⁻¹. Waves of this frequency see only a narrow evanescent layer at r ∼ 10⁻¹ R_⊙ separating the core from the envelope. As a result, a large fraction of the waves can escape into the envelope and arrive the surface for heat deposition.

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Another important feature for massive star evolution is the occurrence of convective shell merger events, driven by convective boundary mixing (Collins et al. 2018; Davis et al.2019; Andrassy et al. 2020; Yadav et al. 2020). Shell mergers not only change the pre-collapse stellar structure of the massive star, but also provide unconventional thermodynamic conditions for the synthesis of minor elements such as Cl, K, and Sc (Ritter et al. 2018). In our case, convective shell mergers drive vigorous nuclear burning, convection, and wave energy generation, so they can lead to a wave-driven outburst (Wu & Fuller 2021).

Our 45 M_⊙ H-rich model exhibits a shell merger that could generate a wave-driven outburst, as shown in Figure 11. When the merger event occurs at 0.005 yr before collapse, the energy deposition rate increases by about 3 orders of magnitude. Even though it has a duration less than 0.001 yr, more than 90 % of the deposited energy of ∼ 10⁴⁸ erg comes from this event. By examining the chemical abundance profiles before and after the shell merger, we see that He has been dredged down below 10⁻¹ R_⊙ during the merger. This occurs when the convective mixing becomes strong during C-shell burning, causing a merger with the overlying He-burning shell that drags the He-rich material to the actively burning C-shell. This drives intense nuclear energy via α-capture reactions that further power convective motion, and wave excitation. The wave frequency also increases due to the larger convective velocities. Consequently, the wave heating rate of the envelope increases by a few orders of magnitude.

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Here we study the hydrodynamical response of the envelope due to wave energy deposition. In Leung et al. (2021), we demonstrated that how fast the energy is deposited affects the envelope expansion. When the energy deposition timescale is shorter than the dynamical timescale, the excited envelope develops a shock and ejects mass in the form of a pulse. On the other hand, when the energy deposition timescale is long, the envelope gradually expands and a steady wind can be driven.

To estimate how much mass can be ejected and its trajectory, we use the total escaped energy E_esc and the duration t_dep. If the wave energy is used efficiently to eject mass, the ejected mass M_ej would be approximately

$$\begin{eqnarray}&&{M}_{\mathrm{ej}}\sim \displaystyle \frac{{E}_{\mathrm{esc}}R}{{{GM}}_{\mathrm{pre} \mbox{-} \mathrm{SN}}},\end{eqnarray} \tag{ 4 }$$

where R is the radius of the pre-explosion star. Equation (4) overestimates the ejecta mass in H-rich stars (Fuller 2017; Linial et al. 2021), so our estimates for H-rich stars should be taken as upper limits. Similarly, if mass is ejected at the star's escape speed, the CSM radius R_CSM would be

$$\begin{eqnarray}&&{R}_{\mathrm{CSM}}\approx {t}_{\mathrm{dep}}{v}_{\mathrm{ej}}\sim {t}_{\mathrm{dep}}\sqrt{\displaystyle \frac{{GM}}{R}}.\end{eqnarray} \tag{ 5 }$$

Fuller & Ro (2018) found that wave heating does efficiently eject mass in H-poor stars, and that the outflow velocity is slightly larger than the escape speed, such that Equations (4) and (5) are reasonable estimates.

In Figure 12 we plot R_CSM against M_ej for all the models computed in this work. The data points cluster into two groups: the H-rich models and the H-poor models. Due to their small binding energy, H-rich models are expected to eject as much as ∼0.5 M_⊙, though the true ejected mass may be substantially smaller. If mass is ejected by an outgoing shock wave, Linial et al. (2021) argued that the ejecta mass will likely be either nearly zero or a large fraction of the H envelope, so more detailed calculations should be performed for reliable estimates of the mass loss in H-rich models.

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The H-poor models exhibit a wide range of M_ej and R_CSM due to their varying wave heating rates and timescales. Most models center around M_ej ∼ 10⁻⁴ M_⊙ and R_CSM ∼ 3 × 10¹³ cm. There are some outliers (corresponding to outliers in Figure 5) that have larger ejected mass (∼10⁻² M_⊙) or a very large R_CSM ∼ 10¹⁴ cm. These are models with large wave energies or long wave heating timescales, respectively. The distribution of the data points do not depend strongly on the initial metallicity.

As shown in Leung et al. (2020, 2021), an ejected mass of ∼10⁻²–10⁻¹ M_⊙ with a radius of 10²–10⁴ R_⊙ can power luminous SNe via CSM interaction, which explains some rapidly brightening transients with a rise time of ∼10 days and a peak luminosity ∼10⁴⁴ erg s⁻¹. The expected M_CSM is much smaller than the required values for most of our models, so we expect rapidly rising H-poor transients to be uncommon (if the CSM is generated by wave heating). The exact structure of the CSM and its impact on the explosion light curve require detailed hydrodynamics and radiative transfer calculations, which we perform for a few of our models.

Having understood the wave deposition history, we may repeat the procedure outlined in Leung et al. (2021) of depositing the energy to the outer part of the star. In that work, the wave luminosity and duration are chosen from analytic estimates. In this work, we directly use the wave energy deposition history recorded from our stellar models above. This approach provides a more accurate prescription to study mass ejection and remove extraneous parameters.

Similar to our previous work, we excise the interior, keeping only about 1 M_⊙ interior of the C shell, so that the simulation is not limited by the small time step during the advanced burning in the core. In our case, the expected mass loss is so small (<10⁻² M_⊙) that we do not expect the surface motion to feedback on the evolution of the core. We add the wave energy as an additional energy source in the stellar models, deposited in the envelope according to Equation (1) in Leung et al. (2021). This accounts for acoustic wave energy dissipation via weak shocks and radiative damping. For detailed implementation we refer readers to our previous work.

For demonstration, we consider the H-poor model with the largest mass ejection shown in Section 4.1, with M_ZAMS = 20 M_⊙ and Z = 0.007. In Figure 13 we plot the density, velocity, mass, and wave heating profiles at different times. The hydrodynamical simulation begins when the total wave heating energy exceeds 10³ L_⊙ for the first time. We see that until 0.01 yr before collapse, the low energy deposition rate does not lead to significant motion in the envelope. When the Ne-shell burning increases the wave heating rate, we see that the envelope quickly expands, reaching a radius ∼10^2.5 R_⊙. The outermost velocity can reach ∼10⁸ cm s⁻¹. However, we emphasize that because of the low density, the ejected mass only amounts to ∼10⁻² M_⊙, which is made of mostly He. The surface luminosity can temporarily increase by 2 orders of magnitude to L ∼ 10⁷ L_⊙. The density profile of the ejected mass is slightly steeper than a r⁻² scaling.

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Our analytical mass ejection and timescale estimates match the expected CSM features fairly accurately for the H-poor model with a large E_dep. For our example, our analytic formulae predict that M_CSM, R_CSM ≈ (0.01 M_⊙, 300 R_⊙), whereas the simulation has M_CSM, R_CSM ≈ (0.007 M_⊙, 758 R_⊙). However, most of the ejected mass is located below ∼300 R_⊙ so the analytical estimate is actually quite good. When the expected mass ejection is very small, the analytic formula can overestimate the mass because the energy deposition becomes more concentrated in matter near the stellar surface.

We plot in Figure 14 the time evolution of the surface luminosity for the same model as Figure 13. When the wave heating peaks about 0.01 yr before collapse, the surface luminosity increases by a factor of ∼100 to reach a peak luminosity of nearly 3 × 10⁷ L_⊙. The temperature initially increases by a factor of a few, but decreases after the initial peak as the photospheric radius moves outward into an extended optically thick wind. The same behavior was seen in Fuller & Ro (2018). High-cadence photometric surveys may be able to detect these progenitor outbursts, like that of SN 2018gep (Ho et al. 2019).

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Our wave heating models can be compared to rapidly rising and fading transients (e.g., Drout et al. 2014), which may be powered by CSM interaction. For the large majority of our models, the wave heating is insufficient to eject enough mass to power observed rapidly evolving transients. The typical mass scale of wave-driven outbursts of ∼10⁻⁴ M_⊙ can only sustain shock-cooling emission for ∼10⁻¹ days, far shorter than the typical evolution times of ∼10 days. The upper end of the distribution explored in this work ejects ∼10⁻² M_⊙, which may sustain shock cooling for ∼1 day, still too short compared to the current population of observed rapidly evolving transients. However, our models predict that a significant fraction of ordinary Type Ib/c SNe will exhibit a bright but very brief phase of CSM interaction within hours of explosion.

Our models also shed light on the rapid rise and fall of the light curve in heavily stripped Type Ib/c SNe such as iPTF14gqr (De et al. 2018b), iPTF16hgs (De et al. 2018a), and SN 2019dge Yao et al. (2020). The short-lived shock cooling for iPTF14gqr indicated a CSM mass and radius of M_CSM ∼ 0.01 M_⊙ and R_CSM ∼ 3 × 10¹³ cm, similar to that of our most energetic H-poor model in Figure 12. Hence, wave-driven mass loss could possibly account for the extended envelope of that event. For the other two, the authors inferred M_CSM ∼ 0.1 M_⊙ and R_CSM ∼ 10¹² cm for iPTF16hgs, and M_CSM ∼ 0.1 M_⊙ and R_CSM ∼ 3 × 10¹² cm for SN 2019dge. Those masses are likely too large to be created by wave-driven mass loss, and the radii are likely too small. Hence, an inflated He envelope as is naturally expected in low-mass He star SN progenitors may be a more likely explanation for those events. All of these events were heavily stripped SNe (likely in binary systems) arising from low-mass progenitors whose structures are quite different from the higher-mass He stars studied here. Future calculations should investigate H-poor low-mass He stars, whose wave heating rates may be increased by degenerate neon/oxygen/silicon burning (Wu & Fuller 2021).

Even though the small amount of CSM predicted by our models will not have a large impact on the optical light curves of typical Type Ib/c SNe, it may affect the shock breakout emission. Even a small amount of optically thick mass (M ≳ 10⁻⁶ M_⊙) above the photosphere may be sufficient to affect the shock breakout duration and its X-ray spectrum.

Our models are roughly consistent with the enhanced CSM density inferred around the progenitor of Type Ib SN 2008D based on its shock breakout emission Soderberg et al. (2008). Svirski & Nakar (2014; see also Balberg & Loeb 2011; Ioka et al. 2019; Ito et al. 2020) demonstrated that the CSM density at R ≲ 10¹⁴ cm must have been ∼ 20 times larger than expected for Wolf–Rayet stars. This entails $\dot{M}\sim {10}^{-3}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ for a wind mass-loss rate of 5 × 10⁻⁵ M_⊙ yr⁻¹. Our typical models have R_CSM ≲ 10¹⁴ cm, consistent with the shock breakout constraint. They also have M_CSM ∼ 10⁻⁴ M_⊙, ejected on timescales of t_CSM ∼ 10⁻² yr, corresponding to mass-loss rates of ∼10⁻² M_⊙ yr⁻¹. This is only slightly larger than the inferred late-time mass-loss rate of SN 2008D. More detailed modeling of shock breakout emission (which is not accurately captured by our SNEC models) can determine whether wave-driven mass can account for the shock breakout signal of 2008D. In any case, we predict that longer-than-expected shock breakout emission may be very common in H-poor SNe, which may be tested by future wide-field UV surveys (Sagiv et al. 2014).

Our work can be compared with other studies of outbursts driven by sudden energy deposition. In Kuriyama & Shigeyama (2020), energy is deposited in the stellar envelope with a given deposition rate and duration, and the amount of energy is scaled with the binding energy of the envelope. The resultant mass loss ranges from ∼10⁻³–1 M_⊙. For red supergiants losing mass via a shock, the actual mass loss sharply drops when the ratio of deposited energy to binding energy is less than roughly 0.5, as explained in Linial et al. (2021). For compact stars with mass loss via super-Eddington winds, most of the deposited energy is used to lift mass out of the gravitational potential, so the total mass lost is closer to our estimate from Equation (4), as explained in Quataert et al.(2016).

In Ouchi & Maeda (2021), a moderate heating rate of of ∼10³⁹ erg s⁻¹ is added to a 12 M_⊙ star, but with a long-lasting duration of 3 yr. The total energy is about 10⁴⁷ erg which is close to our H-rich models, but our models suggest that the expected energy is lower for H-poor stars. The deposition timescale of three years is much longer than our models, allowing the star to expand smoothly rather than eject mass via outbursts. In Owocki et al. (2019) the parameterized energy deposition in a stellar envelope is studied. Half of the envelope energy (∼10⁵⁰ erg) is deposited in a blue supergiant model and a mass outburst of ∼7 M_⊙ is observed, resembling the mass eruption in the η Carinae. Such a high-energy deposition is not seen in our series of models, suggesting that other mechanisms are necessary to explain massive outbursts like that of η-Carinae.

In this work we have assumed that the star loses all of its H envelope due to interactions from its binary companion. This is a good approximation for high-mass or high-metallicity stars where winds will likely remove any residual H envelope during core He burning. For lower-mass and lower metallicity stars, winds might not robustly remove all the H (Götberg et al. 2017; Laplace et al. 2020), and a H envelope may remain until the end of stellar evolution. The less compact H envelope would have a lower binding energy, possibly triggering more significant expansion and/or mass loss compared to the pure He case. This scenario should be investigated in future work.

We have used bolometric radiative transfer for computing the light curves, assuming blackbody radiation. However, given the very low CSM mass, the medium becomes transparent at a very early time (∼10 days), which could mean that photon transport depends on a frequency-dependent opacity. In order to robustly model optically thin ejecta and the associated effective temperature, multiband radiative transport becomes necessary.