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A&A
Volume 641, September 2020
Article Number L10
Number of page(s) 5
Section Letters to the Editor
DOI https://doi.org/10.1051/0004-6361/202038903
Published online 24 September 2020

© ESO 2020

1. Introduction

Long-duration gamma-ray bursts (LGRBs), which are often accompanied with energetic hydrogen-free supernovae (SNe), are considered to be explosions of massive rapidly rotating Wolf-Rayet (WR) stars (Woosley & Bloom 2006). Most LGRBs have a duration on the order of 1 − 100 s (e.g., Levan et al. 2014). The LGRB duration is connected with the duration of the central engine, launching the jet. The central engine is suggested to be accreting black holes (BHs, Woosley 1993; Paczyński 1998), for example, or strongly magnetized neutron stars (so-called magnetars, Usov 1992; Duncan & Thompson 1992). If the central engine is an accreting BH, the LGRB duration can be related to the accretion timescale of the collapsing WR stars that can roughly correspond to the free-fall timescale of WR stars (e.g., Kumar et al. 2008). Indeed, the typical timescales of LGRBs match the free-fall timescales of WR stars that usually have a radius on the order of 1 R⊙ or less (e.g., Yoon et al. 2012).

It has been recently recognized that some LGRBs have a duration of more than 104 s and they are called ultra-long gamma-ray bursts (ULGRBs, e.g., Gendre et al. 2013; Levan et al. 2014). If the duration of more than 104 s is related to the free-fall timescale of the progenitors, they must have a radius that is larger than 10 R⊙. Since the required radius is too large for WR stars, the progenitors of ULGRBs have been linked to hydrogen-rich blue supergiants (BSGs), which typically have a radius on the order of 10 R⊙ and have a free-fall time of more than 104 s (e.g., Suwa & Ioka 2011). However, no hydrogen signatures have ever been observed in ULGRBs (Greiner et al. 2015, G15 hereafter). In the accompanying paper, we show that massive hydrogen-free stars that experience the pulsational pair-instability shortly before the core collapse can keep the extended structure caused by the pair-instability until the collapse and have radii that are well above 10 R⊙ (Marchant & Moriya 2020, MM20 hereafter). They can even have radii exceeding 1000 R⊙ and sustain the accretion to the central BH for far more than 104 s. The jet launched by the long-lasting accretion in the extended progenitor may also escape from the progenitor (Quataert & Kasen 2012). Thus, they are promising progenitor candidates for ULGRBs.

Not only are the extremely long durations of ULGRBs distinct from those of LGRBs, but this is also the case for the accompanying SNe in ULGRBs. SN 2011kl, which was accompanied by ULGRB 111209A, has the peak optical magnitude at around −20 mag and is more luminous than typical SNe associated with LGRBs (G15; Kann et al. 2019). SN 2011kl is difficult to explain with the canonical 56Ni-decay energy input for SNe associated with LGRBs because of the short rise time, high photospheric temperature, and high photospheric velocity. The luminous SNe associated with ULGRBs likely have a different luminosity source (see Ioka et al. 2016 and the references therein). For example, the magnetar powered model, which is also suggested to be the luminosity source of hydrogen-free superluminous supernovae (Quimby et al. 2011), is proposed to explain the accompanying luminous SN (Metzger et al. 2015). SN 2011kl is also linked to the cocoon emission from a hydrogen-rich blue supergiant ULGRB progenitor (Nakauchi et al. 2013; Kashiyama et al. 2013), but SN 2011kl did not show the expected hydrogen signatures (G15).

In this Letter, we investigate the observational properties of the explosions of an extended hydrogen-free ULGRB progenitor presented in MM20. A systematic modeling of the explosions of the extended helium stars up to around 150 R⊙ has been previously performed by Kleiser et al. (2018) and Dessart et al. (2018), but our progenitor has a more extended envelope. We show that the luminous SN components accompanied by ULGRBs appear from our progenitor without 56Ni or any central energy inputs thanks to the long adiabatic cooling phase caused by the large progenitor radius. The overall properties of SN 2011kl can be explained by our progenitor model. Our results show that the extended hydrogen-free ULGRB progenitors presented in MM20 can explain both the extremely long duration and the luminous SNe accompanied by ULGRBs, making them promising progenitors for ULGRBs.

2. Methods

2.1. Progenitor

We took one ULGRB progenitor model from MM20. We refer the reader to MM20 for more details on the progenitor model. Figure 1 shows the density structure of the progenitor model. In short, it is initially an 82.5 M⊙ helium star, rotating with 90% of the critical rotation. It evolves without the Spruit-Tayler dynamo process. The progenitor experiences two pulses at 6749 and 2085 years before the final core collapse. It keeps the extended hydrostatic structure after the second pulse until the core collapse and the radius of the progenitor at the time of collapse is 1962 R⊙. The abundance profile of the progenitor at the time of the collapse is presented in Fig. 2. The progenitor, which was obtained from the one-dimensional hydrostatic stellar evolution calculation, is close to the Eddington limit. There are significant uncertainties and work is in progress related to this regime (e.g., Jiang et al. 2015). We note that the large expansion in our models does not arise from inflation in a star near the Eddington limit, but by the energy deposited in the thermonuclear pulse, which leads to a dynamical expansion by more than two orders of magnitude in a timescale where both convection and radiative transport are irrelevant (Marchant et al. 2019). The exact radius of the stars could be uncertain, but the prediction that they expand significantly is reasonable. The progenitor mass at the collapse is 50 M⊙ and it retains enough angular momentum to be a GRB as presented in MM20. The extended envelope contains 5 M⊙, which is 10% of the progenitor mass.

thumbnail Fig. 1.

Density structure of the ULGRB progenitor adopted in this work. Top panel: radius coordinate and the bottom panel shows it in the mass coordinate. We note that the extended progenitor is a hydrogen-free star.

thumbnail Fig. 2.

Abundance profile of the ULGRB progenitor.

The free-fall time of the progenitor is 4 × 107 s and it is well beyond the duration of ULGRBs (∼104 s). We presume that the accretion toward the central BH can be suppressed at some moment because of, for example, the accompanying SN explosion or the disk wind of BH accretion. The outer layers of the progenitor are less bounded and the accretion would be easily surpressed. Swift 1644+57, which is suggested to be a LGRB with the duration of ∼107 s (Quataert & Kasen 2012), could be a case where the BH accretion was not suppressed, for example.

2.2. Light-curve calculations

The numerical LC calculations were performed with the one-dimensional radiation hydrodynamics code STELLA (Blinnikov et al. 1998, 2000, 2006). STELLA implicitly treats time-dependent equations of hydrodynamics and the angular moments of intensity averaged over a frequency bin with the variable Eddington method. STELLA calculates the spectral energy distributions (SEDs) at each time step.

In this study, we assume an ejecta mass of 15 M⊙ in the LC calculations and set the mass cut at 35 M⊙. This ejecta mass provided the best LC model for SN 2011kl in our investigation. The ejecta mass of around 10 M⊙ is typically estimated in SNe associated with LGRBs (e.g., Iwamoto et al. 1998). We note that the BH mass from the same progenitor is estimated as 45 M⊙ based on its angular momentum distribution in MM20, but here we artificially set the BH mass to have the selected ejecta mass. The explosions are artificially triggered by putting thermal energy required to reach the prescribed explosion energy within 0.5 M⊙ above the mass cut. We show models with an explosion energy of 10 B, 20 B, and 50 B, where 1 B ≡ 1051 erg. An explosion energy of 10 B and above is typically estimated in SNe associated with LGRBs (e.g., Woosley & Bloom 2006). We note that 12 M⊙ exists below 10 000 km s−1 in the ejecta of the 10 B explosion. We included a small amount of 56Ni (M56Ni = 0.1 M⊙) in our standard simulations, but it does not affect the LCs that we present. We also show a model with a 56Ni mass of 1.5 M⊙. The 56Ni mass was also set artificially.

The optical LC of SN 2011kl with which we compared our synthetic LCs was obtained by integrating the SEDs from 3500 Å to 8000 Å (the “quasi-bolometric” LC in G15). Therefore, we constructed the optical LCs from the synthetic models by integrating the synthetic SEDs in the same wavelength range. When we show the photospheric properties, the photosphere is set at the location where the Rosseland mean optical depth became 2/3.

3. Results

Figure 3 shows the synthetic bolometric and optical LCs with a 56Ni mass of 0.1 M⊙. The bolometric LC behaves in the standard way as expected in the cooling phase of the extended progenitor (e.g., Hoflich et al. 1993; Blinnikov et al. 1998; Rabinak & Waxman 2011; Bersten et al. 2012; Nakar & Piro 2014). After the ejecta are heated by the shock wave causing the SN explosion, the ejecta experience adiabatic cooling. The bolometric luminosity steadily declines as the ejecta cool. The adiabatic cooling is less efficient in more extended progenitors and, therefore, the explosions from more extended progenitors have a high temperature for a longer time. This means that it takes more time for the ejecta to be cool enough for optical LCs to be luminous for more extended progenitors. Thus, the optical LCs have longer rise times for larger progenitor radii. The slow cooling also makes the photosphere more extended when the optical luminosity becomes large, making optical LCs more luminous for more extended progenitors. We refer the reader to Grassberg et al. (1971) and Falk & Arnett (1977) for further details on dynamics and LCs in the early phases of extended progenitor explosions.

thumbnail Fig. 3.

Bolometric (solid) and optical (dashed; integrated from 3500 Å to 8000 Å) LCs from the explosions of the extended (1962 R⊙) hydrogen-free ULGRB progenitor. The ejecta mass is 15 M⊙ and the explosion energy is shown in the figure. All the models have 0.1 M⊙ of 56Ni, but it does not affect the LCs presented here as indicated by the total nuclear energy available from 0.1 M⊙ of 56Ni (red; Nadyozhin 1994).

The fast-evolving optical LCs here result from the cooling of extended progenitors. The optical LCs have large peak luminosities and short rise times despite of the small 56Ni mass and massive ejecta (15 M⊙). The 10 B explosion model, for example, reaches its optical peak luminosity of 4 × 1043 erg s−1 (−20.3 mag) in 13 days. We refer the reader to Kleiser et al. (2018) and Dessart et al. (2018) for more detailed information on the LCs from the less extended (≲100 R⊙) hydrogen-free progenitors.

The optical LC of SN 2011kl, which was associated with ULGRB 111209A, is compared with our synthetic optical LCs in Fig. 4. The 10 B explosion model explains the early quick rise and peak luminosity of SN 2011kl well, but the LC decline rate after the peak is larger than that in SN 2011kl. The LC models with 0.1 M⊙ of 56Ni decline too rapidly after the peak. However, a larger amount of 56Ni likely exists because of the large explosion energy. We show the LC model with M56Ni = 1.5 M⊙ in the bottom panel of Fig. 4. The delayed luminosity input from the nuclear decay of 1.5 M⊙ of 56Ni successfully reproduces the slow decline in the optical LC found in SN 2011kl. G15 disfavored the possibility that SN 2011kl is powered by the 56Ni decay because of the short rise. Here, we show that the quick rise time is reproduced by the extended envelope and then the 56Ni decay can contribute to the declining phase. The existence of the extended envelope naturally explains the ultra-long duration of GRB 111209A at the same time.

thumbnail Fig. 4.

Top: synthetic optical (3500 Å to 8000 Å) LCs with M56Ni = 0.1 M⊙ compared with the optical LC of SN 2011kl. Bottom: synthetic optical (3500 Å-8000 Å) LC with M56Ni = 1.5 M⊙ (solid). It matches the observed LC of SN 2011kl well. The quasi-bolometric LC with M56Ni = 0.1 M⊙ is also shown (dashed). We also present the quasi-bolometric LC model from a compact hydrogen-free progenitor having M56Ni = 1.5 M⊙, which does not have a slow cooling phase, in order to illustrate the luminosity contribution from the 56Ni decay with the dot-dashed line. All of the models in the bottom panel have an explosion energy of 10 B. The explosion time for SN 2011kl was set at the time of the ULGRB 111209A trigger.

Figure 5 presents the photospheric velocity and temperature evolution of our explosion models. We can find that our luminous SN models are characterized by large photospheric velocities on the order of 10 000 km s−1 and a hot photospheric temperature exceeding 10 000 K at around the LC peak. The photospheric velocity of SN 2011kl at around the peak luminosity is estimated to be 19 000 km s−1 based on the calcium and carbon lines (G15). Our best LC model for SN 2011kl presented in the bottom panel of Fig. 4 has the photospheric velocity of 15 000 km s−1 at around the LC peak. We estimate the photosphere based on the Rosseland mean opacity. It does not necessarily correspond to where calcium and carbon are absorbed and they could be absorbed above the photosphere. In addition, the photosphere in the model at around the LC peak is located near the outer edge of the ejecta and the photospheric velocity would be sensitive to the structure of the outer layers as well. We, therefore, argue that the photospheric velocity we obtain in the model is consistent with the observation of SN 2011kl. In any case, our model is shown to have very large photospheric velocities close to the observed one. Overall, our extended hydrogen-free progenitor model explains the observed properties of SN 2011kl well.

thumbnail Fig. 5.

Photospheric velocity (top) and temperature (bottom) evolution of the models presented in this work.

4. Discussion

We show that the hydrogen-free GRB progenitor model extended by the pusational pair-instability can be accompanied by luminous fast-evolving SNe in the optical. Our 10 B explosion model has the peak optical luminosity of 4 × 1043 erg s−1 and the rise time of 13 days in the optical. The optical LC properties match those of SN 2011kl well. When ULGRBs are triggered by progenitors on the order of 1000 R⊙, we are likely to observe the luminous SN component. The radius extension by the pulsational pair-instability can also result in less extended ULGRB progenitors on the order of 100 R⊙ or less (MM20). Fewer extended progenitors are expected to make less luminous, (≲1043 erg s−1) faster evolving (≲1 days) SNe in the optical. However, these types of early SN components are likely fainter than the GRB afterglow components and they may be difficult to identify. ULGRBs without the SN component may, therefore, originate from extended progenitors with a radius on the order of 100 R⊙ or less. The difference in the progenitor radii can explain why the luminous SN components in the optical appear only in some ULGRBs.

The luminous SNe that we present here are not necessarily accompanied with ULGRBs because ULGRBs can be off-axis. Alternatively, the jet launched in the progenitors could be choked and the explosions of some ULGRB progenitors may occur without GRBs (e.g., Milisavljevic et al. 2015). The quickly-rising, luminous, blue SNe that we predict here match the properties of fast blue optical transients (FBOTs, Drout et al. 2014; Tampo et al. 2020). They have a rise time of less than 10 days and peak luminosities ranging from ∼1042 erg s−1 to ∼1044 erg s−1. These properties are consistent with our LC models (cf. Kleiser & Kasen 2014; Kleiser et al. 2018). Our LC models are also consistent with those of rapidly rising luminous transients that have peak luminosities between ≃ −20 mag and ≃ −21 mag (Arcavi et al. 2016). Some of these transients can also be related to the explosions of the hydrogen-free stars that are extended by pulsational pair-instability.

The FBOTs and luminous SNe, including superluminous SNe, are often related to the birth of magnetars (e.g., Metzger et al. 2015). Our model presented here does not exclude the magnetar scenario to explain these transients. For SN 2011kl, the quick rise and luminous peak in the optical can be explained by our extended progenitor explosion, but the additional energy source is required to explain the subsequent slow LC decline. The magnetar model can explain the optical LC without an additional energy source, but it is argued that powering both GRB and SN at the same time with a single magnetar is difficult (Ioka et al. 2016). Here, we show that the fast-evolving luminous SNe associated with ULGRBs can be explained even if ULGRBs are triggered with the BH accretion. In our model, the optical luminosity increase is caused by the cooling and the ejecta that are much hotter before the optical luminosity increase, while the magnetar powered models likely predict a cooler temperature before the optical luminosity increase caused by the heating from the magnetar spin down near the center of the ejecta. The two models could be distinguished by the early ultraviolet observations, which can constrain the temperature before the optical LC peak.

In this work, we do not consider the effect of circumstellar matter (CSM) on the LCs. Pulsational pair-instability leads to mass ejection from the progenitors. The extended cool envelope may also experience enhancement in mass loss as found in red supergiants (cf. van Loon et al. 2005). The luminous LC component caused by the extended progenitor can be followed by the interaction-powered LC component. For example, we suggest that the slow decline of SN 2011kl can be due to the 56Ni decay in the previous section. Such a slow decay may also be caused by the interaction between the ejecta and the dense CSM (cf. Moriya et al. 2018).

The progenitor model we adopted in this work experiences the last pulse 2085 years before the core collapse. In other cases, however, the final pulse can occur decades or years before the core collapse (MM20). If the pulsational pair-instability explosions, which occur shortly before the core collapse leading to ULGRBs or FBOTs, become bright enough (e.g., Woosley et al. 2007), they can be observed as precursor transients of ULGRBs or FBOTs.

Finally, if we are lucky enough to have a direct progenitor detection of a ULGRB progenitor, it is observed as a blue or red supergiant star that does not have hydrogen and is dominated by carbon and oxygen. For example, the surface effective temperature of the hydrogen-free progenitor we investigated in this work is only 5228 K.

5. Conclusions

We show that the explosions of the rapidly rotating hydrogen-free GRB progenitor extended by pulsational pair-instability result in luminous, rapidly rising, blue, fast SNe in the optical. The hydrogen-free progenitor investigated in this work has 1962 R⊙ at the time of the collapse. The slow cooling of the extended progenitor makes these types of luminous SNe. The rise time is typically ≲10 days and the peak luminosity can be more luminous than −20 mag, depending on the explosion energy. They have a photospheric velocity that is well above 10 000 km s−1 and the photospheric temperature exceeds 10 000 K around the LC peak. We find that the quick rise and large peak luminosity of the luminous SN 2011kl associated with ULGRB 111209A can be explained by the explosion of our extended progenitor well. Our LC model declines faster than SN 2011kl, but the late-phase LCs could also be powered by the 56Ni decay or the CSM interaction. When the GRB jet is off-axis or chocked, these types of luminous SNe can be observed without accompanying GRBs. Some of the FBOTs and other rapidly rising transients may correspond to cases of this nature. The final pulse due to the pulsational pair-instability can occur ∼1 − 1000 years before the core collapse. If the final pulse occurs decades or years before the core collapse and it gets bright enough, it is possible to detect a precursor transient before an ULGRB or FBOT.

Acknowledgments

T.J.M. is supported by the Grants-in-Aid for Scientific Research of the Japan Society for the Promotion of Science (JP18K13585, JP20H00174). P.M. acknowledges support from the FWO junior postdoctoral fellowship No. 12ZY520N. S.B. has been supported by the grant RSF 18-12-00522 in his work on the supernova and GRB-AG simulations. Numerical computations were in part carried out on PC cluster at Center for Computational Astrophysics (CfCA), National Astronomical Observatory of Japan.

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All Figures

thumbnail Fig. 1.

Density structure of the ULGRB progenitor adopted in this work. Top panel: radius coordinate and the bottom panel shows it in the mass coordinate. We note that the extended progenitor is a hydrogen-free star.
In the text
thumbnail Fig. 2.

Abundance profile of the ULGRB progenitor.
In the text
thumbnail Fig. 3.

Bolometric (solid) and optical (dashed; integrated from 3500 Å to 8000 Å) LCs from the explosions of the extended (1962 R⊙) hydrogen-free ULGRB progenitor. The ejecta mass is 15 M⊙ and the explosion energy is shown in the figure. All the models have 0.1 M⊙ of 56Ni, but it does not affect the LCs presented here as indicated by the total nuclear energy available from 0.1 M⊙ of 56Ni (red; Nadyozhin 1994).
In the text
thumbnail Fig. 4.

Top: synthetic optical (3500 Å to 8000 Å) LCs with M56Ni = 0.1 M⊙ compared with the optical LC of SN 2011kl. Bottom: synthetic optical (3500 Å-8000 Å) LC with M56Ni = 1.5 M⊙ (solid). It matches the observed LC of SN 2011kl well. The quasi-bolometric LC with M56Ni = 0.1 M⊙ is also shown (dashed). We also present the quasi-bolometric LC model from a compact hydrogen-free progenitor having M56Ni = 1.5 M⊙, which does not have a slow cooling phase, in order to illustrate the luminosity contribution from the 56Ni decay with the dot-dashed line. All of the models in the bottom panel have an explosion energy of 10 B. The explosion time for SN 2011kl was set at the time of the ULGRB 111209A trigger.
In the text
thumbnail Fig. 5.

Photospheric velocity (top) and temperature (bottom) evolution of the models presented in this work.
In the text

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