SN 2021dbg: A Luminous Type IIP-IIL Supernova Exploding from a Massive Star with a Layered Shell

SN 2021dbg (ATLAS21gyf) was reported by the Asteroid Terrestrial-impact Last Alert System (ATLAS; Tonry et al., 2018a, b; Heinze et al., 2018) and was first detected at J2000 coordinates $\alpha=09^{\rm h}24^{\rm m}26.801^{\rm s}$, $\delta=-06^{\circ}34^{\prime}53.09^{\prime\prime}$, on 2021-02-15 10:14:52.800 (UTC dates are used throughout this paper). The detected brightness measured with the ATLAS-01 cyan (c) filter was 18.13 (AB magnitude). ATLAS also conducted subsequent observations, acquiring photometric data in the c and o bands. The extended Public European Southern Observatory (ESO) Spectroscopic Survey of Transient Objects (ePESSTO) team (Harvey et al., 2021) observed the initial spectrum using EFOSC2 on the ESO-NTT on 2021-02-16 at 04:05:44. This observation confirmed SN 2021dbg as an SN II. In response, we promptly utilized the 2.4 m Li-Jiang telescope (hereafter referred to as LJT; Fan et al., 2015) at the Li-Jiang Observatory of Yunnan Observatories equipped with the YFOSC (Yunnan Faint Object Spectrograph and Camera; Wang et al., 2019) for continuous photometric and spectral observations.

All images obtained by LJT were processed according to IRAF standard procedures, including template subtraction, background subtraction, flat-fielding, and cosmic ray removal. Instrumental magnitudes were obtained by using the point-spread-function (PSF) fitting method (Stetson, 1987). The instrumental magnitudes were then converted into standard Johnson $BV$ (Johnson et al., 1966) and standard Sloan $gri$ (AB magnitude).

SN 2021dbg was observed by the Ultraviolet/Optical Telescope (UVOT) of the Swift Observatory in the $uvw2$, $uvw1$, $um2$, $u$, $b$, and $v$ bands, but only three images near the luminosity peaks were obtained in each band. Figure 1 displays light curves in all bands we obtained. Table LABEL:tab:A1 presents our all photometric data obtained by LJT, ATLAS and Swift. Figure A1 shows the finder field of SN 2021dbg and local reference stars, whose information is listed in Table A2.

Because of the first detection, we used a simple expanding fireball model, $F(t)=A\times(t-t_{0})^{2}+B$, where $A$ and $B$ are fitting coefficients, to fit the early detections of SN 2021dbg in the cyan band observed by ATLAS to estimate the explosion epoch. The fitting result is shown with the black dashed curve in Figure 1. We adopt MJD = $59258.5\pm 0.5$ as our estimated explosion time, which is 1.9 days prior to the first detection.

LJT captured a total of 15 spectra spanning a period of $\sim 3$ to 81 days post-explosion. The wavelengths and fluxes of these spectra were calibrated according to IRAF standard procedures, telluric absorption was removed by comparison with standard-star spectra, and atmospheric extinction correction was carried out according to the atmospheric extinction information of local stations. Several spectra with large flux-calibration deviations were corrected with multiband photometry. In addition, we used the XingLong 2.16 m telescope (+ BFOSC; at Xing-Long Observatory of the National Astronomical Observatories of China; hereafter referred to as XLT) to take a spectrum $\sim 23$ days after the explosion. The Low-Resolution Imaging Spectrometer (LRIS; Oke et al., 1995) on the Keck I 10 m telescope was used to take a spectrum of the nebular phase $\sim 352$ days after the explosion; use of an atmospheric dispersion corrector (ADC) precluded differential slit losses (Filippenko, 1982). Table A3 lists the journal of spectral observations. Figure 2 displays the spectra observed by the LJT+YFOSC, NTT+EFOSC2, XLT+BFOSC, and Keck I+LRIS. From Figure 2, we can see that the first three spectra exhibit weak flash features, followed by a disappearance of the flash features in the next few spectra, forming a blue featureless phase. Then, low-contrast H lines emerge, and it is until about 30 days after the explosion that clear photospheric features (P-Cygni) appear.

The velocities of H$\alpha$, H$\beta$, Fe \@slowromancapii@ $\lambda 5169$ Å, and Ca \@slowromancapii@ $\lambda 8542$ Å are measured according to the blueshift of the wavelength of the minimum of the spectral line absorption profile relative to the rest wavelength of the emission line. Minima of H$\alpha$, H$\beta$, and Fe \@slowromancapii@ $\lambda 5169$ Å are obtained by polynomial fitting a P-Cygni profile. The minimum of Ca \@slowromancapii@ $\lambda 8542$ Å is obtained by fitting the absorption profile of the Ca\@slowromancapii@ NIR triplet with three Gaussian components. Figure 11 presents the ejecta velocity evolution of SN 2021dbg and compares it with that of SN 2017eaw, SN 2018zd, and SN 2016bkv. These three SNe were chosen as comparison objects because SN 2017eaw has a similar ejecta velocity to SN 2021dbg, while SN 2018zd and SN 2016bkv exhibit hydrogen acceleration behavior in their early stages, similar to what is observed in SN 2021dbg. In Figure 10, those shaded lines are a power-law fitting of the ejecta velocities of SNe \@slowromancapii@P summarized by Faran et al. (2014b).

The velocities of H$\alpha$ and H$\beta$ show an acceleration at $t<29$ d and conform to the power law at $29<t<48$ d. At $t>48$ d, the decline in velocities slows down significantly. However, the velocity of Fe \@slowromancapii@ $\lambda 5169$ Å roughly conforms to the power law at $t>48$ d, although it is lower than predicted by the power law at $t<48$ d. The velocity of H$\beta$ is almost equal to that of Ca \@slowromancapii@ $\lambda 8542$ Å, while lower than the H$\alpha$ velocity by about 2000 km s^-1. Therefore, we think H$\alpha$ came from the outer layer of the ejecta, while H$\beta$ came from the inner layer of the ejecta near the core.

The early H-acceleration behavior observed in SN 2021dbg exhibits similarities to that of SN 2018zd (Zhang et al., 2020) and SN 2016bkv (Nakaoka et al., 2018). According to Zhang et al. (2020), this accelerated H emission originates from either the wind matter or CSM located above the optically thick photosphere. Initially, these ionized winds or CSM are propelled by the shocked ejecta, resulting in the observed spectral lines and acceleration. Meanwhile, well-developed P-Cygni profiles are shaped within the ejecta. The H$\alpha$ P-Cygni profiles of SN 2021dbg have a shallow absorption at $22<t<29$ d, the absorption of the H$\alpha$ P-Cygni profiles thereafter is significantly deepened, and the H velocity accords with the power law at $29<t<48$ d. These findings align with the hypothesis put forth by Zhang et al. (2020).

SN 2018zd showed a significant heating and accelerating behavior of the photosphere within a week after the explosion, which was explained by the reverse-shock heating of the outer layer of the ejecta (Zhang et al., 2020). SN 2021dbg does not have such a heating and accelerating process of the photosphere at early phases. After the P-Cygni profiles develop well, SN 2016bkv, SN 2018zd, and SN 2017eaw have a power-law velocity evolution of H$\alpha$, while the H$\alpha$ velocity of SN 2021dbg declines more slowly and deviates from a power law significantly. A possible explanation for this behavior is that the progenitor of SN 2021dbg may have a thicker H shell, and the shell is likely to be layered because of a steep drop in matter density, electron density, and temperature. As the outermost layers dissipate, deeper H layers become visible.

In the late-time tail, the bolometric light curve is almost entirely powered by the radioactive decay of ⁵⁶Co (⁵⁶Ni$\to$ ⁵⁶Co$\to$ ⁵⁶Fe), so the bolometric luminosity is a good indication of the ⁵⁶Ni mass synthesized in the explosion. Based on this theory, many researchers have given different methods or models to estimate the ⁵⁶Ni mass, such as comparisons made with SN 1987A’s tail luminosity (Elmhamdi et al., 2003), the Hamuy (2003) tail-luminosity method, and the Jerkstrand et al. (2012) tail-luminosity method. By comparing the tail luminosity with that of SN 1987A, the ⁵⁶Ni mass of SN 2021dbg is found to be 0.17 M_⊙. According to the methods of Hamuy (2003) and Jerkstrand et al. (2012) (Eqs. (1) and (2) below, orange and green curves in Figure 11, respectively), the mass of ⁵⁶Ni is 0.165 M_⊙ and 0.173 M_⊙, respectively:

These above methods of calculating ⁵⁶Ni from the tail luminosity assume that the energy released by radioactive decay was completely captured, the deposited energy was instantly re-emitted, and no other energy sources had any effect. Taking into account the case of $\gamma$-photon escape, Wygoda et al. (2019) added a parameter $T_{0}$ ($\gamma$-photon escape time) to the relationship between the energy of ⁵⁶Co decay and the bolometric luminosity, constructing a new method for calculating the mass of ⁵⁶Ni, as shown in Equations (3) and (4) below from Yang & Sollerman (2023):

Taking the matching tail luminosity as the standard, we set $T_{0}=1000$ days and obtained a ⁵⁶Ni mass of 0.175 M_⊙, as seen in the blue curve in Figure 11. Such a large value of $T_{0}$ indicates that almost no photons emitted by ⁵⁶Ni decay escaped (as $T_{0}\to\infty$, Eq. (3) is equivalent to Eq. (2), meaning that ⁵⁶Ni decay photons are completely captured), which implies that SN 2021dbg may have had a thick shell that almost completely captured the gamma-ray photons emitted during the decay of ⁵⁶Ni. This is in agreement with the previous analysis of the spectra and ejecta velocities.

The values obtained from the above methods are all relatively close, indicating a mass of 56Ni in the range of 0.165 to 0.17 M_⊙, which suggests that these methods are reasonable for SN 2021dbg. Since we do not have a more precise and reliable method to determine the mass of ⁵⁶Ni, by combining the results of the aforementioned methods, we estimate the mass of ⁵⁶Ni in SN 2021dbg as 0.17$\pm$ 0.05 M_⊙.

We employ the radiation diffusion model, as outlined by Arnett & Fu (1989) and Fu & Arnett (1989), to reconstruct the explosion parameters of SN 2021dbg. These calculations are facilitated by the LC2 code³³3Accessible at https://titan.physx.u-szeged.hu/~nagyandi/LC2/, as detailed by Nagy & Vinkó (2016). This model segments the ejecta resulting from the progenitor explosion into two distinct components: a high-mass, high-temperature, and high-density core enriched in He and heavier elements, encircled by a low-mass, low-temperature, and low-density shell predominantly composed of H.

At early phases, the elevated luminosity primarily arises from the interaction between the shell and the CSM, while the thermal radiation emanating from the core predominantly contributes to the luminosity during the plateau. As the SN transitions into the tail phase, the luminosity is almost entirely sustained by the radioactive decay of ⁵⁶Ni. Notably, the bolometric light curve of SN 2021dbg exhibits a prolonged linear decline at early times, with a delayed plateau appearance. Attempts to fit the pseudo-bolometric light curve with a model featuring a core with a single shell proved unsuccessful.

Combining with the previous analysis, we considered that the progenitor of SN 2021dbg probably had a very thick H shell whose matter density, electron density, and temperature probably dropped steeply. Hence, we tried to fit the pseudo-bolometric light curve with a core and two shells, achieving a successful result. This model finds that the outermost radius of the progenitor is $\sim 1200$ R_⊙ and the total mass of the ejecta is 18.4 M_⊙; considering a compact remnant, the mass of the progenitor is $\sim 20$ M_⊙.

Figure 12 shows the result of fitting SN 2021dbg’s pseudo-bolometric light curve, and the parameters of the model are presented in Table 2. We divided the shell into inner and outer parts. The thickness of the inner shell is approximately equal to that of the outer shell, but the inner one has a higher mass, temperature, and Thomson scattering coefficient than the outer one. This means that the inner shell is denser and dominated primarily by ionized hydrogen, therefore resulting in a high electron density. The outer shell has a low density and is dominated primarily by neutral hydrogen.

At early times following the explosion, the high-speed shell ejecta collide and interact with the CSM, accelerating the CSM and slowing down the shell ejecta. Much kinetic energy in the shell layer is converted into thermal radiation during this interaction, contributing to the early high luminosity. Most interactions last for $\sim 20$ days, and the luminosity decreases rapidly, then entering a plateau phase dominated by the core thermal radiation contribution. SN 2021dbg took $\sim 50$ days, a longer time than most SNe \@slowromancapii@, for the peak to decline to the plateau, likely owing to the thermal radiation contribution of the inner shell. The luminosity of the plateau and tail is mainly contributed by core thermal radiation and ⁵⁶Ni decay.

Such a layered structure of the shell may be caused by unstable pulsations. This is likely due to the progenitor being in a pulsationally unstable state before the explosion and having entered or being on the verge of entering a phase of enhanced mass loss. Although it still retained a thick hydrogen-rich shell, the shell had already developed a layered structure due to unstable pulsations. Yoon & Cantiello (2010) provided simulation demonstrations showing that stars with initial masses between 17 to 20 M_⊙ may experience enhanced mass loss in the form of pulsation-driven superwinds during the late stages of their evolution. Such pulsation-driven superwinds may be the key factor for the transition of supernova explosions from Type \@slowromancapii@P to Type \@slowromancapii@L.

The single Lorentzian profile fits the H$\alpha$ emission line well, indicating that the emission-line broadening is mainly caused by electron scattering rather than the velocity of the wind. The dual Lorentzian fitting aims to identify the narrow-line component within the emission line, but we cannot fit the effective narrow-line profile of the H$\alpha$ emission, probably limited by the low spectral resolution. The three-Lorentzian fitting is to consider the flux contribution of the emission lines of the possible host galaxy [N \@slowromancapii@] $\lambda\lambda 6548$, 6583 Å, and the results show that this flux contribution can be ignored. The luminosity of the single Lorentzian fitting profile of the H$\alpha$ emission line is $L_{{\rm H}\alpha}=2.1\times 10^{39}$ erg s^-1.

Taking the radius of the blackbody photosphere at the time of this earliest spectrum as $r\approx 3.8\times 10^{14}$ cm) and the radius of the blackbody photosphere at the beginning of the first plateau ($\sim 18$ days after the explosion; see Figure 8) as $r_{1}\approx 1.3\times 10^{15}$ cm), because we think the first plateau indicates that the plateau phase of the photospheric radius around 18 day is attributed to the fact that the CSM beyond this distance is already very thin, and the collision between ejecta and CSM cannot generate sufficient radiation to expand the photosphere any further, then the photosphere gradually shifts to the inner shell. When the shell ejecta expanded to $r_{1}$, their temperature and density were too low to continue expanding the photosphere, until the hotter and denser core ejecta arrived and the photosphere continued expanding. This also explains the temperature exhibiting a slight bump as the photospheric radius expanded 40 days after the explosion.

To estimate the mass loss rate, we also need to obtain the wind velocity. By fitting the H$\alpha$ flash emission line profile in the earliest spectrum, we obtain a velocity broadening of $\sim 1000$ km s^-1. Such a wind velocity is unusually high for the progenitors of SNe \@slowromancapii@P and SNe \@slowromancapii@L, likely due to the fact that our first spectrum was obtained approximately 2.5 days after the explosion, when the wind material had already been accelerated by the ejecta. We compare an example with strong flash emission line and extremely early spectrum, SN 2013fs (Yaron et al., 2017). Assuming that SN 2021dbg and SN 2013fs have comparable wind speed ($\sim 100$ km s^-1), we got a mass loss rate of $\dot{M}\geq 6\times 10^{-4}$ M_⊙ yr^-1, slightly lower than the mass-loss rate of SN 2013fs ($\sim 10^{-3}$ M_⊙ yr^-1). According to Eq. (5) of Ofek et al. (2013), the H mass in the CSM is $\sim 1.7\times 10^{-3}$ M_⊙. If taking the typical wind speed of a red supergiant (RSG; $\sim 15$ km s^-1) as $v_{w}$, we obtain $\dot{M}\geq 7\times 10^{-6}$ M_⊙ yr^-1, which is a typical mass loss rate of RSGs.

The mass loss rate given by the model of Dessart et al. (2017) is on the surface of the progenitor, while the narrow H$\alpha$ emission line we see comes from a farther place. The mass loss rate estimated by the H$\alpha$ flux is lower than the surface mass loss rate given by the model, reflecting the density change of CSM in the spatial scale. Zimmerman et al. (2024) demonstrated that there may be a steep decline in the density of CSM within the distance of $\approx 5\times 10^{13}$ cm to $\approx 5\times 10^{14}$ cm.

Jerkstrand et al. (2012) proposed a model for estimating the mass of the progenitor of SNe from spectra in the nebular phase. As shown in Figure 13, the nebular-phase spectrum, obtained $\sim 352$ days after the explosion using Keck 1, is compared with model spectra corresponding to various progenitor masses. The spectral lines, particularly, Na \@slowromancapi@ D, Mg \@slowromancapi@], and [O \@slowromancapi@], are similar to the model spectra of the progenitor with a mass of 19 M_⊙, implying that the progenitor of SN 2021dbg has a mass of $\sim 19$ M_⊙.

In the nebular phase, Jerkstrand et al. (2012) also gave evolution curves of model spectral line luminosity ([O \@slowromancapi@] $\lambda\lambda 6300$, 6364 Å, Na \@slowromancapi@ D, Mg \@slowromancapi@] $\lambda 4571$ Å, H$\alpha$, [Fe  \@slowromancapii@] $\lambda\lambda 7155$, 7172 Å, [Ca \@slowromancapii@] $\lambda\lambda 7291$, 7323 Å, Ca \@slowromancapii@ NIR triplet) for progenitors with different masses relative to the ⁵⁶Co decay power over time. For the spectrum obtained at $t\approx 352$ days, the flux ratios of the above spectral lines relative to the ⁵⁶Co decay power are shown in Table 3. The values of Mg \@slowromancapi@] $\lambda 4571$ Å and Na \@slowromancapi@ D are $\sim 0.002$ higher, and the values of [Ca \@slowromancapii@] $\lambda\lambda 7291$, 7323 Å and Ca \@slowromancapii@ NIR triplet are $\sim 0.008$ higher, than the model values of the 19 M_⊙ progenitor, while the ratios of [O \@slowromancapi@] $\lambda\lambda 6300$, 6364 Å and H$\alpha$ are lower by $\sim 0.03$ and $\sim 0.05$ (respectively) than model values of the 19 M_⊙ progenitor. The flux ratios of Na, Mg, and Ca are higher, and of H and O are lower, which means that the progenitor mass of SN 2021dbg may be greater than 19 M_⊙.

Spectra from the nebular period can also be used to estimate the ⁵⁶Ni mass produced in the ejecta. Elmhamdi et al. (2003) proposed that the luminosity of the H$\alpha$ emission line in the nebular phase is proportional to the mass of ⁵⁶Ni ejected, and Maguire et al. (2012) obtained the relationship between the FWHM_corr (full width at half-maximum intensity that has been corrected for the instrumental broadening effect) of the nebular H$\alpha$ emission and the mass of ⁵⁶Ni. We obtained FWHM${}_{\rm corr}\approx 92$ Å for the H$\alpha$ emission line in the nebular phase, and according to Eq. (7) below from Maguire et al. (2012), we obtain $M_{\rm Ni}\approx 0.25_{-0.19}^{+0.70}\,{\rm M}_{\odot}$:

Figure 14 shows the correlation between the ⁵⁶Ni mass estimated from the luminosity in the radioactive tail and the FWHM_corr of the nebular H$\alpha$ emission line, where the red data points are from Maguire et al. (2012), and the solid black line is the correlation obtained by Maguire et al. (2012). The uncertainty increases as FWHM_corr increases, and when FWHM_corr exceeds 80 Å, the uncertainty is too large. This is likely due to a lack of samples for high ⁵⁶Ni mass and FWHM_corr. Although the uncertainty is large, this result also supports a high ⁵⁶Ni mass for SN 2021dbg.