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, 2018b; Heinze et al. 2018) and was first detected at J2000 coordinates α = 09^h24^m26801, $\delta =-06^\circ 34^{\prime} 53.^{\prime\prime} 09$, on 2021 February 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 New Technology Telescope (NTT) on 2021 February 16 at 04:05:44. This observation confirmed SN 2021dbg as an SN II. In response, we promptly utilized the Li-Jiang 2.4 m telescope (LJT; Fan et al. 2015) at the Li-Jiang Observatory of Yunnan Observatories equipped with the Yunnan Faint Object Spectrograph and Camera (YFOSC; 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 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 Neil Gehrels Swift Observatory (Swift) 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 the light curves in all bands we obtained. Table A1 presents our all photometric data obtained by LJT, ATLAS, and Swift. Figure A1 shows a finder-field image of SN 2021dbg and local reference stars, whose information is listed in Table A2.

Zoom In Zoom Out Reset image size

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 c 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 ± 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 ∼3 to 81 days postexplosion. 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 Beijing Faint Object Spectrograph and Camera (BFOSC) mounted on the Xing-Long 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 ∼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 ∼352 days after the explosion; use of an atmospheric dispersion corrector precluded differential slit losses (Filippenko 1982). Table A3 lists a 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, where clear photospheric features (P Cygni) appear.

Zoom In Zoom Out Reset image size

3.1.1. Evolution and Comparison of Light Curves

SN 2021dbg attains its peak luminosity nearly concurrently in all optical bands. The light curves for the B and g bands exhibit a linear decline from the peak until 50 days postexplosion, subsequently transitioning into a prolonged plateau phase of slower decline. Meanwhile, the c, V, r, o, and i bands enter this plateau phase earlier, at 43 days. These plateaus persist until ∼110 days after the explosion. Notably, during the plateau phase, there is a subtle brightening in the r, o, and i bands, with increases of ∼0.2 mag in the r and o bands and a more pronounced brightening of ∼0.7 mag in the i band, resulting in a distinct bump in the light curve.

SN 2021dbg stands out as a relatively bright object among SNe II. Its absolute peak magnitudes exceed −18.4 in all optical bands and −19.8 in all UV bands. Table 1 provides peak information and the decline rate from peak to plateau on the optical light curves. The optical and UV bands of SN 2021dbg are brighter than those of typical well-studied SNe IIP, fall within the intermediate level for SNe IIL, and are slightly fainter than the median brightness for SNe IIn. Previously, the optical absolute magnitude range for SNe IIP was reported as −18 ≤ M_op ≤ −15 mag, while for SNe IIn, it was −20 ≤ M_op ≤ −18 mag. In UV bands, SNe IIP had an absolute magnitude of M_UV ≈ −18 mag, and SNe IIn had M_UV ≈ −20 mag (Pritchard et al. 2014). Richardson et al. (2002) conducted a statistical analysis of the brightness in optical bands for SNe IIP and IIL, finding average peaks of M_B = −17.0 ± 1.1 mag for Type IIP and M_B = −18 ± 0.9 mag for Type IIL.

Table 1. Information About the Peaks of Light Curves

	B	V	g	r	i	c	o
Peak Time(days)	10.93	11.69	10.82	12.97	12.70	11.86	12.22
Peak (mag)	−18.58	−18.66	−18.69	−18.46	−18.40	−18.48	−18.45
M50 (mag)	−16.77	−17.54	−17.08	−17.66	−17.57	−17.33	−17.67
Decline rate (mag day−1)	0.046	0.033	0.041	0.027	0.026	0.031	0.023

Note. M50 is the absolute magnitude after 50 days; the decline rate is calculated from peak to 50 days.

Download table as:  ASCIITypeset image

The light curves of SN 2021dbg during the first 50 days resemble those of typical SNe IIL, characterized by a high brightness and a linear decline after the peak. However, after 50 days, the light curves exhibit a prominent plateau, a hallmark feature of SNe IIP. If SNe IIP and IIL are considered two ends of a continuous family of SNe II, SN 2021dbg occupies the brighter end of the transitional zone.

To better analyze the evolution characteristics of the SN 2021dbg light curves, we compared them with those of some other well-studied SNe II after matching the peak values; see Figure 3.

Zoom In Zoom Out Reset image size

In the B band, the decline rate from peak luminosity to 50 days postexplosion is 0.046 mag day⁻¹ for SN 2021dbg. This rate aligns with that observed in SN 2012A (Tomasella et al. 2013), SN 2016X (Huang et al. 2018), and SN 2015bf (Lin et al. 2021), placing it firmly within the midrange of SN II samples in Figure 3. However, several SNe, including SN 2004A (Gurugubelli et al. 2008), SN 2004et (Sahu et al. 2006), SN 2017eaw (Van Dyk et al. 2019), SN 2018zd, and SN 2018aoq (Tsvetkov et al. 2021), exhibit a slower decline and transition into a plateau phase sooner than SN 2021dbg. Conversely, SN 1998S (Fassia et al. 2000), SN 2013by (Valenti et al. 2015), and SN 2013ej (Dhungana et al. 2016) decline more rapidly but lack a discernible plateau phase.

In the V band, the light curve of SN 2021dbg decreases by 1.19 mag from peak to 50 days, with a decline rate of 0.029 mag day⁻¹, which is the fastest among all SN IIP samples; only SN 2013by is comparable, but SN 2013by does not have a significant plateau after that. Valenti et al. (2015) classified SN 2013by as a young SN IIL/IIn based on early optical and near-infrared (NIR) observations. SN 2013ej, SN 2015bf, SN 2016X, and SN 2018zd also do not have a significant plateau, declining linearly nearly from the peak until ∼90–110 days, after which, like all SNe IIP, they rapidly decline to the tail phase. Although an obvious decline before the transition to the ⁵⁶Ni decay tail phase is the feature of typical SNe IIP, Anderson et al. (2014) and Valenti et al. (2015) proposed that all SNe IIL monitored long enough (more than ∼80 days since discovery) demonstrated this decline.

In both the r and i bands, from the peak to the plateau period, the brightness declines by 0.82 mag, with a decline rate of 0.022 mag day⁻¹. Compared to typical SNe IIP, such as SN 2012A, SN 2016X, and SN 2017eaw, the SN 2021dbg peak has a larger peak-to-plateau drop, and takes longer to decline from peak to plateau. This behavior can be explained by interactions between ejecta and the CSM. In the plateau and tail phases, SN 2021dbg is consistent with typical SNe IIP.

Figure 4 shows the position of SN 2021dbg within the SN II population in terms of various photometric indicators. In the left panel, we can see that the brightness of SN 2021dbg is brighter than the SNe IIP samples in the panel, placing it among the SNe IIL samples. In the middle and right panels, we can observe that SN 2021dbg is positioned toward the top of the SN IIP samples provided by Hamuy (2003). These indicators of SN 2021dbg suggest that it possesses the high brightness of SNe IIL, yet does not completely deviate from the range of SNe IIP, implying that SN 2021dbg may be a transitional SN event between SNe IIP and SNe IIL.

Zoom In Zoom Out Reset image size

3.1.2. Evolution and Comparison of Color

Since SN 2021dbg exhibits features of both SNe IIP and SNe IIL in its light curves and spectra, we have selected some well-studied and typical SNe IIP and SNe IIL as comparison samples. Some of them show flash emission features and CSM interaction. Figure 5 shows SN 2021dbg's color evolution and color comparison with these SN II samples.

Zoom In Zoom Out Reset image size

The color evolution trend of SN 2021dbg is consistent with that of typical SNe IIP, but bluer, which may be the result of CSM interaction. The colors curve of SN 2021dbg are very similar to those of SN 2016X and SN 2018zd, which means that they may have comparable CSM interaction. The B − V color curve of SN 2021dbg is very similar to that of SN 2016X, SN 2018zd, and SN 2018aoq during the first 70 days, but SN 2021dbg and SN 2018zd show a brief blue feature at 70–80 days and then slowly turns red. Similar to SN 2016X, SN 2013ej, and SN 2012A, the B − V color curve flattens out and slowly turns blue after ∼110 days, while SN 2004A and SN 2017eaw gradually turn blue after ∼125 days, and SN 2018aoq continues to turn red linearly until ∼170 days (Tsvetkov et al. 2021). The uvw2 − u color curve of SN 2018zd exhibits a "U-turn" feature at early times, indicating that SN 2018zd had a temperature increase and dust may be destroyed by shock waves, which reduces extinction (Zhang et al. 2020). For the first 40 days, SN 2021dbg's g − r color is bluer than that of SN 2016X and SN 2018zd, and has been almost always at the bluest end of these SN II samples in Figure 5.

If such a blue light curve is indeed driven by CSM interaction, it must be exceptionally intense, requiring a significant amount of CSM, similar to the case in SN 2018zd (Zhang et al. 2020). However, this appears to be in contrast with the flash emission lines that disappeared only around 5 days after the explosion, and the typical rapid cooling observed when CSM interaction alone drives the early light curve. As discussed in Section 4.3, we propose that the prolonged bluer light curve of SN 2021dbg may be associated with the presence of a stratified structure in the progenitor's envelope.

3.2.1. Evolution and Comparison of Early Phase Spectra

Early time spectra, especially those showing flash emission lines (e.g., Gal-Yam et al. 2014), can help us understand the composition and structure of matter near the progenitor. To explore the relationship between flash emission lines in early spectra and matter near the progenitor, Dessart et al. (2017) constructed a generation model of spectra and successfully reproduced the flash emission lines.

Figure 6 shows the early time spectra of SN 2021dbg and several other SNe II, as well as the spectra of the r1w5h and r1w5r models (Dessart et al. 2017). The spectra of SN 2021dbg 2.5 and 3 days after the explosion exhibit narrow Hα, Hβ, He ii λ4686, N iii λ λ4334, 4641, and weak C iv λ λ5801, 5812 and C iv λ7110. These flash emission lines are the same as those of SN 2013cu, SN 2015bf, SN 2016bkv, and SN 2018zd, and they also agree with the emission lines produced by the r1w5r model. They are thought to result from the recombination of stellar-wind material near the progenitor after being ionized by X-rays from shocked ejecta. SN 2013cu showed narrow and strong Hα, Hβ, He i, He ii, C iii, C iv, and N iv emission lines within 15.5 hr after the explosion (Gal-Yam et al. 2014), while by 3 days, He i, C iii, C iv, and N iv emission lines disappeared, leaving only weak Hα, Hβ, and He ii lines. Therefore, SN 2021dbg may have had strong and narrow flash emission lines as did SN 2013cu, although we did not obtain SN 2021dbg's spectra at sufficiently early times after the explosion. At 6–10 days, the spectra of SN 2021dbg do not exhibit any significant emission lines except for very weak Hα, consistent with SN 2015bf and also with the spectra of the r1w5h and r1w5r models.

Zoom In Zoom Out Reset image size

In the model by Dessart et al. (2017), w5 represents a mass-loss rate of 5 × 10⁻³ M_⊙ yr⁻¹, which indicates that the progenitor of SN 2021dbg may have experienced enhanced mass loss shortly before the explosion, or undergone a superwind phase, as proposed by Yoon & Cantiello (2010). We discuss the mass loss of the progenitor in more detail in Section 4.4.

3.2.2. Evolution and Comparison of Photospheric-phase Spectra

Figure 7 shows the evolution and comparison of photospheric spectra of SN 2021dbg with those of other well-studied SNe II. The spectral evolution of SN 2021dbg is slower than that of most other SNe II, and the characteristic spectral lines appear later. In spectra during the first 48 days, Hα and Hβ are relatively wide with no obvious P Cygni absorption profile, and the absorption of He i λ5876, the Ca ii NIR triplet, and Fe ii λ5169 are also very shallow. These features are similar to those of SN 2014G (Terreran et al. 2016), SN 2015bf (Lin et al. 2021), and SN 2018hmx (Bracha 2019).

Zoom In Zoom Out Reset image size

After 48 days, Hα, Hβ, and He ii λ4686 begin to appear with obvious P Cygni profiles, and the absorption components of He i λ5876, the Ca ii NIR triplet, and Fe ii λ5169 also begin to deepen, but the absorption depths are still shallower than that of a typical SNe IIP such as SN 2017eaw (Van Dyk et al. 2019). Instead, they are more similar to the line absorption of a typical SN IIL such as SN 2014G. The Hα emission lines of SN 2021dbg, SN 2014G, SN 2015bf, and SN 2018hmx show a large extension on the blue side, and the peaks display a significant blueshift that exceeds 3000 km s⁻¹ at early phases and gradually decreases with time. SN 2017eaw also exhibits such a blueshift, but it is much smaller and decreases rapidly. This behavior has been reported in many SNe II (Chevalier 1976; Taubenberger et al. 2009). Anderson et al. (2014) proposed that this behavior is a direct consequence of a steep density profile in the ejecta, which translates into more confined line emission and higher occultation of the receding part of the ejecta. The rate of decrease of SN 2021dbg's Hα peak blueshift is slower than that of SN 2014G, SN 2015bf, and SN 2018hmx, which indicates that SN 2021dbg may have a thicker ejecta layer with a steep drop in matter density, electron density, and temperature.

3.3.1. Construction of the Bolometric Luminosity Light Curve

Within 100 days after the explosion, we obtained good optical photometric data and applied the SuperBol ¹¹ program (Nicholl 2018) to calculate the pseudobolometric luminosity, temperature, and radius evolution curve in the photosphere phase of SN 2021dbg, as shown in Figure 8. In the UV bands, only three points were obtained by Swift/UVOT. We used them to correct the luminosity at early times, as indicated by the three orange diamond points in Figure 8. Owing to the observation conditions, the photometric data obtained at late times are very limited, and the pseudobolometric luminosity cannot be obtained through multiband photometric data.

Zoom In Zoom Out Reset image size

Valenti et al. (2016) successfully constructed the pseudobolometric luminosity light curves from the beginning of radioactive decay to late times of 30 SNe II only by using V-band data. At late times, we obtained the most data in the r band, and the evolutionary trend of the r-band light curve and the pseudobolometric luminosity light curve are the most similar during the plateau period. Therefore, we applied the method of Valenti et al. (2016) in the r band and multiplied the r-band light curve by a coefficient to make it match the pseudobolometric luminosity light curve during the plateau phase. Then, the pseudobolometric luminosity light curve of SN 2021dbg in the radioactive-decay phase was effectively constructed by replacing the pseudobolometric luminosity light curve with the r-band light curve, as shown with the red curve in Figure 9.

Zoom In Zoom Out Reset image size

3.3.2. Evolution and Comparison of the Bolometric Light Curve

In Figure 8, SN 2021dbg reaches its peak luminosity, ${L}_{\max }\,=\,(1.7\pm 0.9)\times {10}^{43}$ erg s⁻¹, at ∼8 days after the explosion in the bolometric light curve derived from the observed BVgri photometry. We noted that the spectral energy distribution derived from the BVgri photometry at early times was not adequately aligned with the blackbody fitting, resulting in significant errors and potential underestimation of the actual value. To address this issue, we utilized the UV data from Swift in combination with the optical observations for blackbody fitting. The resulting bolometric luminosity value of ${L}_{\max }\,=\,(2.1\pm 0.4)\times {10}^{43}$ erg s⁻¹ is significantly higher than that obtained from the optical bands alone, and the associated uncertainty is reduced.

Figure 10 shows a pseudobolometric light-curve comparison of SN 2021dbg with other SNe II. The evolution trend of the bolometric luminosity light curve of SN 2021dbg is similar to that of SN 1999em, SN 2016X, SN 2017eaw, and other typical SNe IIP, but SN 2021dbg is brighter; the peak bolometric luminosity of SN 2021dbg is about 3 times higher than that of SN 2017eaw, 5 times higher than that of SN 2016X, and about 10 times higher than that of SN 1999em. Peaking in the near-ultraviolet at the same time as the optical light helps produce the high bolometric luminosity. Since SN 2017eaw showed early and moderate CSM interaction (Szalai et al. 2019; Van Dyk et al. 2019), SN 2021dbg with higher luminosity may have had even stronger early time CSM interaction, or a higher total core energy released by the explosion.

Zoom In Zoom Out Reset image size

At t < 50 days, SN 2018zd exhibits the closest luminosity to SN 2021dbg. However, a notable difference lies in the slower decline of SN 2018zd compared to SN 2021dbg, without a pronounced plateau beyond 50 days. At 120 days after the explosion, the bolometric luminosity of SN 2018zd nearly matches that of SN 1999em. Based on this observation, Zhang et al. (2020) postulated that the enhanced luminosity of SN 2018zd relative to SN 1999em within the first 120 days results from the interaction between ejecta and CSM, while the explosion core energy of SN 2018zd remains comparable to that of SN 1999em. Furthermore, the pseudobolometric light curve of SN 2021dbg displays a more prominent radioactive-decay tail than do SN 2017eaw, SN 2018zd, and SN 1999em. This suggests a higher production of ⁵⁶Ni in SN 2021dbg, as further elaborated in Section 4.2.

The velocities of Hα, Hβ, Fe ii λ5169, and Ca ii λ8542 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. The minima of Hα, Hβ, and Fe ii λ5169 are obtained by polynomial fitting their P Cygni profiles. The minimum of Ca ii λ8542 is obtained by fitting the absorption profile of the Ca ii NIR triplet with three Gaussian components. Figure 9 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 11, the shaded lines are a power-law fitting of the ejecta velocities of SNe IIP summarized by Faran et al. (2014b).

Zoom In Zoom Out Reset image size

The velocities of Hα and Hβ show an acceleration at t < 29 days and conform to a power law at 29 < t < 48 days. At t > 48 days, the decline in velocities slows down significantly. However, the velocity of Fe ii λ5169 roughly conforms to a power law at t > 48 days, although it is lower than predicted by the power law at t < 48 days. The velocity of Hβ is almost equal to that of Ca ii λ8542, while lower than the Hα velocity by about 2000 km s⁻¹. Therefore, we think Hα came from an outer layer of the ejecta, while Hβ came from an 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 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 Hα P Cygni profiles of SN 2021dbg have shallow absorption at 22 < t < 29 days; the absorption of the Hα P Cygni profiles thereafter significantly deepened, and the H velocity accords with the power law at 29 < t < 48 days. These findings align with the hypothesis put forth by Zhang et al. (2020).

SN 2018zd showed significant heating and accelerating behavior of the photosphere within a week after the explosion, which was explained by reverse-shock heating of the outer layer of the ejecta (Zhang et al. 2020). SN 2021dbg does not have such a heating and acceleration 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 Hα, while the Hα 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 had a thicker H shell, and the shell was likely 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 → ⁵⁶Co → 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; Equations (1) and (2) below, and orange and green curves in Figure 9, respectively), the mass of ⁵⁶Ni is 0.165 M_⊙ and 0.173 M_⊙, respectively:

$$\begin{eqnarray}&&\begin{array}{l}L(t)=1.271\times {10}^{43}\frac{{M}_{\mathrm{Ni}}}{{M}_{\odot }}\\ {\left(\exp \left[\frac{(t-{t}_{0})/(1+z)-6.1}{111.26}\right]\right)}^{-1}\,\mathrm{erg}\,{{\rm{s}}}^{-1},\end{array}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&L(t)=9.92\times {10}^{41}\frac{{M}_{\mathrm{Ni}}}{0.07\,{M}_{\odot }}({e}^{-t/111.4}-{e}^{-t/8.8})\mathrm{erg}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 2 }$$

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 reemitted, and no other energy sources had any effect. Taking into account the case of γ-ray photon escape, Wygoda et al. (2019) added the parameter T₀ (γ-ray 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):

$$\begin{eqnarray}&&\begin{array}{l}L(t)={M}_{\mathrm{Ni}}(({\epsilon }_{\mathrm{Ni}}-{\epsilon }_{\mathrm{Co}}){e}^{-t/{t}_{\mathrm{Ni}}}+{\epsilon }_{\mathrm{Co}}{e}^{-t/{tCo}})(1-{e}^{-{\left(t/{T}_{0}\right)}^{-2}})\\ +0.034\,{M}_{\mathrm{Ni}}{\epsilon }_{\mathrm{Co}}({e}^{-t/{t}_{\mathrm{Ni}}}-{e}^{-t/{t}_{\mathrm{Co}}}),\end{array}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{T}_{0}=\sqrt{C{\kappa }_{\gamma }{M}_{\mathrm{ej}}^{2}/{E}_{\mathrm{kin}}}.\end{eqnarray} \tag{ 4 }$$

where _Ni = 3.9 × 10¹⁰ erg g s⁻¹ and _Co = 6.8 × 10⁹ erg g s⁻¹ are the specific heating rates of Ni and Co decay, respectively, t_Ni = 8.8 days and t_Co = 111.3 days are their corresponding decay timescales, M_ej is the total mass of the ejecta, E_kin is the kinetic energy of the ejecta, κ_γ is the γ-ray opacity, and C is a constant. The units of M_Ni are grams.

Taking the matching tail luminosity as the standard, we set T₀ = 1000 days and obtained a ⁵⁶Ni mass of 0.175 M_⊙, as seen in the blue curve in Figure 9. Such a large value of T₀ indicates that almost no photons emitted by ⁵⁶Ni decay escaped (as T₀ → ∞, Equation (3) is equivalent to Equation (2), meaning that all ⁵⁶Ni decay photons are completely captured), which implies that SN 2021dbg may have had a thick shell that almost completely captured the γ-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 0.165–0.17 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 ± 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 code, ¹² 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 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 pseudobolometric 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 pseudobolometric light curve with a core and two shells, achieving a successful result. This model finds that the outermost radius of the progenitor is ∼1200 R_⊙ and the total mass of the ejecta is 18.4 M_⊙; considering a compact remnant, the mass of the progenitor is ∼20 M_⊙.

Figure 12 shows the result of fitting SN 2021dbg's pseudobolometric 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.

Zoom In Zoom Out Reset image size

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 ∼20 days, and the luminosity decreases rapidly, then entering a plateau phase dominated by the core thermal radiation contribution. SN 2021dbg took ∼50 days, a longer time than most SNe II, 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 simulations showing that stars with initial masses between 17 and 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 SN explosions from Type IIP to Type IIL.

A large number of observational studies have shown that mass loss occurs at late times in massive stars, but it is still very difficult to directly observe the mass-loss process. The spectral flash emission lines at early phase are closely related to the CSM structure near the SN progenitor, and are thus helpful for us to infer the mass-loss process of the SN progenitor. The early spectra of SN 2021dbg show clear narrow Hα emission, which allows us to estimate the mass-loss rate of its progenitor via the relationship between L_Hα and $\dot{M}$ (Ofek et al. 2013):

$$\begin{eqnarray}&&{L}_{{\rm{H}}\alpha }\leqslant \displaystyle \frac{4\pi h{\nu }_{{\rm{H}}\alpha }{\alpha }_{\mathrm{eff}}\beta {K}^{2}}{\langle {\mu }_{p}\rangle {m}_{p}^{2}r},\end{eqnarray} \tag{ 5 }$$

where m_p is the mass of the proton, 〈μ_p 〉 is the mean number of nucleons per particle (mean molecular weight), β ≡ (r₁ − r)/r, $K\equiv \dot{M}/(4\pi {v}_{w})$, and ${\alpha }_{\mathrm{eff}}\approx 8.74\times {10}^{-14}{\left(\tfrac{{T}_{\mathrm{eff}}}{10,000\,{\rm{K}}}\right)}^{0.89}$ cm³ s⁻¹ (Osterbrock & Ferland 2006). We have:

$$\begin{eqnarray}&&\begin{array}{l}{L}_{{\rm{H}}\alpha }\leqslant 3.68\times {10}^{39}{\left(\frac{\dot{M}}{{10}^{-2}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}}\right)}^{2}\\ \times \,{\left(\frac{{v}_{w}}{500\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right)}^{-2}\beta {\left(\frac{r}{{10}^{15}\,\mathrm{cm}}\right)}^{-1}\,\mathrm{erg}\,{{\rm{s}}}^{-1}.\end{array}\end{eqnarray} \tag{ 6 }$$

Taking T_eff = 20,000 K, which was obtained by blackbody fitting ∼3 days after the explosion, Equation (5) can be simplified to Equation (6). We performed Lorentzian function fitting of the Hα line profile in the earliest spectrum obtained by the NTT, including a single Lorentzian function, two Lorentzian functions, and three Lorentzian functions.

The single Lorentzian profile fits the Hα 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 Hα 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 ii] λ λ6548, 6583, and the results show that this flux contribution can be ignored. The luminosity of the single Lorentzian fitting profile of the Hα emission line is L_Hα = 2.1 × 10³⁹ erg s⁻¹.

The radius of the blackbody photosphere at the time of this earliest spectrum is r ≈ 3.8 × 10¹⁴ cm and the radius of the blackbody photosphere at the beginning of the first plateau (∼18 days after the explosion; see Figure 8) is r₁ ≈ 1.3 × 10¹⁵ cm. The first plateau indicates that the plateau phase of the photospheric radius around 18 days is due to the CSM beyond this distance being already very thin, and the collision between ejecta and CSM cannot generate sufficient radiation to expand the photosphere any further; thus, the photosphere gradually shifts to the inner shell. When the shell ejecta expanded to r₁, 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 Hα flash emission-line profile in the earliest spectrum, we obtain a velocity broadening of ∼1000 km s⁻¹. Such a wind velocity is unusually high for the progenitors of SNe IIP and SNe IIL, 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 speeds (∼100 km s⁻¹), we got a mass-loss rate of $\dot{M}\geqslant 6\times {10}^{-4}$ M_⊙ yr⁻¹, slightly lower than the mass-loss rate of SN 2013fs (∼10⁻³ M_⊙ yr⁻¹). According to Equation (5) of Ofek et al. (2013), the H mass in the CSM is ∼1.7 × 10⁻³ M_⊙. If taking the typical wind speed of a red supergiant (RSG; ∼15 km s⁻¹) as v_w , we obtain $\dot{M}\geqslant 7\times {10}^{-6}$ M_⊙ yr⁻¹, which is a typical mass-loss rate for RSGs.

The mass-loss rate given by the model of Dessart et al. (2017) is on the surface of the progenitor, while the narrow Hα emission line we see comes from a farther place. The mass-loss rate estimated by the Hα flux is lower than the surface mass-loss rate given by the model, reflecting a density change of the CSM with distance. Zimmerman et al. (2024) demonstrated that there may be a steep decline in the density of CSM within the distance of ≈5 × 10¹³ cm to ≈5 × 10¹⁴ cm.

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

Zoom In Zoom Out Reset image size

In the nebular phase, Jerkstrand et al. (2012) also gave evolution curves of model spectral line luminosity ([O i] λ λ6300, 6364, Na i D, Mg I] λ4571, Hα, [Fe ii] λ λ7155, 7172, [Ca ii] λ λ7291, 7323, and the Ca ii NIR triplet) for progenitors with different masses relative to the ⁵⁶Co decay power over time. For the spectrum obtained at t ≈ 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 i] λ4571 and Na i D are ∼0.002 higher, and the values of [Ca ii] λ λ7291, 7323 and the Ca ii NIR triplet are ∼0.008 higher than the model values of the 19 M_⊙ progenitor, while the ratios of [O i] λ λ6300, 6364 and Hα are lower by ∼0.03 and ∼0.05, respectively, than the model values of the 19 M_⊙ progenitor. The flux ratios of Na, Mg, and Ca are higher, and those of H and O are lower, which means that the progenitor mass of SN 2021dbg may have been 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 Hα 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 (FWHM intensity that has been corrected for the instrumental broadening effect) of the nebular Hα emission and the mass of ⁵⁶Ni. We obtained FWHM_corr ≈ 92 Å for the Hα emission line in the nebular phase, and according to Equation (7) below from Maguire et al. (2012), we obtain ${M}_{\mathrm{Ni}}\approx {0.25}_{-0.19}^{+0.70}\,{M}_{\odot }$:

$$\begin{eqnarray}&&{M}_{\mathrm{Ni}}\,=\,A\times {10}^{B\times {\mathrm{FWHM}}_{\mathrm{corr}}}\,{M}_{\odot },\end{eqnarray} \tag{ 7 }$$

where $A={1.8}_{-0.7}^{+1.0}\times {10}^{-3}$ and B = 0.023 ± 0.004.

Figure 14 shows the correlation between the ⁵⁶Ni mass estimated from the luminosity in the radioactive tail and the FWHM_corr of the nebular Hα 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 very 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.

Zoom In Zoom Out Reset image size