Hydrogen-poor Superluminous Supernovae with Late-time Hα Emission: Three Events From the Intermediate Palomar Transient Factory

The main result of this paper is the detection of broad Hα emission in the late-time spectra of the three H-poor SLSNe. Figure 1 displays all of the available spectra for these three events, except two spectra of iPTF15esb at +270 and 320 days, which show only features from the host galaxy. In this figure, the spectra have not been host subtracted. It is apparent that broad Hα emission lines start to emerge at late times between photospheric and nebular phases. Furthermore, they persist until fairly late times, +123, +242, and 251 days for iPTF15esb, iPTF16bad, and iPTF13ehe, respectively, as shown in Figure 2. It is worth noting here that the LCs of iPTF15esb and iPTF16bad decline ∼3 times faster than that of iPTF13ehe (see Section 3.2 for details). Therefore, the last spectrum from iPTF15esb at +123 days could be at a similar late phase as that of iPTF13ehe. In addition, Figure 2 compares our late-time spectra with the spectrum of SLSN-I SN2015bn (Nicholl et al. 2016a), showing prominent broad Hα emission and apparent weak [O i] 6300 Å lines from our three events. Quantitative discussion on [O i] 6300 Å is included in Section 4.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

One important constraint is when Hα is first detected in the available spectra. The answer affects how we calculate the distance the ejecta have traveled since the explosion. We display all of the available spectra for these three events in Figure 1. All spectroscopic data are listed in Table 2, and will be made available via WISeREP (Yaron & Gal-Yam 2012). For comparison, we also include the high SNR spectrum of Gaia16apd, which is the second closest SLSN-I ever discovered (Yan et al. 2017).

It is clear from Figure 1 that the answer to the above question is not obvious because before a spectrum becomes fully nebular, broad absorption features can make it difficult to determine where the true continuum is. For example, does the +52 days spectrum for iPTF15esb (Figure 1) have Hα emission? And is the broad bump near 6500 Å in the $+0$ day spectrum of iPTF16bad Hα, or continuum between two broad absorption features?

To identify possible absorption features near the 6563 Å region, we run SYNOW, the spectral synthesis code (Thomas 2013). This is a highly parametric code, including ion species, temperature, opacity, photospheric velocity, and the velocity distribution. However, it nevertheless provides a useful consistency check for line identifications. Figure 3 illustrates the two model fits to the +52 day and +0 day spectra for iPTF15esb and iPTF16bad. Clearly, the observed features near 6000–6700 Å can be well fit by a combination of Na i, Fe ii 6299, 6248 Å, Si ii 6347, 6371 Å, and C ii 6580, 7234 Å absorption, without any Hα emission. This is confirmed by the actual detections of these lines at +30 days in SLSN-I Gaia16apd (Yan et al. 2017). The broad bumps around 6500 Å in post-peak and pre-nebular spectra are also seen in SN 2007bi and SN 2015bn (Gal-Yam et al. 2009; Nicholl et al. 2016b), and are considered to be a result of multiple absorption features.

Zoom In Zoom Out Reset image size

By visual inspection of the available spectra, we take +73, +97, and +251 days as the first dates when Hα emission lines are clearly detected. This method seems to be subjective; however, lack of full spectroscopic coverage gives much larger uncertainties in determining the true times when Hα first appears.

Figure 4 presents the observed $g,r,i$ LCs of iPTF15esb and iPTF16bad. The derived bolometric LCs are shown in Figures 5 and 6. It is immediately clear that the LCs of iPTF15esb are different from a typical SLSN LC, showing prominent undulations, stronger in the bluer bands. The three peaks are roughly separated by ∼22 days. Detailed discussion on the iPTF15esb LC morphology is presented in Section 4.3.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The peak date for iPTF15esb is chosen as the first peak at MJD = 57363.5 days. iPTF16bad has very limited photometric data. However, its r- and i-band LCs in Figure 4 are initially flat, suggesting that we discovered this event just before peak. Thus we set the peak date as MJD = 57540.4 days, the epoch of the first data. We construct the bolometric LC for iPTF15esb using the following procedure. We start with a pseudo-bolometric LC, which is an integral of the broadband photometry. At each epoch with a spectrum, we calculate a bolometric luminosity using a blackbody fit. The ratio between the bolometric and pseudo-bolometric luminosity gives the bolometric correction. Without sufficient early-time photometry, we fit a power-law $L\propto {t}^{2}$ form to the pre-peak data points, and derived a minimum of ${t}_{\mathrm{rise}}\geqslant 10$ days. The late-time decay rate follows $\propto {\rm{\Delta }}{t}^{-2.5}$, much steeper than the ⁵⁶Co decay rate (solid line in Figure 5). The bolometric LC for iPTF15esb is shown in Figure 5. The similar method was used for iPTF13ehe to get the bolometric LC. iPTF16bad does not have many spectra. We derive its bolometric LC by assuming similar bolometric corrections to the pseudo-bolometric LC as that of iPTF15esb.

One important question is, are these three SLSNe-I with late-time Hα emission special and do they have distinctly different photometric properties compared to other SLSNe-I? The answer is relevant to understanding the nature of these events. Figure 6 compares these three LCs with other events, including two slow evolving SLSN-I PTF12dam, SN2015bn and one fast evolving SLSN-I SN2010gx (Pastorello et al. 2010; Nicholl et al. 2016b; Vreeswijk et al. 2017).

iPTF15esb and iPTF16bad have peak bolometric luminosities of ∼4 × 10⁴³ erg s⁻¹ (−20.57 mag), whereas iPTF13ehe is more energetic, with L_peak ∼ $1.3\times {10}^{44}$ erg s⁻¹ (−21.6 mag).²¹ Although an unbiased SLSN-I sample does not yet exist, a simple compilation of 19 published SLSNe-I (Nicholl et al. 2015) has a median $\langle {L}_{\mathrm{peak}}\rangle \sim 5.7\times {10}^{43}$ erg s⁻¹ (−20.7 mag).

In addition, one striking feature in Figure 6 is the large difference in evolution rates between the three LCs. For iPTF15esb and iPTF16bad, their post-peak decay rates are fast, ∼0.05 mag day⁻¹, three times faster than that of iPTF13ehe, which is 0.016 mag day⁻¹. For comparison, the ⁵⁶Co decay rate is 0.0098 mag day⁻¹. The LC evolution of iPTF15esb and iPTF16bad is similar to the fast evolving SLSN-I SN2010gx (Pastorello et al. 2010), and iPTF13ehe is more like the extremely luminous, slowly evolving SLSN-I SN2007bi (Gal-Yam et al. 2009; Yan et al. 2015). For a naive comparison with the compiled SLSN-I sample by Nicholl et al. (2015), 67% have decay rates of 0.03–0.05 mag day⁻¹, and 33% of 0.01–0.02 mag day⁻¹. In addition, iPTF13ehe has a rise timescale of 83–148 days, implying a large ejecta mass of $70\mbox{--}220\,{M}_{\odot }$. The other two events do not have sufficient pre-peak data, but t_rise in iPTF15esb is likely short, as suggested by the rising rate of the first two available observations before the peak.

We conclude that the photometric properties of these three events are clearly very different from each other. However, they are within the diverse ranges represented by the published SLSNe-I so far, with the possible exception of the unique LC morphology of iPTF15esb. Therefore, it is possible that whatever physical processes responsible for late-time Hα emission could also be relevant to the whole population.

In the following sections, we describe other properties measured from the full spectral data set.

3.3.1. Rapid Spectral Evolution

3.3.2. Higher Ejecta Velocities

Figure 8 shows the ejecta velocity and the blackbody temperature as a function of time. When possible, we use Fe ii 5169 Å, a commonly used feature, to measure the velocity evolution with time. Other Fe ii lines, such as Fe ii 4924, 5018, and 5276 Å are also used to cross-check the results, as is done in Liu et al. (2017). The exception is iPTF15esb at +0 days, whose spectrum does not have a strong Fe ii absorption, and the ejecta velocity is estimated using O ii. The O ii feature in iPTF15esb is blueshifted by 40 Å relative to that of PTF09cnd at −30 day with a velocity of 15,000 km s⁻¹ (Quimby et al. 2011). This implies the velocity of iPTF15esb at +0 day is roughly 17,800 km s⁻¹. The same method is applied to iPTF13ehe and iPTF16bad. We find that at maximum light, our three SLSNe-I have higher ejecta velocities than those of other published SLSNe-I, ranging between 9000 and 12,000 km s⁻¹ (Nicholl et al. 2015).

The blackbody temperatures (T_BB) are estimated by fitting a blackbody function to the spectral continua. At maximum light, the blackbody temperatures of these three SLSNe-I range from ∼8000 to 14,000 K, with iPTF13ehe being the coolest whereas iPTF16bad is the hottest. Compared with other SLSNe-I with strong O ii absorption series, such as PTF09cnd, SN2015bn, PTF11rks, and Gaia16apd with maximum light ${T}_{\mathrm{BB}}\sim {\rm{13,000}}\mbox{--}{\rm{15,000}}$ K (Quimby et al. 2011; Inserra et al. 2013; Yan et al. 2015; Nicholl et al. 2016b), iPTF15esb and iPTF13ehe are indeed cooler at the peak phase. At the peak phase, iPTF16bad has a hotter temperature, which is shown by its steeper and bluer spectra in the early times (Figure 1). This difference is confirmed by their broadband $(g\mbox{--}r)$ color versus time shown by Figure 7. The lack of the full O ii absorption series should not be associated with blackbody temperatures at the peak phase. This is because the excitation of O ii levels are certainly nonthermal.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

3.3.3. Broad Hα Line Luminosities and Velocity Offsets

We perform simultaneous spectral fitting to the spectral continuum plus both narrow and broad Hα components assuming a Gaussian profile. The narrow line fluxes are iteratively measured from the unsmoothed data. Table 5 lists the measured line luminosities and velocity widths. Figure 8 shows these measurements.

Table 5.  Spectral Line Fit Results^a

Name	Phaseb	[O ii]	N.Hα	B.Hα	VFWHM	${\rm{\Delta }}V$
	(day)	(erg s−1)	(erg s−1)	(erg s−1)	(km s−1)	(km s−1)
15esb	30	8.8e+39	5.3e+39	⋯	⋯	⋯
15esb	50	4.9e+39	7.4e+39	⋯	⋯	⋯
15esb	52	1.0e+40	7.4e+39	⋯	⋯	⋯
15esb	73	8.9e+39	5.6e+39	2.6e+41	10800	1051
15esb	102	1.0e+40	7.5e+39	8.4e+40	5382	−160
15esb	122	8.1e+39	1.0e+39	5.4e+40	3768	−69
15esb	270	1.6e+40	8.5e+39	⋯	⋯	⋯
16bad	125	4.8e+39	3.9e+39	1.0e+41	5930	366
16bad	242	2.2e+39	3.6e+39	2.2e+40	3225	−549
13ehe	+251	⋯	6.1e+39	1.5e+41	4852	457
13ehe	+254	⋯	6.2e+39	1.04e+41	4312	457
13ehe	+278	⋯	1.24e+40	9.9e+40	4096	366

Notes.

^aHere N.Hα and B.Hα refer to the narrow and broad Hα component, respectively. ^bThe rest-frame days relative to the peak date.

Download table as:  ASCIITypeset image

One important question is whether the narrow Hα line comes from the host or from the supernova. The top panel in Figure 9 shows the integrated line luminosities as a function of time. The narrow Hα and [O ii] lines show slight variations with time, and the changes are less than a factor of 2. In contrast, the broad Hα line luminosities vary by a factor of 10 with time. Furthermore, the centroids of the narrow Hα emission are always at 6563 Å, whereas the centroids of the broad components change with time (see below). In the case of iPTF13ehe, the spatially resolved 2D spectrum shows that the narrow emission appears to be at the center of the host galaxy (Yan et al. 2015). We conclude that the narrow Hα and [O ii] emission lines are likely dominated by the host galaxies. Narrow Hα emission from the supernovae may exist, but its luminosity is too low to be detected by our data. The observed small variations are due to the combined effects of variable seeing and slit losses.

Zoom In Zoom Out Reset image size

The middle panel in Figure 9 shows the broad Hα line width (FWHM) as a function of time. The FWHM of $\sim 6000\mbox{--}4000$ km s⁻¹ should not be interpreted as the shell expanding velocity. Similar to well studied SNe II powered by ejecta interaction with CSM, the broad line widths likely indicate the velocities of the shocked material. The H-rich CSM expansion velocity is probably much smaller, of an order of a few 100 km s⁻¹.

These three events show an interesting trend in their velocity offsets between the broad and narrow Hα components, as shown in the bottom panel in Figure 9. We find that the broad components initially appear to be blueshifted relative to the narrow components (assuming host emission), and at later times, become redshifted. The velocity offset for iPTF15esb at +73 days is as high as +1000 km s⁻¹, and decreases to $\sim -400$ km s⁻¹ at later epochs. Similarly in iPTF16bad, the offset varies from +400 to −500 km s⁻¹ at +125 and 242 days. iPTF13ehe shows only positive velocity offsets (blueshifted).

Figure 10 shows the +122 day and +242 day spectra for iPTF15esb and iPTF16bad. Although noisy, the spectra show the excess emission at the red side of Hα 6563 Å. One possible explanation is that the expanding H-shell initially could obscure the Hα photons from the back side, which is moving away from us. So we initially see more Hα emission from the material moving toward us (blueshifts). In this model, at later times when ejecta become more transparent, we should see more symmetric line profiles with no velocity offsets. This is clearly not what we see at very late times in our data. So the red excess emission cannot be explained by obscuration. We also note that the observed positive velocity offsets in all three events could be in tension with the binary model proposed by Moriya et al. (2015) for iPTF13ehe, which predicts the equal probability of observing both positive and negative velocity offsets relative to the host galaxies.

Zoom In Zoom Out Reset image size

One important question is where this hydrogen material producing the late-time Hα emission is located. One possibility is a residual hydrogen layer left over from incomplete stripping of the H-envelope. This scenario can be ruled out because if there is any hydrogen in the ejecta, it is very difficult not to have any Hα absorption at all near maximum light, as shown in the detailed modelings carried out by Hachinger et al. (2012). This is because ejecta density is usually much higher than 10⁷ cm⁻³, and the H recombination timescale is $\propto {10}^{13}/{n}_{e}$ seconds $\sim 11{({n}_{e}/{10}^{7})}^{-1}$ days, which is quite short. An actual example is SN 1993J, which is an SN IIb with a very low mass of H ($\lt 0.9\,{M}_{\odot }$). Although its pre-peak spectra have high blackbody temperatures, a weak Hα emission is present at early phases (Filippenko et al. 1993). For our three events, at post-peak before +70 days, the photosphere temperatures are already low and there are no detectable Hα features in all three events, even with ample spectral coverage between +0 days and +122 days for iPTF15esb.

The second possibility is a neutral, detached H-rich shell located at a distance from the progenitor star, possibly produced by a violent mass-loss episode some time prior to the supernova explosion. When the ejecta eventually run into this shell, the shock interaction ionizes H atoms, and subsequent recombination produces Hα emission. This idea was initially proposed for iPTF13ehe in Yan et al. (2015).

The third possibility is proposed by Moriya et al. (2015), where the progenitor is in a binary system with a massive, H-rich companion star ($\gt 20\,{M}_{\odot }$). The explosive ejecta strip off a small amount of H from the companion star, which is then mixed in the inner regions of the ejecta. This H-rich material becomes visible only when the inner layers of ejecta are transparent in the nebular phases. This model predicts that depending on the orientation of the binary, there should be equal probability of seeing H-emitting material moving toward or away from us. The fact that we see blueshifts in all three events could be in tension with this prediction and disfavors this model.

Some quantitative parameters for the H-shell model can be derived from our observations. In this scenario, the progenitor is a massive star, prone to violent mass losses. Several decades before the explosion, it undergoes an eruptive episode, ejecting all of the remaining H envelope. Let us assume that the ejecta average speed is $\langle {v}_{\mathrm{ej}}\rangle$ and the time between the explosion and the time Hα is first detected is ${\rm{\Delta }}t$. The distance traveled by the ejecta, i.e., the radius of this shell, is thus $R=8.6\times {10}^{15}\left(\tfrac{v}{{10}^{4}\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right)\times \left(\tfrac{{\rm{\Delta }}t}{100\,\mathrm{days}}\right)$ cm. Our measured ejecta velocities range from 18,000 to 15,000 km s⁻¹ at maximum light to $\sim 6000\mbox{--}7000$ km s⁻¹ at +100 to +250 days. So the baseline assumption of $\langle {v}_{\mathrm{ej}}\rangle \sim {\rm{10,000}}$ km s⁻¹ is not too far off.

The values of ${\rm{\Delta }}t$ are not well measured for both iPTF15esb and iPTF16bad due to poorly constrained explosion dates. For iPTF15esb, a rough estimate of ${\rm{\Delta }}t$ (Figure 4) is $73+20\sim 93$ days. iPTF13ehe is a slowly evolving SLSN-I (Yan et al. 2015), with ${\rm{\Delta }}t\sim 332$ days. Therefore, for these three events, the sizes of the H-rich shells range between $(9\mbox{--}40)\times {10}^{15}$ cm. If the shell expansion speed is 100 km s⁻¹, the time since the last episode of mass loss before explosion is ${t}_{\mathrm{erupt}}\sim R/{v}_{\mathrm{shell}}\sim R/100$ km s⁻¹ ∼ 30 years. So, approximately, the last episode of mass loss is only 30 years before the supernova explosion. This time could be as short as 10 years if the expansion speed is faster. Such violent instabilities shortly before the supernova explosion could be a very common phenomenon for massive stars in general, as demonstrated, for example, by flash-spectroscopy of SN IIP iPTF13dqy and precursor outbursts in SNe IIn such as SN2009ip (Martin 2013; Margutti et al. 2014; Ofek et al. 2014; Yaron et al. 2017). At lower luminosities, a similar and well studied example as our three events is SN2014C, which was initially discovered as an ordinary SN Ib, then evolved into a strongly interacting SN IIn over ∼1 year timescale (Milisavljevic et al. 2015; Margutti et al. 2017a).

There are two commonly asked questions. (1) If this H-shell is present, why do not we see any H emission in the early-time spectra? (2) Why are our spectra not being obscured or absorbed by this shell? This H-shell is likely to be neutral but optically thin during early times. However, if spectra were taken just hours after explosion, neutral H should have been ionized and we would have detected flash spectral features (Gal-Yam et al. 2014; Yaron et al. 2017), including Hα emission. For these three events, we do not detect any early-time Hα emission because by the time our first optical spectrum is taken, the H-shell has already recombined. At a density of $n\geqslant {10}^{7}$ cm⁻³, the H recombination time is ${t}_{\mathrm{rec}}\leqslant {10}^{13}/n$ s $\leqslant 11$ days. For a H-shell with $R\sim {10}^{16}$ cm and a width of 10% R, this density limit corresponds to a mass limit of $\geqslant 0.01\,{M}_{\odot }$.

If the H-shell is neutral at pre-peak, why do we not observe any Hα absorption? Hα absorption is produced when an excited H atom at n = 2 absorbs a photon with λ = 6563 Å, and moves up to the n = 3 level. At temperatures of several thousands of degree, most H atoms are in the ground state (n = 1) because the excitation energy from n = 1 to n = 2 requires 10 eV, implying a much higher temperature (100,000 K). Without excited n = 2 H atoms, there is no Hα absorption. However, we predict that Lyα absorption (n = 1 −>n = 2 transition) should be strong. Future late-time UV spectroscopy may confirm this for events such as ours.

The mass of this H-shell can be constrained by two other factors. When the ejecta run into the shell, H atoms are ionized again by the thermalized kinetic energy. One constraint is that this ionized H-rich CSM cannot have very high electron scattering opacity, i.e., Thomson scattering opacity, ${\tau }_{\mathrm{thomson}}={\sigma }_{T}{n}_{e}{\rm{\Delta }}R\leqslant 1$ with ${\rm{\Delta }}R$ being the width of the shell. Otherwise, photons from the central supernova would have been absorbed. This condition implies ${M}_{\mathrm{shell}}\leqslant \tfrac{4\pi {{fm}}_{H}{R}^{2}}{{\sigma }_{T}}$, and f is the filling factor, R is the radius of this shell. Here ${\rm{\Delta }}R$ is canceled out when computing the total mass. With the Thomson cross-section ${\sigma }_{T}=6.65\times {10}^{-25}$ cm², we have ${M}_{\mathrm{shell}}\leqslant 1.6f(\tfrac{R}{{10}^{16}\,\mathrm{cm}})\,{M}_{\odot }$. Assuming the width of this shell is only 10% of the radius R, the implied electron volume density is ${n}_{e}\sim 7\times {10}^{9}(\tfrac{R}{{1.0}^{16}\,\mathrm{cm}})$ cm⁻³. The H-shell upper mass limits range from $(1.6\,\mathrm{to}\,30)f\,{M}_{\odot }$ for the three events discussed in this paper. In the case of a small filling factor $f\sim 10 \%$, the shell mass would be less than $0.2\mbox{--}3\,{M}_{\odot }$. One scenario that could naturally explain such a powerful mass loss is the Pulsational Pair-Instability model (PPISN; Woosley et al. 2007; Woosley 2017). Further support of this model is from the weak [O i] 6300 Å emission in the nebular phase spectra, as discussed below.

In the H-shell scenario, the time interval between the supernova explosion and the mass-loss episode, which ejected all of the H-envelope is not very long, only several decades. During this period of time, additional mass-loss episodes could remove some helium layers from the progenitor star, but it is very unlikely that all of the helium can be completely removed. For example, Woosley et al. (2002) presented a model for a star with ${M}_{\mathrm{ZAM}}\sim 25\,{M}_{\odot }$. Their Figure 9 shows before the supernova explosion, the most outer layer has roughly $5\,{M}_{\odot }$ of mixture of H and He, and just underneath that, there is a pure He layer with a mass of $\sim 1.5\,{M}_{\odot }$. If we assume the mass-loss rate of 10⁻⁴ to ${10}^{-6}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, similar to nominal wind mass-loss rates, the time required to completely remove the pure He layer is $1.5\times ({10}^{4}\mbox{--}{10}^{6})$ years, much longer than several decades set by our observational constraint.

This implies that the ejecta of our three events may contain helium. Observationally, our early-time spectra do not detect significant helium features. However, we caution that the presence of weak helium absorption features is very difficult to confidently rule out because He i 3888, 4417, and 6678 Å lines tend to be blended with other features such as strong Fe ii 4515 Å, Si ii 3856 Å, and C ii 6580 Å, as shown in Figure 11. On the other hand, the nondetection of helium features might not be very surprising because helium ionization potential is high, 24.58 eV. This would require much higher temperatures than what our spectra show, or more likely, nonthermal ionization conditions, for example, mixing with radioactive material such as ⁵⁶Ni.

Zoom In Zoom Out Reset image size

Indeed, this condition for nonthermal ionization of He probably exist for SLSNe-I, as suggested by commonly detected five O ii absorption series around 4000 Å. As argued in Mazzali et al. (2016), the excitation of O ii levels is from the nonthermal process, such as energetic particles from radioactive decay. What is relevant here is that these particles can also ionize He i (ionization potential of 24.6 eV). So if helium is present in the ejecta, it is a puzzle why we do not detect any spectral signatures in the early-time data.

Another possible explanation for weak, or the absence of, He features is that all helium is mixed into the outer H-envelope and the H+He outer layers were completely stripped off the progenitor stars before the supernova explosions. The ejecta contain no helium material.

The [O i] 6300 doublet emission is usually very strong for SLSNe-I and SNe Ic because of the following two reasons. First, these supernovae are thought to result from the explosions of massive C+O cores. The ejecta should naturally contain a lot of oxygen. Second, the [O i] 6300 line is a very efficient coolant in the nebular phase (Jerkstrand et al. 2017). Therefore, it is common to see very strong [O i] 6300 Å emission in core collapse SNe. Figure 2 visually illustrates an apparent lack of [O i] 6300 Å emission in the late-time spectra of our three events. Given the noise level in our spectra, it is not immediately clear whether this apparent discrepancy is significant, however.

To address this question, we take three late-time spectra from SLSN-I SN2015bn at +315 and +392 days (Nicholl et al. 2016a) and SN2007bi at +367 days (Gal-Yam et al. 2009), which all have prominent [O i] 6300 Å emission. We scale these three spectra to the distance of iPTF16bad, i.e., multiply by the square of the luminosity distance ratios, and then add the noise measured from the +242 day spectrum for iPTF16bad. The simulated spectra from this procedure are shown in Figure 12. Here the noise added to the input spectra is $\sigma \sim 9\times {10}^{-19}$ erg s⁻¹ s⁻² Å⁻¹, measured from the 240 Å region centered at 6300 Å (excluding Hα) in the +242 day spectrum of iPTF16bad. This noise is then added as a Gaussian random noise to the input spectra. We note that because the input spectra do have their own noises, the output simulated spectra may have slightly higher rms than the true value.

Zoom In Zoom Out Reset image size

From this simple simulation, we conclude that if the +242 day spectrum from iPTF16bad were to have the same [O i] luminosity as that of the three input spectra, we would have detected this feature in our data. This implies that our spectra at $\sim +240$ days likely have intrinsically weaker [O i] 6300 Å emission than the late-time spectra of the three comparison SLSNe-I. Unfortunately, at $z\sim 0.2\mbox{--}0.3$, the Ca ii triplet at 8498 Å is redshifted out of the optical range, so we do not know if the Ca ii triplet is strong, and serves as an alternative cooling line for these three events. In the simulated spectra, the Ca ii triplet is quite strong in SN2015bn, and absent in SN2007bi (see Gal-Yam et al. 2009).

The [O I] 6300, 6364 lines at the nebular phase are very useful diagnostics of supernova ejecta. This is because these lines are efficient coolants and typically re-emit a large fraction of heating energy of the O-material. More importantly, these lines become optically thin, and have line luminosities of $\propto {M}_{{\rm{O}}{\rm{I}}}{n}_{e}{e}^{-{\rm{\Delta }}E/T(t)}$ in the nonlocal thermal equilibrium phase, as discussed in detail in Jerkstrand (2017).

The apparent weakness of the [O i] 6300 doublet and other ionized O emissions in our three events seem to suggest that there is less oxygen emitting at late times. This is puzzling because SLSNe-I are thought to be explosive events of C+O cores with masses greater than several tens of solar masses. There could be several explanations. First, the ejecta of our three events may have lower oxygen masses, and perhaps also lower progenitor masses than that of SN2015bn and SN2007bi. The recent modeling of the nebular spectra of SN2015bn and SN2007bi by Jerkstrand et al. (2016) has derived $M(O)\sim 10\mbox{--}30\,{M}_{\odot }$. The second possible explanation is that these three events could be pulsational pair-instability supernova (PPISN). Calculated optical spectra at the nebular phase, based on pair-instability supernova (PISN) models, seem to show a relatively weak [O i] 6300 doublet (Jerkstrand et al. 2016). At face value, this could be considered to be supporting evidence for a PISN or PPISN model for these events. However, as shown by Jerkstrand et al. (2016), the calculated nebular spectra show very strong [Ca ii] 7300 Å emission lines, which are also not detected in our late-time spectra, but are present in the simulated spectra (Figure 12). The probability of these three events being PPISN or PISN is small. First is because the required progenitor mass is very high, and second, as pointed by Woosley (2017), PPISN still has difficulties producing very energetic SLSNe-I, and iPTF13ehe is such an example.

The third possible explanation is that oxygen in these three events is detached from ⁵⁶Ni, and with very little mixing. If the O-zone is above ⁵⁶Ni, γ-ray photons from ⁵⁶Ni decay will be effectively absorbed by Fe group elements before reaching O. In this case, there is not sufficient photon heating to produce [O i] emission. If ejecta density is very high, it would result in high opacity, and the [O i] line may cool inefficiently. Future better modeling of nebular spectra of SLSNe-I would narrow down these possible explanations.

What makes iPTF15esb stand out is its peculiar LC with strong undulations, particularly in bluer bands. We note that the three peaks are separated from each other equally by ∼22 days. After the first peak, its g-band and also bolometric LC have two additional small bumps (Figures 4 and 5).

LC undulations are also seen in other SN types, such as SN2012aa (between SN Ibc and SLSN-I), other SLSNe-I (SN2015bn), and SN IIn (PTF13z and SN2009ip; Pastorello et al. 2013; Nicholl et al. 2016b; Roy et al. 2016; Inserra et al. 2017; Nyholm et al. 2017). They are probably even present in SN2007bi and PS1-14bj (Gal-Yam et al. 2009; Lunnan et al. 2016). SN2009ip is either an SN IIn or an SN imposter (Fraser et al. 2013; Martin 2013; Graham et al. 2014; Margutti et al. 2014). Figure 13 makes an LC comparison between iPTF15esb, SN2012aa and SN2015bn. The LC undulation in iPTF15esb is quite strong, with some similarity to that of SN2012aa. These LC undulations are clearly very different from the double-peak LCs with initial weak bumps followed by prominent main peaks seen in LSQ14bdq, SN2006oz, PTF12dam, and iPTF13dcc (Leloudas et al. 2012; Nicholl et al. 2015; Smith et al. 2016; Vreeswijk et al. 2017). Their physical nature may also be different.

Zoom In Zoom Out Reset image size

Several ideas were proposed by previous studies to explain the LCs. This includes (1) successive collisions between ejecta and mass shells expelled by previous episodic mass losses; (2) magnetar UV-breakout predicted by Metzger et al. (2014); (3) recombination of certain ionized elements; (4) variable continuum optical/UV opacities, which could modulate the photon diffusion, thus affecting LC morphology, as proposed for ASASSN-15lh (Godoy-Rivera et al. 2017; Margutti et al. 2017b).

In the case of iPTF15esb, interaction based models may explain the data. The second peak has a duration of 20 days and with a net luminosity of $1.5\times {10}^{43}$ erg s⁻¹. The total extra energy in this peak is $\sim 2\times {10}^{49}$ erg. This implies an excess luminosity of $\sim {10}^{43}$ erg s⁻¹ over 10 days. Using a simple scaling relation $L\sim \tfrac{1}{2}{M}_{\mathrm{csm}}{v}^{2}/\delta t$ and taking the ejecta velocity ${v}_{\mathrm{ej}}\sim {\rm{17,000}}$ km s⁻¹, we estimate ${M}_{\mathrm{csm}}\sim 0.01\,{M}_{\odot }$. Eruptive mass losses could produce such mass shells. PPISN models (Woosley 2017) could produce various successive H-poor shells, and the subsequent collisions between shells and/or ejecta-shell would generate additional energy producing the observed LC undulations.

The second possible explanation is due to the change in recombination of elements such as C and O, as shown in Piro & Morozova (2014), CSM with pure CO can undergo recombination at temperatures of roughly 8000 K. Another similar idea is the change of continuum opacity, which can naturally explain the stronger undulation in bluer bands (Godoy-Rivera et al. 2017; Margutti et al. 2017b). Finally, models with central power sources, such as magnetars or fall-back accretion onto a neutron star or black hole, have an energy input function, such as $\tfrac{{E}_{p}}{{\tau }_{p}}\tfrac{1}{{(1+t/{\tau }_{p})}^{2}}$, with E_p and ${\tau }_{p}$ as the magnetic dipole spin-down energy and the spin-down timescale, respectively (Kasen & Bildsten 2010; Dexter & Kasen 2013). At late times, the luminosity should scale like t⁻², close to ${(t-50)}^{-2.5}$, measured from the data (Figure 5). These models seem to be able to explain some data. However, the real test requires detailed calculations, which can meet the challenges of all observed features.