DETECTION OF BROAD Hα EMISSION LINES IN THE LATE-TIME SPECTRA OF A HYDROGEN-POOR SUPERLUMINOUS SUPERNOVA

The iPTF13ehe photometry was obtained mostly with the PTF survey Camera (Rahmer et al. 2008) on the 48 inch Oschin Schmidt telescope (P48) and the imaging camera on the robotic 60 inch (P60) telescope at Palomar Observatory (Cenko et al. 2006). Additional late-time photometry was obtained with the Large Format Camera (LFC) on the Palomar 200 inch (P200), the Keck, and the Discovery Channel Telescope (DCT). P48 data from 2013 February set useful constraints on the explosion date. The P48 images are processed by the PTF imaging processing pipeline written at the Infrared Processing and Analysis Center (IPAC; Laher et al. 2014). The photometry is measured using the PTF Image Differencing Extraction (PTFIDE) software (Masci 2014). This package produces both point-spread function (PSF) fitted photometry as well as aperture photometry on the reference-subtracted images. More importantly, co-added photometry and upper limits based on multi-epoch observations can be derived when the transient object is faint.

The photometry from the P60, the Keck Low Resolution Imager and Spectrograph (LRIS; Oke et al. 1995), and the DCT are measured through an appropriate aperture with diameter (2–2.5) × FWHM of the seeing disk. All photometry is in AB magnitudes, and calibrated onto the SDSS g, r, and i filters. On 2015 February 17, iPTF13ehe was observed by the HST/ACS/WFC camera in the F625W filter (PID: 13858) (A. de Cia et al. 2015, in preparation). The supernova iPTF13ehe is clearly offset from a faint dwarf galaxy. After the subtraction of the supernova light, the host galaxy photometry is 24.24 ± 0.06 mag (AB, r). The g-band decline is leveling out by 2015 March 23, with a total magnitude of 24.77. It faded only 0.1 mag during the two months between 2015 January 22 and March. Thus, we approximate the host brightness in g-band with 24.9. Some of the late-time photometry is taken with LRIS Cousin R_c filter. We transformed R_c magnitude to SDSS r AB magnitude using the late-time spectra. The g, r, and i-band photometry are listed in Table 1. The tabulated photometry are not extinction corrected.

The Schlafly & Finkbeiner (2011) extinction map gives a Galactic extinction $E(B-V)=0.04$ at the position of iPTF13ehe. We assume the extinction law of (Cardelli et al. 1989) with ${A}_{V}/E(B-V)=3.1.$ Specifically, A_g, A_r, and A_i are small, 0.14, 0.1, and 0.07 mag, respectively. In this paper, we have ignored any potential dust extinction from the host galaxy. This assumption is probably not too far off since most dwarf galaxies have low dust extinction and our late-time spectra do not show any significant reddening or Na D absorption lines. Studies of SLSN-I host galaxies also support this assumption (Lunnan et al. 2014; Leloudas et al. 2015).

Spectroscopic observations of iPTF13ehe were obtained on six epochs, three near the LC peak, and three during the late-time nebular phase (∼300 days since the peak). The spectra were taken with the Keck Deep Imaging and Multi-Object Spectrograph (DEIMOS; Faber et al. 2003) and LRIS (Oke et al. 1995) mounted on the Keck 10 m telescopes, and with the Double Spectrograph (DBSP; Oke & Gunn 1983) on the P200. The spectral coverages are ∼3000–10000 Å and 4000–10000 Å for LRIS+DBSP and DEIMOS, respectively. The spectral resolution is moderate, with λ/δλ ∼ 800–2000. DEIMOS observations were reduced using the software developed by the Deep Extragalactic Evolutionary Probe 2 (DEEP2) project (Newman et al. 2013). LRIS and DBSP observations were reduced by us (D. Perley and R. Quimby) using custom written software. The observation information is listed in Table 2.

All six spectra are flux calibrated and corrected for Galactic extinction assuming $E(B-V)=0.04$ (see Section 2.1). We cross-check the spectral calibration against broadband photometry. Overall, the corrections to the spectral calibrations are small. The spectra taken near peak luminosity were not corrected for host galaxy contamination, since it is faint and negligible. For the late-time spectra, we perform host galaxy subtraction, as described below (Section 3.2). All calibrated spectra will be made publicly available via WISeREP (http:/wiserep.weizmann.ac.il; Yaron & Gal-Yam 2012).

Supernova LCs provide several important measurements that can constrain the explosion physics. This includes three observables: the rest-frame rise time from the date of explosion to the maximum brightness (${t}_{\mathrm{rise}}^{\mathrm{rest}}$), the peak bolometric luminosity (${L}_{\mathrm{bol}}^{\mathrm{peak}}$), and the post-peak decay rate (ΔM/Δt).

Figure 1 illustrates the observed g, r, and i-band LCs as a function of Julian Date (JD). iPTF13ehe has a total of 48 images taken eight months prior to the discovery date on 2013 November 25. The upper limit and the two earliest detections in Figure 1 were derived from stacking, each using ∼10 images spanning over 10 days. These early data—often missed for SLSNe—are very useful for constraining the rise timescale, the explosion date, and for searching for SN precursors (e.g., Ofek et al. 2014). The g- and r-band LCs are host-light subtracted, and the i-band LC covers only the peak epochs, which are not significantly affected by the faint host.

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We first determined the peak and explosion dates using polynomial fits to the r-band LC. iPTF13ehe reached its peak at a Julian date (JD) of 2456670.77 days. Here we show how the explosion date, and thus rise time, can be affected by various factors. We define the explosion date as the time when the extrapolated r-band magnitude is fainter than 30 mag. When we use all of the data for a single polynomial fit (Figure 1; blue solid line), the derived explosion date is 2456471.3 days. But if we consider that the two earliest data points may favor a different rising slope, and fit the data with a piece-wise polynomial (red solid line), the derived explosion date is later, at JD = 2456522.5 days. The corresponding rest-frame rise times are ${t}_{\mathrm{rise}}^{\mathrm{rest}}$ = 148.5 and 110 days, respectively. The large uncertainty is due to a lack of early observations, and more importantly, a lack of knowledge of the shape of early SLSN LCs. For example, instead of slower rising slopes indicated by the polynomial fit (blue and red lines in Figure 1), the early LC may have a faster rising exponential form of $L(t)={L}_{\mathrm{peak}}\left(1.0-{e}^{\frac{{t}_{0}-t}{{t}_{e}}}\right),$ as applied to a sample of SN IIn in Ofek et al. (2014). The fit to the data yielded the explosion date t₀ = 2456575.6 days and the exponential rise time t_e = 83 days (shown as black line in Figure 1). The large uncertainty in ${t}_{\mathrm{rise}}^{\mathrm{rest}}$ illustrates one critical and the most difficult aspect of supernova observations—catch them early enough that the physical information can be derived. We conclude that the rise time ${t}_{\mathrm{rise}}^{\mathrm{rest}}$ is in a range of 83–148 days.

Rest-frame LCs require appropriate k-corrections. Here the k-correction, K_QR, is defined as ${M}_{Q}(\mathrm{rest})={m}_{R}(\mathrm{obs})-\mathrm{DM}-{K}_{{QR}},$ with the observed filter being R, the rest-frame filter being Q, and DM being the distance module. We transformed the observed r-band LC to rest-frame M_r and M_g LCs by applying K_rr and K_gr, calculated using the observed spectra at the three separated epochs (2014 January 06, 2014 February 01 and 2014 December 17). K_gr is −0.28, constant for both the early and late epochs. The K_gr correction is almost constant because at z = 0.3434, the observed r filter samples rest-frame 4659.8 Å, very close to the g-band λ_eff at z = 0. Thus K_gr is approximately $2.5{\mathrm{log}}_{10}(1+z)$ (for details see Hogg et al. 2002). The derived rest-frame M_g LC is shown in Figure 3.

K_rr is approximately −0.38 for the pre-peak photometry, −0.5 between the peak and +100 days post-peak (rest-frame), and +0.54 for the rest of the late-time photometry. We note that K_rr = +0.54 is the averaged value based on the three late-time spectra (see Figure 1). This K-correction is large and positive, making the rest-frame M_r LC brighter, as shown in Figure 2. The change of K_rr with time is due to (1) the emergence of a strong, broad Hα emission line at late times (first detected at 2014 December 21); (2) the redder continuum in the supernova spectra. The large variation in K_rr is also responsible for the observed steep (g−r) color evolution with time, from 0.3 near the peak brightness to 1.5 at later times (Figure 1). How much of the M_r brightening is due to the continuum versus Hα? We test this by masking out the Hα line from the late-time spectra and find that the calculated K_rr from the pure continua is +0.3, still quite significant.

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The LCs shown in Figures 2 and 3 indicate a linear decline, except the brightening in the late-time M_r LC. The decay rates are 0.0155 and 0.0149 mag day⁻¹ for the r-band and g-band LCs, respectively. For the r-band LC, we measured the decay rate separately for the late-time and the post-peak photospheric period, and the values are very similar. These decline rates are much slower than those of any normal supernovae in the post-peak photospheric phases. We note that it is close to the pure ⁵⁶Co decay rate of 0.0097 mag day⁻¹.

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Figures 2 and 3 compare the iPFT13ehe M_r and M_g LCs with those of SN2007bi and PTF12dam, two well-studied hydrogen-poor SLSNe (Gal-Yam et al. 2009; Nicholl et al. 2013; Chen et al. 2014). It is interesting to note that the decline rates of the three SLSNe are very similar, except for the elevated M_r bump in iPTF13ehe after the emergence of the broad Hα emission. In addition, iPTF13ehe has a slower rising rate, and thus a wider LC compared to PTF12dam. One argument against PTF12dam being a pair instability supernova (PISN) is that its LC rose much faster than model predictions (Inserra et al. 2013; Nicholl et al. 2013).

The peak bolometric luminosity, ${L}_{\mathrm{bol}}^{\mathrm{peak}},$ is estimated as follows. We have g, r, and i photometry taken around the time when iPTF13ehe reached its peak brightness. Thus, we have fairly good estimates of the peak fluxes in these filters. The integral over the broadband defined SED between g- and i-band results in 6 × 10⁴³ erg s⁻¹, which sets a lower limit on ${L}_{\mathrm{bol}}^{\mathrm{peak}}.$ Figure 4 shows the spectrum in $\lambda {f}_{\lambda }$ versus λ_rest. This spectrum is taken at −9 days pre-peak. We used the broadband photometry taken nearest to this spectrum, and refined the flux calibration to account for slit losses. The continuum shape should reflect the blackbody radiation, and the bolometric flux f_bol is simply

$$\begin{eqnarray}{f}_{\mathrm{bol}} & = & {\displaystyle \int }_{0}^{\infty }\left(\displaystyle \frac{2}{{\lambda }^{2}}\displaystyle \frac{h\nu }{{e}^{h\nu /{k}_{B}T}-1}\right)d\nu \\ & = & \displaystyle \frac{\sigma {T}^{4}}{\pi }=1.386{\nu }_{m}f({\nu }_{m}),\end{eqnarray} \tag{ 1 }$$

where ν_m is the frequency when $\nu {f}_{\nu }$ is at the maximum. From the spectra shown in Figure 4, $\lambda {f}_{\lambda }$ peaks at λ ∼ 4800 Å, with f_bol = 1.386*${\lambda }_{m}f({\lambda }_{m})$ = 1.386 4800.0 4.95 10⁻¹⁷ erg s⁻¹ cm⁻². This yields ${L}_{\mathrm{bol}}^{\mathrm{peak}}$ = 1.3 × 10⁴⁴ erg s⁻¹. This is consistent with the lower limit set by the broadband photometry.

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With ${t}_{\mathrm{rise}}^{\mathrm{rest}}$ and ${L}_{\mathrm{bol}}^{\mathrm{peak}},$ it is clear that iPTF13ehe is an extremely luminous supernova. The total radiative energy can be estimated by, E_rad$\;\geqslant \;$ ${L}_{\mathrm{bol}}^{\mathrm{peak}}\times {t}_{\mathrm{rise}}^{\mathrm{rest}}$ ∼ 1.3 × 10⁴⁴ erg s⁻¹ × 83 days ∼ 9.3 × 10⁵⁰ erg.

iPTF13ehe was observed on six different epochs. Figure 5 presents these data, illustrating the evolution of the spectral features over the rest-frame time interval of 287 days. The color lines in the figure show the smoothed spectra, which are performed using astropy package convolve.Box1DKernel software. The smoothing length ranges from 6 to 8 Å (5–7 pixels) for the P200 and Keck LRIS spectra, and is much smaller, only 3 Å (11 pixels) for the DEIMOS high-resolution spectrum (2014 December 21). In the section below, we discuss in detail the spectral properties in the photospheric and nebular phase separately. An accurate redshift is measured using the multiple narrow emission lines detected in the final spectrum (2015 January 22).

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3.2.1. Photospheric Phase Spectra—Similarity between iPTF13ehe and SN2007bi 

3.2.2. Nebular Phase Spectra—Detection of a Broad Hα Emission Line

As Table 2 shows, we have three nebular-phase spectra taken on ${t}_{\mathrm{rest}}^{\mathrm{peak}}$ = +251, +254, and +278 days (post-peak) or ${t}_{\mathrm{rest}}^{\mathrm{exp}}$ = +322, +325, and +349 days (from explosion JD of 2456575.6 days) respectively. All three spectra display a strong, broad Hα emission line with a velocity width >4000 km s⁻¹, as well as a narrow Hα emission component. Below we discuss in turn the nature of these two components.

The first question is whether the narrow Hα component is from the recombination of ionized hydrogen atoms in a slow-moving shell or from the host galaxy. This type of narrow emission feature is commonly seen in the spectra of SN IIn and usually comes from the slow-moving, outer layer of the H-rich CSM surrounding the supernova. In the case of iPTF13ehe, the complication comes from the fact that all available spectra contain signals from both the supernova and the host galaxy. In the three nebular spectra, the narrow Hα line is unresolved for the two spectra taken with LRIS and resolved in the high-resolution DEIMOS data (FWHM of 1.8 Å) taken on 2014 December 21. The integrated line fluxes for the narrow component are 2.2 × 10⁻¹⁷, 2.1 × 10⁻¹⁷, and 3.88 × 10⁻¹⁷ erg s⁻¹ cm⁻² for 2014 2014 December 17, 21 and 2015 January 22, respectively. The January 2015 spectrum has the highest signal-to-noise ratio (S/N) and also detects Hβ and narrow [O ii] 3727 Å emission lines. The redshifts inferred independently from the narrow Hα and [O ii] lines are the same, at z = 1.3429. The integrated [O ii] 3727 Å line flux is 2.64 × 10⁻¹⁷ erg s⁻¹ cm⁻², implying an SFR of 0.15 M_⊙ yr⁻¹ based on the conversion from Kennicutt (1998). If all of the narrow Hα line flux (3.88 × 10⁻¹⁷ erg cm⁻²) comes from star formation, the inferred SFR is 0.13 M_⊙ yr⁻¹, 15% lower than that inferred from [O ii].

The observed flux variations with time in the narrow Hα line are likely due to the combination of the weather changes and different slit position angles. The consistent redshift and SFR measured from [O ii] and narrow Hα suggest that the narrow Hα line is mostly from the host galaxy and not from the supernova. Additional support for this conclusion comes from the high-resolution DEIMOS spectrum taken on 2014 December 21. Figure 6 shows the reduced, two-dimensional spectrum around the Hα region. We found that the narrow Hα component is resolved in velocity, and is consistent with the host galaxy rotation velocity field of 65 km s⁻¹ (roughly 1 spectral resolution, 1.8 Å). Furthermore, the top panel of Figure 6 shows the DEIMOS slit overlaid on the direct image of iPTF13ehe (red dot) and the host galaxy. The narrow Hα with extended velocity (the bottom panel) does not have any obvious strong emission corresponding to the spatial location of iPTF13ehe (south of the center of the host galaxy). We therefore conclude that the narrow Hα line is most likely from the host galaxy of iPTF13ehe.

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The final piece of evidence supporting this conclusion is discussed in Section 4.2 below, where we argue that the H-rich CSM shell is likely to be mostly neutral because of the shell mass limit constraint by the Thomson optical depth ≤1 in the nebular phases.

For the remainder of this section, we present our analysis of the broad Hα component. Figure 7 presents the first nebular spectrum (${t}_{\mathrm{rest}}^{\mathrm{exp}}$ = +322 days) in comparison with the spectrum of SN2007bi taken at a similar phase. The strongest feature in the iPTF13ehe spectrum is its broad Hα, whereas that of SN2007bi has no traces of either Hα or Hβ from the supernova. This broad Hα line is likely produced when the iPTF13ehe ejecta run into a H-rich CSM and the kinetic energy is converted into thermal emission, a part of which escapes in the Hα and Hβ lines. It is intriguing that the emission from the [O i] 6300,6363 Å is very weak or absent, whereas this feature is very strong in SN2007bi. The cooling ejecta from iPTF13ehe also produced emission such as broad [Mg i] 4570 Å, a possible blend of Na 5890 Å + He I 5876 Å lines, and a blend of broad Fe ii 5169, 5261, 5273, 5333 Å. The weak broad feature around 4861 Å could be Hβ, with a similar physical origin as that of Hα.

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We note that the host galaxy starlight was subtracted from the observed spectra as follows. The host spectrum is constructed using a Bruzual–Charlot model (Bruzual & Charlot 2003), constrained to have the same star formation rate (SFR) measured from the narrow [O ii] 3727 Å from the host galaxy. The continuum decrement around 4000 Å is also used to match the model host spectrum. Our data is inadequate for determining if a fraction of the narrow Hα emission line is from the supernova.

We fit Gaussian profiles to both the broad and narrow Hα lines in the spectra, shown in Figure 8. The broad component has an FWHM between 3870 and 4850 km s⁻¹, which did not change much between 2014 December 17 and 2015 January 22. The integrated Hα fluxes are 5.2–3.8 × 10⁻¹⁶ erg s⁻¹ cm⁻², implying ${L}_{H\alpha }$ = 2.2–1.6 × 10⁴¹ erg s⁻¹, decreasing by 20% over a period of 60 days. We also measured the velocity shifts between the narrow and broad components, δv ∼ 410 and 230 km s⁻¹ for the LRIS spectra taken on 2014 December 17 and 2015 January 22.

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Finally, we conclude that the broad component is from the SN ejecta interaction with an H-rich CSM, similar to the intermediate-velocity-width Balmer lines frequently observed among SN IIn. The ∼4000 km s⁻¹ of the broad component indicates the thermal, random motion of the shock-ionized H atoms. We assume that the velocity difference between the broad and narrow component, ∼300 km s⁻¹, is the H-shell systematic velocity. This assumption affects the calculations of the shell radius and when the shell is ejected by the progenitor star. We speculate that the velocity shell cannot be much larger than a few 100 km s⁻¹, otherwise the wavelength center of the broad component would be significantly shifted from the host galaxy redshift. However, it is possible that the shell could move slower than what we assumed.

3.2.3. Nebular Emission Models

A nebular emission model was computed for two epochs of the iPTF13ehe spectra (2014 December 17 and 2015 January 22) using the code described in Mazzali et al. (2007). The code computes the heating of SN ejecta following the deposition of γ-rays and positrons from ⁵⁶Ni and ⁵⁶Co decay, balancing this by cooling via line emission in non-local thermodynamic equilibrium (NLTE).

In the case of iPTF13ehe, given the low S/N of the nebular spectra, line profiles could not be modeled, so a one-dimensional (1D) version of the code was used. The model spectra are compared with the observed data in Figure 9. Line width was matched to an ejecta velocity inside which all emission was assumed to occur. This velocity is quite low, 4000 km s⁻¹. The intensity of the Fe emission in the blue was used to determine the mass of ⁵⁶Ni, which also depends on cooling from other species. The [O i] 6300,6363 Å emission line is unusually weak in iPTF13ehe in comparison with the nebular spectra of SN2007bi and other SN Ic events. Ignoring all material at velocities above 4000 km s⁻¹, we obtain a reasonable match to the spectra (excluding Hα) for M(⁵⁶Ni) ∼ 2.5 M_⊙. This would correspond to a progenitor star of ∼95 M_⊙ in the models of Heger & Woosley (2002). However, the oxygen mass in our model is only 13 M_⊙, much less than the predicted value of 45 M_⊙ (Heger & Woosley 2002). Although more oxygen may be located at velocities above 4000 km s⁻¹ and may not be significantly excited by radiation coming from the core. It is possible that a significant part of the CO core of the star was lost before the explosion. This is clearly in contradiction to the Heger & Woosley (2002) model prediction. In addition, we have kept the masses of Si and S at the values of the 95 M_⊙ model of Heger & Woosley (2002; 20 and 8 M_⊙, respectively). This leads to strong cooling lines of these elements, which are not in contradiction with the optical data but are predicted to be very strong in the near-infrared, which is unobserved. Should these elements be reduced in mass, the ⁵⁶Ni mass would also be reduced. This naive comparison of model and data is to illustrate the obvious limitations and contradictions in the existing models of SLSNe. In the case of iPTF13ehe, the lack of any [O i] 6300 Å emission imposes a challenge to the models assuming massive progenitors.

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The LCs and spectra provide measurements of ${t}_{\mathrm{rise}}^{\mathrm{peak}},$ ${L}_{\mathrm{bol}}^{\mathrm{peak}},$ and v_ej, which allow us to make the following physical parameter estimates.

We begin with the supernova ejecta mass M_ej. The SN rise time is determined by how long it takes photons to radiatively diffuse out to the emitting surface. This radiative diffusion time t_diff can be derived based on electron Thomson scattering and expressed in terms of M_ej, t_diff = $f(\kappa {M}_{\mathrm{ej}}/{Rc}),$ where f = $\frac{9}{4{\pi }^{3}}$ and κ is mass opacity in cm² g⁻¹ (Arnett 1996; Padmanabhan 2000). The characteristic timescale for a supernova LC is defined as t_c = $\sqrt{2{t}_{h}{t}_{\mathrm{diff}}},$ where t_h is hydrodynamic scale, $R/{v}_{\mathrm{ej}}.$ Thus, t_c = $\sqrt{2f\kappa {M}_{\mathrm{ej}}/(c\times {v}_{\mathrm{ej}})}.$

This equation is the basis for an empirical scaling relation, ${t}_{\mathrm{rise}}^{\mathrm{rest}}$ $\;\propto \;$t_c$\;\propto \;$ $\sqrt{({M}_{\mathrm{ej}}/{v}_{\mathrm{ej}})}.$ Using this relationship and another well-studied Type Ib event, SN 2008D, with ${v}_{\mathrm{ej}}\;=\;$ 10,000 km s⁻¹, ${t}_{\mathrm{rise}}^{\mathrm{rest}}$ = 19 days, and M_ej = 7 M_⊙ (Mazzali et al. 2008), we derive M_ej(iPTF13ehe) = 173 M_⊙. Using t_c ≃ ${t}_{\mathrm{rise}}^{\mathrm{rest}},$ we calculate M_ej ∼ 67–219 ${M}_{\odot }$ assuming κ = 0.1 cm² g⁻¹ for an ejecta composed of heavy elements. The mass opacity (κ) due to electron scattering is determined by the ionization fractions of C, O, and Fe, as well as line opacity. For ejecta composed of heavy elements, various studies have used κ in the range of (0.01–0.2) cm² g⁻¹ (Arnett 1982; Bersten et al. 2011, 2012). The M_ej estimate is quite sensitive to κ and t_c, which are very uncertain with our current knowledge. Regardless of the large uncertainty in M_ej, we can conclude that the exploding core mass of iPTF13ehe is >67 M_⊙. This implies that the progenitor star of iPTF13ehe must be very massive.

The second physical parameter is the supernova kinetic energy, E_kin = $\frac{1}{2}{M}_{\mathrm{ej}}{v}_{\mathrm{ej}}^{2}$ = 0.5 × (67–220) M_⊙ × (13,000)²km s⁻¹ = (1–4) × 10⁵³ erg. The implied kinetic energy E_kin to the ejecta mass M_ej ratio in units of 10⁵¹ erg per 1 M_⊙ is ∼1.6. Comparing to the lower limit on the supernova radiative energy, ${E}_{\mathrm{rad}}\;\geqslant \;$ 0.93 × 10⁵¹ erg, this implies that <1% of E_kin is being converted into visible radiation. Most of the kinetic energy from this extreme power explosion has gone into expansion.

Our inferred E_kin is extreme in comparison with typical values observed among Type Ia and core-collapse SNe. Specifically, for a normal core-collapse supernova, the total gravitational energy available from forming a neutron star is of an order of 10⁵³ erg, and a very large fraction of that is lost to free-streaming neutrinos. So it is difficult to explain within a standard core-collapse model how iPTF13ehe could get such an extremely large kinetic energy. This imposes a challenge to models that use magnetars as energy sources. One possible mechanism for producing such a large explosion energy is PPISN or PISN models for the most massive stars from Heger & Woosley (2002). However, we note that it is also possible that the ejecta mass M_ej is overestimated by a factor of (5–10). As discussed earlier, the commonly used methods have serious limitations, and it is not clear how to measure ejecta masses more accurately for SLSN events.

The third physical parameter is the ⁵⁶Ni mass. If the power source for the observed luminous emission is radioactive decay of ⁵⁶Ni, how much of this material would be required? The bolometric peak luminosity, 1.3 × 10⁴⁴ erg s⁻¹, can constrain the amount of ⁵⁶Ni and ⁵⁶Co, based on L_bol = 8 × 10⁴² erg s⁻¹$\;\times \;{M}_{\mathrm{Ni}}/{M}_{\odot }$ (Arnett 1982; Smith et al. 2007). The inferred M_Ni is 16 M_⊙. Katz et al. (2013) discussed another method, ${\displaystyle \int }_{0}^{t}Q({t}^{\prime }){t}^{\prime }{{dt}}^{\prime }={\displaystyle \int }_{0}^{t}{L}_{\mathrm{bol}}({t}^{\prime }){t}^{\prime }{{dt}}^{\prime },$ with t $\gg$ 40 days, Q as the radioactive heating function (⁵⁶Ni$-\gt {\;}^{56}\mathrm{Co}$ $-\;\gt$ Fe), and can be expressed as $Q(t)=3.9\times {10}^{10}{e}^{-t/7.6e+5}$ + 6.78 × 10⁹$({e}^{-t/9.59e+6}$ $-\;{e}^{-t/7.6e+5}).$ All are in cgs units. Using this relation and the r-band absolute magnitude LC, we derive a lower limit on M_Ni of 13 M_⊙. These numbers are much larger than those of any classical supernovae. The calculations assuming ${}^{56}\mathrm{Ni}$ as the single power source yield much larger estimates than the prediction from our nebular emission model. This may indicate that multiple power sources could be in play for producing the iPTF13ehe emission. Radioactive decay could be one of them, and the total ⁵⁶Ni mass does not have to be so extremely large.

Finally, if the emission at the peak luminosity is considered to be a blackbody, the energy can be estimated as E_rad = $\frac{4\pi }{3}{R}_{\mathrm{ph}}^{3}$ $\;\times \;{{aT}}_{\mathrm{eff}}^{4},$ where R_ph is the photospheric radius at the peak luminosity, and T_eff is the blackbody effective temperature. As discussed in Section 3.2.1, T_eff is quite low, 7000 K. With the lower limit on E_rad, this equation implies that the size of the photosphere is R_ph ∼ 1.8 × 10¹⁶ cm, a very large radius at peak luminosity compared to that of normal SNe. This is mostly due to the low value of T_eff. It is not clear why some SLSNe-I seem to have much cooler temperatures at similar early phases than others.

The key new result we present here is the discovery of a broad Hα line with a velocity width of 4000 km s⁻¹ in the late-time spectra. The question is how this emission might be produced. The simple explanation is the interaction of the SN ejecta with a H-rich CSM, as commonly seen in SLSN-II spectra. However, the key difference here is that this H-rich material is in a shell, located at a distance much further away from the explosion site. The reason for a discrete shell rather than continuous CSM material such as wind-driven mass loss is because the early-time spectra do not show any signatures of the ejecta-CSM interaction. This interaction only appears at late times.

At the rest-frame −9 days pre-peak, the SLSN ejecta velocity was 13,000 km s⁻¹. Let us take the estimated explosion date as 2456575.6 days (the latest explosion date from the exponential fit). The first detection of Hα is on JD = 2457008.5, giving an interval in the rest-frame ${\rm{\Delta }}{t}_{\mathrm{rest}}$ = 322 days. As Figure 2 shows, there is no spectroscopy between +13 and +251 days (post-peak, rest-frame), therefore the precise time when Hα emission lines first appear cannot be determined. The date of the third spectrum without Hα (JD = 2456689.5) can be used to set the lower limit on ${\rm{\Delta }}{t}_{\mathrm{rest}}$ = 85–322 days. In practice, the lower limit value of 85 days is unlikely. In the rest of the calculations we use only ${\rm{\Delta }}{t}_{\mathrm{rest}}$ = 332 days for simplicity. Assuming that the ejecta did not slow down significantly before running into the CSM shell, the approximate distance traveled by the ejecta is R_rest = ${v}_{\mathrm{ej}}\times {\rm{\Delta }}{t}_{\mathrm{rest}}$ = 4e + 16 cm. The broad Hα line has a width of ∼4000 km s⁻¹, and is separated from the narrow Hα by roughly (400–230) km s⁻¹. We interpret the 4000 km s⁻¹ line width as the thermal motion of shock-ionized hydrogen atoms, and the velocity shift of ∼300 km s⁻¹ is v_csm, the CSM shell velocity. We can set a limit on the timescale, ${\rm{\Delta }}t,$ when this material was ejected by the progenitor star, using ${\rm{\Delta }}t\times {v}_{\mathrm{csm}}$ = R_rest, giving ${\rm{\Delta }}{t}^{\mathrm{rest}}\leqslant 40$ years. This is an upper limit since the CSM shell could initially have had a higher speed.

Let us consider an H-rich CSM shell with a radius of 4 × 10¹⁶ cm surrounding iPTF13ehe. This naturally begs two questions: (1) is this material from the progenitor star or a part of the galactic ISM? and (2) why does this CSM not produce any observable signatures—either in emission or absorption—in the early spectra when the UV photons from the early explosion would have interacted with this material?

This H-rich CSM shell is only 4 × 10¹⁶ cm from the location of the progenitor star, which is several orders of magnitudes smaller than the typical size of a H ii region. Therefore, this H-rich CSM is probably not a part of the galactic ISM, but rather more likely produced by either wind mass loss or ejection due to some other mechanism, such as pulsational pair instability, occurring in massive stars (>67 M_⊙).

As early as—days pre-peak, the follow-up spectra reveal strong supernova signatures, which implies that at this phase, the CSM shell must be optically thin to visible photons. The fact that we also do not detect any narrow hydrogen recombination lines from the H-rich CSM shell, commonly seen in the spectra of SN IIn, could suggest two possibilities. First is that this H-shell had already become neutral when the first spectrum was taken. Second is that this H-shell is ionized, but the early spectra are dominated by the supernova light, and the exposure times are too short to detect any H-recombination signals from this ionized shell. However, as shown below, this second scenario is unlikely because of a short recombination timescale.

When this CSM shell was initially ejected by the progenitor star 50 years ago, the medium was very likely fully ionized. This ionized state was maintained by the heat sources from the progenitor star, and probably continued to the early phase of the supernova explosion. However, when the supernova photosphere cools down, there are no more heat sources and the ionized H atoms in this shell will recombine. This recombination timescale must be less than 62 days (rest-frame, from the explosion date of 2456575.6), i.e., the recombination is completed before the date of the first optical spectrum. Assuming Case B recombination, the recombination timescale is ${t}_{\mathrm{rec}}\sim {10}^{13}/n$ s < 62 days, with n being the volume density, and n = ${M}_{\mathrm{csm}}/4\pi {m}_{H}{R}_{\mathrm{rest}}^{2}w,\;$R_rest = 4 × 10¹⁶ cm (radius of the shell), m_H as the hydrogen mass, and w as the width of this shell. Assuming that the shell width w is only 10% of the shell radius, the above equations yield ${M}_{\mathrm{csm}}\gt 0.03{M}_{\odot }.$

As shown below, the shell mass M_csm is constrained to be <30 M_⊙. At the upper limit of 30 M_⊙, the H-recombination timescale t_rec ∼ 10⁵ s. Thus, at the early phases of the spectral observations, the H-shell is already neutral.

Once this CSM shell becomes neutral, without any other heat sources, it stays neutral until the SN ejecta run into this shell. The shock front generates high-energy photons that ionize the hydrogen atoms again. These ionized H atoms recombine, and produce the observed Hα and Hβ emission lines. The important question is if this shock-ionized shell (or partially ionized shell) is optically thick to Thomson scattering. The fact that the late-time spectra do display SN spectral signatures, such as [Mg i] 4570 Å, suggests that this shock-ionized shell is probably not optically thick to Thomson scattering. Other evidence that the CSM shell is not extremely dense comes from the SWIFT soft X-ray observation taken on 2014 December 23, yielding a 3σ limiting luminosity of 3 × 10⁴³ erg s⁻¹. In addition, the ejecta interaction with extremely dense CSM would produce elevated continuum emission, which is not observed in the late-time absolute g-band LC.

So if the shock-ionized CSM shell is optically thin, we have ${\tau }_{\mathrm{thomp}}=\kappa \rho w$ $\;\leqslant \;1,$ where ρ is the density, and w is the width of this CSM shell. With $\rho =\frac{{M}_{\mathrm{csm}}}{4\pi {R}^{2}w},$ the above equation is simplified as ${M}_{\mathrm{csm}}\leqslant \frac{4\pi {R}^{2}}{\kappa },$ independent of the width of this shell. Assuming κ = 0.34 cm²/g for an H-rich medium, we have ${M}_{\mathrm{csm}}\leqslant 30{M}_{\odot }.$ This mass value corresponds to a volume number density and a column density of 4 × 10⁸ cm⁻³ and 10²⁴ cm^−2, respectively. We predict that this shell should produce strong Lyα absorption features if any UV spectra were taken. There should not be much Hα absorption because without an external excitation source, most of the H atoms are in the n = 1 ground state. To have a significant population in the n = 2 state with collisional excitation, it would require the gas to have a very high temperature, such that ${KT}\sim {\rm{\Delta }}{E}_{21}=10$ ev ∼ 100,000 K. The shell around iPTF13ehe is unlikely to have such a high temperature.

With the estimated M_csm, we can calculate the kinetic energy of this CSM shell, $\frac{1}{2}{M}_{\mathrm{csm}}{v}_{\mathrm{csm}}^{2}=2\times {10}^{49}$ erg s⁻¹. Here we assume that the CSM shell systematic velocity is ∼300 km s⁻¹, roughly the velocity shift observed between the broad and narrow Hα lines. The initial v_csm could be larger. The energetics of this shell is within the predictions of PPISN models (Woosley et al. 2007).

We note that the CSM shell may be partially ionized. This would lead to higher M_csm value and suggests that collisional excitation might be important for producing Hα. The shock heated CSM shell with Balmer dominated emission is a complex system. The broad Hα emission is likely produced by charge exchange between fast moving neutral H atoms (Chevalier et al. 1980; Morlino et al. 2013). Better quantitative estimates will need to apply the theory of Balmer dominated emission shock. This is beyond the scope of this paper.

Detection of a H-rich CSM shell around a H-poor SLSN is a natural prediction from the PPISN model (e.g., Woosley et al. 2007; Waldman 2008). Table 1 in the supplemental material from Woosley et al. (2007) illustrates that in the cases of He-core masses greater than 53 M_⊙, the time interval between the first and the second instability pulses could be as long as 6 × 10⁹ s, and the subsequent instabilities would happen more frequently. iPTF13ehe lost its H-shell about 40 years (10⁹ s, rest) before the SN explosion. In addition, the kinetic energy of this CSM shell is about 2 × 10⁴⁹ erg s⁻¹, similar to what is predicted in Table 1 of Woosley et al. (2007). Both the timescale and energetics support the hypothesis that iPTF13ehe could be a PPISN candidate. In this scenario, iPTF13ehe started with a progenitor star with an initial mass of >70 M_⊙, ejected about <30 M_⊙ from the H envelope about 40 years ago (rest), during the first episode of pulsational pair instability. Following the first mass ejection, there is at least one, possibly more pulsational pair instabilities before the supernova explosion. The later ejected H-poor CSM shell tends to be faster and more energetic than the previous one, naturally leading to shell-shell collision (Woosley et al. 2007). The reason for possible additional instability pulses is that the H-poor CSM shell-shell collision could provide one of the power sources for the observed LC and spectral features.

However, this PPISN model could have one potential problem. The highest kinetic energy generated by these pulsational pair instabilities is predicted to be 8 × 10⁵⁰ erg, no more than 10⁵¹ erg. The relative kinetic energy between the 2nd and 3rd pulses would be even smaller. Therefore, even with the most efficient kinetic and thermal energy conversion, it may be hard to produce the peak radiative energy measured for iPTF13ehe (>9.3 × 10⁵⁰ erg). One solution proposed in Quimby et al. (2011) is that after several episodes of pulsational pair instabilities, the core undergoes supernova explosion. The ejecta interaction with the last H-poor CSM shell could provide a more energetic reservoir for powering the observed emission. This is derived from an earlier idea proposed for SLSNe-II by Woosley et al. (2007).

The second caveat regarding the PPISN model is that the spectra of iPTF13ehe do not show much [O i] 6300 Å emission in all of the phases for which we had data. The iPTF13ehe ejecta seems not to have much oxygen material. This is clearly in contradiction with the models calculated by Heger & Woosley (2002), which predict an oxygen-dominated core with the mass >50 M_⊙. Our estimated ejecta mass has a lower limit of 70 M_⊙, suggesting a very massive core. However, this calculation depends on the assumed value of opacity, κ. If adopting a higher value of 0.2, the ejecta mass would be a factor of two smaller. These uncertainties may suggest a less massive progenitor star that does not go through pulsational pair instabilities. For example, a luminous blue variable (LBV) could eject a massive H envelope from the progenitor star during its instability episode, like Eta Carina. Then a massive core-collapse model, such as the one proposed by Moriya et al. (2010), is needed to explain the energy output of iPTF13ehe.

With very low metallicity and rotation, a variation of the PPISN model could have a progenitor star with a much lower mass than the 95–150 M_⊙ predicted in the Woosley et al. (2007) study. As pointed out in the studies of Chatzopoulos & Wheeler (2012) and Yoon et al. (2012), low metallicity and rotating stars could undergo pulsational pair instabilities at initial stellar masses as low as ∼50–70 M_⊙. Our constraint on the iPTF13ehe progenitor mass is not very stringent; the lower limit is less than the initial mass of 95 M_⊙ predicted by the Woosley et al. (2007) model. If low metallicity and rotation are relevant, iPTF13ehe could be a PPISN candidate.

Finally, there is another alternative physical model, which was briefly mentioned in Woosley et al. (2007). A 95–150 M_⊙ star with rotation and magnetic torques would initially evolve in a similar fashion to one without rotation and magnetic field. It will undergo episodes of pulsational pair instability that eventually produce a C/O core with a mass in the range of 40–60 M_⊙. However, the difference is that the rotating star with magnetic torque can end up forming a neutron star with a fast spin-period of a few milliseconds and a magnetic field strength of 10¹⁵ G—i.e., a magnetar (Duncan & Thompson 1992; Heger et al. 2005). The spin-down of a magnetar can provide sufficient power for a SLSN, as shown in several studies (Kasen & Bildsten 2010; Inserra et al. 2013; Nicholl et al. 2013). For iPTF13ehe, it is possible that its massive progenitor star experiences several episodes of pulsational pair instabilities, ejecting several shells, and the final supernova explosion leaves behind a magnetar. The power sources for the observed LC and early-time H-poor spectra could well be a combination of a magnetar and the collision between H-poor CSM shells. The magnetar scenario clearly needs more scrutiny in the future.

If PPISN is a possible model to explain iPTF13ehe, a related question is how common such an event is among all SLSNe-I. This question is difficult to answer because it depends on when spectroscopic observations are taken. Of the 23 SLSNe-I at z < 0.4 PTF discovered during 2009–2013, 13 events have at least 1 spectrum taken after 100 days post-peak. Of these 13 events, we found 2 cases with Balmer emission lines in the late-time spectra. The second case is PTF10aagc, an H-poor SLSN at z = 0.207. Figure 10 shows the spectra taken at the phase of +75 days post-peak (rest-frame), revealing a broad Hα and the corresponding weak, but detected Hβ. PTF10aagc may be another case of a SLSN-I with ejecta interaction with a H-rich CSM at late times, although in many ways PTF10aagc is different from iPTF13ehe. Detailed discussion of this object is included in R. M. Quimby et al. (2015, in preparation). Our data suggest that at least 15% of all SLSNe-I have late-time (>100 days post-peak) Balmer emission lines from ejecta interactions with H-rich CSM. It is possible that much higher fractions of SLSNe-I would eventually show late-time spectral signatures of interaction with H-rich CSM. However, the answer must depend on the mass loss mechanism of the SLSN-I progenitor stars.

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