LSQ14bdq: A TYPE Ic SUPER-LUMINOUS SUPERNOVA WITH A DOUBLE-PEAKED LIGHT CURVE

LSQ14bdq was discovered by La Silla QUEST (LSQ; Baltay et al. 2013), at coordinates $\alpha ={10}^{{\rm{h}}}{01}^{{\rm{m}}}41\buildrel{\rm{s}}\over{.} 60$, $\delta =-{12}^{{\rm{o}}}22\prime 13\buildrel{\prime\prime}\over{.} 4$ (J2000.0), in images taken on April 5.1 UT (though earlier detections exist; Section 2.2). It was classified by Benitez et al. (2014), as part of the Public ESO Spectroscopic Survey of Transient Objects (PESSTO; Smartt et al. 2014), as a SLSN Ic. This spectrum (1500 s) was taken on 2014 May 4.9 UT with the ESO 3.58 m New Technology Telescope, using EFOSC2 and Grism#13, and was followed by a longer exposure (2 × 1800 s) on the next night. A third spectrum was taken using Grism#11 (2400 s), on 2014 May 7.0 UT. These were reduced using the PESSTO pipeline, applying bias-subtraction, flat-fielding, wavelength and flux calibration and telluric correction (Smartt et al. 2014). The absolute fluxes were matched to contemporaneous photometry. PESSTO data are available from the ESO archive¹⁸ or WISeREP¹⁹ (Yaron & Gal-Yam 2012).

Figure 1 shows the spectrum summed over these three nights. The Grism#11 spectrum (resolution 13.8 Å) shows interstellar Mg ii $\lambda \lambda$ 2795.528, 2802.704 absorption, giving a redshift of z = 0.345 from Gaussian fits. We estimate that the mean rest-frame phase of the combined spectrum is 19 d before maximum brightness (Section 2.2). Also shown are SLSNe Ic PTF12dam (Nicholl et al. 2013) and PTF09cnd (Quimby et al. 2011). The broad absorption features in LSQ14bdq are ubiquitous in such objects before maximum light. The O ii lines are a defining feature of the class (Quimby et al. 2011) and the deep Mg ii absorption matches that in PTF09cnd and other objects with near-ultraviolet spectroscopy (e.g., Chomiuk et al. 2011).

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The observed light curve of LSQ14bdq is shown in Figure 2. The rise from 2014 March 22.1 UT was measured with the automated LSQ pipeline (Baltay et al. 2013), employing point-spread function (PSF) fitting forced photometry, and are calibrated to SDSS r (AB system). Inspection of pre-discovery LSQ data showed clear variable flux at the SN position before this first pipeline detection. Applying manual PSF photometry (using SNOoPY)²⁰ revealed that this was an early peak prior to the main rise. Non-detections (Table 1) suggest the explosion occurred on MJD = 56721 ± 1, assuming a smooth rise to the first peak. A stack of all LSQ images from 2012–2013 shows no host galaxy to a limiting magnitude of r = 24.1, hence image subtraction is unimportant.

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Table 1.  Observed Photometry of LSQ14bdq

Date	MJD	Phasea	g	r	i	z	Telescope
2014 Mar 02	56718.0	−66.2	⋯	>22.85	⋯	⋯	LSQ
2014 Mar 04	56720.0	−64.7	⋯	>22.40	⋯	⋯	LSQ
2014 Mar 06	56722.0	−63.2	⋯	21.78 (0.32)	⋯	⋯	LSQ
2014 Mar 08	56724.0	−61.7	⋯	21.24 (0.20)	⋯	⋯	LSQ
2014 Mar 10	56726.0	−60.2	⋯	21.08 (0.32)	⋯	⋯	LSQ
2014 Mar 12	56728.0	−58.7	⋯	21.16 (0.25)	⋯	⋯	LSQ
2014 Mar 14	56730.0	−57.3	⋯	20.99 (0.23)	⋯	⋯	LSQ
2014 Mar 18	56734.0	−54.3	⋯	22.04 (0.08)	⋯	⋯	LSQ
2014 Mar 20	56736.1	−52.7	⋯	22.05 (0.28)	⋯	⋯	LSQ
2014 Mar 22	56738.1	−51.2	⋯	22.21 (0.21)	⋯	⋯	LSQ
2014 Mar 24	56740.1	−49.7	⋯	22.21 (0.03)	⋯	⋯	LSQ
2014 Mar 26	56742.1	−48.3	⋯	22.06 (0.08)	⋯	⋯	LSQ
2014 Mar 28	56744.1	−46.8	⋯	21.55 (0.16)	⋯	⋯	LSQ
2014 Mar 30	56746.1	−45.3	⋯	21.44 (0.10)	⋯	⋯	LSQ
2014 Apr 03	56750.1	−42.3	⋯	21.05 (0.02)	⋯	⋯	LSQ
2014 Apr 05	56752.1	−40.9	⋯	20.84 (0.15)	⋯	⋯	LSQ
2014 Apr 07	56754.0	−39.4	⋯	20.67 (0.08)	⋯	⋯	LSQ
2014 Apr 09	56756.1	−37.9	⋯	20.47 (0.03)	⋯	⋯	LSQ
2014 Apr 13	56760.1	−34.9	⋯	20.18 (0.06)	⋯	⋯	LSQ
2014 Apr 15	56762.1	−33.4	⋯	20.12 (0.03)	⋯	⋯	LSQ
2014 Apr 17	56764.0	−31.9	⋯	19.93 (0.05)	⋯	⋯	LSQ
2014 Apr 19	56766.0	−30.5	⋯	19.88 (0.02)	⋯	⋯	LSQ
2014 Apr 21	56768.0	−28.9	⋯	19.89 (0.07)	⋯	⋯	LSQ
2014 Apr 23	56770.0	−27.5	⋯	19.74 (0.01)	⋯	⋯	LSQ
2014 Apr 25	56772.1	−25.9	⋯	19.71 (0.05)	⋯	⋯	LSQ
2014 Apr 28	56775.5	−23.4	⋯	19.64 (0.19)	⋯	⋯	PS1
2014 May 06	56783.1	−17.8	19.55 (0.09)	19.35 (0.12)	19.45 (0.05)		NTT
2014 May 07	56784.7	−16.6	19.29 (0.11)	19.31 (0.20)			LCOGT
2014 May 12	56789.9	−12.7	19.27 (0.04)	19.26 (0.12)	19.18 (0.06)	19.48 (0.12)	LT
2014 May 20	56797.9	−6.8	19.27 (0.04)	19.16 (0.02)	19.16 (0.06)	19.40 (0.04)	LT
2014 Nov 23	56984.2	131.8	⋯	21.15 (0.23)	⋯	⋯	LSQ
2014 Nov 23	56984.3	131.8	⋯	20.99 (0.10)	20.89 (0.06)	⋯	NTT
2014 Nov 27	56988.2	134.7	⋯	21.05 (0.24)	⋯	⋯	LSQ
2014 Nov 28	56989.2	135.5	⋯	21.36 (0.30)	⋯	⋯	LSQ
2014 Dec 18	57009.2	150.3	⋯	21.27 (0.33)	⋯	⋯	LSQ
2014 Dec 20	57011.5	152.0	⋯	21.51 (0.24)	⋯	⋯	PS1
2014 Nov 23	57024.2	161.5	⋯	21.78 (0.38)	⋯	⋯	LSQ
2015 Jan 02	57033.2	168.2	⋯	21.65 (0.23)	⋯	⋯	LSQ
2015 Jan 20	57042.0	174.3	⋯	22.16 (0.20)	⋯	⋯	PS1
2015 Feb 12	57065.3	192.0	23.29 (0.11)	22.41 (0.04)	22.30 (0.08)	22.00 (0.17)	GROND
2015 Feb 26	57079.2	202.4	23.74 (0.14)	22.89 (0.13)	22.82 (0.31)	22.79 (0.41)	NTT
2015 Mar 13	57094.1	213.5	24.35 (0.13)	23.43 (0.16)	22.87 (0.24)	22.45 (0.32)	NTT
Host (2012–2013 stack)				>24.08			LSQ
K-correctionsb			${K}_{g\to u}$	${K}_{r\to g}$	${K}_{i\to r}$	${K}_{z\to i}$
Phase < 0 (LSQ14bdq spectrum, −19d)			−0.30	−0.32	−0.49	−0.38
Phase > 0 (PTF12dam spectrum, +171d)			−0.22	−0.16	−0.18	−0.20
Near-infrared (Vega system)			J	H	K
2015 Feb 12	57065.3	192.0	20.70 (0.17)	>20.03	>18.39		GROND

Notes.

^aRest-frame days relative to the estimated date of r-band maximum, MJD = 56807. ^bDefined by $m=M+\mu +K$.

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We obtained multicolor imaging using EFOSC2, the 2.0 m Liverpool Telescope and Las Cumbres Observatory Global Telescope 1 m network. PSF magnitudes were calibrated using a sequence of local field stars, themselves calibrated against standard fields on photometric nights. LSQ14bdq set for the season just before reaching maximum brightness. Subsequent data are a combination of PESSTO, LSQ, Pan-STARRS1 (PS1; Magnier et al. 2013), and GROND (Greiner et al. 2008) images. The PS1 data were taken in the ${w}_{{\rm{P}}1}$-band (effectively a gri composite; Tonry et al. 2012) from the Pan-STARRS NEO Science Consortium survey (Huber et al. 2015), and also calibrated to r.

We converted observed r-band magnitudes to rest-frame g-band for comparison with other SLSNe (at this redshift, observed $g,r,i,z$ are similar to rest-frame $u,g,r,i$). The K-correction before peak is calculated from synthetic photometry on the LSQ14bdq spectrum (${K}_{r\to g}\;\simeq \;-0.3$). As we only have one spectrum, our post-peak data use a K-correction calculated in a similar manner, but from the spectrum of PTF12dam at +171 d (Nicholl et al. 2013). LSQ14bdq has a broad light curve like PTF12dam. A polynomial fit suggests ${M}_{g}=-21.96$ at maximum light. The initial peak (${M}_{g}=-20.01$) is much faster, with a rise of 5 days and a total width of ∼15 days.

Leloudas et al. (2012) presented pre-rise data for SN 2006oz with multi-color detections. Figure 3 shows that the two are qualitatively similar. The rise to peak is not as pronounced as for LSQ14bdq, although time-sampling was sparser. Leloudas et al. (2012) suggested a luminosity plateau powered by oxygen-recombination in extended CSM. Of the other SLSNe with strict explosion constraints, SN 2011ke (Inserra et al. 2013) shows a similar rise to SN 2006oz, but non-detections shortly before discovery limit any early peak to be fainter than those observed for LSQ14bdq and SN 2006oz.

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We constructed the bolometric light curve of LSQ14bdq in two steps. First we integrated the flux in the rest-frame u- to i-bands, following the procedure described in Inserra et al. (2013). Before −20 d, we caution that points are derived using the earliest available color information. To estimate the full bolometric light curve, we take the fractional flux outside of this range to be the same as for PTF12dam (Nicholl et al. 2013; Chen et al. 2014). This seems reasonable, at least in the late-time NIR, from the J-band detection at 192 days (Table 1). Both the observed ugri-pseudobolometric and the estimated full bolometric light curve are shown in Figure 2.

We can reproduce the main peak with models powered by a central engine (we take a magnetar as representative) or by ejecta–CSM interaction. For details of the models, see Inserra et al. (2013), Chatzopoulos et al. (2012), and Nicholl et al. (2014). The magnetar fit has magnetic field $B=0.6\times {10}^{14}\;$ G, spin period $P=1.7\;\mathrm{ms}$, and diffusion time ${\tau }_{m}=90$ d. We have fixed the time of explosion to coincide with the first detection on the precursor peak. The CSM model has ejected mass ${M}_{\mathrm{ej}}$ $=\;30.0\;$ ${M}_{\odot }$, CSM mass ${M}_{\mathrm{CSM}}$ $=\;16.0\;$ ${M}_{\odot }$ (assuming $\kappa =0.2\;{\mathrm{cm}}^{2}\;{{\rm{g}}}^{-1}$), density ${\rho }_{\mathrm{CSM}}=3.0\times {10}^{-13}\;{\rm{g}}\;{\mathrm{cm}}^{-3}$, and explosion energy ${E}_{{\rm{k}}}=5.0\times {10}^{51}\;$ erg.

We also compare to the brightest PISN model of Kasen et al. (2011; a 130 ${M}_{\odot }$ bare helium core), which reproduces the peak luminosity. However, the rise-time is discrepant: the well-constrained main rise of LSQ14bdq lasts for 50 days, whereas the PISN model rises for over 100 days, and declines more slowly than LSQ14bdq. We therefore reach the same conclusion as Nicholl et al. (2013) and McCrum et al. (2014), who found that the rise-time ruled out PISN models for two slowly declining SLSNe, PTF12dam and PS1-11ap.

The first scenario we investigate for the early peak is an initially normal SN, powered by the radioactive decay of ⁵⁶Ni, before the mechanism powering the super-luminous second peak kicks in. We compare our early light curve to ⁵⁶Ni-powered SNe (core-collapse and thermonuclear) in Figure 3, choosing filters with similar effective wavelengths. As the late-time spectra of Type Ic SLSNe closely resemble SNe Ic, we first compare to SN 1994I, a well-observed object with a narrow light curve, suggesting ${M}_{\mathrm{ej}}$ $\;\lesssim 1\;$ ${M}_{\odot }$ (Richmond et al. 1996). The width of the LSQ14bdq peak is slightly narrower, but comparable to SN 1994I. However, it is 2.3 magnitudes brighter. Using the Arnett (1982) model, as implemented by Inserra et al. (2013), we find that matching the photometry²¹ requires an almost pure ⁵⁶Ni ejecta of $\simeq 1\;$ ${M}_{\odot }$, which is difficult to produce with core-collapse SNe. SNe Ia produce $\approx 0.5$–1 ${M}_{\odot }$ of nickel, but comparing with SN 2005cf (Pastorello et al. 2007) shows that SNe Ia have light curves that are too broad. The fast rise of LSQ14bdq would necessitate a very large explosion energy, even for the lowest possible ejecta mass, ${M}_{\mathrm{ej}}$ = ${M}_{\mathrm{Ni}}$. A fit shows that we require ${E}_{{\rm{k}}}=25$ B, where 1 B(Bethe)$\;=\;{10}^{51}\;$erg. Because complete burning of 1 ${M}_{\odot }$ of carbon/oxygen to nickel liberates only ∼1 B, an additional energy source is required. Thus, if the early peak is "a supernova in itself," it cannot be a normal ⁵⁶Ni-powered event.

In Figure 4, we show an alternative scenario, comparing the early emission from LSQ14bdq to other SNe with two observed peaks. The basic light curve morphology of SNe 1987A, 1993J and 2008D has been interpreted as an initial cooling phase, releasing heat deposited by the shock wave, before a second peak is driven by delayed heating from ⁵⁶Ni (Shigeyama & Nomoto 1990; Woosley et al. 1994; Modjaz et al. 2009). The light curve of LSQ14bdq is qualitatively similar to these objects, suggesting that the light curve could be explained by a shock cooling phase, followed by internal reheating. While bolometric luminosity in the cooling phase should decline monotonically, single-filter light curves show maxima as the peak of the spectral energy distribution moves into and out of the optical.

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We fit the early rise using analytic approximations from Rabinak & Waxman (2011), giving the parameters in Figure 4. We use their blue supergiant (radiative envelope), red supergiant (convective envelope), and Wolf–Rayet models for SN 1987A, 1993J and 2008D, respectively. The progenitor radius, ${R}_{\star }$, determines the slope and duration of the rise, while the luminosity scale is set by both ${R}_{\star }$ and by the explosion energy per unit mass, ${E}_{{\rm{k}}}/{M}_{\mathrm{ej}}$. The values of ${R}_{\star }$ and ${E}_{{\rm{k}}}/{M}_{\mathrm{ej}}$ used to fit the literature objects are in line with previous estimates. As noted by Rabinak & Waxman (2011), the model assumptions begin to break down after a few days; we end the simulations at the cut-off time prescribed by their Equation (17). The model for SN 1993J is still rising slowly as it goes through the peak. The discrepancy with observations may be due to the very simple density profile assumed in the model. Detailed models of SN 1993J have had $\lesssim 0.1$ ${M}_{\odot }$ in the extended envelope, with most of its mass in the core.

To model LSQ14bdq, we set ${E}_{{\rm{k}}}/{M}_{\mathrm{ej}}$ $=\;C$ B/${M}_{\odot }$, where C is arbitrary. To try to break the degeneracy between ${E}_{{\rm{k}}}$ and ${M}_{\mathrm{ej}}$, we assume that the diffusion time during the early peak is the same as in our central-engine fit to the main peak. We neglect late-time kinetic energy input from the magnetar, ≈10⁵¹ erg for our model, because this is small compared to the initial energy found for the shock cooling, as will be seen below. We then have

$$\begin{eqnarray}&&{\tau }_{m}=\displaystyle \frac{1.05}{{(13.7c)}^{1/2}}{\kappa }^{1/2}{\left(\displaystyle \frac{{M}_{\mathrm{ej}}^{3}}{{E}_{{\rm{k}}}}\right)}^{1/4}=90\;\mathrm{days}.\end{eqnarray} \tag{ 1 }$$

For $\kappa =0.2\;{\mathrm{cm}}^{2}\;{{\rm{g}}}^{-1}$, this leads to

$$\begin{eqnarray}&&{M}_{\mathrm{ej}}=40.1\;{C}^{1/2}\;{M}_{\odot };\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{E}_{{\rm{k}}}=40.1\;{C}^{3/2}\;{\rm{B}}.\end{eqnarray} \tag{ 3 }$$

The uncertainty in ${\tau }_{m}$ (taking the range where ${\chi }^{2}\lt 2{\chi }_{\mathrm{min}}^{2}$) is $\sim 30\%$, meaning ${M}_{\odot }$ and ${E}_{{\rm{k}}}$ are constrained to within a factor of 2.

Figure 4 shows models for 3 progenitors: a Wolf–Rayet with ${R}_{\star }$ $=10$ ${R}_{\odot }$, and extended stars with ${R}_{\star }$ $=100,500$ ${R}_{\odot }$ (extended models are insensitive to the choice of radiative/convective envelope). For the compact model, we derive ${M}_{\mathrm{ej}}$ $\approx \;270\;$ ${M}_{\odot }$; depending on the precise mass, the implied progenitor should either explode as a PISN or collapse totally (hence invisibly) to a black hole (Heger & Woosley 2002), neither being consistent with the light curve. The inferred energy, ${E}_{{\rm{k}}}$ $\gt {10}^{54}$ erg, is also unrealistic.

An extended envelope (or wind; Ofek et al. 2010) is therefore a requirement in this scenario. The 100 ${R}_{\odot }$ model requires ${M}_{\mathrm{ej}}$ $\approx \;60\;$ ${M}_{\odot }$ and ${E}_{{\rm{k}}}$ $\approx \;150$ B. This energy is greater than the canonical neutron star gravitational binding energy of 10⁵³ erg (of which $\sim 1\%$ is normally accessible to power the explosion). The energy released in black hole-formation is higher than for neutron stars and could meet the requirement, if it could couple to the ejecta. A possible mechanism is an accretion disk, such as in the collapsar model (Woosley 1993) of gamma-ray bursts (GRBs). In this case the engine would be black hole accretion (Dexter & Kasen 2013) rather than a magnetar. This accretion engine has a characteristic power law, $L\propto {t}^{-n}$, similar to the magnetar, with ${n}_{\mathrm{mag}}=2$ and ${n}_{\mathrm{acc}}=5/3$. Therefore we would expect a similar ${\tau }_{m}$, and that Equations (2) and (3) would still hold.

The final model shown is for ${R}_{\star }$ $=\;500$ ${R}_{\odot }$. The inferred mass is ${M}_{\mathrm{ej}}$ $\approx 30\;$ ${M}_{\odot }$, with ${E}_{{\rm{k}}}$ $\approx 20$ B, which may also favor a black hole engine over a neutron star (it is similar to the kinetic energy in GRB-SNe), but not so definitively as in the more compact models. The radius is very large for a hydrogen-free star, but similar to SN 1993J, which had only a very diffuse hydrogen envelope, and by maximum light had evolved to resemble a SN Ib. For this model, the velocity, $v\sim \sqrt{10{E}_{{\rm{k}}}/(3{M}_{\mathrm{ej}})}=10,000$ km s⁻¹, is in good agreement with the observed spectrum.

An alternative scenario to consider is that the main peak arises from CSM interaction on scales of $\sim {10}^{4}$ ${R}_{\odot }$, as has been suggested for other SLSNe (e.g., Chatzopoulos et al. 2013). CSM fits for the main peak (Figure 2) require ${E}_{{\rm{k}}}/{M}_{\mathrm{ej}}$ ∼ 0.2 B/${M}_{\odot }$, lower than any of the shock cooling models shown in Figure 4. This is fairly inflexible for the CSM model, as ${E}_{{\rm{k}}}$ and ${M}_{\mathrm{ej}}$ are the two strongest drivers of the peak luminosity—e.g. models with ${E}_{{\rm{k}}}/{M}_{\mathrm{ej}}$ ∼ 0.4 B/${M}_{\odot }$ are too bright by about 0.5 dex (and rise too quickly). To reproduce the early emission with shock cooling and ${E}_{{\rm{k}}}/{M}_{\mathrm{ej}}$ ∼ 0.2 B/${M}_{\odot }$, we would need initial radius ${R}_{\star }$ $\;\sim \;2000$ ${R}_{\odot }$. This is uncomfortably large for any reasonable progenitor. However models have been proposed in which the cooling phase arises from shock breakout in an inner region of dense CSM rather than the progenitor envelope (Ofek et al. 2010); this may be a viable explanation for LSQ14bdq, but would require a novel CSM structure to get two distinct peaks.

A model was put forward by Moriya & Maeda (2012) to explain the data for SN 2006oz, in which a single CSM interaction produces a double-peaked light curve due to a sudden increase in CSM ionization (and hence opacity) in the collision. However, this model does not specify the source of the early emission before the collision, which for LSQ14bdq we have shown rises too steeply to be explained as a conventional SN. Multi-peaked light curves from interaction could also arise within the pulsational pair-instability model (Woosley et al. 2007). Here, multiple shells are ejected and could produce distinct interaction events with a range of luminosities and timescales. Suppose SN ejecta collide with an inner shell at the beginning of our observations, and the resulting merged ejecta/shell then hit an outer shell fifteen days later, generating the second peak. For a shell separation ${R}_{\mathrm{CSM}}\sim {10}^{15}$ cm (from our CSM fit and the Woosley et al. 2007 models), this would require ${v}_{\mathrm{ej}+\mathrm{inner}}\sim {10}^{4}$ km s⁻¹, which is similar to the observed line widths. This may provide a reasonable alternative to the shock cooling scenario, although the massive outer shell must also be accelerated to avoid showing narrow spectral lines. We note that the Woosley et al. (2007) models are much redder than our observations. Hence, further detailed modeling is needed to assess the viability of this scenario for LSQ14bdq.