PTF13efv—AN OUTBURST 500 DAYS PRIOR TO THE SNHUNT 275 EXPLOSION AND ITS RADIATIVE EFFICIENCY

Some supernova (SN) progenitors exhibit vigorous variability or possible explosive outbursts shortly (weeks to years) prior to the SN explosion (Foley et al. 2007; Pastorello et al. 2007; 2013, Fraser et al. 2013; Mauerhan et al. 2013; Ofek et al. 2013a, 2013b, 2014a; Margutti et al. 2014). SNe showing such activity are mostly of Type IIn (and Ibn), with spectra showing a blue continuum and hydrogen Balmer (and helium) emission lines (Schlegel 1990; Filippenko 1991, 1997; Pastorello et al. 2008; Kiewe et al. 2012). Moreover, it is possible that other classes of SNe also have precursors as well (e.g., Corsi et al. 2014; Strotjohann et al. 2015). Some of the SNe IIn are presumably powered by conversion of the large reservoir of kinetic energy to radiated energy via interaction of the ejecta with circumstellar material (CSM; e.g., Chugai & Danziger 1994; Svirski et al. 2012; Ofek et al. 2014b). We note that the classification of SNe IIn is not well-defined; some SNe display similar spectral features on timescales of a few days after the explosion, which subsequently disappear (Niemela et al. 1985; Fassia et al. 2001; Gal-Yam et al. 2014; Khazov et al. 2016; Shivvers et al. 2015; Smith et al. 2015; Yaron et al. 2016). It is possible that these flash-ionized SNe have lower CSM mass, and/or a CSM that is confined to short distances from the progenitor (e.g., Gal-Yam et al. 2014; Groh 2014; Yaron et al. 2016).

Ofek et al. (2014a) systematically searched for pre-explosion outbursts (precursors) among a sample of 16 SNe IIn in which the hydrogen Balmer lines persist at least until the SN maximum light. Five possible precursors were found. Based on this analysis, they conclude that precursor events among SNe IIn are common: assuming a homogeneous population, at the one-sided 99% confidence level, more than 98% of all SNe IIn have at least one pre-explosion outburst that is brighter than 3 × 10⁷ L_⊙ (absolute magnitude −14) that takes place up to 2.5 years prior to the SN explosion. The average rate of such precursor events during the year prior to the SN explosion is likely larger than one per year (i.e., multiple events per SN per year), and fainter precursors are possibly even more common. They also find possible correlations between the integrated luminosity of the precursor, and the SN total radiated energy, peak luminosity, and rise time. These correlations are expected if the precursors are mass ejection events, and the early-time light curve of these SNe is powered by interaction of the SN ejecta with optically thick CSM. No precursors were found in a similar search among five SNe IIn that was recently reported by Bilinski et al. (2015). They do not provide the absolute-magnitude-dependent search time of their sample, so direct comparison of the two surveys is not straightforward.

The nature of the SN precursors is unknown, although several theoretical mechanisms have been suggested to explain this high mass-loss in the final stages of stellar evolution. These include the pulsational pair instability (e.g., Rakavy et al. 1967; Woosley et al. 2007; Waldman 2008; Moriya & Langer 2015), bursty shell oxygen burning (Arnett & Meakin 2011), binary evolution (e.g., Chevalier 2012; Soker & Kashi 2013), and internal gravity waves excited by core convection (Quataert & Shiode 2012; Shiode & Quataert 2014). In addition to the nature of the engine driving the precursors, another relevant question is how the mass-loss arises and the origin of the radiated luminosity. In the context of luminous blue variables and η Carinae in particular, one can envision mass-loss as arising from explosions—i.e., shock waves accelerating material at the surface, later converting the kinetic energy to radiation through the interaction of the freshly ejected material with previously ejected mass (e.g., Smith 2013). In this case, we expect the radiated energy to be less or comparable to the kinetic energy of the ejecta. In an opposite scenario, a super-Eddington radiative field drives mass through radiation pressure. Here we expect the radiated energy to be larger than the kinetic energy of the ejecta (Shaviv 2000, 2001).

SNHunt 275 (PSN J09093496+3307204) was discovered by Howerton.¹³ Classification of the transient (Elias-Rosa et al. 2015) by the Asiago Transient Classification Program using a spectrum taken on 2015 February 9.93 (UTC dates are used throughout this paper) revealed a narrow P-Cygni Hα line with an emission width of about 900 km s⁻¹ and an expansion velocity, derived from the absorption component, of 950 km s⁻¹. The P-Cygni profile is superposed on broad Hα emission, having a FWHM intensity of ∼6800 km s⁻¹. Elias-Rosa et al. (2015) also reported on the detection of a possible source at the transient location in Hubble Space Telescope (HST) images with apparent magnitudes of 22.8, 21.5, and 22.5 (F606W filter) on 2009 February 9, 2008 March 30, and 2009 February 25, respectively. These correspond to absolute magnitudes of about −9.7, −11.0, and −10.0, respectively. Observations on 2015 March 9, April 9, and April 14 showed that the transient brightness had increased (de Ugarte Postigo et al. 2015a, 2015b, 2015c). Furthermore, spectroscopic observations on 2015 April 14 (with resolution R ≈ 500) did not detect the P-Cygni absorption component. Vinko et al. (2015) reported that the absolute magnitude of the transient reached −17 on 2015 May 18, and suggested that the transient has exploded as a SN.

Here we present Palomar Transient Factory (PTF) observations of the field of this transient in the years prior to its recent discovery and the detection of a precursor event reaching an absolute magnitude of about −12 (Duggan et al. 2015). We use these observations to put limits on the ejected mass and the radiative efficiency of the precursor. The radiative efficiency is defined here as the ratio of the radiated energy to the kinetic energy. Although the results have an uncertainty of several orders of magnitude, they provide the foundations for better future measurements.

We assume a distance to the transient of about 30 Mpc and a Galactic reddening of E_B−V = 0.023 mag (Schlegel et al. 1998). In Section 2 we present our photometric and spectroscopic observations, as well as Swift observations. The results are discussed in Section 3 and summarized in Section 4.

The Palomar Transient Factory (PTF and iPTF; Law et al. 2009; Rau et al. 2009), using the 48 inch Oschin Schmidt telescope, observed the field of SNHunt 275 starting in 2009 March. On 2013 December 12, PTF detected a new source at the location of the event, and the transient was named PTF 13efv (Figure 1). Spectroscopic classification obtained on 2013 December 13 suggested that this is a "SN imposter" (e.g., Van Dyk & Matheson 2012). All of the PTF observations are reduced using the PTF-IPAC pipeline (Laher et al. 2014) and the photometric calibration and magnitude system are described by Ofek et al. (2012a, 2012b).

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Photometry of the source was derived using point-spread function fitting photometry on the subtracted images (see, e.g., Firth et al. 2015 for details). Three images obtained between 2014 January 23 and April 25 were used as a reference. The PTF R-band photometry is listed in Table 1 and the light curve is presented in Figure 2. The R-band light curve clearly shows a precursor detected toward the end of 2013 November. The first detection of this outburst was on 2013 November 26. The next observations, about two weeks later, do not show an indication for flux variations. Therefore, it is possible that the outburst started much earlier than November 26. Observations obtained on 2013 December 21 indicate that the source returned to the levels of the reference image. We note that our PTF g-band light curve includes a single nondetection on 2013 April 22 with a limiting magnitude of 21.1. The precursor disappeared in the third week of 2013 December. We note that in Figure 2 there is a single point, on 2009 September 10, that looks like an outburst. In order to test its reality, we ran the newly developed image subtraction code (Zackay et al. 2016) on the images, where we constructed a reference image using the optimal image coaddition algorithm described in Zackay & Ofek (2015a, 2015b). This image subtraction code is optimal in the background dominated noise limit, and unlike the popular image subtraction methods it is numerically stable, returns a subtraction image with uncorrelated noise, and preserves the shape of cosmic rays and bad pixels. We found out that the residual causing the detection on 2009 September 10 has a sharp shape, indicating that it is likely a bad pixel or radiation hit event. Therefore, we conclude that it is not an outburst.

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We note that there are 21 observations obtained between 2010 February 13 and 16. All these observations have negative fluxes and their weighted mean count is −68 ± 9, where the error was estimated using the Bootstrap method (Efron 1982). This is likely due to real variability of the progenitor, specifically a decline in luminosity relative to the reference image. We note that the formal error on the mean (12 counts) is consistent with the bootstrap error. This consistency indicates that our error estimate is reasonable. For additional tests regarding systematics in our image subtraction and photometry we refer the reader to Ofek et al. (2014a).

Most of the optical spectra (see Table 2) were obtained with the Low Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) on the Keck I 10 m telescope, although a few spectra were also taken with the DEep Imaging Multi-Object Spectrograph (DEIMOS; Faber et al. 2003) on the Keck II 10 m telescope, the Kast spectrograph (Miller & Stone 1993) on the Shane 3 m telescope at Lick Observatory, and the Gemini-North Multiobject Spectrograph (GMOS; Hook et al. 2004) on the 8 m Gemini-N telescope. Spectral reductions followed standard techniques (e.g., Matheson et al. 2000; Silverman et al. 2012). All spectra are publicly available online via the Weizmann Interactive Supernova Data Repository, WISeREP¹⁴ (Yaron & Gal-Yam 2012). The spectra are presented in Figure 3 and a close-up view of the Hα line is shown in Figure 4.

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The first spectrum was obtained during the 2013 December outburst. It exhibits a strong and narrow Hα emission line ($\mathrm{FWHM}\lesssim 500$ km s⁻¹) with a narrow P-Cygni absorption component at a velocity of ∼1300 km s⁻¹ (measured relative to the peak of the emission line). The spectrum continuum is consistent with an effective temperature of about 5750 K and a radius of ∼4 × 10¹⁴ cm (see Table 2). We note that, blueward of the Hα line, there is a minor decrement in the flux level. If this is due to a P-Cygni profile, in addition to the narrow P-Cygni at 1300 km s⁻¹, then this indicates velocities of up to 15,000 km s⁻¹. However, the nature of this decrement is not clear. The Hα luminosity at this epoch is roughly 1.2 × 10³⁹ erg s⁻¹.

After the 2015 May rebrightening, the spectra become bluer, and the Hα emission line in the Keck/DEIMOS spectrum is well-described by a two-component Gaussian with component widths of $\lesssim 500$ and ∼2000 km s⁻¹. A month later, the spectra become redder and two P-Cygni absorption features are detected in all of the Balmer lines: one with a velocity of ∼1000 km s⁻¹ (as before), and a new absorption feature with a velocity of ∼2000 km s⁻¹. We note that the DEIMOS spectrum shows the Na i absorption doublet (5890, 5896 Å) at zero redshift and at the host-galaxy redshift. The equivalent width of the Na i doublet at the host-galaxy redshift is about 2.3 times stronger than the Galactic Na i absorption line. Therefore, it is likely that there is host-galaxy extinction in the direction of this event.

The Hα line luminosity as measured in the Keck/DEIMOS spectrum on 2015 May 20 is about 1.2 × 10⁴⁰ erg s⁻¹. This is over an order of magnitude stronger than the luminosity during the 2013 outburst. We verified the flux calibration is correct by calculating the V_UVOT-band synthetic magnitude from the spectrum and comparing it with the Swift-UVOT photometry.

SNHunt 275 exploded in NGC 2770, which has been the home of several SNe (e.g., Thöne et al. 2009), among which was SN 2008D (Soderberg et al. 2008; Modjaz et al. 2009). Thus, the host galaxy has been observed many times and by various instruments. Specifically, since 2008, it was observed by the Ultra-Violet/Optical Telescope (UVOT; Roming et al. 2005) on board the Swift satellite (Gehrels et al. 2004). Some of these observations have already been reported (e.g., Campana et al. 2015). The data were reduced using standard procedures (e.g., Brown et al. 2009). Flux from the transient was extracted from a 3''-radius aperture, with a correction applied to transform the photometry on the standard UVOT system (Poole et al. 2008). The resulting measurements, all of which have been converted to the AB system (Oke & Gunn 1983), are listed in Table 3 and displayed in Figure 5. Since there are no UVOT detections of the object prior to t₀ (=2457157.36, see definition below), Figure 5 shows only measurements taken after t₀. We note that the contribution from the host galaxy was subtracted by removing the (coincidence-loss corrected) mean count rate observed prior to 2015 January.

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Table 3.  Swift-UVOT Photometric Observations

Filter	JD $-\;{t}_{0}$	Counts	Counts error
	(day)
V	−2685.8316	−0.016	0.054
V	−2682.2874	0.087	0.074
V	−2680.7415	−0.007	0.040
V	−2679.6697	0.004	0.052
V	−2678.8016	0.000	0.047

Note. Time is given relative to t₀ = 2,457,157.36. The counts are background-subtracted, where the background is estimated as the mean of all the observations in a given filter obtained before 2015 January 1. The subtracted backgrounds are 0.892, 1.496, 0.743, 0.085, 0.206, and 0.146 counts for the V, B, U, UVM2, UVW1, and UVW2 filters, respectively. The zero points to convert these counts to AB magnitudes are 17.88, 18.99, 19.36, 18.97, 18.53, and 19.07 mag, for the V, B, U, UVW1, UVM2, and UVW2 filters, respectively.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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We used the UVOT observations to construct the bolometric light curve of the transient. This was done by correcting the measurements for Galactic reddening of ${E}_{B-V}=0.023$ mag (Schlegel et al. 1998; Cardelli et al. 1989), and fitting a blackbody continuum to all of the observations in one-day bins (only in bins having observations in more than three bands). The fitted bolometric light curve, effective temperature, and radius are presented in Figure 6, while the fitted measurements are listed in Table 4. Figure 7 presents the UVOT spectral energy distribution, along with the best-fit blackbody curve, on three epochs, 1.8, 4.5, and 14.3 days after t₀. The uncertainties were estimated using the bootstrap method (Efron 1982) applied to each time bin. Following Ofek et al. (2014c), we further estimated the rise timescale of the event by fitting the luminosity (L) with an exponential rise of the form

$$\begin{eqnarray}&&L={L}_{{\rm{max}}}(1-\mathrm{exp}[-(t-{t}_{0})/{t}_{{\rm{rise}}}]),\end{eqnarray} \tag{ 1 }$$

where L_max is the fitted maximum luminosity and t₀ is the fitted time of zero flux. We fitted the first four detections and estimate that t_rise ≈ 2.2 ± 1.6 days, L_max = (2.0 ± 0.3) × 10⁴² erg s⁻¹, and t₀ = 2, 457, 157.36 ± 2.2 day. We note that t₀ does not necessarily mark the time of explosion.

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Table 4.  Swift-UVOT Bolometric Light Curve

JD $-\;{t}_{0}$	Lbol	Temp.	Radius
(day)	(×1042 erg s−1)	(K)	(×1014 cm)
1.860	1.14 ± 0.05	11,500 ± 600	4.0 ± 0.5
3.126	1.50 ± 0.03	11,900 ± 300	4.3 ± 0.2
4.540	1.78 ± 0.02	12,200 ± 100	4.4 ± 0.1
5.176	1.79 ± 0.36	12,300 ± 600	4.4 ± 1.7
7.325	1.98 ± 0.04	12,100 ± 200	4.7 ± 0.2
10.260	1.81 ± 0.03	10,900 ± 200	5.5 ± 0.2
11.416	1.67 ± 0.04	10,200 ± 200	6.1 ± 0.3
12.582	1.54 ± 0.04	10,000 ± 300	6.1 ± 0.4
13.257	1.43 ± 0.04	9800 ± 200	6.1 ± 0.3
14.335	1.32 ± 0.05	9200 ± 300	6.8 ± 0.5

Note. Bolometric luminosity, effective temperature, and radius estimated from a blackbody fit to the Swift-UVOT observations (Table 3) corrected for Galactic extinction. Just as in Table 2, the temperature measurements should be regarded as lower limits on the effective temperature. Assuming the host extinction is twice as large as the Galactic extinction (i.e., as suggested by the Na i absorption doublet), the lower limit on the temperature will be higher by up to about 1000 K.

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For each Swift-XRT image of the transient, we extracted the number of X-ray counts in the 0.2–10 keV band within an aperture of 9'' radius centered on the transient position. This aperture contains ∼50% of the source flux (Moretti et al. 2004). The background count rates were estimated in an annulus around the transient location, with an inner (outer) radius of 50'' (100''). The log of Swift-XRT observations, along with the source and background X-ray counts in the individual observations, is given in Table 5. While binning the observations in 10-day bins, we did not detect X-rays from this position with a false-alarm probability lower than 4%. In the two weeks after t₀, we can set a 2σ upper limit of 0.26 count ks⁻¹ in the 0.2–10 keV range. Assuming a Galactic neutral hydrogen column density of n_H = 1.8 × 10²⁰ cm⁻² and an intrinsic power-law spectrum with a photon index of Γ = 2, this translates to an upper limit on the luminosity of L_X < 1.1 × 10³⁹ erg s⁻¹ within the Swift-XRT energy range.

Throughout this paper we assume a distance to SNHunt 275 of 30 Mpc (distance modulus 32.38 mag). The reduction and analysis presented here is based mainly on tools available as part of the MATLAB astronomy and astrophysics package (Ofek 2014).

Here, we briefly review the properties of the 2013 event (Section 3.1), and discuss the question of whether SNHunt 275 marks the final disruption of the star (Section 3.2). Furthermore, by analyzing the properties of the 2013 precursor and the latest explosion (2015 May), we attempt to constrain the physical setup of this explosion, and specifically the radiative efficiency of the precursor explosions (Section 3.3). In Section 3.4 we discuss the question of whether the possible mass-loss is driven by a radiation field, or the radiation is generated by the mass-loss interaction with previously emitted material.

3.1. The 2013 Event

3.2. The Nature of the 2015 Event

3.3. The Radiative Efficiency of Precursors

Table 6 lists the measured properties of the precursor and the possible SN explosion. These properties were estimated based on the PTF light curve, the spectra, the Swift-UVOT data, and the HST observations (Elias-Rosa et al. 2015). Next, we use these properties to estimate the radiative efficiency of the precursor. The goal of this section is to roughly estimate the CSM mass ejected in the 2013 outburst, and to estimate the ratio between the radiated luminosity and kinetic energy of the precursor. This measurement has the potential to resolve the key question: what drives the CSM ejection? For example, a ratio much smaller than one favors models in which the radiation is generated by conversion of the kinetic energy of the ejected mass to radiation via interaction (forming collisonless shocks; e.g., Katz et al. 2011; Murase et al. 2011, 2014) with previously emitted material, over models in which a super-Eddington luminosity drives the ejection of the CSM.

Since the precursor has super-Eddington luminosity (for a $\lesssim 100$ M_⊙ progenitor), it is likely that the outburst was associated with mass ejection. Here we attempt to estimate the physical parameters of the precursor (e.g., ejected mass) and to use it to estimate the ratio of the radiated energy of the precursor to its kinetic energy, which we call the precursor radiative efficiency:

$$\begin{eqnarray}{\epsilon }_{R} & \equiv & \displaystyle \frac{2\displaystyle \int {Ldt}}{{M}_{{\rm{CSM}}}{v}_{{\rm{CSM}}}^{2}}\\ & \approx & 3\times {10}^{-3}\left(\displaystyle \frac{\langle L\rangle }{1.7\times {10}^{40}\;\mathrm{erg}\;{{\rm{s}}}^{-1}}\right)\left(\displaystyle \frac{{\rm{\Delta }}t}{20\;{\rm{day}}}\right)\\ & & \times {\left(\displaystyle \frac{{M}_{{\rm{CSM}}}}{{M}_{\odot }}\right)}^{-1}{\left(\displaystyle \frac{{v}_{{\rm{CSM}}}}{1000\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{-2}.\end{eqnarray} \tag{ 2 }$$

Here, L is the precursor luminosity as a function of time t, Δt is the precursor duration, M_CSM is the precursor ejecta mass, and v_CSM is the precursor ejecta velocity. The CSM mass can be expressed as

$$\begin{eqnarray}&&{M}_{{\rm{CSM}}}=\left(\displaystyle \frac{1}{{\epsilon }_{R}}\right)\left(\displaystyle \frac{2\langle L\rangle {\rm{\Delta }}t}{{v}_{{\rm{CSM}}}^{2}}\right).\end{eqnarray} \tag{ 3 }$$

The radiative efficiency allows us to relate between the observed luminosity integrated over time, the CSM velocity, and mass. Furthermore, the exact value of the radiative efficiency likely depends on the CSM ejection mechanism, and therefore it may be useful for testing some theoretical ideas regarding the precursor physical mechanism (see Section 3.4).

However, our derivation is an order-of-magnitude estimate that relies on several assumptions, which are not necessarily correct. For example, we assume that the CSM has spherical symmetry and is not heavily clumped. Nevertheless, as far as we know, this is the only existing estimate for the radiative efficiency of a precursor.

The distance the precursor ejecta can travel during its 20 days ejection is

$$\begin{eqnarray}{r}_{{\rm{CSM}}} & \approx & {v}_{{\rm{CSM}}}{\rm{\Delta }}t\\ & \approx & 1.7\times {10}^{14}\left(\displaystyle \frac{{v}_{{\rm{CSM}}}}{1000\;\mathrm{km}\;{{\rm{s}}}^{-1}}\right)\left(\displaystyle \frac{{\rm{\Delta }}t}{20\;{\rm{days}}}\right){\rm{cm}},\end{eqnarray} \tag{ 4 }$$

where Δt is the duration of the precursor (≥20 days). An order-of-magnitude estimate of the mean density of the ejected CSM (during its ejection) is

$$\begin{eqnarray}n & \approx & \displaystyle \frac{{M}_{{\rm{CSM}}}}{{\mu }_{{\rm{p}}}{m}_{{\rm{p}}}4/3\pi {r}_{{\rm{CSM}}}^{3}}\\ & \approx & 2.7\times {10}^{11}\left(\displaystyle \frac{1}{{\epsilon }_{R}}\right)\left(\displaystyle \frac{\langle L\rangle }{1.7\times {10}^{40}\;\mathrm{erg}\;{{\rm{s}}}^{-1}}\right){\left(\displaystyle \frac{{\mu }_{{\rm{p}}}}{0.6}\right)}^{-1}\\ & & \times {\left(\displaystyle \frac{{\rm{\Delta }}t}{20{\rm{day}}}\right)}^{-2}{\left(\displaystyle \frac{{v}_{{\rm{CSM}}}}{1000\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{-5}\;{{\rm{cm}}}^{-3}.\end{eqnarray} \tag{ 5 }$$

Here, μ_p is the mean molecular weight (assumed to be 0.6).

Another constraint comes from the fact that the precursor radiation disappeared on a timescale shorter than one week (Figure 2); thus, the cooling timescale is ≲1 week. The Bremsstrahlung cooling timescale, which gives an upper limit on the cooling timescale, is given by

$$\begin{eqnarray}{t}_{{\rm{cool}}} & \lesssim & 1.76\times {10}^{13}{\left(\displaystyle \frac{T}{{10}^{4}{\rm{K}}}\right)}^{1/2}{\left(\displaystyle \frac{n}{1{{\rm{cm}}}^{-3}}\right)}^{-1}\\ & & \times {\left(\displaystyle \frac{Z}{1}\right)}^{-2}\;{\rm{s}},\end{eqnarray} \tag{ 6 }$$

where T is the gas temperature and Z is the atomic number (number of protons), and thus can be translated to a lower limit on the density of the emitting region. If we require that t_cool < 7 days, and assume $\langle Z\rangle \approx 1.7$ and T ≈ 10⁴ K, we find that $n\gtrsim 7\times {10}^{7}$ cm⁻³. Combining this limit on n along with Equation (5) and the fact that ${\rm{\Delta }}t\geqslant 20$ days, we get

$$\begin{eqnarray}&&{\epsilon }_{R}\lesssim 3.4\times {10}^{3}.\end{eqnarray} \tag{ 7 }$$

Next, an order-of-magnitude estimate for the photon diffusion timescale (e.g., Popov 1993; Padmanabhan 2001) is given by

$$\begin{eqnarray}{t}_{{\rm{diff}}} & \approx & \displaystyle \frac{9\kappa {M}_{{\rm{CSM}}}}{4{\pi }^{3}{{cr}}_{{\rm{CSM}}}}\\ & \approx & 0.32\left(\displaystyle \frac{1}{{\epsilon }_{R}}\right)\left(\displaystyle \frac{\kappa }{0.34\;\mathrm{cm}\;{\mathrm{gr}}^{-1}}\right)\left(\displaystyle \frac{\langle L\rangle }{1.7\times {10}^{40}\;\mathrm{erg}\;{{\rm{s}}}^{-1}}\right)\\ & & \times {\left(\displaystyle \frac{{v}_{{\rm{CSM}}}}{1000\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{-3}\;{\rm{day}}.\end{eqnarray} \tag{ 8 }$$

Assuming that ${t}_{{\rm{diff}}}\lesssim 7$ days, we can set the following lower limit:

$$\begin{eqnarray}&&{\epsilon }_{R}\gtrsim 0.04.\end{eqnarray} \tag{ 9 }$$

Until now, our constraints on the radiative efficiency are based on the properties of the precursor. Next, we will use the properties of the 2015 May event to derive additional constraints.

Assuming v_CSM ≈ 1000 km s⁻¹, after 500 days (i.e., the time between the 2013 December precursor and the 2015 May event), the CSM traveled a distance of r_CSM ≈ 4 × 10¹⁵ cm. Since the rise time of the 2015 May event is about 2 days (Table 6), we can use the diffusion timescale (Equation (8)) to set an order-of-magnitude upper limit on the mass of the CSM:

$$\begin{eqnarray}{M}_{{\rm{CSM}}} & \lesssim & 0.4\left(\displaystyle \frac{{t}_{{\rm{diff}}}}{2\;{\rm{day}}}\right)\left(\displaystyle \frac{{r}_{{\rm{CSM}}}}{4\times {10}^{15}\;{\rm{cm}}}\right)\\ & & \times {\left(\displaystyle \frac{\kappa }{0.34\mathrm{cm}{{\rm{g}}}^{-1}}\right)}^{-1}\;{M}_{\odot }.\end{eqnarray} \tag{ 10 }$$

Inserting this limit on M_CSM into Equation (2) gives

$$\begin{eqnarray}&&{\epsilon }_{R}\gtrsim 0.007\left(\displaystyle \frac{{\rm{\Delta }}t}{20\;{\rm{day}}}\right){\left(\displaystyle \frac{{v}_{{\rm{CSM}}}}{1000\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{-2}.\end{eqnarray} \tag{ 11 }$$

We note that currently we also have the following upper limit on the duration and luminosity of the precursor. Since we did not find a transient at the location of PTF 13efv in the Catalina Real Time Survey¹⁵ (CRTS; Drake et al. 2009), and assuming CRTS can detect magnitude 19 transients, we can conclude that the luminosity of the precursor was not larger by more than a factor of about four than the observed luminosity of 1.7 × 10⁴⁰ erg s⁻¹ seen during 2013 December. Furthermore, the PTF g-band nondetection prior to the 2013 December event sets an upper limit of about 240 days on Δt. Since the precursor was not detected in the UV (Table 6), the bolometric correction is likely small.

To conclude, combining all the constraints, we set the following limits on the radiative efficiency:

$$\begin{eqnarray}&&0.04\lesssim {\epsilon }_{R}\lesssim 3400.\end{eqnarray} \tag{ 12 }$$

We stress that this is an order-of-magnitude estimate and it includes several assumptions that are not necessarily correct. Therefore, the results of this analysis should be viewed with caution. Since we cannot determine whether the efficiency is smaller or larger than unity, we cannot point definitively toward one of two types of scenarios: kinetic energy converted into radiation or radiation-driven mass-loss. However, with improved observational constraints this analysis can be used in the future to obtain better estimates of the radiative efficiency of precursors.

3.4. What Drives the Mass Loss and Radiation?

In the case that the 2013 event is caused by a super-Eddington continuum-driven wind, we expect that it will satisfy a mass-loss versus luminosity relation. In this case, Shaviv (2001) has shown that the total mass-loss is given by

$$\begin{eqnarray}&&M\approx { \mathcal W }\displaystyle \frac{L-{L}_{{\rm{Edd}}}}{c\;{c}_{{\rm{s}}}}{\rm{\Delta }}t,\end{eqnarray} \tag{ 13 }$$

where ${ \mathcal W }$ is a dimensionless constant that empirically was found to be of the order of a few, c_s is the speed of sound at the base of the wind (estimated to be 60 km s⁻¹), and L_Edd is the Eddington luminosity. For $L\gg {L}_{{\rm{Edd}}}$ we can write

$$\begin{eqnarray}M & \approx & 4\times {10}^{-5}\left(\displaystyle \frac{{ \mathcal W }}{5}\right)\\ & & \times \left(\displaystyle \frac{L}{1.7\times {10}^{40}\;\mathrm{erg}\;{{\rm{s}}}^{-1}}\right)\left(\displaystyle \frac{{\rm{\Delta }}t}{20\;{\rm{day}}}\right)\;{M}_{\odot }.\end{eqnarray} \tag{ 14 }$$

This estimate is below the derived upper limits on the CSM mass, and hence we cannot rule out this model.

The second option that we would like to consider is that the radiation is generated from conversion of the kinetic energy of the ejected mass to radiation via interaction with previously emitted material (e.g., Smith et al. 2014). One possible problem with this scenario is that the interaction will produce mostly hard X-ray photons (e.g., Fransson 1982; Katz et al. 2011; Murase et al. 2011, 2014; Chevalier & Irwin 2012; Svirski et al. 2012). Presumably, it is possible to convert these X-ray photons to visible light by Comptonization or bound-free absorption (e.g., Chevalier & Irwin 2012; Svirski et al. 2012). Comptonization requires larger than unity Thompson optical depth, while the bound-free absorption will need neutral CSM mass with column densities above ∼10²³ cm⁻². We note that in the current observations there is no evidence for a large Thompson optical depth, but we cannot rule out strong bound-free absorption. Moreover, this scenario may still work, if we introduce large departures from the spherical symmetry that we have assumed so far.

We present observations of a precursor, peaking at an absolute magnitude of about −12, ∼500 days prior to the SNHunt 275 2015 May event. Also included are Swift-UVOT observations of the 2015 May event that peaked at an absolute magnitude of −17. We discuss the nature of the 2015 May event, and conclude that it is not yet clear whether this event signals the final explosion of the progenitor or is still another eruption. If the latter, then we may detect an SN taking place within months to a few years.

Finally, we use the observations to constrain the ratio of the radiated energy to the kinetic energy of the precursor (i.e., the radiative efficiency). Under some simplistic assumptions, our order-of-magnitude estimate suggests that the radiative efficiency of PTF 13efv is $\gtrsim 0.04$. However, this still does not necessarily mean that all precursors have similar radiative efficiencies.

We thank M. Graham, P. Kelly, A. Bostroem, I. Shivvers, and W. Zheng for their help obtaining some of the optical spectra. We are also grateful to the staffs of the Palomar, Lick, and Keck Observatories for their excellent assistance. Research at Lick Observatory is partially supported by a generous gift from Google. Some of the data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and NASA; the observatory was made possible by the generous financial support of the W.M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. E.O.O. is the incumbent of the Arye Dissentshik career development chair and is grateful for support by grants from the Willner Family Leadership Institute Ilan Gluzman (Secaucus NJ), the Israel Science Foundation, Minerva, Weizmann-UK, and the I-Core program by the Israeli Committee for Planning and Budgeting and the Israel Science Foundation (ISF). N.J.S. is grateful for the IBM Einstein Fellowship. A.G.Y. is supported by the EU/FP7 via ERC grant No. 307260, the Quantum universe I-Core program by the Israeli Committee for Planning and Budgeting and the ISF; by Minerva and ISF grants; by the Weizmann-UK "making connections" program; and by Kimmel and ARCHES awards. M.S. acknowledges support from the Royal Society and EU/FP7-ERC grant No. 615929. A.V.F.'s research is supported by the Christopher R. Redlich Fund, the TABASGO Foundation, and NSF grant AST-1211916.