RAPIDLY EVOLVING AND LUMINOUS TRANSIENTS FROM PAN-STARRS1

PS1 is a wide-field imaging system dedicated to survey observations. Located on Haleakala, Hawaii, it possesses a 1.8 m diameter primary mirror and a 33 diameter field of view (Kaiser et al. 2010). The imager consists of an array of sixty 4800 × 4800 pixel detectors with a pixel scale of 0258, providing an instantaneous field of view of 7.1 deg² (Tonry & Onaka 2009). Observations are obtained with a set of five broadband filters (g_P1r_P1i_P1z_P1y_P1, hereafter grizy_P1) which are similar, although not identical, to those used by the Sloan Digital Sky Survey (SDSS; Ahn et al. 2012). Details of the filters and photometry system are given in Tonry et al. (2012) and Stubbs et al. (2010).

The PS1-MDS consists of 10 fields, each a single PS1 imager footprint, distributed throughout the sky. Approximately 25% of PS1 observing time is dedicated to revisiting the PS1-MDS fields on a nightly basis in griz_P1 to a 5σ depth of ∼23.3 mag with a nominal cadence of 3 days in any given filter. In optimal observing conditions, g_P1 and r_P1 are observed on the same night with i_P1 and z_P1 observations following on consecutive evenings. y_P1 is observed during times of full moon to a depth of ∼21.7 mag.

Initial reduction and processing of all PS1-MDS images are carried out with the PS1 Image Processing Pipeline (Magnier 2006; Magnier et al. 2008). This includes standard reductions, astrometric solution, and stacking of nightly images as well as source detection and photometry. The nightly PS1-MDS stacks are then transferred to the Harvard FAS Research Computing cluster where difference images are produced and potential transients identified by the photpipe pipeline (Rest et al. 2005, 2013). Potential transients are visually inspected for possible promotion to status of transient alert. This visual inspection acts to filter out false positives due to time varying trails from saturated sources and poorly subtracted galaxy cores (with obvious large-scale dipole patterns). Once a transient reaches alert status it is flagged for potential spectroscopic follow-up. Spectra are acquired for ∼10% of PS1-MDS alerts, with final selections left to the spectroscopic observers.

As part of the normal operation of the PS1-MDS described above, we identified a number of transients that evolved on rapid timescales and reached peak luminosities associated with SNe (−16 > M > −21 mag). Objects identified in this way (i.e., flagged by a human operating the pipeline) are certainly useful for determining the properties of rapidly evolving transients. However, calculating volumetric rates based on the number of transients identified in a survey requires a well defined set of selection criteria. To systematically identify objects that lie in this portion of transient phase space, we initiated a search within the ∼5000 transient sources discovered with the photpipe pipeline during the duration of the PS1-MDS. As a first cut, we required that the transient satisfy the following three criteria in a minimum of two photometric bands (all times are observer frame).¹⁷

• 1.  
  The transient must rise by ≳1.5 mag in the 9 days immediately prior to observed maximum light.
• 2.  
  The transient must decline by ≳1.5 mag in ∼25 days post observed maximum.
• 3.  
  The transient must be present (>3 σ) in at least three sequential observations. This criteria selects a unique population of transients than those discussed in Berger et al. (2013; which possess timescales shorter than 1 day).

These criteria are motivated by the observed timescales of known SNe and are intended to exclude the bulk of Type Ia, Type Ib/c, and Type II SNe. In V-band, typical Type Ia and Type Ib/c SNe will rise by 0.6–0.75 mag in the 10 days immediately prior to maximum light and decline by 1.0–1.2 mag in the 25 days post-maximum (Riess et al. 1999; Drout et al. 2011; Li et al. 2011). At higher redshifts PS1 will probe bluer wavelengths (which typically evolve more rapidly) but this will compete with the effects of time dilation. Many Type II SNe would easily pass the rise time requirement, but they decline by ≲0.5 mag in the 25 days post maximum (Li et al. 2011; Hamuy 2003). The most rapid Type Ic SNe (e.g., SN 1994I; Richmond et al. 1996) and most rapid SN1991bg-like Type Ia SNe (Taubenberger et al. 2008) would barely pass all three of our requirements if caught at maximum light. However, any given PS1 band is only observed every three days and we require the same band to pass both our rise and decline cuts. We therefore expect our selected objects to evolve more rapidly than these events.¹⁸

A number of known low-luminosity transients (nova, CVs, M dwarf flares, etc.) could pass these selection criteria if located within the Milky Way or a nearby galaxy. Thus, all objects that passed these initial criteria were then examined by eye in order to select objects that were likely of extragalactic origin. Objects were removed from consideration if there was a clear stellar source at the location of the transient. In several cases, spectra were obtained of rapidly evolving transients, which revealed Balmer lines in emission at zero redshift, indicating the transient was likely galactic. Our search identified a handful (∼10) of these low-luminosity events. If a transient was either host-less, or exploded near a low signal to noise, unresolved, source (such that the stellar versus galactic nature of the host could not be robustly determined) it was kept in the sample and is discussed below.

In the end, by combining the results from this systematic search with results from the normal operation of the PS1-MDS pipeline, we identify 14 transients of interest. For 10 of these transients we have obtained spectra of their underlying hosts, confirming their extragalactic origin. In Section 3 we provide an overview of the selected objects and divide them into three groups based on the quality of their light curves and constraints available for their distance. In the rest of this section we describe the observations obtained for all 14 transients.

The 14 objects in our sample were discovered in the PS1-MDS imaging spanning 2010–2013. Discovery dates, coordinates, and other basic information are listed in Table 1. Detailed information on the production of final point-spread function (PSF), template subtracted, griz_P1 photometry is given in Rest et al. (2013) and Scolnic et al. (2013). For transients discovered before 2011 October, object specific deep templates were constructed from pre-explosion images. For transients discovered after this time, template subtraction was performed using the PS1 "deep stacks" constructed from high quality PS1 images obtained between 2010 and 2011.

In Figures 1–3 we plot the griz_P1 light curves for all 14 transients. This includes 3σ pre- and post-explosion limits. To give perspective on the rapid timescale of these events, we have also plotted the Type Ibc template light curve (gray area; normalized to the PS1 transient peak magnitude) from Drout et al. (2011). Photometry is listed in Table 2.

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In addition to the PS1 photometry, we also obtained one epoch of r-band imaging for PS1-11bbq with Gemini GMOS (Hook et al. 2004), one epoch of ri-band imaging for PS1-12brf with Magellan IMACS (Dressler et al. 2006) and one epoch of r-band imaging for PS1-13ess with Magellan IMACS. This additional photometry was obtained at +2, +45 and +12 rest-frame days for the three objects, respectively. The images were processed using standard tasks in IRAF¹⁹ and calibrated using PS1 magnitudes of field stars. We subtracted contributions from the host galaxies using PS1 template images and the ISIS software package as described in Chornock et al. (2013). These points are also shown (squares) in Figures 1 and 2, and listed in Table 2.

For our entire sample we compile griz-band photometry for any underlying galaxy/source. When possible, we utilize the SDSS DR9 Petrosian magnitudes, which account for galaxy morphology. For cases where the underlying galaxy/source was too faint for a high signal-to-noise SDSS detection, we perform aperture photometry on the PS1 deep template images, choosing an aperture to encompass all of the visible light. Cross-checks show the PS1 and SDSS magnitudes are consistent. In Figures 4 and 6 we show the environments immediately surrounding the transients.

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Spectroscopic follow-up for the PS1-MDS is carried out on a number of telescopes, with the MMT, Magellan and Gemini bearing most of the load. Spectra are acquired for roughly 10% of the transients identified by the photpipe pipeline, with final selections left to the observer. We obtained spectra of five transients while they were active, including two observations of PS1-12bb. The epochs on which these spectra were taken are indicated by a dashed vertical line in the appropriate panels of Figures 1 and 2. Host galaxy spectra were also obtained for six transients. A summary of our spectroscopic data is given in Table 3.

Initial reduction (overscan correction, flat fielding, extraction, wavelength calibration) of all long slit spectra was carried out using the standard packages in IRAF. Flux calibration and telluric correction were performed using a set of custom idl scripts (see, e.g., Matheson et al. 2008; Blondin et al. 2012) and standard star observations obtained the same night as the science exposures. Spectra obtained with the Hectospec multi-fiber spectrograph (Fabricant et al. 2005) were reduced using the IRAF package "hectospec" and the CfA pipeline designed for this instrument.

Together our gold and silver samples contain 10 objects. For these events, we obtained spectroscopic redshifts of their host galaxies, allowing us to constrain their true luminosity scale.

Our gold sample is composed of six objects. These are our highest quality events, all of which satisfy the photometric selection criteria listed in Section 2.2. The absolute magnitude, rest-frame, light curves for these events are shown in Figure 1.

Our silver sample is composed of four objects. These are events that were noted as rapidly evolving during the normal operations of the PS1-MDS but that possess sparser light curves (Figure 2). In all cases the observed light curves are sufficient to characterize them as rapidly evolving, but sparse enough such that they fail the systematic selection criteria described above. For instance, PS1-13ess only has one band with a deep limit in the 9 days prior to observed maximum (as opposed to the requisite two). For a majority of this manuscript, the silver objects will be analyzed with our gold sample, as they further inform the properties of rapidly evolving transients. However, in Section 7 when calculating volumetric rates, only objects that pass the well defined set of selection criteria outlined above will be considered.

In Figure 4 we show the 25' × 25' region surrounding the gold and silver transients, all of which have an associated host. Narrow emission and absorption lines were used to measure the redshift to each host. These range from z = 0.074 (PS1-10ah) to z = 0.646 (PS1-11bbq) with a median redshift of z = 0.275. In Table 1 we list the redshift, luminosity distance, and Milky Way reddening in the direction of each transient (Schlafly & Finkbeiner 2011). Throughout this paper we correct only for Milky Way extinction. All calculations in this paper assume a flat ΛCDM cosmology with H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_m = 0.27, and Ω$_\Lambda$ = 0.73.

In Figure 5 we plot peak absolute magnitude versus redshift in griz_P1 for the gold/silver transients. Stars represent our observed magnitudes corrected for distance and MW extinction. Circles represent absolute magnitudes that have been k-corrected to the rest-frame griz_P1 bandpasses based on best-fit blackbodies (see Section 4). We see that our sample spans a wide range of absolute peak magnitude (−17 > M > −20).

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Our bronze sample is composed of four objects. These events have light curves that were flagged by the selection criteria in Section 2.2 but for which we were unable to spectroscopically confirm the extragalactic nature of their hosts. The 25' × 25' region surrounding our bronze sample is shown in Figure 6. All four transients have a faint (25 mag < m_i < 22 mag) underlying source visible in the PS1 deep stacks, although in several cases there is ambiguity about the true host (for instance, PS1-13aea exploded in the region between NGC 4258 and NGC 4248; see Figure 6). In the Appendix we quantify the most likely hosts and discuss the consequences of each probable host for the nature of these transients. We find it likely that a subset of our bronze sample events are extragalactic, and therefore additional rapidly evolving and luminous transients. However, due to the uncertainty in the distance to any individual bronze event, for a majority of this manuscript we will focus on the properties of the gold and silver transients.

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In Table 4 we summarize the photometric properties of the gold/silver transients, including their observed/absolute magnitudes and several measurement of their rise and decline timescales. The t_{1/2, rise} and t_{1/2, decline} timescales as well as the number of magnitudes the light curves decline in the first 15 days post-maximum (Δm₁₅) were determined by linearly interpolating our observed light curve.²⁰ All values are determined with respect to the time of observed maximum, and are therefore influenced by the three day cadence in each band. However, this should not strongly affect our qualitative assessment of these objects. The quoted rise time values encompass the entire range of values permitted by the observed photometry/limits in each band.

In general the transients have faster rise than decline timescales. This is shown in Figure 8 where we plot the t_{1/2, rise} versus t_{1/2, decline} timescales. Most events fall well below the dashed line denoting equality, indicating that decline timescale is not a good proxy for overall timescale in these events. In fact, for six events, our data do not exclude a transient that rose on a timescale ≲1 day. In contrast, the typical Δm₁₅ values for these transients (1–2 mags) are slightly more rapid than typical stripped envelope core-collapse SNe (CC-SNe) (Δm₁₅ ∼ 0.5–1.0; Drout et al. 2011) but slower than the rapidly declining Type I SN 2005ek, SN 2010X, and SN 2002bj (Drout et al. 2013; Kasliwal et al. 2010; Poznanski et al. 2010), which possess Δm₁₅ ≳ 3 mag.

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Three of the transients (PS1-10ah, PS1-12brf, PS1-13ess) show evidence for a change in decline timescale. PS1-10ah initially declines very rapidly, with a linear decline rate of ∼0.15 mag day⁻¹, which then shallows to ∼0.02 mag day⁻¹ around 10 days post-maximum. PS1-13ess shows an initial decline very similar to PS1-10ah, but then rises again as evidenced by our final i_P1 and z_P1 data points. This may liken it to the double peaked Type IIb SN 1993J (see Section 8). The other objects in our sample show no discernible change in slope out to ∼10–20 days post-maximum.

In the normal operation mode of the PS1-MDS only g_P1 and r_P1 observations are acquired on the same day, with i_P1 and z_P1 observations following on consecutive evenings. In the upper panel of Figure 9 we plot the g_P1 − r_p1 colors from every epoch on which both bands were observed. The colors are generally blue (g_P1 − r_p1 ≲ 0.0) and redden slightly with time. In the lower panel of Figure 9 we plot g_P1 − r_P1 color at maximum as a function of transient redshift. A majority of objects possess −0.2 > g_P1 − r_P1 > −0.3. Only PS1-12bb shows significantly redder colors with g_P1 − r_p1 = 0.0. For comparison, we also show a randomly selected sample of PS1 Type Ia SNe (gray dots). The Type Ia SNe are significantly redder than our rapidly evolving transients, especially at redshifts greater than z = 0.2 where the g_P1 and r_P1 filters probe the portion of the Type Ia spectrum where line blanketing greatly reduces the UV flux.

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In order to gain a more complete view of the spectral energy distribution (SED) evolution of our sample, we interpolate our griz_P1 light curves to a set of common epochs. The uncertainly involved in such an interpolation is accentuated due to the rapidly evolving nature of our sample, and we take care to only interpolate to epochs for which there was a cluster of griz_P1 observations within a few days. In Figure 10 we plot the SEDs. For a majority of the events, no turnoff is seen in the SED at blue wavelengths. This is true even for our highest redshift object, PS1-11bbq, for whom the g_P1 extends out to a rest fame wavelength of ∼2500 Å.

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Also shown in Figure 10 are the best-fit blackbody curves for each epoch. For nine (of 10) transients the best-fit blackbodies yield temperatures and radii that cool/expand with time, as one expects for an explosion with expanding ejecta (e.g., SNe). The best-fit blackbody temperatures and radii for these events are plotted as a function of time in Figure 11. On average, the temperatures cool from ∼20,000 K near maximum to ∼7000 K at ∼20 days, and the radii expand from ∼10¹⁴ cm to a few ×10¹⁴ during the time period over which they are constrained. Dashed lines in Figure 11 show fiducial cooling rates and photosphere expansion speeds, which are based on our best observed object: PS1-10bjp (orange). The presence of extragalactic extinction along the line of sight would slightly increase these temperatures and radii, but would not affect our conclusion that their evolution is consistent with explosions that possess an expanding ejecta.

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The temperature/radius evolution of three transients warrant further note: (1) PS1-12brf displays an initial best-fit blackbody temperature of ∼50,000 K. This exact value is uncertain because our data lies far down the Rayleigh–Jeans tail, but from Figure 1 we see that it possesses extreme colors near maximum light. This is also the only transient for which our data shows longer wavelengths reaching maximum at later times. (2) PS1-10ah shows tentative evidence for a temperature that rises to maximum and then cools. (3) PS1-12bb is our only object that does not show a characteristic cooling/expanding behavior. The best-fit blackbody temperature shows little variation and is consistent with ∼7000 K from 0 < t < 20 days.

Finally, by assuming the spectra of our objects can be approximated by these best-fit blackbodies, we can perform rough k-corrections on our observed magnitudes to rest-frame griz_P1 bandpasses. This will allow us to directly compare the magnitudes observed for objects with differing redshifts. We perform synthetic PS1 photometry on these blackbodies and find the "rest" griz_P1 peak magnitudes listed in Table 4. These "k-corrected" peak magnitudes are shown as circles in Figure 5 and are used to produce "rest-frame" g_P1 − r_P1 colors, which are plotted in Figure 9.

To constrain the total energy radiated in these explosions, we construct pseudo-bolometric light curves from our multi-band data. We first perform a trapezoidal interpolation to our observed griz_P1 light curves and then account for missing IR flux by attaching a blackbody tail based on the best-fit values described above. In order to account for missing UV flux and the varied wavelength coverage of our observations (due to differing redshifts) we then extend the same blackbody from the edge of the observed g_P1 band back to 2500 Å (rest-frame). This represents the blue edge of the wavelength range covered by our highest redshift event, and the approximate range of our spectra in Section 5.

Using this formulation, our peak pseudo-bolometric luminosities span a range of approximately 2 × 10⁴² erg s⁻¹ < L < to 3 × 10⁴³ erg s⁻¹, and are plotted in Figure 7. If we had instead utilized a UV bolometric correction that integrated the entire best-fit blackbody, these values would be approximately a factor of two higher. In the left panel of Figure 12 we plot our derived pseudo-bolometric light curves. The number of epochs for which we can constrain the luminosity is limited for the silver transients. The energy radiated by the six gold transients between −3 and +20 days ranged from 2 × 10⁴⁸ erg (PS1-12bb) to 2 × 10⁴⁹ erg (PS1-11qr).

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For comparison, we also show the pseudo-bolometric light curves of several other rapidly evolving events (right panel): SN 2002bj (Poznanski et al. 2010), PTF 09uj (Ofek et al. 2010), SN 2010X (Kasliwal et al. 2010), and SN 2005ek (Drout et al. 2013), as well as the double peaked SN 1993J (Schmidt et al. 1993). The curves for SN 2005ek, SN 2002bj, and SN 1993J were calculated from multi-band photometry in a manner similar to that utilized here, while the curves for SN 2010X and PTF 09uj were derived based on r-band data only. We note that SN 2005ek and SN 2010X, which have been proposed to be powered mainly by radioactive decay (Drout et al. 2013; Kasliwal et al. 2010; Tauris et al. 2013), are less luminous than the PS1-MDS events, while the more luminous PTF 09uj and the first peak of SN 1993J are thought to be powered by cooling envelope emission/interaction. These power sources will be discussed further in Section 8.

From Figure 13 we see that the spectra are dominated by continua as opposed to strong P Cygni features. Four of the events, PS1-11bbq, PS1-12bv, PS1-12brf and PS1-13duy, show blue continua²¹, while PS1-12bb is consistent with a blackbody of 6000–7000 K. PS1-12bb also showed redder photometric colors and a distinct SED evolution (Section 4). Of the events, PS1-12bv shows the strongest evidence for broad spectral features, with the most evident near 3900 Å.

Spectra dominated by blue continua have been observed in previous SNe. They are typically found in objects that are hot, optically thick, and powered by cooling envelope emission or interaction. For instance, although SN 1993J later went on to develop a plethora of P Cygni features indicative of a Type IIb SNe, during its initial light curve peak (attributed to cooling envelope emission and recombination) its spectrum was dominated by continua with only a few features between 4000–5000 Å. Hydrogen lines were not evident in the early spectra. In addition, the rapidly evolving Type IIn SN PTF 09uj (attributed to shock breakout/interaction) has only weak narrow emission lines in its spectra near maximum, and is dominated by a blue continuum. Given the signal to noise of our spectra, it is unlikely that we would be able to identify similar emission features in our events if they were present. Thus, based on the quality and coverage of our spectra, we are unable to conclude whether the objects in our sample are hydrogen-rich or hydrogen-poor. We plot spectra of SN 1993J and PTF 09uj, as well as the blue rapidly evolving SN 2002bj (whose power source is still under debate), in the top panel of Figure 13.

In contrast, SNe that are powered mainly by radioactive decay (Type Ia/b/c SNe) are typically dominated by P Cygni features formed in the outer ejecta layers. In particular, they often possess strong line blanketing in the blue due to the presence of iron peak elements. We plot several examples in the lower panel of Figure 13. We see that our spectra more closely resemble events that are powered by interaction/recombination, as opposed to radioactive decay.

We obtained two spectra for PS1-12bb. At the time of the second epoch (+33 days) the i-band light curve of PS1-12bb had declined by ∼3 mag. Similar to the spectrum obtained near maximum light, this spectrum is dominated by continuum (with some contribution from its host galaxy's light). This is in contrast to any other "late time" spectra of a rapidly declining SN that has been obtained to date. Both SN 2005ek (Drout et al. 2013) and SN 2010X (Kasliwal et al. 2010) were observed between 10 and 35 days post-maximum. Both events (Type Ic) displayed a growing emission component in the Ca ii NIR triplet. By +23 days the spectrum of SN 2010X was dominated by the Ca ii NIR triplet between 8000 and 9000 Å. This is not the case for PS1-12bb. We can place a limit on the luminosity in the Ca ii NIR triplet between 8300–8700 Å at +33 days in PS1-12bb of <3 × 10³⁹ erg s⁻¹. This is approximately 4 times lower than the feature observed in SN 2010X at a similar time. PS1-12bb was also our only object whose best-fit blackbodies did not show radii that expanded with time. Thus, this transient may be of a different kind than a SN with an expanding ejecta that eventually becomes optically thin.

The emission lines present in Figure 13 are unresolved and attributed to the host galaxies. However, in the spectrum of PS1-12bv there is tentative evidence for circumstellar material (CSM) absorption in the Mg ii (λλ 2796,2803) feature. A view around this feature is shown in the left panel of Figure 14. The spectrum of PS1-12bv shows unresolved nebular emission lines of [O ii] λ3727 and Hβ at a redshift of z = 0.405. In contrast, the two deepest features of the Mg ii (λλ 2796,2803) absorption feature are blue shifted by ∼700 km s⁻¹ relative to the galaxy emission lines (z = 0.402) and there is a resolved blue wing to the feature. This blue wing spans an additional ∼1000 km s⁻¹ from the minimum of the absorption feature. Our resolution corresponds to ∼400 km s⁻¹ in this wavelength region.

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A similar blue absorption wing was seen in the spectra of the Type IIn SN 1998S (Bowen et al. 2000), although in this case the wing spanned only ∼350 km s⁻¹ from the absorption minimum. Both Bowen et al. (2000) and Chugai et al. (2002) credit this "shelf" of absorption to the CSM around the explosion and Chugai et al. (2002) invoked radiative driving to accelerate relatively slow moving CSM material (40–50 km s⁻¹) to these velocities. In our case, if the blue component is due to CSM absorption, we would require either stronger radiative driving or a faster CSM wind speed. The CSM wind speed found for SN 1998S was typical for a RSG wind, whereas the speeds required for PS1-12bv would be more indicative of a wind from a WR or luminous blue variable star. PS1-12bv is one of our four most luminous objects and is very similar photometrically to PS1-11qr, PS1-11bbq, PS1-13duy and PTF 09uj (which was hypothesized to be due to the shock breakout from an optically thick wind; Ofek et al. 2010). This broad feature may therefore point to a progenitor star that possesses a strong wind in the years before explosion for these transients.

Alternatively, this feature could be explained by either a complex interstellar medium (ISM) absorption system along the line of sight or an outflow from the host galaxy. In order to investigate this possibility, we fit pairs of Mg ii (λλ 2796,2803) doublets with varying redshifts and FWHM to this portion of the spectrum. An example fit is shown in the right panel of Figure 14. Blue and green lines show the individual Mg ii (λλ 2796,2803) doublets, and the red line shows their sum. In all cases, we required absorption components that were both resolved and significantly broader than typical ISM absorptions (≲100 km s⁻¹).

After correcting the host griz-band photometry for Milky Way extinction we use the FAST stellar population synthesis code (Kriek et al. 2009) to calculate the total stellar mass contained within our host galaxies. Our models utilized the Maraston (2005) stellar library and assumed an exponential star formation history and Salpeter IMF. The total extinction was restricted to <0.05 (motivated by the Balmer decrement in our highest quality host spectra and the blue colors of our transients; the assumed extinction does not significantly affect the resulting mass). The results from this analysis are listed in Table 5.

Table 5. Host Galaxy Properties

Event	mobs, i	log (O/H) + 12a	Methodb	log(Mgal/M☉)	SFR	sSFR	Offset	Offset	Norm. Offsetc
	(mag)	(measured)			(M☉ yr−1)	(Gyr−1)	(arcsec)	(kpc)
PS1-10ah	18.08 (0.02)	8.49 (0.03)	PP04N2	9.12$^{+0.18}_{-0.21}$	∼1.2	∼0.9	0.42	0.68	0.21
PS1-10bjp	19.22 (0.03)	8.38 (0.05)	PP04N2	9.12$^{+0.18}_{-0.24}$	∼2.1	∼1.6	0.95	2.39	0.85
PS1-11qr	19.80 (0.06)	8.85 (0.08)	PP04N2	10.17$^{+0.20}_{-0.37}$	∼4.3	∼0.3	1.54	12.58	0.98
PS1-11bbq	24.40 (0.15)	8.67 (0.14)	Z94	8.01$^{+0.61}_{-0.70}$	>0.3	>2.4	0.47	8.81	1.05
PS1-12bb	16.59 (0.01)	8.79 (0.11)	PP04N2	10.54$^{+0.43}_{-0.12}$	∼2.3	∼0.06	4.93	10.99	1.92
PS1-12bv	22.01 (0.20)	⋅⋅⋅	⋅⋅⋅	9.89$^{+0.62}_{-0.52}$	>0.3	>0.03	0.97	10.29	0.50
PS1-12brf	22.04 (0.21)	8.6 (0.2)	KD02	8.73$^{+0.20}_{-0.17}$	>0.3	>0.5	0.42	2.90	0.69
PS1-13duy	22.20 (0.04)	8.6 (0.2)	KD02	8.78$^{+0.15}_{-0.12}$	>0.1	>0.2	0.33	2.16	0.44
PS1-13dwm	21.38 (0.08)	<8.4	PP04N2	8.96$^{+0.27}_{-0.01}$	∼1.9	∼2.0	1.40	8.28	0.82
PS1-13ess	22.54 (0.08)	8.43 (0.03)	M91	8.68$^{+0.07}_{-0.13}$	∼4.5	∼9.3	0.14	1.04	0.32

Notes. ^aMetallicity measured from host galaxy spectra. Diagnostics utilized varied between objects. ^bDiagnostic used to obtain Column 2. PP04N2 = Pettini & Pagel (2004); Z94 = Zaritsky et al. (1994); KD02 = Kewley & Dopita (2002); M91 = McGaugh (1991). ^cOffset normalized by the g-band half-light radius of the host galaxy.

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The total stellar mass in the host galaxies ranges from 8.0 < log  (M/M_☉) < 10.6 with a median value of log  (M/M_☉) = 9.0. In the first panel of Figure 16 we plot the cumulative distribution of our host masses in comparison to the CC-SN and long gamma-ray burst (LGRB) samples from Svensson et al. (2010). A larger fraction of our sample's hosts appear at relatively low masses in comparison to the CC-SN. A Kolmogorov–Smirnov (K-S) test yields a 14% (37%) probability that the rapidly evolving transients hosts are drawn from the same population as the CC-SN (LGRB) hosts. Thus, while our host galaxies skew slightly toward lower masses, there is no statistical evidence for a different parent population from either LGRBs or CC-SNe.

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Using the Markov Chain Monte Carlo method described in Sanders et al. (2012) we measure the emission line fluxes and metallicities of nine of the host galaxies. Due to the varying wavelength coverage and quality of our spectra, it was not possible to use the same strong line diagnostic for all of the galaxies. In Table 5 we list both the measured value and the diagnostic utilized. For the purposes of comparison, we then convert all of the values to the R23 system of Kewley & Dopita (2002) using the calibration relations from Kewley & Ellison (2008).

Many of the host galaxies have metallicities that are roughly solar, with a median value of log  (O/H) + 12 = 8.8. In the second panel of Figure 16 we plot their cumulative distribution. Our hosts are offset to a significantly higher metallicity than either LGRB hosts (Svensson et al. 2010; Savaglio et al. 2009; Levesque et al. 2010a; Levesque et al. 2010b; Graham & Fruchter 2013) or the untargeted Type Ibc hosts from Sanders et al. (2012) (black line and dashed green line, respectively) with a ≲0.5% probability of being drawn from the same population. The entire CC-SN sample from Kelly & Kirshner (2012) (solid green line) is shifted to even higher metallicities than our sample, although we caution a fraction of these events were discovered by targeted surveys (which bias toward higher metallicities).

In Figure 17 we plot the stellar mass versus metallicity for nine of the transients (red stars) versus the ∼53,000 SDSS star-forming galaxies from SDSS (Tremonti et al. 2004, shaded regions). Also shown are the low redshift LGRB hosts from Levesque et al. (2010b, black). The hosts of the PS1-MDS rapidly evolving SNe appear to be consistent with the bulk of star-forming galaxies in SDSS. This is in contrast to the hosts of LGRBs and Type I SLSNe, both of which have been shown to obey a relation in the mass–metallicity plane that is offset below the bulk of star-forming galaxies (Levesque et al. 2010b; Lunnan et al. 2014).

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We estimate host galaxy SFRs for the six events for which we possess galaxy spectra (Figure 15) by measuring their Hα line fluxes and applying the relation of Kennicutt (1998). In each case we apply a rough correction for the covering fraction of our spectra by scaling to our PS1 photometry of the hosts. We do not correct for intrinsic extinction. In the three cases where both Hα and Hβ are detected the decrement is reasonably consistent with zero extinction. The resulting SFRs range from 1–5 M_☉ yr⁻¹ and are listed in Table 5. For the four remaining objects we may place lower limits on the SFR by measuring the Hβ emission line flux from the explosion spectra (Figure 13) and assuming zero extinction. We do not attempt to correct for the covering fraction in these cases. The lower limits range from 0.1–0.3 M_☉ yr⁻¹. In the second and third panels of Figure 16 we plot the cumulative distribution of our SFRs and specific SFRs in comparison to the CC-SN and LGRB hosts from Svensson et al. (2010). Although the small number of events limits the conclusions we can draw, there is no statistical evidence that the samples are drawn from different progenitor populations. The SFRs measured for our hosts are clustered around the median value observed for both CC-SNe and LGRBs.

Using the PS1 centroid positions (good to ∼01) we measure the separation between the location of the transient and the center of its host galaxy. The cumulative distribution of these offsets (in physical units) are shown in the left panel of Figure 18 (red line). Also shown are distributions of Type Ia, Type Ibc and Type II SNe (Prieto et al. 2008, blue, green, and cyan, respectively), short-duration GRBs (Fong & Berger 2013, dashed black; SGRBs), and LGRBs (Bloom et al. 2002, solid black).

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In the right panel of Figure 18 we normalize these offsets by the g-band half-light radius of the host. Also shown are Type Ia SN (Galbany et al. 2012, blue), Type Ibc, and Type II SNe (Kelly & Kirshner 2012, green and cyan, respectively), and the same LGRB and SGRB samples as described above. For objects with high signal to noise SDSS detections, we use the Petrosian half-light radius from SDSS DR9. For others (PS1-11bbq, PS1-13duy, and PS1-13ess), we estimate the half-light radius based on the light within a 3'' radius of the centroid location within the PS1 deep stacks (we caution that these values are more uncertain). Both the physical and normalized offsets are listed in Table 5. Our sample most closely resembles the normalized offsets of Type Ibc and Type II SNe, indicating that, at least in this context, our explosion sites are consistent with the environments in which one can expect to find massive stars.

As described in Section 5, the continuum dominated spectra of our objects more closely resemble those of explosions powered by cooling envelope emission or interaction than those powered by radioactive decay. In addition, the rapid timescale and high peak luminosity of several of our events are difficult to reconcile with an explosion powered entirely by ⁵⁶Ni. This is demonstrated in Figure 20 where we plot the rise time versus peak luminosity for the gold/silver transients along with SNe from the literature that are powered by radioactive decay. Using the models of Arnett (1982) and Valenti et al. (2008) we map these parameters onto a grid of ⁵⁶Ni mass (M_Ni) and a parameter proportional to the total ejecta mass (M_ej) and kinetic energy (E_K) of the explosion. These results rely on the assumptions of spherical symmetry, centrally localized ⁵⁶Ni, and an optically thick ejecta.

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The M_Ni required to reproduce the peak luminosity of our events span a wide range (0.03 M_☉ < M_Ni < 0.7 M_☉). This range is similar to that spanned by Type Ib/Ic SNe, however, the devil is in the details. The degeneracy between M_ej and E_K can be broken by using the photospheric velocity of the explosion near maximum light. For a given velocity, a smaller characteristic time implies a lower ejecta mass. Thus, for objects with short overall timescales, it is possible to obtain the unphysical result that M_Ni > M_ej.

The photospheric velocities of our objects are unknown, so in Figure 20 we plot curved lines that represent M_Ni = M_ej for a variety of velocities. Any object to the upper left of a given line is physically disallowed for the simplified photospheric model. While the radioactively powered explosions from the literature fall comfortably in the region where M_Ni ≪ M_ej, several of our transients would require relatively high ejecta velocities (≳0.1c) to remain physical. In all cases the rise times and peak luminosities imply that the required nickel mass makes up a significant fraction of the total ejecta mass.

One caveat is that the models represented in Figure 20 assume the ejecta is optically thick. If this assumption breaks down, incomplete gamma-ray trapping at early times can produce a faster initial light curve evolution (Drout et al. 2013). For our objects, we can estimate the level of gamma-ray trapping required such that a ⁵⁶Co → ⁵⁶Fe decay tail would fall below our late-time PS1 photometry limits. For five of our ten gold objects, the late-time PS1 limits require incomplete gamma-ray trapping at early times if the peak is truly powered by ⁵⁶Ni. Using the parameterization of Valenti et al. (2008) to relate the level of trapping to M_ej and E_k we find that only two of our objects (PS1-10ah and PS1-12bb) have lower limits for M_Ni/M_ej that are less than 0.3.

Thus, if our objects are powered primarily by ⁵⁶Ni, they would require either (1) progenitors that can produce a relatively small ejecta mass composed almost entirely of ⁵⁶Ni—a scenario that seems inconsistent with the lack of strong UV line blanketing in our spectra—or (2) a explosion scenario in which either a significant amount of the radioactive material is mixed into the outer ejecta layers or there is a significant breakdown in spherical symmetry.

We are therefore converging on a situation where the early emission from many of our rapidly evolving events is powered by a source other than radioactive ⁵⁶Ni. In this case, it is useful to place limits on the amount of ⁵⁶Ni that could power a subsequent peak in the light curve (such as that observed in SN 1993J or Type Ibn SN iPTF13beo; Gorbikov et al. 2014) without exceeding our observed light curve points or late-time limits. SN 1993J possessed two peaks of similar optical luminosity. The first was due to cooling envelope emission and the second to the radioactive decay of ∼0.07 M_☉ of ⁵⁶Ni. Only one of our objects, PS1-13ess, shows evidence for a second peak in its light curve. The M_Ni required to power this second peak for PS1-13ess is 0.2–0.3 M_☉ (depending on the rise time, which is not well constrained). This is approximately four times higher than the amount that powered SN 1993J. In Figure 20 we use our observations to put upper limits on the amount of ⁵⁶Ni that could power such a secondary peak in the remainder of our transients.

For each object, we present a colored region which represents the maximum nickel mass that could power an optically thick explosion with a given rise time. For three of our objects (PS1-10ah, PS1-10bjp, and PS1-12bb) we can put an upper limit on the amount of ⁵⁶Ni that could power a secondary peak to ≲0.03 M_☉. This is lower than the amount inferred for all but a few Type Ibc and peculiar Type Ia SNe. Several Type II SNe have been constrained to have M_Ni < 0.03 M_☉, although over half of those analyzed in Hamuy (2003) have M_Ni larger than this. The limits on the more luminous transients are less constraining in comparison to Type Ib/Ic SNe.

The blue colors and spectra of several of our objects resemble those observed in SNe powered by cooling envelope emission or interaction with a dense CSM (e.g., Type IIb, Type IIn and Type Ibn SNe, several of which have peak luminosities and timescales, which also resemble the PS1 transients presented here). In this section we examine both the shock breakout from the surface of a star and a shock breakout that occurs within an optically thick wind surrounding the progenitor as possible power sources for our transients.

8.2.1. Shock Breakout from the Surface of a Star

First, we consider the case where these events are powered by the cooling envelope portion of the explosion of a massive star. While the shock breakout from a massive star lasts only a matter of seconds (WR stars) to hours (RSGs) the process shock heats the ejecta, which then cools and recombines, giving rise to optical emission which is independent from later emission powered by radioactive decay. The luminosity reached by the cooling envelope emission can give insight into the radius of the progenitor, with larger progenitors yielding more luminous events (due to both a larger emitting surface and reduced effects of adiabatic cooling), while the timescale of the event is related to the envelope mass that is cooling/recombining (see, e.g., Nakar & Sari 2010; Rabinak & Waxman 2011).

Several of our transients (e.g., PS1-10ah, PS1-12brf, PS1-13dwm, PS1-13ess) have peak luminosities and timescales that are similar to those observed for the cooling envelope portion of Type IIb SNe with extended progenitors. In Figure 21 we compare the light curve of SN 1993J to several of our gold sample objects and see that the initial decline of SN 1993J is well matched to the initial decline of our object PS1-10ah. This is consistent with the initial light curve signature expected for the explosion of progenitors with extended low-mass envelopes (Nakar & Piro 2014). However, with the exception of PS1-13ess, we do not observe a second peak due to the decay of ⁵⁶Ni as is observed in other Type IIb SNe. In fact, these intermediate luminosity objects are the transients for which we can place the strictest limits on the amount of ⁵⁶Ni that powers a secondary peak. For PS1-10ah we constrain M_Ni ≲ 0.03M_☉, which is more than a factor of two lower than that found for the second peak of SN 1993J (Woosley et al. 1994). This implies that some stripped envelope CC-SNe may eject a very small amount of radioactive isotopes. A similar point was raised in Kleiser & Kasen (2014) who modeled the rapidly declining Type Ic SN 2010X as an oxygen recombination event.

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While this power source seems reasonable for our intermediate luminosity events, a number of our other transients (PS1-11qr, PS1-11bbq, PS1-12bv, and PS1-13duy) possess peak luminosities that are a factor of 10 higher than that observed for SN 1993J (see Figure 21). Woosley et al. (1994) invoked a progenitor radius of ∼4 × 10¹³ cm in order to reproduce the light curve of SN 1993J. This is only a factor of two below the radii of the largest known RSGs (Levesque et al. 2009). Thus, if these events can be explained by the cooling envelope emission after shock breakout from the surface of a massive star, we would seem to require a progenitor that is both extremely extended, but also possesses a relatively low envelope mass. Alternatively, these events could represent cases where the shock breakout occurs not directly from a stellar surface, but inside a dense, optically thick, wind surrounding the star. This hypothesis was also put forth for the rapidly evolving Type IIn event, PFT09uj (Ofek et al. 2010), whose light curve bears striking resemblance to our higher luminosity events (Figure 21).

8.2.2. Shock Breakout within a Dense Wind

The case of a shock breakout from a dense wind has been examined from a theoretical perspective by Chevalier & Irwin (2011), Balberg & Loeb (2011), Ofek et al. (2010) and Ginzburg & Balberg (2014). For a wind environment, the density profile around the star goes as ρ_w∝r⁻². While the actual situation for the case of an optically thick mass-loss region may be more complex (e.g., due to shell ejections), this approximation has been made in previous works and will also be utilized here. These models have been applied to explain a number of super-luminous SNe (both Type I and Type II; Chevalier & Irwin 2011) as well other Type IIn SNe such as SN2009ip (Margutti et al. 2014) and PTF 09uj (Ofek et al. 2010) and the first peak of Type Ibn iPTF13beo (Gorbikov et al. 2014).

In their Appendix, Margutti et al. (2014) solve the equations given in Chevalier & Irwin (2011) for the case where the wind radius, R_w, is larger than the radius at which diffusion becomes important, R_d. These equations give the ejecta mass and kinetic energy of the explosion, as well as the opacity and density of the mass-loss region (as parameterized by a mass-loss rate $\dot{M}$) in terms of three observables: the rise time of the explosion (t_rise), the energy radiated on the rise (E_rad), and the radius at breakout (R_bo). Using our first measured blackbody radius for each transient (Figure 22) as an order of magnitude estimate for R_bo, we can utilize these models to estimate the physical parameters of the explosion and mass-loss region surrounding the progenitor. From Figure 22 we see that the breakout radius for our events is relatively small. All the events (including those whose first radius constraint was measured at maximum light) have values below that measured for SN 2009ip and an order of magnitude smaller than those measured for several SLSNe (Chevalier & Irwin 2011).

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These models are degenerate in M_ejE⁻² and we find values for the ejecta mass ranging from 1.0 (E/10⁵¹ erg) M_☉ ≲ M_ej ≲ 45.0 (E/10⁵¹ erg) M_☉. In comparison, Margutti et al. (2014) found M_ej = 50.5 (E/10⁵¹ erg) M_☉ for the 2012b outburst of SN2009ip. In Figure 23 we plot diagonal lines that represent the value of M_ejE⁻² obtained for each object. The shaded gray region in each panel represents an excluded region where the explosion energy (vertical axis) is lower than the total radiated energy calculated in Section 4. Horizontal lines in each panel then represent explosion energies that are 10 and 100 times the radiated energy.

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For these models we infer mass-loss rates ranging from 2 × 10⁻³(v_w/1000 km s⁻¹) M_☉ yr⁻¹ ≲ $\dot{M}$ ≲ 2 × 10⁻¹(v_w/1000 km s⁻¹) M_☉ yr⁻¹. A histogram of these values are shown in the first panel of Figure 24. We have normalized to a wind speed of 1000 km s⁻¹ based on the tentative CSM absorption observed in PS1-12bv (Section 5). These values exceed the mass-loss rates of WR stars (typically ≲10⁻⁴ M_☉ yr⁻¹) and may hint at a more complex or eruptive mass-loss history.

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In order to obtain more information about the mass-loss environment implied by these models, we next use the time when the bolometric luminosity calculated in Section 4 falls below that expected from continued interaction (Chevalier & Irwin 2011 Equation (9); Margutti et al. 2014 Equation (A6)) to estimate the time at which the shock reaches the outer radius of the dense wind region. For all of our objects, with the exception of PS1-10ah, this occurs within a few days after maximum light. For PS1-10ah the flattening of the light-curve at +10 days is consistent with the emission expected for continued interaction. Using this information and Equation (A7) from Margutti et al. (2014), we find that the dense wind extends to a few × 10¹⁵ cm for all of our objects (second panel, Figure 24). For three events (PS1-11bbq, PS1-12brf, and PS1-13duy) we were only able to put lower limits on the extent of the mass-loss region. These values are comparable to the dense wind radius of 1.2 ×10¹⁵ cm found by Margutti et al. (2014) for the 2012b explosion of SN 2009ip.

From this we find that the total mass contained within the region of dense mass-loss is only a few hundredths of a solar mass for most of our objects (third panel, Figure 24). This is an order of magnitude lower than the CSM mass found by Margutti et al. (2014) for the 2012b explosion of SN 2009ip. In addition, the timescale over which the ejection of this mass from the progenitor would have occurred is very short. For wind speeds of 1000 km s⁻¹ the mass-loss would have occurred in the ≲1 yr prior to explosion (fourth panel, Figure 24).

Chevalier & Irwin (2011) predict that the temperature of the explosion should rise to maximum in the case of shock breakout within a region of dense mass-loss. Unfortunately, for many of our objects we do not robustly constrain their temperature evolution on the rise. However, one of our best observed objects on the rise, PS1-10ah, does show evidence for a rise in temperature to maximum. Our best-fit blackbody for this object at maximum light is ∼18,000 K, but several days before max is only 10,000 K. This trend is also reflected in the observed g–r colors, which get bluer at maximum light.

If this physical scenario is an accurate representation of our transients, then they (along with PTF09uj) add to the interesting picture painted by Type IIn, Type Ibn, SLSN-II, and other transients about the (possibly eruptive) mass-loss that some massive stars undergo in the year(s) immediately prior to explosion. The rates of these short-duration transients are not insignificant compared to the rates of longer duration Type IIn SNe (8%–9% of CC-SNe; Smith et al. 2011). While the mass-loss rates and dense wind radii required for our transients are similar to those derived for other Type IIn events, the total mass contained in the dense CSM is a factor of 10 lower than that inferred for a majority of Type IIn SNe (see Smith 2014 and references therein). This, in turn, leads to a smaller break-out radius and shorter transient duration.

We now turn our attention to a set of non-explosive transients whose predicted properties bear some resemblance to several of our objects: the super-Eddington phase of a tidal disruption flare. To date, a majority of tidal disruption event candidates have been discovered in the UV and X-rays. This is expected given the high predicted blackbody temperature of material close to the supermassive black hole (SMBH) (∼3 × 10⁵ K; see, e.g., Lodato & Rossi 2011). However, for SMBHs with M ≲ 10⁸ M_☉, there may be a period of time after the initial disruption when accretion is super-Eddington, which can drive an outflow of material. Strubbe & Quataert (2009) model the light curves and spectra for this type of emission. They find that the transients are short-lived (≲30 days), luminous (L ∼ 10⁴³ erg s⁻¹), and peak in the optical/UV.

Cenko et al. (2012) argue that a super-Eddington outflow may explain the event PTF 10iya, which has several properties in common with the PS1-MDS transients. PTF 10iya has a rapid timescale (∼10 days), high peak luminosity (∼10⁴⁴ erg s⁻¹) and a blackbody temperature of ∼20,000 K. However, there are several difficulties in interpreting our objects similarly. First, and most obviously, PTF 10iya was coincident with the nucleus of its host galaxy to within 350 mas. The same is not the case for many of the transients presented here. Only PS1-10ah lies in the very central region of its host. While, in principle, a non-nuclear event could be due to a tidal disruption by an intermediate-mass black hole (IMBH), in the models of Strubbe & Quataert (2009) a characteristic timescale of ∼10 days requires a SMBH with a mass between 10⁶ and 10⁸ M_☉. The timescale for an IMBH would be ≲1 day.

In addition, Strubbe & Quataert (2009) predict that the observed temperature should increase slightly as the transient declines. In contrast, our objects show ejecta which cool with time. Finally, Cenko et al. (2012) argued that the blackbody radii measured for PTF 10iya (∼10¹⁵ cm) are too large for SN ejecta traveling at typical velocities to reach in such a short period of time. The same argument does not hold for our objects, whose blackbody radii are an order of magnitude smaller. Thus, despite sharing several observational properties with PTF 10iya, it is not obvious that any of our events are consistent with the emission predicted for the super-Eddington phase of a tidal disruption flare.

In contrast, Strubbe & Quataert (2009) predicted that the PS1-MDS should detect approximately 20 tidal disruption flares in their super-Eddington phase per year. Using their models and detection rates as a function of BH mass and the black hole mass function from Hopkins et al. (2007) we estimate that roughly 40% of these should fall in the rapidly evolving parameter space that was systematically examined in this paper. In addition, Strubbe & Quataert (2009) calculate their rates using a limiting flux of 25 AB mag for the PS1-MDS, which is 1–1.5 mag fainter than what the survey actually achieved. Using Equation (32) in Strubbe & Quataert (2009) to scale their derived rates to the true sensitivity obtained by PS1-MDS we produce a modified predicted detection rate of one to two events per year within the parameter space we have examined. Thus, given the stringent detection criteria we utilized in Section 2.2 it is possible that our lack of detections in four years of the PS1-MDS is not in conflict with the models of Strubbe & Quataert (2009).

In some cases, the merger of two low-mass neutron stars (NS) may produce a stable massive NS as opposed to collapsing to a black hole. Both Yu et al. (2013) and Metzger & Piro (2014) investigate the electromagnetic counterparts that would be produced from the formation of such a system if the magnetar spin-down energy is channeled into the ejecta from the merger, as opposed to a collimated jet. They predict optical/UV transients with peak bolometric luminosities of 10⁴³–10⁴⁴ erg s⁻¹, rise timescales of ≲1 day and overall timescales of ∼10 days. Although these predicted luminosities and timescales are slightly higher/shorter than those observed for the PS1-MDS transients presented here, their properties are broadly comparable.

However, both the derived rates for the PS1-MDS transients and their explosion site offset distribution disfavor a significant fraction originating from this channel. The "realistic" NS–NS merger rate from Abadie et al. (2010) is 1000 events yr⁻¹ Gpc⁻³ and the "high" rate is 10,000 events yr⁻¹ Gpc⁻³. The rates we derive in Section 7 are 4800–8000 events yr⁻¹ Gpc⁻³. Thus, if all of our events originated from this channel we would require a high NS–NS merger rate of which a significant fraction produce stable NS remnants. In addition, the offset distribution observed for our transients is consistent with that observed for CC-SNe rather than SGRBs (which are also thought to originate from NS–NS mergers). However, while this progenitor channel cannot explain the entire population of rapidly evolving objects we identify in the PS1-MDS, we cannot rule it out for some individual objects. To do so, we would require models with more detailed radiation transport to determine if the blue colors and continuum dominated spectra we observe are consistent with predictions.