THE NEEDLE IN THE 100 deg² HAYSTACK: UNCOVERING AFTERGLOWS OF FERMI GRBs WITH THE PALOMAR TRANSIENT FACTORY

A program called the iPTF TOO Marshal monitors the stream of Gamma-ray Coordinates Network (GCN) notices³⁷ from the three redundant, anonymous NASA/GSFC VOEvent servers. It listens for notices of type FERMI_GBM_GND_POS, sent by GBM's automated on-ground localization, or FERMI_GBM_FIN_POS, sent by the GBM burst advocate's human-in-the-loop localization.³⁸

Upon receiving either kind of notice, the TOO Marshal determines if the best-estimate sky position is observable from Palomar at any time within the 24 hr after the trigger. The criterion for observability is that the position is at an altitude $\gt 23\buildrel{\circ}\over{.} 5$ (i.e., airmass $\lesssim 2.5$), at least $20{}^\circ$ from the center of the moon, at an hour angle between $\pm 6\buildrel{\rm{h}}\over{.}5$, and that the Sun is at least $12{}^\circ$ below the horizon at Palomar.

If the position is observable and the 1σ statistical error radius r_stat reported in the GCN notice is less than $10{}^\circ$, the TOO Marshal selects a set of 10 P48 fields that optimally cover the error region.³⁹ It converts the GBM position estimate and radius into a probability distribution by applying a well-known empirical prescription of the systematic errors of the GBM localization. Paciesas et al. (2012b) state that the total effective error radius in the FERMI_GBM_FIN_POS localizations is well described by the quadrature sum of the statistical radius and a systematic contribution, where the systematic is $2\buildrel{\circ}\over{.} 6$ for 72% of bursts and $10\buildrel{\circ}\over{.} 4$ for 28% of bursts. We use the weighted rms of these two values, ${{r}_{{\rm sys}}}=\sqrt{0.72{{(}^{2\buildrel{\circ}\over{.} 6)2}}+0.28{{(}^{10\buildrel{\circ}\over{.} 4)2}}}\approx 6{}^\circ$. The total error radius is then ${{r}_{{\rm eff}}}=\sqrt{{{r}_{{\rm stat}}}^{2}+{{r}_{{\rm sys}}}^{2}}$. We construct a Fisher–von Mises distribution, centered on the best-estimate position, with a concentration parameter of

$$\begin{eqnarray}&&\kappa ={{\left[ 1-{\rm cos} \left( \frac{\pi }{180{}^\circ }{{r}_{{\rm eff}}} \right) \right]}^{-1}}.\end{eqnarray} \tag{ 1 }$$

With the FERMI_GBM_FIN_POS alert, the Fermi GBM team also distributes a detailed localization map that accounts for the systematic effects (Connaughton et al. 2015). The TOO Marshal retrieves from the Fermi data archive a file that describes the 1σ, 2σ, and 3σ significance contours. If the localization has significant asymmetry, we also retrieve a 2D FITS image whose pixel values correspond to the GBM localization significance, and use this instead of the Fisher–von Mises distribution.

Giving preference to fields for which deep co-added reference images exist, the TOO Marshal selects 10 P48 fields spanning an area of $\approx 72$ deg² to maximize the probability of enclosing the true (but as yet unknown) location of the source, assuming the above distribution.

The Marshal then immediately contacts a team of humans (the authors) by SMS text message, telephone, and e-mail. The humans are directed to a mobile-optimized web application to trigger the P48 (see Figure 11 in the Appendix).

Within the above constraints, we decide whether to follow up the burst based on the following criteria. The event must be ≲12 hr old when it first becomes observable from Palomar, and we must cover enough of the error circle to have a ≳30% chance of enclosing the position of the source. We discard any bursts that are detected and accurately localized by Swift BAT, because these are more efficiently followed up by conventional means. We also give preference to events that are out of the Galactic plane and that are observable for at least 3 hr.

There are some exceptional circumstances that override these considerations. If the burst's position estimate is accessible within an hour after the burst, we may select it even if the observability window is very brief. If the burst is very well localized or has the possibility of a substantially improved localization later due to a LAT or IPN detection, we may select it even if it is in the Galactic plane.

The default observing program is three epochs of P48 images at a 30-minute cadence. The human may shorten or lengthen the cadence if the burst is very young or old (see the discussion of Equation (2) in Section 2.4 below), change the number of epochs, or add and remove P48 fields. When the human presses the "Go" button, the TOO Marshal sends a machine-readable e-mail to the P48 robot. The robot adds the requested fields to the night's schedule with the highest possible priority, ensuring that they are observed as soon as they are visible.

As the night progresses, the TOO Marshal monitors the progress of the observations and the iPTF real-time image subtraction pipeline (P. E. Nugent et al. 2015, in preparation). The real-time pipeline creates difference images between the new P48 observations and co-added references composed of observations from months or years earlier. It generates candidates by performing source extraction on the difference images. A machine learning classifier assigns a real/bogus score (RB2; Brink et al. 2013) to each candidate that predicts how likely the candidate is to be a genuine astrophysical source (rather than a radiation hit, a ghost, an imperfect image subtraction residual, or any other kind of artifact).

Table 1 lists the number of candidates that remain after each stage of candidate selection. First, requiring candidates to have signal-to-noise ratio (S/N) > 5 gives us a median of 35,000 candidates. This number varies widely with galactic latitude and the area searched (a median of ∼500 deg⁻²). Second, we only select candidates that have RB2 > 0.1, reducing the number of candidates to a median of 36% of the original list.⁴⁰ Third, we reject candidates that coincide with known stars in reference catalogs (Sloan Digital Sky Survey (SDSS) and the PTF reference catalog), cutting the list to 17%. Fourth, we eliminate asteroids cataloged by the Minor Planet Center, reducing the list to 16%. Fifth, we demand at least two secure P48 detections after the GBM trigger, reducing the list to a few percent, or ∼500 candidates.

Table 1.  Number of Optical Transient Candidates Surviving Each Vetting Stage

	S/N	RB2	Not	Not in	Detected	Saved for
GRB	$\gt 5$	$\gt 0.1$	Stellar	MPCa	Twice	Follow-up	RB2b
130702A	14 629	2 388	1 346	1 323	417	11	0.843
131011A	21 308	8 652	4 344	4 197	434	23	0.198
131231A	9 843	2 503	1 776	1 543	1 265	10	0.137
140508A	48 747	22 673	9 970	9 969	619	42	0.730
140606B	68 628	26 070	11 063	11 063	1 449	28	0.804
140620A	152 224	50 930	17 872	17 872	1 904	34	0.826
140623A	71 219	29 434	26 279	26 279	442	23	0.873
140808A	19 853	4 804	2 349	2 349	79	12	0.318
Median reduction		36%	17%	16%	1.7%	0.068%

^aNot in Minor Planet Center database. ^bRB2 score of optical afterglow in earliest P48 detection.

Download table as:  ASCIITypeset image

When the image subtraction pipeline has finished analyzing at least two successive epochs of any one field, the TOO Marshal contacts the humans again and the surviving candidates are presented to the humans via the Treasures portal.

The remaining candidate vetting steps currently involve human participation and are informed by the nature of the other transients that iPTF commonly detects: foreground SNe (slowly varying and in low-z host galaxies), active galactic nuclei (AGNs), cataclysmic variables, and M-dwarf flares.

In the Treasures portal, we visually scan through the automatically selected candidates one P48 field at a time, examining ∼10 objects per field (see Figure 12 in the Appendix for a screenshot of the Treasures portal). We visually assess each candidate's image subtraction residual compared to the neighboring stars of similar brightness in the new image. If the residual resembles the new image's point-spread function, then the candidate is considered likely to be a genuine transient or variable source.

Next, we look at the photometric history of the candidates. Given the time, t, of the optical observation relative to the burst and the cadence, $\delta t$, we expect that a typical optical afterglow that decays as a power law ${{F}_{\nu }}\propto {{t}^{-\alpha }}$, with $\alpha =1$, would fade by $\delta m=2.5{{{\rm log} }_{10}}(1+\delta t/t)$ mag over the course of our observations. Any source that exhibits statistically significant fading ($\delta m/m\gg 1$) consistent with an afterglow decay becomes a prime target.⁴¹

Note that a $1\sigma$ decay in brightness requires such a source to be

$$\begin{eqnarray}&&-2.5{{{\rm log} }_{10}}\left( \frac{\delta t}{t\sqrt{2}} \right)\end{eqnarray} \tag{ 2 }$$

brighter than the $1\sigma$ limiting magnitude of the exposures. For example, given the P48's typical limiting magnitude of R = 20.6 and the standard cadence of $\delta t=0.5$ hr, if a burst is observed t = 3 hr after the trigger, its afterglow may be expected to have detectable photometric evolution only if it is brighter than R = 18.3. Noting that long GRBs preferentially occur at high redshifts and in intrinsically small, faint galaxies (Svensson et al. 2010), we consider faint sources that do not display evidence of fading if they are not spatially coincident with any sources in SDSS or archival iPTF observations.

If a faint source is near a spatially resolved galaxy, then we compute its distance modulus using the galaxy's redshift or photometric redshift from SDSS. We know that long GRB optical afterglows at t = 1 day typically have absolute magnitudes of $-{\mkern 1mu} 25\lt {{M}_{B}}\lt -21$ mag (1σ range; see Figure 9 of Kann et al. 2011). Most SNe are significantly fainter: Type Ia are typically ${{M}_{B}}\sim -19$ mag, whereas Type Ibc and II are ${{M}_{B}}\sim -17$ mag, with luminous varieties of both Type Ibc and II extending to ${{M}_{B}}\sim -19$ mag (Richardson et al. 2002; Li et al. 2011). Therefore, if the candidate's presumed host galaxy would give it an absolute magnitude ${{M}_{R}}\lt -20$ mag, it is considered promising. This criterion is only useful for long GRBs because short GRB afterglows are typically ∼6 mag fainter than long GRB afterglows (Kann et al. 2011).

The human saves all candidates that are considered promising by these measures to the iPTF Transient Marshal database. This step baptizes them with an iPTF transient name, which consists of the last two digits of the year and a sequential alphabetic designation.

Once named in the Transient Marshal, we perform archival vetting of each candidate using databases including VizieR (Ochsenbein et al. 2000), NED,⁴²  the High Energy Astrophysics Science Archive Research Center (HEASARC),⁴³  and Catalina Real-time Transient Survey (Drake et al. 2009), in order to check for any past history of variability at that position (see Figure 13 in the Appendix for a screenshot of the Transient Marshal).

We check for associations with known quasars or AGNs in Véron-Cetty & Véron (2010) or with AGN candidates in Flesch (2010).

M dwarfs can produce bright, blue, rapidly fading optical flares that can mimic optical afterglows. To filter our M dwarfs, we check for quiescent infrared counterparts in WISE (Cutri et al 2014). Stars of spectral type L9–M0 peak slightly blueward of the WISE bandpass, with typical colors (Wright et al. 2010)

$$\begin{eqnarray*}\begin{array}{ccccccccccccccc} 3\;\lesssim & [R-W1] & \lesssim 12 \\ 0.1\;\lesssim & [W1-W2] & \lesssim 0.6 \\ 0.2\;\lesssim & [W2-W3] & \lesssim 1 \\ 0\;\lesssim & [W3-W4] & \lesssim 0.2. \\ \end{array}\end{eqnarray*}$$

Therefore, a source that is detectable in WISE but that is either absent from or very faint in the iPTF reference images suggests a quiescent dwarf star.

The above stages usually result in ∼10 promising optical transient candidates that merit further follow-up. If, by this point, data from Fermi LAT or from IPN satellites are available, we can use the improved localization to select an even smaller number of follow-up targets.

For sources whose photometric evolution is not clear, we perform photometric follow-up. We may schedule additional observations of some of the P48 fields if a significant number of candidates are in the same field. We may also use the P48 to gather more photometry for sources that are superimposed on a quiescent source or galaxy, in order to make use of the image subtraction pipeline to automatically obtain host-subtracted magnitudes. For isolated sources, we schedule one or more epochs of r-band photometry with the P60. If, by this point, any candidates show strong evidence of fading, we begin multicolor photometric monitoring with the P60.

Next, we acquire spectra for one to three candidates per burst using the P200, Gemini, Keck, Magellan, or Himalayan Chandra Telescope (HCT). A spectrum that has a relatively featureless continuum and high-redshift absorption lines secures the classification of the candidate as an optical afterglow.

Once any single candidate becomes strongly favored over the others based on photometry or spectroscopy, we trigger X-ray and UV observations with Swift and radio observations with VLA, CARMA, and AMI. Detection of a radio or X-ray afterglow typically confirms the nature of the optical transient, even without spectroscopy.

Finally, we promptly release our candidates, upper limits, and/or confirmed afterglow discovery in GCN circulars.

The reported P48 magnitudes are all in the Mould R band and in the AB system (Oke & Gunn 1983), calibrated with respect to either r' point sources from SDSS or for non-SDSS fields using the methods described in Ofek et al. (2012).

To monitor the optical evolution of afterglows identified by our program, we typically request nightly observations in ri (and occasionally gz) filters for as long as the afterglow remained detectable. Bias subtraction, flat-fielding, and other basic reductions are performed automatically at Palomar by the P60 automated pipeline using standard techniques. Images are then downloaded and stacked as necessary to improve the S/N. Photometry of the optical afterglow is then performed in IDL using a custom aperture-photometry routine, calibrated relative to SDSS secondary standards in the field (when available) or using our own solution for secondary field standards constructed during a photometric night (for fields outside the SDSS footprint).

For some bursts (GRB 140606B), we also obtain photometry with the Large Monolithic Imager (LMI) mounted on the 4.3 m Discovery Channel Telescope (DCT) in Happy Jack, AZ. Standard CCD reduction techniques (e.g., bias subtraction, flat-fielding) are applied using a custom IRAF pipeline. Individual exposures are aligned with respect to astrometry from the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) using SCAMP (Bertin et al. 2006) and stacked with SWarp (Bertin et al. 2002).

Where GROND (Greiner et al. 2008) and RATIR (Butler et al. 2012) have reported multicolor photometry in GCN circulars, we include their published data in Table 2 and our light-curve plots.

We monitor GBM–iPTF afterglows with CARMA, a millimeter-wave interferometer located at Cedar Flat near Big Pine, California. All observations are conducted at 93 GHz in single-polarization mode in the array's C, D, or E configuration. Targets are typically observed once for 1–3 hr within a few days after the GRB, establishing the phase calibration using periodic observations of a nearby phase calibrator and the bandpass and the flux calibration by observations of a standard source at the start of the track. If detected, we acquire additional observations in approximately logarithmically spaced time intervals until the afterglow flux falls below detection limits. All observations are reduced using MIRIAD using standard interferometric flagging and cleaning procedures.

We look for radio afterglows at 6.1 and/or 22 GHz with VLA. VLA observations are reduced using the Astronomy Software Applications package. The calibration is performed using the VLA calibration pipeline. After running the pipeline, we inspect the data (calibrators and target source) and apply further flagging when needed. The VLA measurement errors are a combination of the rms map error, which measures the contribution of small unresolved fluctuations in the background emission and random map fluctuations due to receiver noise, and a basic fractional error (here estimated to be $\approx 5\%$), which accounts for inaccuracies of the flux density calibration. These errors are added in quadrature, and total errors are reported in Table 3.

Starting in 2014 August, we also look for radio emission with AMI. AMI is composed of eight 12.8 m dishes operating in the 13.9–17.5 GHz range (central frequency of 15.7 GHz) when using frequency channels 3–7 (channels 1, 2, and 8 are disregarded due to their currently susceptibility to radio interference). For further details on the reduction and analysis performed on the AMI observations please see Anderson et al. (2014b).

This is the first GBM burst whose afterglow we discovered with iPTF (Singer et al. 2013b), indeed the first afterglow ever to be pinpointed based solely on a Fermi GBM localization. It is also the lowest-redshift GRB in our sample, so it has the richest and most densely sampled broadband afterglow data. It has two other major distinctions: its associated SN (SN 2013dx, Schulze et al. 2013; Pozanenko et al. 2013; Cenko et al. 2013a; D'Elia et al. 2013) was detected spectroscopically, and its prompt energetics are intermediate between low-luminosity GRBs (llGRBs) and standard cosmic bursts (see below).

Based on the Fermi GBM ground localization with an error radius of $4{}^\circ$, we imaged 10 fields twice with the P48 at ${\Delta }t=t-{{t}_{{\rm GBM}}}=4.2$ hr after the burst.⁴⁴ We scheduled P60 imaging and P200 spectroscopy for three significantly varying sources. Of the three, iPTF13bxl showed the clearest evidence of fading in the P48 images. Its spectrum at ${\Delta }t=1.2$ days consisted of a featureless blue continuum. We triggered Swift, which found a bright X-ray source at the position of iPTF13bxl (Singer et al. 2013c; D'Avanzo et al. 2013). Shortly after we issued our GCN circular (Singer et al. 2013c), Cheung et al. (2013) announced that the burst had entered the FOV of LAT at ${\Delta }t=250$ s. The LAT error circle had a radius of $0\buildrel{\circ}\over{.} 5$, and its center was $0\buildrel{\circ}\over{.} 8$ from iPTF13bxl. An IPN triangulation with MESSENGER (GRNS), INTEGRAL (SPI-ACS), Fermi-GBM, and Konus-Wind (Hurley et al. 2013) yielded a $0\buildrel{\circ}\over{.} 46$-wide annulus that was also consistent with the OT.

The afterglow's position is $0\buildrel{\prime\prime}\over{.} 6$ from an R = 23.01 mag source that is just barely discernible in the P48 reference images. A spectrum from NOT+ALFOSC (Leloudas et al. 2013) determined a redshift of z = 0.145 for a galaxy $7\buildrel{\prime\prime}\over{.} 6$ to the south of iPTF13bxl. At ${\Delta }t=2.0$ days, we obtained a Magellan+IMACS spectrum (Mulchaey et al. 2013) and found weak emission lines at the location of the afterglow that we interpreted as Hα and [O iii] at the same redshift. Kelly et al. (2013) characterized the burst's host environment in detail and concluded that it exploded in a dwarf satellite galaxy.

Joining the two P48 observations at ${\Delta }t\lt 1$ day to the late-time P60 light curve requires a break at ${\Delta }t=1.17\pm 0.09$ days, with slopes ${{\alpha }_{{\rm O},1}}=0.57\pm 0.03$ and ${{\alpha }_{{\rm O},2}}=1.05\pm 0.03$ before and after the break, respectively. The XRT light curve begins just prior to this apparent break and seems to follow the late-time optical decay (until the SN begins to dominate at ${\Delta }t=5$ days), although the automated Swift light-curve analysis (Evans et al. 2009) also suggests a possible X-ray break with about the same time and slopes. This hints at an achromatic break, normally a signature of a jet. However, the late slope and the change in slope are both unusually shallow for a jet break. Furthermore, the radio light curve does not exhibit a break. The change in slope is also a little too large for cooling frequency crossing the band (for which one would expect ${\Delta }\alpha =1/4$). An energy injection or a structured jet model may provide a better fit (Panaitescu 2005).

Late-time ${\Delta }t\gt 1$ day observations include several P60 gri observations, three RATIR $r^{\prime} i^{\prime} ZYJH$ epochs, an extensive Swift XRT and UVOT light curve, and radio observations with VLA and CARMA (although of the VLA data, we only have access to the first observation). The optical and X-ray spectral slopes are similar, ${{\beta }_{{\rm O}}}=0.7\pm 0.1$ and ${{\beta }_{{\rm X}}}=0.8\pm 0.1$. An SED at $2\lt {\Delta }t\lt 2.3$ days is well explained by the standard external shock model (Sari et al. 1998) in the slow cooling regime, with ${{\nu }_{m}}$ lying between the VLA and CARMA frequencies and ${{\nu }_{c}}$ in the optical. This fit requires a relatively flat electron spectrum, $d{{n}_{{\rm e}}}/d{{\gamma }_{{\rm e}}}\propto \gamma _{{\rm e}}^{-p}$ with $p\approx 1.6$, cut off at high energies. Applying the relevant closure relations (for the case of $1\lt p\lt 2$; see Dai & Cheng 2001) to ${{\alpha }_{X}}$ and ${{\beta }_{X}}$ permits either an ISM or wind environment.

Our late-time spectroscopy and analysis of the SN will be published separately (S. B. Cenko et al. 2015, in preparation).

We started P48 observations of Fermi trigger 403206457 (Jenke 2013) about 11.6 hr after the burst. The optical transient iPTF13dsw (Kasliwal et al. 2013) faded from R = 19.7 mag to R = 20.2 mag from 11.6 to 14.3 hr. The latest pre-trigger image on 2013 September 25 had no source at this location to a limit of $R\gt 20.6$ mag. The optical transient continued to fade as it was monitored by several facilities (Xu et al. 2013a, 2013c; Perley et al. 2013; Sudilovsky et al. 2013; Volnova et al. 2013).

At 15.1 hr after the burst, we obtained a spectrum of iPTF13dsw with the Gemini Multi-object Spectrograph (GMOS) on the Gemini South telescope. GMOS was configured with the R400 grating with a central wavelength of 7200 Å and the 1'' slit, providing coverage over the wavelength range of 5100–9300 Å with a resolution of $\approx 3$ Å. No prominent features were detected over this bandpass, while the spectrum had a typical S/N of $\approx 3$–4 per 1.4 Å pixel. Rau et al. (2013) observed the optical transient with the X-Shooter instrument on the ESO 8.2 m VLT. In their spectrum extending from ∼3000 to ∼24000 Å, they identified several weak absorption lines from which they derived a redshift of z = 1.874. Both spectra are shown in Figure 5.

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The source was detected by Swift XRT (Page 2013), but with insufficient photons for spectral analysis. The source was observed with ATCA, but no radio emission was detected. Largely because in our sample this is the oldest afterglow at the time of discovery, there are not enough broadband data to constrain the blast wave physics.

GRB 131231A was detected by Fermi LAT (Sonbas et al. 2013) and GBM (Jenke & Xiong 2014), with photons of energies up to 9.7 GeV. Xu et al. (2013b) observed the LAT error circle with the 1 m telescope at Mt. Nanshan, Xinjiang, China. At 7.9 hr after the burst, they detected a single $R=\sim 17.6$ mag source that was not present in SDSS images. At 17.3 hr after the burst, Malesani et al. (2013) observed the afterglow candidate with the MOSaic CAmera on the 2.56 m Nordic Optical Telescope (NOT). The source had faded to R = 18.6.

Although we had imaged 10 P48 fields shortly after the Fermi trigger (Singer et al. 2013a), due to the short visibility window at Palomar we were only able to obtain one epoch. At 1.45 hr after the burst, we detected an R = 15.7 mag optical transient iPTF13ekl at the position of the Nanshan candidate. Though our single detection of iPTF13ekl could not by itself rule out that the source was a moving solar system object, the Nanshan detection at 6.46 hr, fitting a decay with a power-law index of $\alpha =1.03$, was strong evidence that the transient was the optical afterglow of GRB 131231A.

On January 1.09 UT (21.5 hr after the trigger), we observed the afterglow with Gemini South using the GMOS camera (Hook et al. 2004) in Nod&Shuffle mode: we obtained 32 dithered observations of 30 s each at an average airmass of 2. We analyzed this data set using the dedicated GEMINI package under the IRAF environment and extracted the one-dimensional spectrum using the APALL task. We determined the redshift of the GRB, based on the simultaneous identification of forbidden nebular emission lines ([O ii], [O iii]) and absorption features (CaH&K) at the same redshift of z = 0.6419. In Figure 5, we show the normalized spectrum.

The source was also detected by Swift XRT (Mangano et al. 2014b) and UVOT (Holland & Mangano 2014), as well as CARMA (Perley 2014).

With only the millimeter, optical, and X-ray observations, the SED is highly degenerate. Contributing to the degeneracy, the X-ray and optical observations appear to fall on the same power-law segment. It is consistent with either fast or slow cooling if the greater of ${{\nu }_{c}}$ or ${{\nu }_{m}}$ is near the optical, assuming a flat electron distribution with $p\sim 1.5$. It is also consistent with slow cooling if ${{\nu }_{c}}$ is above the X-ray band and $p\sim 2.6$.

This burst was detected by Fermi GBM and INTEGRAL SPI-ACS (Yu & Goldstein 2014), as well as by Konus-Wind, Mars Odyssey (not included in the GCN circular), Swift BAT (outside the coded FOV), and MESSENGER, yielding a $1\buildrel{\circ}\over{.} 5\times 12^{\prime}$ IPN error box (Hurley et al. 2014c).

Due to poor weather early in the night, P48 observations started 6.7 hr after the trigger (Singer et al. 2014a). We found one optical transient candidate within the IPN triangulation, iPTF14aue, which faded from $r=17.89\pm 0.01$ mag with a power-law fit of $\alpha =1.12\pm 0.1$ over a timescale of 1.5 hr.

We triggered a Swift TOO. From 0.8 to 8.1 days after the trigger, Swift XRT detected a coincident X-ray source that faded with a power law $\alpha =1.48\ (+0.15,-0.14)$ (Amaral-Rogers 2014a, 2014b). The source was also detected by Swift UVOT (Marshall & AmarelRogers 2014).

Moskvitin et al. (2014) obtained a 20-minute, 3800–7200 Å spectrum of iPTF14aue with the 6 m BTA telescope in Zelenchukskaia. Exhibiting no absorption features, this established an upper limit of $z\lt 2.1$. Malesani et al. (2014) used the Andalucia Faint Object Spectrograph and Camera (ALFOSC) on NOT to get an 1800 s spectrum spanning 3200–9100 Å, and found several absorption features at redshift z = 1.03. Consistent redshifts were reported by Wiersema et al. (2014) with the ACAM instrument on the 4.2 m William Herschel Telescope and by Bhalerao & Sahu (2014) with Himalaya Faint Object Spectrograph and Camera (HFOSC) on the 2 m HCT. This last spectrum is shown in Figure 5.

Due to the brightness of the optical transient, optical photometry was available from several facilities up to 4.5 days after the burst (Butler et al. 2014a, 2014b; Gorosabel et al. 2014b; Moskvitin et al. 2014; Malesani et al. 2014; Masi 2014; Fujiwara et al. 2014; Volnova et al. 2014a).

Horesh et al. (2014) detected the source with VLA 5.2 days after the Fermi trigger, at 6.1 GHz (C band) and at 22 GHz (K band). A broadband SED constructed from P60 and XRT data from around this time is consistent with $p\approx 2$. Because p is not distinguishable from 2, we cannot discriminate between fast and slow cooling based on this one time slice. However, given the late time of this observation, the slow cooling interpretation is more likely, putting ${{\nu }_{m}}$ between the radio and optical bands and ${{\nu }_{c}}$ between the optical and X-ray. Because the VLA light curve is decreasing with time, an ISM circumburst density profile is favored.

Fermi trigger 423717114 (Burns 2014) was observable from Palomar for several hours, starting about 4.3 hr after the time of the burst. Based on the final GBM localization, we searched 10 P48 fields and found several plausible optical transient candidates (Singer et al. 2014c).

iPTF14bfu had no previous detections in iPTF between 2013 May 23 and October 13. Its position was outside the SDSS footprint, but it had no plausible host associations in VizieR (Ochsenbein et al. 2000). From 4.3 to 5.5 hr after the burst, it faded from $R=19.89\pm 0.10$ to 20.32 ± 0.14 mag, fitting a power law of $\alpha =-1.6\pm 0.7$ relative to the time of the GBM trigger. iPTF14bfw ($R=19.96\pm 0.06$ mag) was coincident with an r = 21.27 galaxy in SDSS DR10 and displayed no statistically significant photometric variation over the course of our P48 observations. iPTF14bgc ($R=18.44\pm 0.02$ mag) was coincident with an $R=21.07\pm 0.08$ mag point source in our co-added reference image composed of exposures from 2013 July 31 through September 24. iPTF14bga ($R=19.75\pm 0.06$ mag) was likewise coincident with a $R=20.42\pm 0.17$ mag point source in our reference image composed of exposures from 2011 July 29 through October 20.

On the following night, we observed all four candidates again with P48 and P60 (Perley & Singer 2014). iPTF14bfw and iPTF14bga had not faded relative to the previous night. iPTF14bgc had faded to $R=20.68\pm 0.21$ mag, consistent with the counterpart in our reference images but significantly fainter than the previous night. A power-law fit to the decay gave a temporal index of $\alpha =-1.1\pm 0.1$, entirely consistent with typical GRB afterglows. iPTF14bfu was not detected in our P48 images to a limiting magnitude of $R\lt 21.1$, but it was detected in stacked P60 images ($r=21.1\pm 0.2$), consistent with a power law of $\alpha \sim -0.5$.

An IPN triangulation from Fermi, Konus–Wind, and MESSENGER yielded a long, slender $14\buildrel{\circ}\over{.} 18\times 0\buildrel{\circ}\over{.} 414$ error box that contained iPTF14bfu and iPTF14bfw (Hurley et al. 2014d).

We obtained two 900 s spectra with the DEIMOS spectrograph on the Keck II 10 m telescope (Perley et al. 2014a). On a blue continuum, we found [O ii], [O iii], and H α emission features and Ca ii absorption features, at a common redshift of z = 0.384. A galaxy offset by $\sim 2^{\prime\prime}$ along the slit showed the same emission lines at the same redshift.

Swift XRT observed the location of iPTF14bfu for a total of 9 ks from 2.1 to 9.3 days after the GBM trigger, and found a source that faded with a power-law fit of $\alpha =-1.0\ (+0.7,-0.6)$ (Mangano 2014; Mangano & Burrows 2014; Mangano et al. 2014a).

At 18.4 days after the trigger, we obtained a 1200 s spectrum of iPTF14bfu with the Low Resolution Imaging Spectrometer on the Keck I 10 m telescope (Perley et al. 2014b). The spectrum had developed broad emission features. A comparison using Superfit (Howell et al. 2005) showed a good match to SN 1998bw near maximum light, indicating that the source had evolved into an SN Ic-BL. Our late-time photometry and spectroscopy will published separately (Cano et al. 2015).

Although there were three radio detections of GRB 140606B, only during the first CARMA detection does the optical emission appear to be dominated by the afterglow. We can construct an SED around this time using nearly coeval DCT and XRT data. Because of the faintness of the X-ray afterglow, the spectral slopes ${{\beta }_{{\rm X}}}$ and ${{\beta }_{{\rm OX}}}$ are only weakly determined. As a result, there is a degeneracy between two plausible fits. The first has ${{\nu }_{m}}$ anywhere below the CARMA band, ${{\nu }_{c}}$ just below the X-rays, and $p\approx 2$. The second has ${{\nu }_{m}}$ just above the radio and ${{\nu }_{c}}$ in the middle of the XRT band, with $p\approx 2.2$.

The early P48 observations do not connect smoothly with the P60 and DCT observations from ${\Delta }t=1$ to 4 days. This may indicate a steep–shallow–steep time evolution requiring late-time energy injection, or it may just indicate that the afterglow is contaminated by light from the host galaxy or the SN at relatively early times.

This burst is distinctive in our sample for two reasons. First, it is the earliest afterglow detection in the iPTF sample at ${\Delta }t=0.25$ hr. Second, its broadband SED is not clearly explainable by the standard forward shock model.

Fermi trigger 424934131 (Fitzpatrick & Connaughton 2014) was observable from Palomar for about 6 hr from the time of the burst. Based on the ground localization, we started observing 10 P48 fields about 10 minutes after the trigger. Based on the final localization, we added 10 more fields, for a total of 20, about an hour after the trigger.

The candidate iPTF14cva (Kasliwal et al. 2014) was contained within one of the early 10 fields. From 14.9 to 87.2 minutes after the trigger, the candidate faded from $R=17.60\pm 0.01$ to 18.80 ± 0.02 mag, consistent with a somewhat slow power law of $\alpha =0.62\pm 0.01$.

We observed the candidate with GMOS on the 8 m Gemini North telescope. Starting 8.8 hr after the trigger, we obtained two 900 s spectra extending from 4000 to 9300 Å. We detected Mg ii and Fe ii absorption lines at z = 0.88 and many absorption features at a common redshift of z = 2.04. The lack of Lyα absorption implied an upper limit of $z\sim 2.3$ and suggested that z = 2.04 was the redshift of the source.

We triggered Swift and VLA follow-up. In a 3 ks exposure starting 10.4 hr after the Fermi trigger, Swift XRT detected an X-ray source with a count rate of $1.2\times {{10}^{-1}}$ counts s⁻¹ (De Pasquale 2014b). Over the next 4 days of Swift observations, the X-ray source faded with a slope $\alpha =1.32\pm 0.16$ (De Pasquale 2014a). A fading source was also detected by Swift UVOT (Siegel & De Pasquale 2014).

The source was detected by VLA on June 23 at 6.1 GHz (C band) at 108 ± 15 μJy and at 22 GHz (K band) at 62 ± 15 μJy. On June 30, there was a marginal detection in C band with 48 ± 12 μJy and no detection in K band with a noise level of 15 μJy rms.

The optical transient was also observed in R band by the Konkoly Observatory (Kelemen 2014) and the 1 m telescope at the Tien Shan Astronomical Observatory (Volnova et al. 2014b).

The SED of this afterglow cannot be explained by a standard forward shock model. If we place the peak frequency near the radio band, the optical and X-ray fluxes are drastically underpredicted, whereas if we place the peak frequency between the optical and X-ray bands, we miss the radio observations by orders of magnitude. This seems to require an additional component. One possibility is that there is a forward shock peak in the UV and a reverse shock peak at low frequencies (similar to GRB 130427A; see Laskar et al. 2013; Perley et al. 2014d). Another possibility is that there is an inverse Compton peak in the UV (similar to GRB 120326A; Urata et al. 2014).

Fermi trigger 425193729 (von Kienlin 2014) was observable from Palomar for about 6 hr from the time of the burst. Based on the ground localization, we started imaging 10 fields 11 minutes after the trigger. The final Fermi localization, which was avilable 2.6 hr later, shifted by 134. Due to the large change in the localization, we calculated only a 4% chance that the source was contained within the P48 fields.

Candidate iPTF14cyb (Kasliwal et al. 2014), situated at an extreme edge of the P48 tiling, was within the 1σ confidence region for both the ground and final localizations. From 16 to 83 minutes after the trigger, the source faded from $R=18.04\pm 0.01$ to 19.69 ± 0.06 mag, consistent with a power-law decay with an index $\alpha =0.94\pm 0.03$.

Starting 2.8 hr after the trigger, we obtained two 900 s GMOS spectra extending from 4000 to 9300 Å. We detected Mg ii and Fe ii absorption lines at z = 1.06 and many absorption features at z = 1.92. The lack of Lyα absorption implied that this was the redshift of the burst.

We triggered Swift, VLA, and CARMA follow-up. In a 3 ks exposure starting 10.7 hr after the burst, Swift XRT detected an uncataloged X-ray source with a count rate of $(2.2\pm 0.6)\times {{10}^{-3}}$ counts s⁻¹ (D'Elia et al. 2014). By 79 hr after the trigger, the source was no longer detected in a 5 ks exposure (D'Elia & Izzo 2014). No radio source was detected with VLA in C band (6.1 GHz) to an rms level of 17 μJy, or in K band (22 GHz) to an rms level of 18 μJy.

Because of the lack of radio detections and the extreme faintness of the X-ray afterglow, the broadband behavior of the afterglow does not constrain the shock physics.

Fermi trigger 429152043 (Zhang 2014) was observable from Palomar about 3 hr after the burst. We imaged 13 fields with P48 and found one promising optical transient. iPTF14eag was situated on the extreme edge of one of the P48 tiles that was just outside the GBM 1σ contour. It faded from $R=18.91\pm 0.06$ to 19.29 ± 0.10 mag from 3.35 to 4.91 hr after the trigger and had no archival counterparts in SDSS or in our own reference images.

Due to Hurricane Iselle, we were unable to use our TOO programs on Keck or Gemini North. We requested photometric confirmation of the fading from HCT (Sahu et al. 2014), submitted a Swift TOO, and sent our GCN circular (Singer et al. 2014b) to encourage others to obtain a spectrum.

Swift observed the position of iPTF14eag from 11.6 to 14.4 hr after the burst (Page et al. 2014). An X-ray source was detected with a count rate of $1.5\times {{10}^{-2}}$ counts s⁻¹. In a second observation starting 62.2 hr after the trigger (Page & Cenko 2014), the source had faded to below $2.46\times {{10}^{-3}}$ counts s⁻¹. No source was detected by UVOT (Oates & Cenko 2014).

We obtained a spectrum with the OSIRIS instrument (Cepa et al. 2000) on Gran Telescopio Canarias (GTC) in four 900s exposures with a mean epoch of 21.340 hr after the burst. We used the R1000B grism and a 1'' slit, with a resolution of R 1000. We determined a redshift of 3.293 (improved from the one given by Gorosabel et al. 2014a) through the identification of strong absorption features. The flux-calibrated spectrum is shown in Figure 5.

The source was detected in radio with VLA (Corsi & Horesh 2014) and AMI (Anderson et al. 2014a). The broadband SED around the time of the VLA detection broadly fits a forward shock model but is poorly constrained due to the lack of a contemporaneous X-ray detection. The spectral slope between the two VLA bands is somewhat steeper than the standard low-frequency value of $\beta =-1/3$, possibly indicating that the radio emission is self-absorbed. We obtained 14 AMI observations every 2 or 3 days from 2014 August 8 until 2014 September 12. Observations were 2–4 hr in duration. AMI first detected the afterglow 4.6 days post-burst. The AMI light curve peaked ∼10.6 days post-burst at 15.7 GHz, which is characteristic of forward shock emission at radio wavelengths (Chandra & Frail 2012).

A peculiar feature of the optical light curve is that the P60 r- and i-band observations at ${\Delta }t\approx 2$ days appear to be inverted, with a rising rather than falling spectral shape, compared to the earlier P60 photometry at ${\Delta }t\approx 1$ day. However, this feature is within the error bars and may be merely a statistical fluctuation.

This is the highest-redshift burst in our sample and also had the weakest prompt emission in terms of the fluence observed by GBM .

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View figure set (8 panels)

Tarball of figure set images

First, we investigate the properties of the subset of GBM bursts followed up by iPTF compared to the GBM bursts as a whole. It is known that, on average, GRBs with larger prompt fluences have brighter optical afterglows, though the correlation is very weak (Nysewander et al. 2009). In Figure 6, we plot the fluence in the 10–1000 keV band and 1σ localization radius of all GBM bursts from the beginning of our experiment, retrieved from the Fermi GBM Burst Catalog at HEASARC.⁴⁵  As expected, there is a weak but clearly discernible correlation between fluence and radius, $F\propto {{r}^{-1.3}}$, with a Pearson correlation coefficient of R = 0.64.⁴⁶ The subset of bursts that we followed up spans a wide range in fluence and error radii up to $\sim 10{}^\circ$. The bursts for which we detected optical afterglows are preferentially brighter, with the faintest burst having a fluence as low as 3 × 10⁻⁶ erg cm⁻². There are some bright ($\gt 3\times {{10}^{-5}}$ erg cm⁻²) and well-confined ($\lt 1\buildrel{\circ}\over{.} 8$) events for which we did not find afterglows: those at 2013 August 28 07:19:56, 2013 November 27 14:12:14, and 2014 January 04 17:32:00 (see Table 5). However, these non-detections are not constraining given their ages of 20.28, 13.46, and 18.57 hr, respectively. Conversely, there were two especially young bursts (followed up at ${\Delta }t=0.11$ and 0.17 hr) for which we did not detect afterglows. The non-detection of the burst at 2014 July 16 07:20:13 makes sense because we searched only 28% of the GBM localization. The non-detection on 2014 April 04 04:06:48, for which we observed 69% of the localization, is a little more surprising, especially given its relatively high fluence of 8 × 10⁻⁶ erg cm⁻²; this is a possible candidate for a "dark GRB." On the whole, however, we can see that (1) we have followed up bursts with a large range of error radii and fluences, (2), there is a weak preference toward detecting bursts with small error radii, and (3) the detections tend toward bursts with high fluences. Naively one might expect higher fluences to translate into lower redshifts, but the interplay between the GRB luminosity function and detector threshold greatly complicates such inferences (Butler et al. 2010).

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Second, the rich sample of all of the GRB afterglows that we have today is undeniably the result of the success of the Swift mission. It is therefore interesting to consider how the GBM–iPTF sample is similar to or different from the Swift sample, given the differences in bandpasses and our increased reliance on the optical afterglow. In Figure 7, we plot the cumulative redshift distribution of our sample, alongside the distribution of redshifts of long GRBs detected by Swift.⁴⁷ Indeed, we find that our sample is at lower redshifts; the former distribution lies almost entirely to the left of the latter, and the ratio of the median redshifts (z = 1.5 versus z = 1.9) of the two populations is about 0.75. However, with the small sample size, the difference between the two redshift distributions is not significant: a two-sample Kolmogorov–Smirnov test yields a p-value of 0.26, meaning that there is a 26% chance of obtaining these two empirical samples from the same underlying distribution. More GBM–iPTF events are needed to determine whether the redshift distribution is significantly different.

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Amati et al. (2002) pointed out a striking empirical correlation in the rest-frame prompt emission spectra of BeppoSAX GRBs, with the peak energy (in the $\nu {{F}_{\nu }}$ sense) E_peak related to the bolometric, isotropic-equivalent energy release E_iso by ${{E}_{{\rm peak}}}\propto E_{{\rm iso}}^{m}$. It was quickly realized that such a relation, if intrinsic to the bursts, could be used to measure the redshifts of GRB non-spectroscopically (Atteia 2003). As with the Phillips relation for SNe Ia (Phillips 1993), with such a relation GRBs could serve as standardizable candles in order to measure cosmological parameters (Dai et al. 2004; Friedman & Bloom 2005; Ghirlanda et al. 2006; etc.).

However, there has been a vigorous debate about whether the Amati relation and related correlations are innate to GRBs or reflect a detector-dependent selection bias (Band & Preece 2005; Ghirlanda et al. 2005; Nakar & Piran 2005; Sakamoto et al. 2006; Butler et al. 2007; Cabrera et al. 2007; Schaefer & Collazzi 2007; Butler et al. 2009; Firmani et al. 2009; Krimm et al. 2009; Butler et al. 2010; Shahmoradi & Nemiroff 2011; Collazzi et al. 2012; Kocevski 2012). One alternative interpretation is that bursts to the upper-left boundary of the Amati relation are selected against by photon-counting instruments because, being relatively hard, there are fewer photons. The lack of bursts to the lower right of the Amati line may be due to a genuine lack of relativistic explosions that are much softer than, but as energetic as, standard GRBs.

It has been difficult to directly test the Amati relation in the context of Fermi bursts because most lack known redshifts, since bursts that were coincidentally observed and localized by the Swift BAT do not directly sample the selection bias of Fermi GBM. However, Heussaff et al. (2013) showed that many Fermi bursts that lack known redshifts would be inconsistent with the Amati relation at any distance. (See also Urata et al. 2012 for outlier events detected by Fermi LAT and Suzaku WAM.) Here, we have a small sample of Fermi bursts with known redshifts. One of them, GRB 140606B/iPTF14bfu at z = 0.384, is a clear outlier, over $2\sigma$ away from the mean Amati relation. This burst is not alone: in Figure 8, we have marked a selection of previous long GRBs with spectroscopically identified SNe. Three among them are also outliers. (A possible caveat is that the prompt emission mechanism for GRB 140606B could be different from typical cosmological bursts; we explore this in the next section.) To be sure, most of the bursts in our GBM–iPTF sample fall within a $1\sigma$ band of the Amati relation. This includes the nearest event to date, GRB 130702A/iPTF13bxl at z = 0.145. However, the one outlier in our admittedly small sample strengthens the case that the boundary of the Amati relation is somewhat influenced by the detector thresholds and bandpasses.

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Two GRBs in our sample, GRB 130702A/iPTF13bxl and GRB 140606B/iPTF14bfu, have ${{E}_{{\rm iso}}}\sim {{10}^{51}}$ erg (rest frame), energetically intermediate between "standard" luminous, cosmically distant bursts and nearby llGRBs. Prototypes of the latter class include GRB 980425/SN 1998bw (Galama et al. 1998; Kulkarni et al. 1998), which was also the first SN discovered in association with a GRB. They offer an interesting test case for competing theories to explain the wide range of prompt gamma-ray energy releases observed from GRBs (e.g., Schulze et al. 2014b).

It has been suggested that the two luminosity regimes correspond to different prompt emission mechanisms (Bromberg et al. 2011). The llGRBs could be explained by the breakout of a mildly relativistic shock from the progenitor envelope (Nakar & Sari 2012). High-luminosity bursts, on the other hand, are thought to be produced by internal shocks within an ultra-relativistic jet (Rees & Meszaros 1994) that has successfully punched through the star. A central engine that sometimes fails to launch an ultra-relativistic jet is one way to unify the luminosity functions of standard GRBs and llGRBs (Pescalli et al. 2014).

The smoking gun for the relativistic shock breakout model is a cooling, thermal component to the prompt X-ray emission, as in the case of GRB 060218 (Campana et al. 2006). Unfortunately, this diagnostic is not possible for GRB 130702A and GRB 140606B because we lack early-time Swift observations.

However, Nakar & Sari (2012) propose a closure relation (their Equation (18)) between the prompt energy, temperature, and timescale that is valid for shock breakout-powered GRBs. We reproduce it here:

$$\begin{eqnarray}&&t_{{\rm bo}}^{{\rm obs}}\sim 20\;{\rm s}{{\left( \frac{{{E}_{{\rm bo}}}}{{{10}^{46}}{\rm erg}} \right)}^{\frac{1}{2}}}{{\left( \frac{{{T}_{{\rm bo}}}}{50\;{\rm keV}} \right)}^{-\frac{9+\sqrt{3}}{4}}}.\end{eqnarray} \tag{ 3 }$$

If we very crudely assume that all of the prompt emission is from a shock escaping from the progenitor envelope, then we can use E_iso, E_peak, and T₉₀ as proxies for those observables. This gives us a simple discriminator of which bursts are plausible shock breakout candidates, the ratio

$$\begin{eqnarray}&&\xi =(1+z)t_{{\rm bo}}^{{\rm obs}}/{{T}_{90}},\end{eqnarray} \tag{ 4 }$$

which should be close to 1. As expected, most of the energetic (${{E}_{{\rm iso}}}\gt {{10}^{52}}{\rm erg}$), cosmic ($z\gt 0.5$) GRBs in our sample are inconsistent with the closure relation. They are all much shorter in duration, given their γ-ray spectra, than would be expected for a shock breakout. The exception is GRB 140623A/iPTF14cyb, which yields $\xi =0.5\pm 0.5$. In this particular case, one possible explanation is that the central engine simply remained active for much longer than the timescale of the shock breakout.

Surprisingly, of the two low-luminosity, low-redshift bursts in our sample, GRB 130702A/iPTF13bxl's prompt emission was much too brief to be consistent with this shock breakout model, with $\xi =(1.6\pm 0.7)\times {{10}^{3}}$. Most likely, this means that the prompt emission of GRB 130702A is simply a very soft, very sub-luminous version of an otherwise "ordinary" long GRB. Any early-time shock breakout signature, if present, was not observed either because it occurred at energies below GBM's bandpass or because it was much weaker than the emission from the standard GRB mechanism. However, GRB 140606B/iPTF14bfu's prompt emission is consistent with the closure relation, with $\xi =0.5\pm 0.3$. Though we must interpret this with caution because we cannot disentangle a thermal component from the GBM data, if we naively apply linear least squares to (the logarithm of) Equations (14), (16), and (17) of Nakar & Sari (2012),

$$\begin{eqnarray}&&{{E}_{{\rm bo}}}\approx 2\times {{10}^{45}}R_{5}^{2}\gamma _{f,0}^{\frac{1+\sqrt{3}}{2}}{\rm erg},\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{{T}_{{\rm bo}}}\sim 50{{\gamma }_{f,0}}{\rm keV},\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&t_{{\rm bo}}^{{\rm obs}}\approx 10\frac{{{R}_{5}}}{\gamma _{f,0}^{2}}{\rm s},\end{eqnarray} \tag{ 7 }$$

then we find the breakout radius and Lorentz factor to be

$$\begin{eqnarray*}\begin{array}{ccccccccccccccc} {{R}_{{\rm bo}}} & = & (1.3\pm 0.2)\times {{10}^{3}}\;{{R}_{\odot }}, \\ {{\gamma }_{f,0}} & = & 14\pm 2. \\ \end{array}\end{eqnarray*}$$

The breakout radius is comparable to that which Nakar & Sari (2012) find for GRB 060218 and GRB 100316D, suggestive of breakout from a dense wind environment, rather than the star itself.⁴⁸ However, the derived Lorentz factor of GRB 140606B is a bit higher than those of the other two examples.

Another way to constrain the nature of the explosion is to look at the kinetic energy ${{E}_{k,{\rm iso}}}$ of the blast compared to the promptly radiated energy ${{E}_{\gamma ,{\rm iso}}}\equiv {{E}_{{\rm iso}}}$ and the radiative efficiency $\eta ={{E}_{\gamma ,{\rm iso}}}/({{E}_{k,{\rm iso}}}+{{E}_{{\rm iso}}})$. After the end of any plateau phase, the X-ray flux is a fairly clean diagnostic of ${{E}_{k,{\rm iso}}}$ assuming that the X-rays are above the cooling frequency (Freedman & Waxman 2001). During the slow-cooling phase and under the typical conditions where $p\approx 2$ and ${{\nu }_{{\rm c}}}\lt {{\nu }_{{\rm X}}}$, the X-ray flux is only weakly sensitive to global parameters such as the fraction of the internal energy partitioned to electrons and to the magnetic (${{\epsilon }_{e}}$, ${{\epsilon }_{B}}$). Even the radiative losses, necessary for extrapolating from the late-time afterglow to the end of the prompt phase, are minor, amounting to order unity at ${\Delta }t=1$ day (Lloyd-Ronning & Zhang 2004). We calculate the isotropic-equivalent rest-frame X-ray luminosity from the flux at ${\Delta }t=1$ day using Equation (1) of Racusin et al. (2011), reproduced below:

$$\begin{eqnarray}&&{{L}_{{\rm X}}}(t)=4\pi D_{{\rm L}}^{2}{{F}_{{\rm X}}}(t){{(1+z)}^{-{{\alpha }_{{\rm X}}}+{{\beta }_{{\rm X}}}-1}}.\end{eqnarray} \tag{ 8 }$$

Then we estimate the kinetic energy at the end of the prompt emission phase using Equation (7) of Lloyd-Ronning & Zhang (2004):

$$\begin{eqnarray}\begin{array}{ccccccccccccccc} {{E}_{k,{\rm iso}}} & = & \left( {{10}^{52}}\;{\rm ergs} \right)\times R\times {{\left( \frac{{{L}_{{\rm X}}}(1\;{\rm day})}{{{10}^{46}}\;{\rm ergs}\;{{{\rm s}}^{-1}}} \right)}^{-4/(p+2)}}{{\left( \frac{1+z}{2} \right)}^{-1}} \\ {} & {} & \times \epsilon _{e,-1}^{4(1-p)/(2+p)}\epsilon _{}^{B,-2(2-p)/(2+p)}t_{}^{10\,{\rm hr}(3p-2)/(p+2)} \\ {} & {} & \times \nu _{18}^{2(p-2)/(p+2)}. \\ \end{array}\end{eqnarray} \tag{ 9 }$$

The correction factor R for radiative losses is given by Equation (8) of Lloyd-Ronning & Zhang (2004), adopted here:

$$\begin{eqnarray}&&R={{\left( \frac{t}{{{T}_{90}}} \right)}^{(17/16){{\epsilon }_{e}}}}.\end{eqnarray} \tag{ 10 }$$

The numeric subscripts follow the usual convention for representing quantities in powers of 10 times the cgs unit, i.e., ${{\epsilon }_{e,-1}}={{\epsilon }_{e}}/{{10}^{-1}}$, ${{\epsilon }_{B,-2}}={{\epsilon }_{B}}/{{10}^{-2}}$, and ${{\nu }_{18}}\equiv \nu /({{10}^{18}}\;{\rm Hz})$. We assume ${{\epsilon }_{e}}=0.1$ and ${{\epsilon }_{B}}=0.01$. For bursts that have XRT detections around ${\Delta }t=1$ day (GRB 130702A, 131231A, 140508A, 140606B, and 140620A), we calculate L_X by interpolating a least-squares power-law fit to the X-ray light curve. Some of our bursts (GRB 131011A, 140623A, and 140808A) were only weakly detected by XRT; for these we extrapolate from the mean time of the XRT detection assuming a typical temporal slope of ${{\alpha }_{{\rm X}}}=1.43\pm 0.35$ (Racusin et al. 2011). The kinetic and radiative energies of our eight bursts are shown in Figure 9. Half of our bursts are reasonably well constrained in E_k–${{E}_{\gamma }}$ space; these are shown as red points. The other half (GRB 131011A, 131231A, 140620A, and 140623A) have highly degenerate SEDs, so their position in this plot is highly sensitive to model assumptions; these are shown as gray points. Dotted lines are lines of constant radiative efficiency.

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Within our sample, there are at least three orders of magnitude of variation in both ${{E}_{k,{\rm iso}}}$ and ${{E}_{\gamma ,{\rm iso}}}$. The two GRB–SNe have radiative and kinetic energies of $\sim {{10}^{51}}$ erg, both two to three orders of magnitude lower than the other extreme in our sample or the average values for Swift bursts. In our sample, they have two of the lowest inferred radiative efficiencies of $\eta \sim 0.1$–0.5, but these values are not atypical of BATSE bursts (e.g., Lloyd-Ronning & Zhang 2004) and are close to the median value for Swift bursts. These are, therefore, truly less energetic than cosmological bursts, not merely less efficient at producing gamma rays.