GRB 080503: IMPLICATIONS OF A NAKED SHORT GAMMA-RAY BURST DOMINATED BY EXTENDED EMISSION

The Swift Burst Alert Telescope (BAT) detected GRB 080503 at 12:26:13 on 2008 May 3 (UT dates and times are used throughout this paper). The GRB light curve (Figure 1) is a classic example of a short GRB with extended emission: a short, intense initial spike with a duration of less than 1 s followed by a long episode of extended emission starting at ∼10 s and lasting for several minutes. The overall T₉₀ for the entire event is 232 s.

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Similar extended emission has been seen before in many short bursts detected by both Swift and BATSE (Figure 2). All such events to date have remarkably similar general morphologies. However, the fact that the long component is so dominant in this case (factor of ∼30 in total fluence) raises the question of whether this is truly a "short" (or Type I) GRB and not an event more akin to the traditional LGRBs (Type II) in disguise. To this end we have reanalyzed the BAT data in detail and applied additional diagnostics to further investigate the nature of this event. We also downloaded and reanalyzed BAT data from all other SGRBs (and candidate SGRBs) with and without extended emission through the end of 2007. A summary of the results of our analysis is presented in Table 1.

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The BAT data analysis was performed using the Swift HEAsoft 6.5 software package. The burst pipeline script, batgrbproduct, was used to process the BAT event data. In addition to the script, we made separate spectra for the initial peak and the extended emission interval by batbinevt, applying batphasyserr to the PHA files. Since the spectral interval of the extended emission includes the spacecraft slew period, we created the energy response files for every 5 s period during the time interval, and then weighted these energy response files by the 5 s count rates to create the averaged energy response. The averaged energy response file was used for the spectral analysis of the extended emission interval. Similar methods were employed for previous Swift SGRBs.

For GRB 080503, the T₉₀ durations of the initial short spike and the total emission in the 15–150 keV band are 0.32 ± 0.07 s, and 232 s respectively. The peak flux of the initial spike measured in a 484 ms time window is (1.2 ± 0.2) × 10⁻⁷ erg cm⁻² s⁻¹. The hardness ratio between the 50–100 keV and the 25–50 keV bands for this initial spike is 1.2 ± 0.3, which is consistent with the hardness of other Swift SGRBs, though it is also consistent with the LGRB population. In Figure 3, we plot the hardness and duration of GRB 080503 against other Swift bursts, resolving this burst and other short events with extended emission separately into the spike and the extended tail. The properties of the initial spike of GRB 080503 match those of the initial spikes of other SGRBs with extended emission (and are consistent with the population of short bursts lacking extended emission), while the hardness and duration of the extended emission are similar to that of this component in other short bursts.

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The fluence of the extended emission measured from 5 s to 140 s after the BAT trigger in the 15–150 keV bandpass is (1.86 ± 0.14) × 10⁻⁶ erg cm⁻². The ratio of this value to the spike fluence is very large (∼30 in the 15–150 keV band), higher than that of any previous Swift short (or possibly short) event including GRB 060614. It is not, however, outside the range measured for BATSE members of this class, which have measured count ratios up to ∼40 (GRB 931222, Norris & Bonnell 2006). In Figure 4, we plot the fluences in the prompt versus extended emission of all Swift SGRBs to date. BATSE bursts are overplotted as solid gray diamonds; HETE event GRB 050709 is shown as a circle. The two properties appear essentially uncorrelated, and the ratio has a wide dispersion in both directions. Although only two Swift events populate the high extended-to-spike ratio portion of the diagram (and the classification of GRB 060614 is controversial), the difference in this ratio between these and more typical events is only about a factor of 10, and the intermediate region is populated by events from BATSE and HETE¹⁸, suggesting a continuum in this ratio across what are otherwise similar events.

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Lag analysis (Norris et al. 2000) has also been used as a short–long diagnostic. For GRB 080503, the spectral lag between the 50–100 keV and the 25–50 keV bands using the light curves in the 16 ms binning is 1 ± 15 ms (1σ error), consistent with zero and characteristic of short-hard GRBs. Unfortunately, the signal is too weak to measure the spectral lag for the extended emission which dominates the fluence. While lag can vary between pulses in a GRB (Hakkila et al. 2008) and short pulses typically have short lags, even very short pulses in canonical long GRBs have been observed to have non-negligible lags (Norris & Bonnell 2006).

Based on all of these arguments, we associate GRB 080503 with the "short" (Type I) class. Regardless of classification, however, the extremely faint afterglow of this burst appears to be a unique feature. In fact, as we will show, while the extremely low afterglow flux is more reminiscent of SGRBs than LGRBs, relative to the gamma-rays the afterglow is so faint that this event appears quite unlike any other well studied member of either population to date.

The Swift UV-Optical Telescope (UVOT) began observations of the field of GRB 080503 at 83 s after the trigger, starting with a finding chart exposure in the White filter at t = 85–184 s. No source is detected within the XRT position to a limiting magnitude of >20.0 (Brown & Mao 2008). A sequence of filtered observations followed, and then additional White-band exposures. The transient is not detected in any exposure. Because of the deep Gemini data shortly thereafter, these additional limits do not constrain the behavior of the optical counterpart and are not reported or reanalyzed here. A summary of the subsequent UVOT observations is given by Brown & Mao (2008).

Shortly after the GRB trigger we slewed with the 10 m Keck-I telescope (equipped with LRIS) to the GRB position. After a spectroscopic integration on a point source near the XRT position that turned out in later analysis to be a faint star, we acquired (between 13:38:37 and 13:57:02) imaging in the B and R filters simultaneously. Unfortunately, because the instrument had not been focused in imaging mode prior to the target of opportunity, these images are of poorer quality and less constraining than Gemini images (see below) taken at similar times. The optical transient (OT) is not detected in either filter. Magnitudes (calibrated using the Gemini-based calibration, Section 2.4) are reported in Table 2.

On May 8 we used long-slit (1'' wide) spectroscopy with LRIS (Oke et al. 1995) on Keck I to obtain spectra of two relatively bright galaxies 13'' SE of the afterglow position. We calibrated the two-dimensional spectra with standard arc and internal flat exposures. We employed the 600 line mm⁻¹ grism (blue camera) and 600 line mm⁻¹ grating blazed at 10,000 Å (red camera). The data were processed with the LowRedux¹⁹ package within XIDL²⁰. Both objects show the same emission lines, at common observed wavelengths of λ_obs≈ 5821, 6778.8, 7592.2, 7745.6, and 7820 Å. The latter two are associated with the Hβ and [O III] λ5007 lines, respectively, identifying this system to be at z = 0.561.

While the placement of the slit in the target-of-opportunity spectroscopic on May 3 did not cover the location of the transient, a third, serendipitous object along the slit shows a single emission line at λ_obs ≈ 6802.9 Å and a red continuum. We tentatively identify this feature as unresolved [O II] λ3727 emission and estimate its redshift to be 0.8245. This source is far (31'') from the OT position, at α = 1906311, δ = +68°48'043.

We also initiated a series of imaging exposures using GMOS on the Gemini-North telescope. The first image was a single 180 s r-band exposure, beginning at 13:24, 58 minutes after the Swift trigger. We then cycled through the g, r, i, and z filters with 5 × 180 s per filter. A second g epoch was subsequently attempted, but the images are shallow due to rapidly rising twilight sky brightness.

The following night (May 4) we requested a second, longer series of images at the same position. Unexpectedly, the transient had actually brightened during the intervening 24 hr, so we continued to observe the source for several additional epochs. The next night (May 5), we acquired r-band images (9 × 180 s), followed by a long nod-and-shuffle spectroscopic integration, and concluded with 4 × 180 s exposures in each of the g and i bands. On May 6 and 7, we acquired long r-band imaging only (14 × 180 s on May 6 and 16 × 180 s on May 7). Finally, on May 8, we acquired a long K-band integration using NIRI, nearly simultaneous with the HST observations (Section 2.5) at the same epoch.

Optical imaging was reduced using standard techniques via the Gemini IRAF package.²¹ Magnitudes were calculated using seeing-matched aperture photometry and calibrated using secondary standards. The standard star field SA 110 was observed on the nights of May 3, May 4, May 5, and May 8; catalog magnitudes (Landolt 1992) were converted to griz using the equations from Jester et al. (2005) and used to calibrate 23 stars close to the GRB position (Table 3).

In an attempt to measure or constrain the redshift of GRB 080503, we obtained a nod-and-shuffle long-slit spectroscopic integration of the positions of the optical transient and the nearby faint galaxy S1 (Figure 5). Two exposures of 1320 s each were obtained starting at 12:20 on 2008 May 05. Unfortunately, even after sky subtraction and binning, no clear trace is observed at the position, and no line signatures are apparent. The redshift of the event is therefore unconstrained, except by the g-band photometric detection which imposes a limit of approximately z < 4.

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We began near-infrared observations of GRB 080503 on 2008 May 08 at 12:46, roughly simultaneous with the Hubble Space Telescope (HST) measurement (Section 2.5). All images were taken in the K_s band with NIRI. We employed the standard Gemini-N dither pattern for each of the 30 s exposures. In all, 92 images were taken yielding a total time on target of ∼1.5 hr. The data were reduced and the individual frames were combined in the usual way using the "gemini" package within IRAF. There is no detection of a source at the location of the optical transient. The nearby faint galaxies (S1 and S4) are also undetected. Calibrating relative to the 2MASS catalog (excluding stars near the edge of the image because NIRI is known to suffer from fringing), we derive an upper limit of K_s > 22.47 mag (3σ).

All optical photometry, in conjunction with the space-based measurements from Swift  and Chandra, is plotted in Figure 6.

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Given the unusual nature of the afterglow, and the indications of a Li-Paczyński-like light curve in the first two days, we proposed²² to observe the field of GRB 080503 with the Wide-Field Planetary Camera (WFPC2) on HST. Filter changes, depth, and cadences were chosen to confirm or refute the basic predictions of the Li & Paczyński (1998) model (see Section 3.4). The localization region was observed in three epochs on 2008 May 8, May 12, and July 29. A set of F450W (one orbit), F606W (two orbits), and F814W (one orbit) observations were obtained during the first visit, with F606W (two orbits) and F814W (two orbits) in the second visit, and finally a deep (four orbit) observation in F606W in the third visit. Observations were dithered (a three-point line dither for the first epoch of F450W and F814W, and a standard four-point box for all other observations). The data were reduced in the standard fashion via multidrizzle, while the pixel scale was retained at the native ∼01 pixel⁻¹.

At the location of the afterglow in our first-epoch F606W image we found a faint point source, with a magnitude of F606W = 27.01 ± 0.20 after charge-transfer efficiency correction following Dolphin (2000). Our other observations show no hint of any emission from the afterglow or any host galaxy directly at its position. We derived limits on any object at the GRB position based on the scatter in a large number (∼100) of blank apertures placed randomly in the region of GRB 080503. The limits for each frame are shown in Table 2. In addition, a stacked frame of all our F814W observations yields F814W >27.3 mag. A combination of all but our first-epoch F606W observations provides our deepest limit of F606W >28.5 mag (3σ), in a stacked image with exposure time 13,200 s. Therefore any host galaxy underlying GRB 080503 must be fainter than that reported for any other short burst (Figure 7).

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Although there is no galaxy directly at the GRB position, there are faint galaxies close to this position which are plausible hosts. In particular, our stacked image of all the F606W observations shows a faint galaxy ∼08 from the afterglow position, with F606W(AB) = 27.3 ± 0.2 mag (designated "S4" in Figure 5). Although faint, this galaxy is clearly extended, with its stellar field continuing to ∼03 from the GRB position. (It is plausible that deeper observations or images in redder wavebands may extend its disk further, but we have no evidence that this is the case.) Additionally, there is a brighter galaxy ("S1," F606W ≈26.3 mag) ∼2'' to the north of the afterglow position, also visible in the Gemini images. Given the faintness of these galaxies and the moderate offset from the afterglow position, the probability of chance alignment is nontrivial (a few percent, following Bloom et al. 2002), and we cannot make firm statements about their association with GRB 080503.

The extremely deep limit on a host galaxy puts GRB 080503 in very rare company. Among short bursts, no comparably deep limit exists for any previous event except GRB 061201, although a study with deep HST imaging of short-burst hosts has yet to be published. However, ground-based searches for hosts of other SGRBs with subarcsecond positions have identified coincident host galaxies in nine of 11 cases. The two exceptions are GRB 061201 (Stratta et al. 2007) and GRB 070809 (Perley et al. 2008); both of these appear at relatively small physical offset from nearby spirals which have been claimed as host candidates. Short GRB 070707 has a coincident host with R = 27.3 mag (Piranomonte et al. 2008), about the same as the magnitude of the nearest galaxy to the GRB 080503 OT position. In fact, even compared with long bursts, the lack of host galaxy is unusual; only five events have host-galaxy measurements or limits fainter than 28.5 mag.

There are two general possibilities to explain this extreme faintness. First, GRB 080503 could be at high redshift (z > 3), or at moderately high redshift in a very underluminous galaxy (at z ≈ 1, comparable to the highest-z SGRBs detected to date, M_B < −15 mag).²³ A bright "short" GRB at very high redshift would impose a much larger upper end of the luminosity distribution of these events than is currently suspected. An extremely underluminous host would also be surprising under a model associating SGRBs with old stars, since the bulk of the stellar mass at moderate redshifts is still in relatively large galaxies (Faber et al. 2007).

Second, GRB 080503 could be at low redshift but ejected a long distance from its host. To further examine this possibility, we have estimated the probabilities (following Bloom et al. 2002) of a statistically significant association with other bright galaxies in the field. A rather faint spiral galaxy is located 13'' SE of the afterglow position (J2000 coordinates α = 1906317, δ = 68°47'279; visible in the bottom-left corner of Figure 5) and has r = 21.7 mag and z = 0.561 (Section 2.3). The probability that this is a coincidence is of order unity. We also searched NED and DSS image plates for very bright nearby galaxies outside the field. The nearby (D ≈ 5 Mpc) dwarf galaxy UGC 11411 is located at an offset of 15; again the chance of random association is of order unity. There are no other nearby galaxies of note. While a low probability of random association does not rule out an association with one of these objects (a progenitor that escapes its host-galaxy potential well and has a sufficiently long merger time will be almost impossible to associate with its true host), it prevents us from making an association with any confidence.

The Swift X-ray telescope began observing GRB 080503 starting ∼82 s after the burst, detecting a bright X-ray counterpart. Observations continued during the following hour and in several return visits.

The XRT data were reduced by procedures described by Butler & Kocevski (2007b). The X-ray light curve, scaled to match the optical at late times, is shown in Figure 6. Despite the bright early afterglow, the flux declined precipitously and no significant signal is detected during the second through fourth orbits. A marginally significant detection is, however, achieved during a longer integration a day later.

The X-ray hardness ratio decreases, as does the 0.3– 10.0 keV count rate, during the course of the early observations (Figure 8(a) and (b)). Absorbed power-law fits to the evolving spectrum are statistically acceptable (χ²/dof ≈ 1) and yield a photon index Γ which increases smoothly with time and an H-equivalent column density N_H that apparently rises and then falls in time (Figure 8(c) and (d)). This unphysical N_H variation is commonly observed in power-law fits to the XRT emission following BAT GRBs and XRT flares (see, e.g., Butler & Kocevski 2007a); it suggests that the intrinsic spectrum, plotted on a log-log scale, has time-dependent curvature. In fact, we find that the combined BAT and XRT data are well fit by a GRB model (Band et al. 1993) with constant high- and low-energy photon indices and a time-decreasing break energy that passes through the XRT band during the observation.

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The amount of physical column density that contributes to the effective N_H in Figure 8(c) can be estimated at early or late times, when the effective N_H is near its minimum, or from the Band et al. (1993) GRB model fits. We find N_H = 5.5^+1.5_−0.9 × 10²⁰ cm⁻², comparable to the Galactic value of N_H = 5.6 × 10²⁰ cm⁻², indicating that the host-galaxy hydrogen column is minimal.

Under Director's Discretionary Proposals 09508297 and 09508298, we conducted imaging using the Chandra X-Ray Observatory ACIS-S on two occasions. During the first integration (2008 May 07 19:18:23 to 2008 May 08 04:09:59) an X-ray source is detected at α = 19062876, δ = +68°47'35''3 (J2000, 0.5'' uncertainty), consistent with the position of the optical afterglow. This source was not detected during the second epoch (2008 May 25 18:11:36 to 2008 May 26 03:04:28), limiting the decay rate to steeper than approximately t^−1.6.

Minimizing the Cash (1976) statistic, we find the Chandra spectrum to be acceptably fit by an absorbed power law with β = 0.5 ± 0.5 and unabsorbed flux F_X = (1.5 ±  0.7) × 10⁻¹⁴ erg cm⁻² s⁻¹ (0.3–10 keV). We assume Galactic absorption only.

We attempted to use the photon arrival times to constrain the temporal index (α) assuming power-law brightening or fading behavior (Butler et al. 2005). The exposure time is short compared with the time elapsed since the GRB, precluding strong constraints. Although the data do marginally favor brightening behavior (α = −13 ± 7), in contrast to the well established optical fading at this point, we do not consider this to be a strong conclusion.

Immediately after the prompt emission subsides, the X-ray light curve (Figure 9) is observed to decline extremely rapidly (α = 2–4, where α is defined by F_ν ∝ t^−α), plummeting from a relatively bright early X-ray flux to below the XRT detection threshold during the first orbit. Although a similar rapid early decline is seen in nearly all GRBs for which early-time X-ray data are available (O'Brien et al. 2006), GRB 080503 probably constitutes the most dramatic example of this on record: the decline of ∼6.5 orders of magnitude from the peak BAT flux is larger by a factor of ∼100 than observed for the reportedly "naked" GRB 050421 (Godet et al. 2006) and comparable to the decline of two other potentially naked Swift events described by Vetere et al. (2008). The lack of contamination of this phase of the GRB by any other signature (X-ray flares or a standard afterglow) affords an excellent test for models of this decay component.

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An afterglow interpretation can be ruled out almost immediately. In addition to the difficulties faced by such a model in explaining the very sharp decay index, continuous spectral softening, and smooth connection with the prompt emission (all of which are commonly observed in the rapid decay phase of other GRBs), the early UVOT White measurement (≲220 μJy at 85–184 s) imposes a limit on the X-ray to optical spectral slope of β_OX < −0.5 (using the convention F_ν ∝ ν^−β) which is very difficult to explain as afterglow emission, but is consistent with the low-energy tail of prompt-emission spectra.

While the origin of the rapid-decay phase observed in most X-ray light curves is still not settled, the most popular interpretation is high-latitude emission (Kumar & Panaitescu 2000), also referred to as the curvature effect. In this scenario, after the prompt emission ends some photons still reach us from increasingly larger angles relative to the line of sight (to the central source) due to a longer path length induced by the curvature of the (usually assumed to be quasi-spherical) emitting region (or shell). Such late photons correspond to a smaller Doppler factor, resulting in a relation between the temporal and spectral indices, α = 2 + β, that holds at late times (t − t₀ ≫ Δt) for each pulse in the prompt light curve (of typical width Δt and onset time t₀) where β = −dlog F_ν/dlog ν and α = −dlog F_ν/dlog(t − t₀). The total tail of the prompt emission is the sum of the contributions from the different pulses. At the onset of the rapid-decay phase the flux is usually dominated by the tail of the last spike in the light curve, and therefore can potentially be reasonably fit using a simple single-pulse model with t₀ set to near the onset of this last spike. At later times the tails of earlier pulses can become dominant. At sufficiently late times both t − t₀ ≫ Δt and t ≫ t₀ (i.e., t − t₀ ≈ t) for all pulses, and the relation α = 2 + β is reached for t₀ = 0 (i.e., setting the reference time t₀ to the GRB trigger time). In GRB 080503 the large dynamic range enables us to probe this late regime; as shown in Figure 9, which displays α versus 2 + β for the rapid-decay phase using t₀ = 0, the relation α = 2 + β roughly holds, as expected for high-latitude emission.

While the above discussion suggests that high-latitude emission is a viable mechanism for the rapid-decay phase in GRB 080503, a more careful analysis is called for, especially since assuming an intrinsic power-law spectrum during the rapid-decay phase requires an unphysical time-variable N_H; a better and more physical description is provided by using a fixed Galactic value for N_H and an intrinsic Band et al. (1993) spectrum whose peak energy passes through the XRT range (see Section 2.6). A more detailed analysis of this event (and others) in the context of the high-latitude model and possible alternatives using this model will be forthcoming in future work.

The faintness of the early afterglow is very striking. Any afterglow emission for this event was unlikely to be brighter than about ∼1μJy at optical wavelengths and 10⁻²μJy in X-rays at any time after about 1 hr (and if the late afterglow peak were due to a nonafterglow signature, a possibility we consider in Section 3.4, these limits would be even more stringent.) Our early optical limits are the deepest for any GRB on record at this epoch (Kann et al. 2008). If the observed emission at t > 1 d is due to a mini-SN or other process, the absence of an afterglow is even more notable. Figure 10 shows the X-ray flux at 11 hr, F_X(11 hr), and the fluence of the prompt γ-ray emission, S_γ, for GRB 080503 together with a large sample of both LGRBs and SGRBs (data taken from Figure 4 of Nysewander et al. 2008, but modified slightly as described in the caption). GRB 080503 immediately stands out as a dramatic outlier, with an F_X/S_γ several orders of magnitude below that of the general population, indicating a poor conversion of the energy left in the flow after the prompt gamma-ray emission into afterglow (emission from the external forward shock). A natural explanation for this difference is a very low external density.

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Using the upper limit on the X-ray flux, F_X(11 hr) < 8.4 × 10⁻¹⁵ erg cm^-2 s⁻¹, and the measured fluence, S_γ = (1.7 ± 0.1) × 10⁻⁶ erg cm^-2, we derive constraints on the external density, n = n₀ cm^-3. Following Granot et al. (2006), it is convenient to use the X-ray afterglow efficiency, _X(t) ≡ tL_X(t)/E_k,iso(t). We can relate the isotropic equivalent kinetic energy in the afterglow shock, E_k,iso, to the measured fluence by using the ratio η_kγ ≡ E_k,iso/E_γ,iso, which is expected to be of order unity. This gives

$$\begin{equation} \epsilon _X = \frac{t F_X(t)}{\eta _{\rm k\gamma }S_\gamma },\quad \quad \epsilon _X(t = 11\,{\rm hr}) < 8.0\times 10^{-5}\eta _{\rm k\gamma }^{-1},\, \end{equation} \tag{ 1 }$$

where L_X(t) in the definition of _X is interpreted here as evaluated at t = 11 hr and an energy range of 2–10 keV (converted from our reported 0.3–10 keV value assuming β ≈ −1) in the observer frame. This makes it easier to compare this value to the one derived from standard afterglow theory, as is done next.

The value of β_OX ≈ 0.7 suggests p ≈ 2.4 if the cooling break frequency is above the X-rays, ν_c > ν_X, and a smaller value of p if ν_c < ν_X. If ν_c < ν_X, then for p ≈ 2.2 and _B ≪ _e (using Equation 7 of Granot et al. 2006),

$$\begin{equation} \epsilon _X(t = 11\,{\rm hr}; \nu _c < \nu _X) \approx 10^{-3}\epsilon _{e,-1}^{p-3/2}\epsilon _{B,-2}^{p/4}E_{\rm k,iso,52}^{(p-2)/4} \end{equation} \tag{ 2 }$$

$$\begin{equation} \hphantom{\epsilon _X(t = 11\,{\rm hr}; \nu _c < \nu _X) }\sim 10^{-3}\epsilon _{e,-1}^{0.7}\epsilon _{B,-2}^{0.55}E_{\rm k,iso,52}^{0.05}, \end{equation} \tag{ 3 }$$

where _e = 0.1_e,−1, _B = 0.01_B,−2, and E_k,iso = 10⁵²E_k,iso,52 erg. There is no dependence on the external density as long as ν_c < ν_X, and the dependence on E_k,iso is extremely weak. It does have some dependence on _e and _B. However, reproducing the value derived in Equation (1) requires these shock microphysical parameters to assume very low values—not out of the question but on the low end of the values inferred from modeling of the best-monitored GRB afterglows. This is assuming a reasonable efficiency of the gamma-ray emission, _γ ≲ 0.5, leaving at least a comparable kinetic energy in the outflow that was transferred to the shocked external medium before 11 hr, η_kγ ≈ (1 − _γ)/_γ ≳ 1. For typical values of the shock microphysical parameters (_e ≈ 0.1 and _B ≈ 0.01), Equations (1) and (2) can be reconciled either if ν_c(11 hr) ≫ ν_X (which as is shown below implies a very low external density), or if 1 − _γ ≈ η_kγ ≪ 1 (i.e., an extremely high gamma-ray efficiency that leaves very little energy in the afterglow shock, compared with that emitted in gamma-rays).

For a reasonable gamma-ray efficiency (_γ ≲ 0.5) this suggests that ν_c > ν_X. In this case the value of _X is reduced by a factor of (ν_c/ν_X)^1/2 compared with its value for ν_c < ν_X (that is given in Equation (2) for p ≈ 2.2) and is smaller by a factor of ∼1.48 for p ≈ 2.4 (that is inferred from the observed value of β_OX for ν_c > ν_X). For a ν_X ≈ 10¹⁸ Hz (corresponding to ∼4 keV) this suggests ν_c(11 hr) ≳ 10²⁰ Hz, which in turn (using the expression for ν_c from Granot & Sari 2002) implies

$$\begin{equation} n \lesssim 5 \times 10^{-6}E_{\rm k,iso,52}^{-1/2}\epsilon _{e,-1}^{-1}\epsilon _{B,-2}^{-1/2}\;{\rm cm^{-3}}. \end{equation} \tag{ 4 }$$

This dependence on the parameters is valid in the limit of _B ≪ _e, where Y ≈ (_e/_B)^1/2 ≫ 1 and ν_c ∝ n⁻¹E^−1/2_k,iso(1 + Y)^−2−3/2_B ∝ n⁻¹E^−1/2_k,iso⁻¹_e^−1/2_B. Therefore, the upper limit on the external density cannot easily be increased by a large factor. This suggests a very low external density compared with typical disk values (n ≈ 1 cm⁻³) or even a galactic halo (n ≈ 10⁻³ cm⁻³; Basu 2003) but is of the same order as the intergalactic particle density (n ≈ 10⁻⁶ cm⁻³; Hinshaw et al. 2008). This result therefore provides strong evidence that this explosion occurred far outside any galaxy. (An intriguing alternative to this, however, would be if the burst occurred in a low-density pulsar cavity inflated by one of the NSs in the precursor binary; Rosswog & Ramirez-Ruiz 2003.)

The counterpart rebrightened during the second night of observations, rising again above detectability in both the optical and X-ray bands. The optical is far better constrained than the X-rays in this case: the rise is at least 1.5 mag (a factor of ∼3) and peaks between 0.1 d and 2 d after the event, though most likely the peak is toward the end of this period as the optical observations at 1–2 d are consistent with constant flux. Although the faint afterglow and sparse observations preclude a careful search for chromatic behavior, the X-ray emission shows a broadly similar temporal behavior as the optical and is consistent with being on the same segment of a power-law spectrum (F_ν ∝ ν^−β), with a very reasonable value of the optical to X-ray spectral slope for GRB afterglows, β_OX ≈ 0.7. This suggests that they arise from the same physical region, and probably also from the same emission mechanism (most likely synchrotron emission from the forward external shock, i.e., the afterglow; we will consider other models in Section 3.4).

A late peak (t ≈ 1 d) is unusual for an afterglow but not unprecedented. Most such events are rebrightenings and not global maxima. The most prominent examples of this have been long bursts, though some modest X-ray flaring has been observed in a few short GRBs (Fox et al. 2005; Campana et al. 2006), and notably the classification-challenged GRB 060614 peaked in the optical band between 0.3–0.5 d. Without deep imaging before our first Gemini exposure, we cannot constrain the nature of an optical afterglow in the earliest phases of GRB 080503. However, it is clear that since this behavior is consistent with that observed for at least some previous GRB afterglows, the observed light curve, like the SED, is consistent with an afterglow model. The cause of this delayed peak, however, remains an open question, which we will now turn our attention to.

The similar temporal behavior of the X-ray and optical flux around the observed peak argues against a passage of a spectral break frequency (e.g., the typical synchrotron frequency ν_m passing through the optical) as the source of the late time peak in the light curve, and in favor of a hydrodynamic origin. One possibility for such a hydrodynamic origin is the deceleration time, t_dec. However, such a late deceleration time implies either an extremely low initial Lorentz factor of the outflow, Γ₀, or an unreasonably low external density

$$\begin{equation} n_0 \approx \left[\frac{t_{\rm dec}}{42(1+z)\,{\rm s}}\right]^{-3} E_{\rm k,iso,51} \left(\frac{\Gamma _0}{100}\right)^{-8} \end{equation} \tag{ 5 }$$

$$\begin{equation} \approx 10^{-10}E_{\rm k,iso,51} \left(\frac{\Gamma _0}{100}\right)^{-8}\hphantom{aaaaaa\,} \end{equation} \tag{ 6 }$$

$$\begin{equation} \approx E_{\rm k,iso,51} \left(\frac{\Gamma _0}{5.7}\right)^{-8}\hphantom{aaaaaaaaaaa\,} \end{equation} \tag{ 7 }$$

(see, e.g., Granot 2005; Lee et al. 2005a), where we have used t_dec/(1 + z) ≈ 1 d.

An initial Lorentz factor of Γ₀ ≳ 100 is typically required in order to overcome the compactness problem for the prompt GRB emission. This would in turn imply in our case an external density of n ≲ 10⁻¹⁰ cm^-3 that is unrealistically low, even for the intergalactic medium (IGM). An external density typical of the IGM, n_IGM ∼ 10⁻⁶ cm^-3 would require Γ₀ ∼ 30. This may or may not be a strong concern in this case: the constraints on the high-energy spectrum of the extended-emission component of short GRBs are not yet well established,²⁴ and it is not yet certain that existing compactness constraints apply to this emission component, potentially allowing a lower minimum Lorentz factor than is required for SGRB initial spikes (Fermi has detected high-energy emission up to ∼3 GeV from the short GRB 081024B, Omodei 2008) or for classical LGRBs.

An alternative hydrodynamic explanation for the late peak is if the afterglow shock encounters a large and sharp increase in the external density into which it is propagating. However, it would be very hard to produce the required rise in the light curve up to the broad peak due to a sudden jump in the external density (Nakar & Granot 2007) unless a change in the microphysical parameters accompanies the sharp density discontinuity (as may occur inside a pulsar cavity inflated by one of the NSs in the precursor binary). Below we discuss other possible causes for such a broad and largely achromatic peak in the afterglow light curve. The main features these models need to explain are the extremely low value of F_X(11 hr)/S_γ and the late-time peak (a few days) in the afterglow light curve.

Off-axis jet. The bulk of the kinetic energy in the afterglow shock might not be directed along our line of sight, and could instead point somewhat away from us. For such an off-axis viewing angle (relative to the region of bright afterglow emission, envisioned to be a jet of initial half-opening angle θ₀) the afterglow emission is initially strongly beamed away from us (this can be thought of as an extreme version of the "patchy shell" model— Kumar & Piran 2000a; Nakar et al. 2003). As the afterglow jet decelerates the beaming cone of its radiation widens, until it eventually reaches our line of sight, at which point the observed flux peaks and later decays (Rees 1999; Dermer et al. 2000; Granot et al. 2002; Ramirez-Ruiz et al. 2005). This interpretation can naturally account for the dim early afterglow emission (without necessarily implying an extremely low external density), as well as the rapid decay after the peak (if our viewing angle from the jet axis is θ_obs ≳ 2θ₀). The possibility of a slightly off-axis jet is particularly intriguing given the fact that the initial spike is much fainter relative to the extended emission in this event (and in GRB 060614, which also exhibits a late light curve peak) than for most SGRBs; one may envision a unified short-burst model in which the short-spike component of the prompt emission is beamed more narrowly than the component associated with the extended emission. However, since a low circumstellar density is no longer needed, there is no natural means of supressing the early afterglow that should be created by the extended-emission-associated component, and producing the large ratio of the gamma-ray fluence and early-time X-ray afterglow flux would require that the gamma-ray emission along our line of sight is bright and the gamma-ray efficiency is very large (Eichler & Granot 2006). Regardless of whether the jet is seen off-axis, there is good evidence that this GRB is significantly collimated, with a decay index α>2 at late times (t > 3 d) in both the optical and X-ray bands.

Refreshed shock. A "refreshed shock" (Kumar & Piran 2000b; Ramirez-Ruiz et al. 2001; Granot et al. 2003) is a discrete shell of slow ejecta that was produced during the prompt activity of the source and catches up with the afterglow shock at a late time (after it decelerates to a somewhat smaller Lorentz factor than that of the shell), colliding with it from behind and thus increasing its energy. This interpretation also requires a very large gamma-ray efficiency, (_γ ≳ 95%) corresponding to _γ/(1 − _γ) ∼ η⁻¹_kγ ≳ 30. In this picture, the sharp decay after the peak (at least as steep as ∼t⁻²) requires that the collision occur after the jet-break time.

The rather sparse afterglow data make it hard to distinguish between these options. Nevertheless, the overall observed behavior can be reasonably explained as afterglow emission in the context of existing models for afterglow variability.

Under any scenario, the absence of a bright afterglow associated with GRB 080503, together with the late-time optical rise suggests that a substantial fraction of this event's energy may be coupled to trans- and nonrelativistic ejecta. Nonrelativistic outflows from the central engine are sufficiently dense to synthesize heavy isotopes, which may power transient emission via reheating of the (adiabatically cooled) ejecta by radioactive decay (Li & Paczyński 1998). Since at most ∼0.1 M_☉ is expected to be ejected from any short GRB progenitor, the outflow becomes optically thin earlier and traps a smaller fraction of the decay energy than for a normal SN; these "mini-SNe" therefore peak earlier and at fainter magnitudes than normal SNe.

Current observational limits (Bloom et al. 2006; Hjorth et al. 2005a; Castro-Tirado et al. 2005; Kann et al. 2008) indicate that any supernova-like event accompanying an SGRB would have to be over 50 times fainter (at peak) than normal Type Ia SNe or Type Ic hypernovae, five times fainter than the faintest known SNe Ia or SNe Ic, and fainter than the faintest known SNe II. These limits strongly constrain progenitor models for SGRBs. Unless SGRBs are eventually found to be accompanied by telltale emission features such as the SNe associated with LGRBs, the only definitive understanding of the progenitors will come from possible associations with gravitational wave or neutrino signals.

The most promising isotope to produce bright transient emission is ⁵⁶Ni because its decay timescale of ∼6 d is comparable to the timescale over which the outflow becomes optically thin. Compact object mergers, however, are neutron rich and are not expected to produce large quantities of Ni (Rosswog et al. 2003). Metzger et al. (2008b) estimated that in the best cases only ⩽10⁻³ M_☉ of Ni is produced by outflows from the accretion disk. On the other hand, neutron-rich material may be dynamically ejected from a NS–NS or a NS–BH merger. Its subsequent decompression may synthesize radioactive elements through the r process, whose radioactive decay could power an optical transient (Li & Paczyński 1998). Material dynamically stripped from a star is violently ejected by tidal torques through the outer Lagrange point, removing energy and angular momentum and forming a large tail. These tails are typically a few thousand kilometers in size by the end of the disruption event. Some of the fluid (as much as a few hundredths of a solar mass) in these flows is often gravitationally unbound, and could, as originally envisaged by Lattimer & Schramm (1976), undergo r-process nucleosynthesis (Rosswog et al. 1999; Freiburghaus et al. 1999). The rest will eventually return to the vicinity of the compact object, with possible interesting consequences for SGRB late-time emission. A significant fraction (∼10%–50%) of the accretion disk that initially forms from the merger will also be ejected in powerful winds (Lee et al. 2005b) from the disk at late times; this material is also neutron rich and will produce radioactive isotopes (Metzger et al. 2008c).

In the case of GRB 080503, the amount (mass M) of radioactive material synthesized in the accompanying SGRB wind necessary to provide the observed luminosity is constrained to be (M/M_☉)f ≈ (1.5 − 1.8) × 10⁻⁷(z/1)². A larger uncertainty is the value of f, which is the fraction of the rest mass of the radioactive material that is converted to heat and radiated around the optical near the peak of the light curve (∼1–2 d). Generally f ≲ 10⁻⁴ since ∼ 10⁻³ of the rest mass is converted to gamma-rays during the radioactive decay, only part of the gamma-ray energy is converted to heat (some gamma-rays escape before depositing most of their energy), and only part of the mass in the synthesized radioactive elements decays near the peak of the light curve (so that f can easily be much less than 10⁻⁴, but it is hard for it to be higher than this value). We note here that the most efficient conversion of nuclear energy to the observable luminosity is provided by the elements with a decay timescale comparable to the timescale it takes the ejected debris to become optically thin (t_τ). In reality, there is likely to be a large number of nuclides with a very broad range of decay timescales. Current observational limits thus place interesting constraints on the abundances and the lifetimes of the radioactive nuclides that form in the rapid decompression of nuclear-density matter—they should be either very short or very long when compared with t_τ so that radioactivity is inefficient in generating a high luminosity.

In Figure 11, we show two light-curve models for a Ni-powered mini-SN from GRB 080503 calculated according to the model of Kulkarni (2005) and Metzger et al. (2008b). Shown with asterisks and triangles are the r-band and F606W-band detections and upper limits from Gemini and HST. The solid and dashed lines correspond to a low-redshift (z = 0.03) and high-redshift (z = 0.5) model, respectively. Qualitatively, both models appear to be reasonably consistent with the flux light curve. To reproduce the peak of the optical emission at t ≈ 1 d, a total ejected mass of ∼0.1 M_☉ is required in either model. In order to reproduce the peak flux, the Ni mass required in the high- and low-redshift models is M_Ni ≈ 0.3 M_☉ and 2 × 10⁻³ M_☉, respectively. Since the former is unphysically large in any SGRB progenitor model, a high-redshift event appears inconsistent with a mini-SN origin for the optical rise.

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If GRB 080503 originates at very low redshift (z < 0.1), a mini-SN model would still appear viable. However, most mini-SN models also predict that the spectrum should redden significantly with time and possess a negative spectral slope once the outflow becomes optically thin after the peak at t ≈ 1 d. This is not observed: the HST detection in F606W and nondetections in F814W and F450W at 5.35 d suggest that the spectrum is approximately flat at late times. While the detected optical emission may be attributed to a mini-SN type of event, the expected spectrum in such a case is quasi-thermal, resulting in no detectable emission in the X-rays. (Rossi & Begelman 2008 have proposed a fallback model in which X-rays can rebrighten days or weeks after the event, but the luminosity is extremely low, and to explain the Chandra count rate a very close distance of ∼8 Mpc would be required; while not excluded by our data, this is orders of magnitude closer than any known nonmagnetar short GRB.) Therefore, the late X-ray detections a few days after the GRB are most likely afterglow emission.