THE AFTERGLOW OF GRB 130427A FROM 1 TO 10¹⁶ GHz

GRB 130427A triggered the Burst Alert Telescope (BAT; Barthelmy et al. 2005) on board the Swift satellite (Gehrels et al. 2004) on 2013 April 27 at 07:47:57 (UT dates are used throughout this paper). This trigger time actually corresponds to a point near the end of burst activity, as the BAT was in the middle of a preplanned slew when burst emission began and could not trigger until the slew was complete. Consequently, the BAT trigger time does not provide a useful reference time for the burst; we instead employ the Fermi Gamma-Ray Burst Monitor (GBM; Meegan et al. 2009) trigger time of 07:47:06.42 (von Kienlin 2013) as t₀ in all of our subsequent analyses, an adjustment of 50.58 s for times referenced to the BAT trigger.

Following the end of its preplanned slew and trigger, Swift slewed immediately to the BAT location and began observations with the X-Ray Telescope (XRT; Burrows et al. 2005) beginning at 07:50:17.7 (t − t₀ = 190.8 s). Observations continued until t − t₀ = 1984 s, at which point Swift slewed to another location owing to orbital visibility constraints. After a gap of about 20 ks (0.23 days), Swift returned to the source for further observations; regular additional observing epochs continued as long as the position remained visible to Swift.

We downloaded the Swift BAT and XRT light curves and spectral analysis from the Swift Burst Analyser (Evans et al. 2010)²⁶ and Swift XRT repository (Evans et al. 2007, 2009). Specifically, we obtained the 15–50 keV BAT flux light curve (in 64 ms, 1 s, 10 s, and signal-to-noise ratio (S/N) = 7 binning modes) and the 0.3–10 keV XRT flux light curve; each light curve was appropriately rebinned by our own scripts depending on the application. Where necessary, these bandpass-integrated fluxes were converted to flux-density values in Jy using a smoothed value of the photon index Γ for each bin and a correction factor of 1.16 for X-ray absorption (taken from the ratio of absorbed to unabsorbed fluxes on the XRT spectral analysis page for this event²⁷).

Ultraviolet–Optical Telescope (UVOT) data were also acquired by Swift in parallel with XRT follow-up observations beginning at t − t₀ = 197 s. The GRB field is at high Galactic latitude (b = +72°), and there are relatively few bright stars nearby; consequently, the spacecraft experienced difficulties guiding and most of the initial exposures are trailed, though this difficulty was corrected in subsequent epochs.

We reduced the UVOT data using standard procedures within the HEASoft²⁸ environment (e.g., Brown et al. 2009). Flux from the transient was extracted from a 3'' radius aperture for images with good star lock (a much larger aperture was used on trailed exposures to include all of the trailed flux), with a correction applied to put the photometry on the standard UVOT system (Poole et al. 2008). For observations after t = 8 days the object is not detected in individual epochs, so we stacked observations in three blocks spanning the time periods t = 9–15 days, 16–30 days, and 30–60 days. The resulting measurements are listed in Table 1.

The Palomar 60 inch telescope (P60; Cenko et al. 2006) responded automatically to the BAT trigger and began imaging the field starting at 07:52:21.7 (Figure 2), detecting a bright source at the location reported by Elenin et al. (2013). This initial set of observations consisted of a repeating cycle of 60 s exposures in the r, i, and z filters. P60 temporarily slewed away from the target after completing this sequence ∼90 minutes later, but was manually instructed to return to the field and continue observations, this time in a repeating cycle of 60 s exposures in the g, r, and i filters. Observations continued until a telescope limit was reached at airmass 4.2. P60 was not available for observations the following night, but the GRB was monitored the night after that (and for a majority of the next several nights) in the g, r, i, and z filters for most of the window in which it was observable, switching to 120 s and then 180 s exposures. As the source faded and the Moon brightened, the z and g exposures were dropped in favor of r and i; observations continued nightly (except during periods of bad weather) until May 31, after which a less regular cadence was used.

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Basic reductions (bias subtraction, flat-fielding, and astrometry) are provided in real time by an automated IRAF²⁹ pipeline. During periods when the Moon was up significant scattered moonlight was visible in the frames; we subtract it using a scaled model of the moonlight pattern, which is approximately constant with phase. In addition, z-band frames are significantly fringed and i-band frames very marginally fringed; we create a fringe frame from observations taken during dark time and subtract it to remove this pattern. Observations are then stacked using SWarp³⁰ to improve the S/N in observations taken after the first night.

We performed point-spread function (PSF) matched photometry of the afterglow using the DAOPHOT package. The afterglow mildly saturated the first few frames; we include these data by fitting only to the nonsaturated pixels. Pixels affected by bad columns (e.g., Figure 2) were also excluded. The resulting photometry was calibrated with respect to nearby point sources from Data Release 9 (DR9; Ahn et al. 2012) of the Sloan Digital Sky Survey (SDSS) and is in the AB system (Oke 1974). Because the underlying host galaxy contributes non-negligible flux to the afterglow, for all frames after the initial riz observation sequence we subtracted reference SDSS frames from our P60 imaging using the publicly available High Order Transform of PSF ANd Template Subtraction (HOTPANTS³¹) before performing photometry. (We note that this procedure differs from the technique of simply subtracting the galaxy in flux space employed for all other instruments; see Section 2.18.) Results are reported in Table 1; for consistency with the magnitudes from other instruments reported in this table (which are not host-subtracted), our estimate of the total host flux (Section 2.18) is re-added to the magnitude column.

Shortly following the discovery of GRB 130427A and its afterglow, we initiated observations with the Gemini-North telescope on Mauna Kea. A spectroscopic sequence of four 400 s exposures began at 09:19 (91 minutes after the GRB), using the B600 grating and covering a wavelength range of 3824–6707 Å. A second sequence of three 300 s exposures was obtained starting at 10:44 (177 minutes after the GRB), again utilizing the B600 grating but set to a bluer central wavelength for a coverage of 3080–5955 Å (but the sensitivity is poor shortward of ∼3300 Å).

The data were reduced and combined in IRAF via the usual GMOS pipeline. No standard star was observed on the same night, so we plot in Figure 3 the normalized spectrum. We clearly identify lines of Ca ii, Mg ii, and Mg i, providing the first measurement of the redshift of GRB 130427A of z = 0.340 (Levan et al. 2013). Despite the exceptionally high S/N (the afterglow was at R = 14.9–15.3 mag during the observations), the spectrum is essentially featureless outside these transitions, with the exception of a weak detection of Ti ii λ3384, Galactic (z = 0) Ca ii and Na i, and a possible detection of Mn ii in the UV at low S/N. This is not unexpected; at z = 0.340 the strongest metal lines remain in the UV and lie blueward of our spectral range. The overall spectrum is broadly comparable to the composite long-duration GRB spectrum of Christensen et al. (2011) at these wavelengths.

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The spectrum also shows some weak Galactic features. The S/N and resolution of the GMOS spectra are sufficient to fit the two components of the Galactic Na i D doublet absorption feature (the D₁ and D₂ components). We fit Gaussian functions to the two lines in the first GMOS spectrum, which has the highest continuum S/N in the region of interest. We find a summed equivalent width of the two components of EW(D₁ + D₂) = 0.193 ± 0.017 Å. Using the empirical relation between sodium absorption strength and dust extinction as derived by Poznanski et al. (2012; their Equation (9)), this implies E_{B − V} = 0.024 mag. This is in agreement with the value as derived from the Schlegel et al. (1998) maps, but we note that at the low resolution of GMOS there may be a component of atmospheric sodium contaminating the measurement.

Follow-up observations of the associated SN were conducted on 2013 May 16 and 17. While the primary motivation of both epochs was for spectroscopy of the SN (which we do not discuss here; a detailed multi-epoch study of the SN spectroscopic properties will be left for future work), both observations were preceded by a short imaging acquisition sequence. Specifically, on the first night a four-filter sequence of griz was employed, but the second-night acquisition was performed with only the r-band filter. We reduce these imaging observations using the Gemini reduction tools in IRAF and measure the magnitude of the host+afterglow using a 30 radius error circle.

We observed the field of GRB 130427A with the United Kingdom Infrared Telescope (UKIRT) using the Wide Field Camera in the JHK filters at a range of epochs from a few hours to a few weeks post-burst. The images were pipeline processed by the Cambridge Astronomical Survey Unit. Aperture photometry was performed using the Gaia software and calibrated relative to seven Two Micron All Sky Survey (2MASS) stars in the field (each having typical quoted errors of 0.02–0.03 mag, leading to a zero-point statistical uncertainty of about 0.01 mag). We extracted the photometry with both 15 and 30 radii apertures and use a constant flux offset (calculated from the median flux difference between the two radii for each filter) to correct the 15 aperture photometry for the contribution of the outer parts of the host galaxy. The final magnitudes (corresponding to an effective 30 radius aperture and including all of the host flux) are reported in Table 1.

Imaging observations were carried out each night between 2013 April 27 and April 30 with the Yunnan Faint Object Spectrograph and Camera instrument of the Lijiang 2.4 m Gao-Mei-Gu (GMG) telescope in Yunnan Observatories, China. Data were taken with the Briz filters³² on the first night following the GRB and with the r filter exclusively during the three subsequent nights. Bias correction and flat-fielding were performed using standard IRAF routines, and the magnitude of the transient was measured with respect to SDSS comparison stars using a 3'' radius aperture. The S/N of each individual image is high (∼50), and the uncertainty of most observations is dominated by the calibration to the standard stars.

Images of GRB 130427A were also acquired with the 1.0 m Telescope (T100) at TUBITAK National Observatory in Turkey. We obtained six sets of R-band observations on April 27.75, 28.73, 29.77, and 30.73, and on May 1.80 and 2.79. Initial reduction (bias subtraction and flat-fielding) was performed with the European Southern Observatory Munich Image Data Analysis System (ESO-MIDAS) software environment (version 12FEBpl1.3) and IDL codes. Significant variations are observed in sky brightness across the chip even after flat-fielding using standard reference flats, so we further flat-fielded the observations by median-combining a series of exposures from the first night of observations and dividing all images by the resulting super-sky flat; observations were stacked as appropriate to improve the S/N per image. Aperture photometry on all images was performed with a custom IDL routine using SDSS field stars as calibrators and an aperture radius of 3''.

Imaging was acquired with the simultaneous seven-color Gamma-Ray burst Optical and Near-infrared Detector (GROND; Greiner et al. 2008) mounted on the 2.2 m Max Planck Gesellschaft (MPG)/ESO telescope at La Silla Observatory, Chile. We observed the field on 2013 April 28, April 29, May 11, May 13, and May 19, the long hiatus being caused by detector downtime. Owing to the northerly declination of the source, all observations were obtained at moderate to high airmass and bad seeing conditions. Data reduction was performed via a custom pipeline calling upon IRAF routines, comparable to the methods described in more detail by Krühler et al. (2009) and Yoldaş et al. (2008). During the first night, the afterglow is still very bright and easily detected in single exposures, but due to the sparse field and bad observing conditions, data had to be stacked to allow astrometric and photometric analysis. Calibration was performed against SDSS (optical) and 2MASS near-infrared (NIR) field stars for the late (SN) epochs, and the resulting catalogs for these images were used as input catalogs to astrometrize the early images. Photometry was then performed versus catalogs of reference stars derived from higher-quality P60 (griz) and UKIRT (JHK) images. Early measurements were obtained using PSF photometry in the optical and seeing-matched aperture photometry in the NIR, whereas SN-epoch measurements were obtained using a fixed 3'' radius aperture in all bands to encompass the entire host galaxy.

GRB 130427A was also observed with the 0.76 m Katzman Automatic Imaging Telescope (KAIT; Filippenko et al. 2001; Li et al. 2003), the 1 m Nickel Telescope, and the 3 m Shane telescope at Lick Observatory. KAIT and Nickel observations were performed in the BVRI filters from one to several days after the burst when the afterglow was still bright, while late-time Shane data were in BVR using the Kast spectrograph (Miller & Stone 1993) in imaging mode. We performed photometry on the images with a 25 radius aperture and calibrated to nearby SDSS stars, transformed to BVRI using the equations of Lupton³³. Both KAIT and Kast have relatively small fields of view, and only a small number of comparison stars (two to three for KAIT and one for Kast) were available for calibration, possibly producing a small amount of additional systematic uncertainty in the photometry.

We observed the location of GRB 130427A with the Large-Format Camera on the Palomar 200 inch telescope on 2013 May 5. We acquired five dithered exposures in the g band and four in r. The data were reduced with a Python code written by B. Sesar. Photometry was performed on each image individually in IDL using a 3'' radius aperture, and individual exposures were averaged together in flux space for each filter.

We obtained two epochs of observations on May 5 and May 12 using the 1.34 m Schmidt telescope of the Thüringer Landessternwarte Tautenburg, Germany. Images were acquired using the 4k camera in the first and the 2k camera in the second epoch. Photometry was calibrated against SDSS field stars transformed to R_C magnitudes using the transformations of Lupton. Magnitudes were derived using a fixed 3'' radius aperture to encompass the entire host galaxy.

Images of GRB 130427A were taken using the Low Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) on 2013 May 9 in the g and V filters and on 2013 May 10 in the g and R filters. These data were reduced via standard techniques using a custom IDL pipeline. Further imaging was conducted with the Deep Imaging Multi-Object Spectrograph (Faber et al. 2003) on 2013 June 9 in the R band and also reduced using standard techniques. Photometry was performed in IDL using a 3'' radius aperture relative to unsaturated SDSS stars in the field of view, with riz transformed to R using the Lupton transformation equations.

Observations of GRB 130427A were completed with the 22 m radio telescope RT-22 at 36.8 GHz in the Crimean Astrophysical Observatory using modulation radiometers. We applied the standard "ON–ON" observing technique, when antenna temperatures are recorded while pointing the two different beam lobes with orthogonal polarizations at the target in turn. We took several series containing from 30 to 36 measurements of 300 s exposure. The average temperature value and its dispersion were estimated. The orthogonal polarization of the beam lobes provides an intensity estimate irrespective of source polarization. The antenna temperature was corrected for extinction in the atmosphere, and a flux density was estimated using observations of calibration sources. The flux was also corrected for an elevation dependence of the effective area of the radio telescope.

We observed the position of GRB 130427A with the Combined Array for Research in Millimeter Astronomy (CARMA) on several occasions over 3 days following the burst, including two separate epochs on the first day after the GRB. All observations were conducted in single-polarization mode with the 3 mm receivers tuned to a frequency of 93 GHz, and were reduced using MIRIAD using observations of 3C 84 and 3C 273 to calibrate the flux scale.

The IRAM Plateau de Bure Interferometer (PdBI; Guilloteau et al. 1992) using the Wideband Express correlator was pointed to the GRB 130427A location on six occasions at 86.7 GHz in configurations of six and five antennas. The millimeter counterpart was detected 3 days after the GRB onset with a high (∼10) S/N at a distance of δ_R.A. = −052(± 013) and δ_Decl. = −030(± 015) from the phase center coordinates. Photometry at each epoch was performed using UV point-source fits to the phase center using the GILDAS software package. The primary flux calibrator was MWC 349. It was used on June 15 to derive the flux of the amplitude/phase calibrator 1156+295 to 1.35 Jy at the observing frequency. This flux was then used over the whole monitoring period.

The position of GRB 130427A was observed with the Karl G. Jansky Very Large Array (VLA) in its D, DnC, and C configurations, under programs 13A-411 (PI: A. Corsi), 13A-046 (PI: E. Berger), S50386 (PI: S. B. Cenko), and SE0851 (PI: A. Fruchter). The data were taken between 2013 April 27 and 2013 September 2 in several bands (K, Ka, Ku, X, C, and S; L observations were also acquired but are not presented here owing to contamination from sidelobes of a nearby object), covering overall a frequency range between 1.4 GHz and 37 GHz (see Table 2). All of the observations were conducted using the standard WIDAR correlator setting (8-bit sampling, yielding a total bandwidth of 2 GHz per band), except a few X-band observations used in reference pointing (which employed a narrower bandwidth).

Data were reduced using the Common Astronomy Software Applications, with the exception of a few observations in mid-May that were reduced using the Astronomical Image Processing System. 3C 286 was used for bandpass and flux calibration; J1125+2610 and J1159+2914 were used for gain and phase calibration. Uncertainties in the measured flux were calculated as the quadrature sum of the map rms and a fractional systematic error (of order 5%) to account for uncertainty in the flux-density calibration.

While nearly all of the optical photometry of the burst and afterglow is from our own observations, we use some data from the literature and other sources to supplement these during gaps in our temporal coverage: specifically, the early-time R measurements of Wren et al. (2013) (taken during prompt emission and only used in plotting), ugriz photometry of Xu et al. (2013b), BVRI photometry from Hermansson et al. (2013), and JH photometry from Butler et al. (2013a, 2013b, 2013c). The uncertainties in all of these GCN-derived points are increased to 0.05 mag in our modeling if a smaller error was quoted. Our late-time observations of the SN are also supplemented by the r-band photometry of Xu et al. (2013a), although we note that their earlier r-band measurements show an offset from our own P60 photometry at similar epochs. We also take LAT observations from Figure 2 of Tam et al. (2013) and radio observations (GMRT and a few supplementary CARMA and VLA points) from Laskar et al. (2013).

A relatively bright, extended host galaxy is present underlying the GRB in SDSS archival images. If not taken into account, the additional flux from this source would have significant impact on the modeling of the afterglow and SN. While we correct for this directly in the P60 reductions via image subtraction against SDSS reference imaging, this technique is not applicable for non-SDSS filters and would be impractical for use across our entire data set given the large number of instruments employed.

To correct for the host contribution to the afterglow, we first downloaded optical (ugriz) photometry of this object from the online DR9 catalog of the SDSS. While this is adequate for constraining the contribution of the host to the gri filters, the SDSS u and z detections are marginal, and other filters are not covered by the survey. For other bands in which we have late-time observations (t > 20 days) and that are far from the spectral energy distribution (SED) peak of the expected SN (specifically, the UVOT UV filters and the NIR H and K bands), we proceed by assuming that the late-time decay is fit by a power-law extrapolation of the earlier measurements using our model and fit a constant component to the late-time data to estimate the host contribution to these bands.

Finally, we interpolate to the remaining filters (including u and z) by fitting a stellar population to the UV/optical/NIR photometry (using the same technique as in Perley et al. 2013) fixed at the GRB redshift and performing synthetic photometry in the remaining desired filters. The corresponding fluxes were then subtracted from all (non-P60) photometry measurements before modeling and analysis. The magnitudes used in this procedure are presented in Table 3.

A more detailed analysis of the host galaxy is reserved for future work, although for completeness we report the basic parameters of the host as determined by our SED fit here: we find a stellar mass of M_* = (2.1 ± 0.7) × 10⁹ M_☉, a mean population age of 250 Myr, and a small amount of extinction (A_V ≲ 0.5 mag). These properties—indicating a blue, young, low-mass galaxy—are quite typical of the low-z GRB host population (Savaglio et al. 2009).

GRB 130427A is unquestionably an exceptional event. Its bolometric fluence of 2.68 × 10⁻³ erg cm⁻² is the largest of any GRB detected by the all-sky Konus satellite in almost two decades of operation (Golenetskii et al. 2013c); indeed, it is the first GRB with a fluence value exceeding 10⁻³ erg cm⁻² recorded since 1988 (Mitrofanov et al. 1990; Atteia et al. 1991). Only one GRB in history is known to have exceeded it, GRB 840304 (Klebesadel et al. 1984)³⁴.

The brightest GRBs originate from events that are in relatively close proximity to Earth (as in the case of GRB 030329; e.g., Price et al. 2003; Hjorth et al. 2003) or have exceptional luminosity (as in GRBs 990123 or 080319B; e.g., Andersen et al. 1999; Kulkarni et al. 1999; Bloom et al. 2009; Racusin et al. 2008; Woźniak et al. 2009). In the case of GRB 130427A, both factors play a role. At the observed redshift of this GRB, the observed fluence corresponds to an isotropic-equivalent (that is, not beaming-corrected) energy release of E_{γ, iso} = 8.5 × 10⁵³ erg (=0.5 M_☉c²). In Figure 1 we plot this value in comparison to a wide range of other GRBs taken from the literature: Swift (from Butler & Kocevski 2007, using the most up-to-date catalogs online³⁵), Konus (from a search of the GCN Circulars from 2005 onward), Fermi-GBM (from Goldstein et al. 2012 and Paciesas et al. 2012), and a variety of pre-Swift satellites from Amati (2006). Fluences were converted to E_{γ, iso} when the latter was not calculated explicitly. To avoid redundancy in cases where multiple satellites detected a GRB, we plot the Konus value in preference to GBM, and GBM in preference to Swift.

GRB 130427A is comparable to the most energetic bursts in any of these populations; its E_{γ, iso} is one to two orders of magnitude above the median value for Swift GRBs and significantly higher, even, than the average for GRBs detected by Konus (which is insensitive to the faintest events). It would be easily detectable at almost any redshift; events with 1/10 this E_{γ, iso} routinely trigger Swift out to z > 5 (and even z > 8). Nevertheless, GRB 130427A is not unprecedented by GRB standards; several dozen known events outrank it in E_{γ, iso}. GRB 130427A is remarkable because it is by far the closest event with a large energy release: all previous events of similar or greater energetics have been at z > 0.9 (corresponding to a factor of 10 in $d_L^2$); the next-most-luminous event to occur comparably close (at z < 0.5) was GRB 030329, which was a full factor of 50 lower in E_{γ, iso}.

In brief, in terms of apparent energetics, GRB 130427A constitutes a highly but not exceptionally luminous GRB, seen closer than any burst of comparable luminosity in the afterglow era. It therefore represents the best chance to date to study the properties of a high-luminosity GRB in the extreme detail afforded by such nearby events.

The hard X-ray temporal profile of the GRB (15–50 keV) from the BAT is plotted in Figure 4. While the burst appears very long in the BAT band (T₉₀ = 163 s, with detectable emission continuing to ∼2000 s; Barthelmy et al. 2013), this is largely because of the presence of a long-lived, shallow power-law component extending throughout the initial period of observations following the burst itself and a rebrightening episode beginning at t = 120 s. Beyond these two features, the burst is dominated by an initial pulse complex from −1 s to 18 s that contributes about 60% of the fluence in BAT's softer channels and the large majority of the fluence in the true gamma-ray bands; for example, the Konus light curves of Golenetskii et al. (2013c) suggest that in the 300–1160 keV band encompassing E_pk, over 95% of the total fluence was emitted between 4 s and 11 s.

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The rebrightening episode from 120 s to 350 s was caught starting at 195 s by the Swift XRT and shows some interesting features in that band. While the overall peak energy E_pk ≈ 240 keV reported by Konus is well inside the gamma-ray band, the XRT spectral index (Figure 5) evolves strongly during the observation and is softer than β > 1.0 at the end of the flare (t > 220 s), indicating a peak below ∼1 keV at that time. Only minimal evolution is seen in BAT, and the spectral index is never particularly hard even at the start of the flare, which may indicate unusual spectral structure. As this paper does not focus on the details of the prompt emission, we leave further study for future work. Its most pertinent characteristics for our analysis of the afterglow are that it is clearly associated with the prompt emission (on the basis of its peaked spectral profile and hard-to-soft evolution), is energetically subdominant compared to the primary pulse, and (as discussed in the next paragraph) appears to have only minimal effect on the underlying afterglow light curve.

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The nature of the long-lived shallow power-law component, however, is of significant interest for our subsequent analysis. The appearance of such a component in a γ-ray light curve is unusual; to our knowledge the only previous Swift GRB showing a similar signature is GRB 080319B, although similar features have been searched for in bright BATSE bursts (Giblin et al. 2002) and probably seen in at least one case (Giblin et al. 1999; Fraija et al. 2012). A logarithmically binned BAT light curve is plotted in the inset to Figure 4 along with a rescaled XRT light curve; the dashed line shows a power-law fading as F∝t⁻¹, which (except in the region of the flare discussed in the previous paragraph) matches both light curves reasonably well both before and after the late-time prompt emission episode. The photon index is close to Γ = 2 (spectral index β = 1) in both the BAT and XRT bands, as is the spectral index connecting the two bands. These properties—namely, a power-law SED with β ≈ 1 and power-law light curve with a shallow decay index—are highly suggestive of afterglow emission associated with the forward shock. Indeed, our later modeling (Section 4) strongly supports this hypothesis as the existence of emission in the BAT band with flux, temporal evolution, and spectral index similar to what is observed is inevitably predicted based on simple extrapolation of the X-ray flux in time and frequency.

The X-ray light curve (Figure 5) shows very simple evolution. After the end of the prompt emission episode at ∼400 s, the X-ray flux fades as an effectively unbroken power law (a small amount of excess is seen during a short observation at t = 0.27 days) for the entire remainder of the observation, a span of five orders of magnitude in time. In particular, the light curve does not show any sign of steepening at late times, indicating a very late jet break (t > 100 days), placing a limit on the collimation angle, and giving a lower bound on the true energy scale (see Section 4.6).

Like the GRB itself (and like the optical afterglow; Figure 6), the X-ray afterglow is remarkably bright. In the top panels of Figure 7 we plot the Swift XRT light curve against a sample of other XRT light curves (limited for clarity to subsamples of the closest events, the most energetic events, and an effectively random subsample of all Swift GRBs). Except between 0.02 and 0.4 days (when it is exceeded by GRB 111209A), GRB 130427A is the brightest X-ray afterglow to be observed by the satellite at any common time of comparison. (By comparison to Jakobsson et al. 2004, it is also brighter than any pre-Swift X-ray afterglow.) In an absolute sense, however, its properties are much less exceptional: its X-ray luminosity is only slightly above average for Swift GRBs.

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The wide-field RAPTOR monitored the evolution of the optical afterglow throughout the gamma-ray activity, recording a peak of R ≈ 7 mag (Wren et al. 2013), which would make this the second-brightest (at peak) optical afterglow yet observed, brighter than GRB 990123 (Akerlof et al. 1999) but not as bright as GRB 080319B, the "naked eye" burst (Racusin et al. 2008). Our own observations do not cover this prompt phase, but begin at 315 s after the GBM trigger and provide nearly continuous coverage (in the r/R band, and more partial coverage in other bands) for the next two days, followed by nightly coverage for the next several weeks through the emergence and peak of the associated SN.

A plot of the flux of the optical afterglow in various filters as a function of time is shown in Figure 6. Generically, the optical afterglow evolution during the course of our observations can be described as three power-law segments: a moderately rapid decay at early times (<0.02 days; decay index α = 1.15), a more gradual decay at intermediate times (0.02–0.6 days; α = 0.85), and then another moderately rapid decay at late times (>0.6 days; α = 1.45). Beyond about 6 days the optical afterglow flux is significantly contaminated by host and SN emission; while our observations are consistent with an unbroken decay (particularly in the NIR bands, where the SN and host are relatively faint), we will ultimately require late-time reference images to confirm this unambiguously.

We fit the optical afterglow observations (for points at t < 6 days; later points are not used owing to uncertainty about the SN and host contributions) in all filters simultaneously using the empirical model of Perley et al. (2008b), which treats the light curve as a sum of Beuermann et al. (1999) smoothly broken power laws; color evolution is incorporated in this model as the result of different intrinsic spectral indices underlying each component, as well as the rising and falling power-law segments of each component.³⁶ Only two components are required to reproduce the optical behavior without introducing any significant residual trends: a relatively fast-decaying component at early times plus a more gradually evolving component (with a break at t = 0.7 days) to explain the remainder of the evolution. The early- and late-time colors are similar, but the shallow-decay period at 0.1–0.7 days shows a significantly flatter (bluer) spectral index (although the difference is relatively small; Δβ = 0.34). This color evolution can be seen more clearly in the middle panel of Figure 6.

To examine the temporal evolution of the optical SED of this GRB in more detail and verify that the color evolution indicated by our model fits is real, we subdivided the afterglow into seven temporal ranges: t = 0.0045–0.009, 0.019–0.03, 0.05–0.12, 0.19–0.3, 0.45–0.95, 1.1–3.2, and 3.5–5.1 days. We then performed separate fits to the light curve on these epochs individually to create an optical SED at approximately the midpoint of each of these epochs. The interpolated SEDs, corrected for Galactic extinction (E_{B − V} = 0.02 mag; Schlegel et al. 1998; Schlafly & Finkbeiner 2011, ³⁷), are presented in Table 4.

It is also desirable to constrain and correct for the effects of host extinction. To do so, we take the SED at t = 2 days (which is after the temporal break and should be minimally affected by intrinsic curvature in the SED resulting from a break passage or contribution from the early-time component) and fit these observations assuming an intrinsic power law with spectral index β_O and a Fitzpatrick (1999) extinction model with a profile similar to that of the Large Magellanic Cloud (Misselt et al. 1999) and R_V = 3. (The extinction column toward this GRB is too low to robustly constrain the choice of actual extinction law, although models with a 2175 Å bump marginally better reproduce the SED than the featureless Small Magellanic Cloud like curve.) We measure a small but significant amount of extinction (A_V = 0.13 ± 0.06 mag) from this fit. We then fit to all seven epochs for the spectral slope β_O after correcting for host extinction using this value. The result (see the bottom panel of Figure 6) confirms the blue-to-red evolution between moderately early (t = 10⁻²–10⁻¹ days) and late (t > 1 days) times. The red-to-blue transition from the earliest observations during the initial steep decay to t > 10⁻² s is also seen, although it is not highly significant as we do not have NIR observations during this early period.

While the optical afterglow of GRB 130427A is the second brightest (in terms of apparent magnitude, compared at a common time-post-GRB) of any GRB observed to date for the large majority of its evolution (GRB 030329 was brighter by about 1.0 mag), as at other wavelengths this apparent brightness relative to other GRBs is primarily a function of the burst's proximity: as shown in Figure 7, its overall luminosity and decay rate are quite characteristic of other optical afterglows observed for moderately luminous bursts.

While we were not able to begin observing at radio wavelengths for several hours following the burst and cannot directly constrain the early-time behavior, GRB 130427A nevertheless represents one of the most thoroughly observed radio afterglows to date, with observations spanning <1–95 GHz in frequency and 0.36–128 days in time. Interestingly, the properties of the afterglow at these wavelengths (luminosity, spectral shape, and temporal behavior) are quite unlike those of most other GRB afterglows detected at radio wavelengths thus far.

First, the GRB 130427A afterglow is actually remarkably faint given the close proximity and large energetics of the GRB (Figure 8). For example, its millimeter afterglow is a factor of 100 less luminous than that of GRB 030329 at t = 3 days. At t = 10 days the radio afterglow is ∼10 times less luminous than that of GRB 030329 at the same epoch and a factor of 100 below the most luminous late-time radio GRBs. While lower-luminosity afterglows are not unprecedented, nearly all of them correspond to very nearby events that were also underluminous in gamma rays (and indeed at all other wavelengths).

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The light curve is also remarkable. The early CARMA observations show rapid fading beginning at t = 0.7 days (α ≈ 1.4). This rapid evolution slows down at later times: the later CARMA and subsequent PdBI points are consistent with approximately α ≈ 0.4, and the high-frequency VLA bands show slow similar temporal evolution. In contrast, most well-studied radio afterglows are flat or even rising over the first week and fade steeply after that time (Chandra & Frail 2012).

Finally, the SED is unusual: typically the early-time radio spectral index of a GRB is relatively hard either because of synchrotron self-absorption (which predicts β ≈ −2 below the self-absorption frequency) or because the observations are below the synchrotron peak (in which case β ≈ −1/3). We do not see any sign of self-absorption here except possibly during the first epoch, when the spectral index as measured by a comparison of the two C-band intermediate frequencies (5.1 and 6.8 GHz, acquired simultaneously) is remarkably hard and consistent with β ≈ −2. At all other times the radio spectral index is very close to flat (β ≈ 0) with no sign of a turnover toward low frequencies.

Given that the GRB is "normal" in nearly all other ways, it would seem like a curious coincidence that its radio properties are so unusual. However, it is important to recognize that in the radio and millimeter bands, the comparison sample of GRBs is highly flux limited: only about 50% of all GRBs are detected at radio wavelengths (Chandra & Frail 2012).³⁸ Indeed, GRB 130427A would likely not have been detected itself at radio wavelengths prior to the VLA's upgrade had it occurred at a "typical" Swift redshift of z > 1.5. It is therefore more likely that this otherwise entirely ordinary GRB is not particularly exceptional or unusual at radio wavelengths, but instead that we have obtained our first clear look at a member of the (large, but previously poorly understood) radio-faint population by virtue of this event's close proximity. We will return to the discussion and interpretation of the radio behavior of this GRB afterglow in Section 4.5.1.

Radio observations of point-like sources can be affected by interstellar scintillation. We do not see any obvious effects of scintillation in our observations (all well-sampled radio light curves and SEDs show a relatively smooth appearance, except perhaps for the first C-band epoch), but scintillation nevertheless could represent a significant additional source of uncertainty if present. To estimate the possible scintillation contribution, we use the angular-diameter version of Equation (2) in Taylor et al. (2004) (using our inferred values of E_K and A_* from Section 4) to estimate the size of the GRB as a function of time relative to the angular scintillation scale in Figure 2 of Walker (2001). The point-source scintillation scale at this Galactic latitude of 4.5 μas is much smaller than the expected angular size of ${\sim }40\, t_{\rm days}^{0.75}$ μas, indicating that any scintillation should be strongly damped at high frequencies (ν ≳ ν_o; the transition frequency ν_o is ∼5 GHz at this Galactic latitude) and effectively negligible. The angular scale, however, is larger at lower frequencies where the strong scattering regime applies, scaling as θ∝(ν/ν_o)^−11/5 (Walker 1998). At the time of the first low-frequency observations (∼5 days), the scintillation scale at 1.5 GHz is ∼100 μarcsec, which is similar to the source size at that time, and modulation of up to (ν/ν_o)^17/30 or about 40% can be expected, which should be considered when interpreting the GMRT and L/S-band observations.

The appearance and fading of an SN are unmistakable in the late-time data. Some caution must be used in interpreting these observations in more than a qualitative sense, since large systematic uncertainties are introduced at late times owing to the contribution of the host and afterglow, which are known approximately but have significant uncertainty.

Nevertheless, the current observations are sufficient for a preliminary investigation into the basic properties of the associated SN. In Figure 9(a) we plot the excess flux after subtraction of the power-law afterglow (based on our preferred model fit in Section 3.4, which only uses data from the first 5 days after explosion to minimize any SN contribution), which shows the clear rise and fall of an additional, red component. The i-band signature currently has large systematic errors because of the uncertain host contribution in this band, which we expect will be significantly reduced after late-time reference imaging is available; for now we do not include these bands in the SN fit. The g- and r-band observations are fit with an SN 1998bw template taken from an interpolation of the observations of Galama et al. (1998) and Clocchiatti et al. (2011), scaled independently by linear factors in time and luminosity. We find that an SN with an apparent luminosity (not corrected for extinction) ∼0.6 × that of SN 1998bw and a timescale 0.8× that of SN 1998bw provides a reasonable fit to our observations, in good agreement with the analysis of Xu et al. (2013a). After correction for host extinction based on our estimate of A_V = 0.13 mag (Section 3.4), the intrinsic luminosity is 0.7× that of SN 1998bw.

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A more detailed examination of the SN properties will be left for further work and will not be discussed here. We did verify that the SN should not contribute a large amount of flux to the UV or optical filters that might have affected our host-galaxy subtraction in Section 2.18; assuming colors similar to those of Šimon et al. (2010) and Kocevski et al. (2007), the contribution to these bands is relatively small (≲15% of the host+afterglow flux) at all times.

Our multifrequency, multi-epoch data provide a powerful test of basic afterglow models. The optical, X-ray, and radio fluxes and spectral slopes are well observed and independently constrained at almost every epoch, permitting us to construct an evolving SED spanning many orders of magnitude in both time and frequency.

To provide the best constraints possible and minimize the uncertainties associated with the nonsimultaneity of observations in each band for this exercise, it is necessary to interpolate measurements to construct coeval SEDs at a series of semiregularly spaced epochs spanning the full range of observations. Optical observations have already been interpolated in this way using the technique described in Section 3.4; here we extract the XRT, millimeter, and multi-frequency radio fluxes (as well as BAT observations during the first epoch) and XRT spectral index at each of these same epochs (0.007, 0.023, 0.07, 0.23, 0.7, 2.0, and 4.5 days), plus at a series of later-time epochs (10, 30, 60, and 130 days) after the optical light becomes dominated by host and SN.

The BAT and XRT bands are simply directly interpolated in flux and in β using the curves in Section 2.1. We also interpolate (logarithmically in time and flux) the LAT data of Tam et al. (2013) in the 0.2–10 and 10–100 GeV bins. The radio observations are relatively sparsely sampled and the radio behavior at these wavelengths is complex and frequency dependent, so the choice of interpolation procedure is not straightforward: fortunately, since our epoch times were deliberately chosen to be very close to the times of radio observations, the results are largely independent of the procedure. Nevertheless, using the observed behavior of the light curves at both low and high frequencies, we choose temporal indices that provide a reasonable approximation of the observed behavior at all times to perform the interpolation as accurately as possible. Specifically, at high frequencies (>50 GHz) we interpolate assuming t^−1.4 behavior at t < 1 days, t^−1.0 at t = 1–3 days, and t^−0.4 at later times. At low frequencies (<50 GHz) we interpolate assuming t^−0.4 at t < 1 days, t⁻¹ at t = 1–4 days, t^−0.4 at t = 4–100 days, and t⁻¹ after 100 days. Results, color-coded by epoch over the full range from 0.007 to 130 days, are shown in Figure 10.

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We first attempted to fit these SEDs with a simple single-component synchrotron SED using the standard model of Sari et al. (1998): a thrice-broken power law in frequency with breaks at the synchrotron self-absorption frequency ν_a, the minimum electron energy ν_m, and the cooling frequency ν_c; spectral indices (β, where F_ν∝ν^−β) between the breaks are −2, −1/3, {1/2 or (p − 1)/2}, and (p/2), where p is the electron power-law index (typically p ≈ 2–2.5) and the slope of the third segment depends on whether the electrons are fast-cooling (ν_c > ν_m) or slow-cooling (ν_m < ν_c). Breaks are softened by means of the Beuermann et al. (1999) function.

Even in a qualitative sense, this spectral shape can provide a reasonable fit to the radio–optical–X-ray data only at or after t ≈ 30 days. At earlier times, the flat or soft radio spectral index cannot be made to match the other bands as it would require ν_m ≲ ν_radio, which is not consistent with extrapolation from the optical band (it also has some difficulty explaining the shallow slope between the X-ray and optical bands β_OX at the earliest times). We therefore added a second synchrotron SED to the model with the ν_m peak at low frequencies. This two-component model was found, in general terms, to be capable of providing an excellent description of the data at every epoch.

The need for two components in this fashion is highly suggestive of the presence of both reverse and forward shocks simultaneously contributing to the afterglow, the reverse shock dominating at lower frequencies and the forward shock at higher frequencies. The case for this interpretation grows even stronger when the temporal behavior is also considered: the steep-shallow-steep evolution of the optical light curve and steep-shallow evolution of the millimeter light curve are very similar to the behavior of previous GRB afterglows with claimed early-time reverse shocks at these frequencies (e.g., Akerlof et al. 1999; Kulkarni et al. 1999; Kobayashi & Zhang 2003b; Li et al. 2003; Wei 2003; Shao & Dai 2005; Perley et al. 2008a; Gomboc et al. 2008; Racusin et al. 2008; Bloom et al. 2009; Pandey et al. 2010; Gruber et al. 2011; Cucchiara et al. 2011; Zheng et al. 2012; Gendre et al. 2012). In the remainder of the discussion we therefore refer to the low-frequency and high-frequency synchrotron components of the model as the reverse-shock and forward-shock components, respectively.

With this paradigm in mind, we attempted to reproduce the temporal evolution of the multiwavelength SED within the standard forward/reverse-shock fireball model of GRB afterglows (e.g., Meszaros & Rees 1993; Sari et al. 1998; Piran 1999). In general, we started with attempting to reproduce the SED at t = 2 days post-trigger and extrapolated the SED forward and backward in time under various assumptions about the evolution of the key synchrotron parameters (F_{ν, max}, ν_a, ν_m, and ν_c) for both the forward and reverse shocks, adjusting the assumptions as necessary to reproduce the earlier and later SEDs. We determine the values of these parameters and do not yet attempt to solve for the underlying fundamental burst/microphysical parameters (with the exception of the electron index p). Our procedure parallels the approach taken by Laskar et al. (2013), but was developed largely independently and is applied here to a much larger data set, including radio observations out to t = 128 days, significantly improved optical observations, and consideration of the spectral indices as well as the absolute fluxes.

The ingredients, assumptions, and basic results of the model are described in the following sections.

4.3.1. Forward Shock

4.3.2. Reverse Shock

This model (which has only a few significant free parameters in the form of the initial placement of the breaks, plus p, g, and the modified cooling-break index) does a remarkably good job fitting the data. As can be seen in Figure 10, the model curves are within about a factor of two, and often much better, of each observation at all frequencies and at all epochs. This is true for observations at intermediate epochs not shown in the discrete SEDs as well: in Figure 11 we plot synthetic light curves from our model versus data at a series of frequencies spanning from the radio to high-energy gamma rays. All of the qualitative features of the GRB afterglow noted previously are represented by the model, including the relatively faint radio afterglow, the clear spectral index and steep-shallow-steep optical evolution, and the lack of X-ray spectral or temporal evolution.

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The model is not perfect; in particular, it tends to underpredict the NIR flux slightly and implies a somewhat shorter-lived shallow-decay component in the optical bands relative to what is observed. Nevertheless, given the only very limited flexibility in both the shape of the SED at any epoch and its evolution with time, the accuracy to which the observations are matched is remarkable.

So far we have only taken the temporal scalings of the break frequencies and peak fluxes from theory, with their initial values treated as free parameters. However, these values are prescribed by theory as well, depending on the properties of the burst and its environment and microphysical parameters describing the partition of energy within the shock wave. The parameters underlying the forward-shock evolution are _B (the fractional energy in magnetic fields), _e (the fractional energy in accelerated electrons), E_K (the total energy of the shock), and the circumburst density normalization (in the case of a wind medium, A_*). Additional fundamental parameters that are relevant to the reverse shock are t_X (the shock crossing time, which is t_GRB in the thick-shell model and t_dec in the thin-shell model), γ₀ (the initial Lorentz factor of the outflow, which is also the inverse baryon fraction of the initial fireball), and the magnetization R_B (which permits _B in the ejecta to differ from that in the forward shock). The electron index p, for which we have already solved, constitutes a final parameter.

4.5.1. Forward Shock

To determine the forward-shock parameters, we took the values of the spectral breaks and peak at the earliest epoch at which we have data (t = 0.007 days) and inverted the standard equations governing the locations of the breaks to solve for _B, _e, E_K, and A_*. (We choose this early epoch to try to minimize the impact of the subsequent noncanonical evolution of ν_c.) This solution is actually underdetermined because we could not measure ν_a directly, as it is below the observed bands at all times. However, the physical requirement that _B + _e < 1.0 narrows down the allowed parameter space to a relatively narrow range. We infer (assuming that neither efficiency exceeds its equipartition value; i.e., _B < 1/3, _e < 1/3)

$$\begin{equation*} 0.03 < \epsilon _B < 0.33, \end{equation*}$$

$$\begin{equation*} 0.33 > \epsilon _e > 0.14, \end{equation*}$$

$$\begin{equation*} 1.9\times 10^{53} < E_K < 4.2\times 10^{53}, \end{equation*}$$

$$\begin{equation*} 0.005 > A* > 0.001, \end{equation*}$$

where E_K is in erg. These ranges refer only to the range of "best-fit" parameters allowed given our constraints on _e (which determines the left bound) and _B (which determines the right bound). Our inferred values are all consistent with the numbers presented by Laskar et al. (2013) with the exception of E_K, which we find to be larger than their estimate.

The observed properties of the afterglow, in particular the radio faintness, can largely be explained as a product of the parameters observed for this GRB. The large values of E_K and _e and the low wind density A* produce a shock with a great deal of energy distributed among a relatively small number of electrons, which therefore move very rapidly and radiate mostly at high frequencies (high ν_m) at the expense of the lower-energy emission. Specifically, ν_m is located in the optical band at early times, explaining why the afterglow appears blue at t < 0.5 days but shifts to the red (and fades more rapidly) at later epochs.

4.5.2. Reverse Shock

The observed properties of the reverse shock are determined by the same physical parameters as the forward shock with the addition of a direct dependence on the initial Lorentz factor γ₀ and the magnetization ratio R_B = _{B, RS}/_{B, FS}. At the time of shell crossing (∼t_X), the values of ν_{m, RS} and F_{ν, max} are easily determined by simple scaling relations versus the equivalent values of the forward shock (for the thin-shell case, Zou et al. 2005; and including the magnetization parameter as defined by Gomboc et al. 2008):

$$\begin{equation*} F_{\nu,{\rm max,RS}}/F_{\nu,{\rm max,FS}} = 1.2 \gamma _0 R_B^{1/2}, \end{equation*}$$

$$\begin{equation*} \nu _{m,{\rm RS}}/\nu _{m,{\rm FS}} = 0.31 \gamma _0^{-2} R_B^{1/2}, \end{equation*}$$

$$\begin{equation*} \nu _{c,{\rm RS}}/\nu _{c,{\rm FS}} = R_B^{-3/2}. \end{equation*}$$

While ν_{c, RS} is generally hidden inside the forward shock at all times, ν_m and F_{ν, max, RS} are tightly constrained observationally. Based on their temporal scalings, their values can then be extrapolated back to t_X, which is bounded by the burst duration (t ≈ 20 s for the period of strongest emission) and the appearance of the afterglow in the BAT band (t ≈ 50 s); this in turn can be used to solve for γ₀ and R_B.

As previously mentioned, there are two possible cases: ν_{a, RS} < ν_{m, RS} and ν_{m, RS} < ν_{a, RS}. The first possibility is strongly disfavored by this exercise as the Lorentz factor derived is extremely low (γ₀ ≈ 14). This would be in conflict with the independent constraint on γ₀ set by the deceleration time of the afterglow (which in the thin-shell case must be less than the afterglow peak time); e.g., from Zou et al. (2005),

$$\begin{equation*} t_{\rm dec} = 2.9\times 10^3\, {\rm s} (1+z) E_{53} \gamma _{1.5}^{-4} A_{*,-1}^{-1}. \end{equation*}$$

For t_dec < 20–50 s this would imply γ₀ ≳ 120–250, which is not consistent with the value set by the reverse-to-forward-shock ratio.

We therefore adopt the ν_{m, RS} < ν_{a, RS} model. In this case, we find more reasonable values of γ and R_B; e.g., for an assumed t_X = 50 s,

$$\begin{equation*} 230 < \gamma _0 < 430, \end{equation*}$$

$$\begin{equation*} 2.3 < R_B < 2.7, \end{equation*}$$

which is self-consistent with the deceleration constraint on γ₀.

A further consistency check can be performed by examining the location of the self-absorption break ν_{a, RS}, the peak value (at t_X) of which is predicted as a function of (_B,_e,E_K,Γ,A_*) by (for example) Equation (38) of Zou et al. (2005), and the time-evolution after that point is given by the power-law scalings discussed previously. Its value at t = 0.7 days is well constrained by observations (ν_{a, RS} = 18 GHz); this value is fully consistent with its expected value from our theoretical model under the range of values derived above (33 GHz >ν_{a, RS} > 18 GHz).

As seen in many other Swift GRBs (Racusin et al. 2009), the afterglow of GRB 130427A shows no break in the XRT light curve in observations taken to date indicative of a jet. Given that GRBs are believed to be narrowly collimated, this might initially seem surprising. However, the jet break time is not just a function of beaming angle but also of other factors, including the energy of the shock and (in particular) the circumburst density. The jet opening angle is related to these observable parameters by the relation (Li & Chevalier 2003)

$$\begin{eqnarray*} &&\theta _{\rm jet} = 5{.\!\!^\circ }4 \left(\frac{t_{\rm jet}}{\rm d}\right)^{1/4} A_*^{1/4} \left(\frac{1+z}{2}\right)^{-1/4} \left(\frac{E_{\rm K}}{10^{53}\, {\rm erg}}\right)^{-1/4}. \end{eqnarray*}$$

For the range of forward-shock parameters derived in Section 4.5.1, we derive a constraint on the jet opening angle of θ_jet > 5° and a corresponding beaming-corrected E_K > 5 × 10⁵⁰ erg and E_γ > 2.2 × 10⁵¹ erg. These limits are still consistent with previous GRBs and the canonical energy scale of ∼10⁵¹ erg (Frail et al. 2001), and the lack of a jet break through to the present time is no surprise—in this case it is primarily a consequence of the very low density surrounding the burst. In fact, a continued lack of a jet break out to extremely late times remains entirely consistent with the model; the burst is consistent with E_K + E_{γ, iso} < 10⁵² erg even for jet break times as late as 4 yr.