AN ACHROMATIC BREAK IN THE AFTERGLOW OF THE SHORT GRB 140903A: EVIDENCE FOR A NARROW JET

GRB 140903A triggered the Swift Burst Alert Telescope (BAT; Barthelmy et al. 2005) at 15:00:30 UT on 2014 September 3 (Cummings et al. 2014). The Swift X-ray Telescope (XRT; Burrows et al. 2005) began settled observations of the GRB field 74 s after the BAT trigger and monitored the X-ray afterglow during the following 3 days, until the source faded below the detector sensitivity threshold. The XRT data comprise 24 ks acquired in Photon Counting (PC) mode.

BAT and XRT data were processed using the Swift software package distributed within HEASOFT (v. 6.17). We used the latest release of the BAT and XRT Calibration Database and followed standard data reduction procedures.

The Chandra X-ray Observatory performed two Target of Opportunity (ToO) observations in order (1) to precisely localize the X-ray afterglow (PI: T. Sakamoto) and (2) to characterize its late-time temporal evolution and search for a possible jet break (PI: E. Troja). Our first observation (ObsId 15873) started 3 days after the burst and observed the field for a total exposure of 19.8 ks. Our second Chandra observation (ObsId 15986) was performed on 2014 September 18 for a total exposure of 59.3 ks. Chandra data were reduced using version 4.6.1 of the CIAO software with CALDB version 4.6.3. Events from the GRB afterglow were selected using a source extraction radius of 2 pixels, and the derived count rates were corrected for vignetting effects and point-spread function (PSF) losses. The background contribution was estimated from an annular, source-free region centered on the afterglow position.

The GRB afterglow is detected at both epochs. In our first Chandra observation we detect 80 net source counts in the 0.5–8.0 keV energy band. We corrected the native Chandra astrometry by aligning our X-ray and optical images (see Section 2.3). Based on the match of five bright X-ray and optical sources, we determine a refined X-ray (J2000.0) position of $\alpha \,=\,{15}^{{\rm{h}}}{52}^{{\rm{m}}}03\buildrel{\rm{s}}\over{.} 273$, $\delta \,=\,+27^\circ 36^{\prime} 10\buildrel{\prime\prime}\over{.} 83$ with an error radius of 04 (90% confidence level). In our second and last Chandra observation only 6 counts are measured at the source position, corresponding to a detection significance >99.99% (Kraft et al. 1991).

We initiated an observing campaign with the Large Monolithic Imager (LMI) mounted on the 4.3 m DCT in Happy Jack, AZ. Observations in the griz filters started on 2014 September 04 at 3.17 UT, approximately 12 hr after the Swift trigger, and continued to monitor the field for the next 3 weeks. Late-time images in the r and i filters were acquired on 2016 March 17 (561 days after the burst) and used as templates for image subtraction. Standard CCD reduction techniques (e.g., bias subtraction, flat-fielding, etc.) were applied using a custom IRAF¹⁹ pipeline. Individual short (10–20 s) exposures were aligned with respect to astrometry from the Sloan Digital Sky Survey (SDSS; Ahn et al. 2014) using SCAMP (Bertin 2006) and stacked with SWarp (Bertin et al. 2002).

As shown in Figure 1, the field of GRB 140903A is quite complex: the optical afterglow lies on top of a relatively bright host galaxy (see below), and only 12'' away from an extremely bright (V ≈ 9 mag) star. In order to extract the afterglow brightness from our DCT images, we performed digital image subtraction with the High Order Transform of PSF ANd Template Subtraction (HOTPANTS; Becker 2015). The resulting photometry, calibrated with respect to nearby point sources from SDSS, is presented in Table 1. The transient is detected with high significance in our first epoch at Δ t = 12.5 hr, and possibly at 2.5 days, although the significance of this last detection is only marginal (≲3σ).

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Using the images from 2016 March 17, we measure the following magnitudes for the underlying host galaxy: r'= 20.58 ± 0.09 and i' = 20.12 ± 0.05. From earlier observations we also measure g' = 21.97 ± 0.16 and z' = 19.66 ± 0.08, although we caution that these fluxes may include some afterglow contribution. The host is unresolved in all of our DCT images (seeing ranging from 08 to 20). Using astrometry from nearby SDSS point sources for reference, we measure a (J2000.0) position of $\alpha \,=\,{15}^{{\rm{h}}}{52}^{{\rm{m}}}03\buildrel{\rm{s}}\over{.} 278$, δ = +27°36'1068. The excess afterglow flux measured in our subtracted images is consistent with this location, within the estimated uncertainty of our astrometric tie (≈100 mas in each coordinate).

NIR images were acquired in zJHK_s bands using the 2.0 m Liverpool (LT) and the 3.5 m Calar Alto telescopes (CAHA). The LT images were taken in the z band with the IO:O camera, which provides a 100 × 100 field of view and a 03 pixel scale. The CAHA data were acquired in the JHK_s bands with the Ω₂₀₀₀ instrument, yielding a 154 × 154 field of view and a 045 pixel scale. In order to reduce the contamination of the nearby bright star, these observations were taken in relatively short (20–30 s) exposures. The reduction followed standard steps: bad pixel masking, bias and flat-field correction, sky subtraction, plus stacking, performed by calling on IRAF tasks (Tody 1993). The resulting photometry, calibrated with respect to nearby point sources from SDSS and the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006), is presented in Table 1. We used the offsets from Blanton & Roweis (2007) to convert the 2MASS Vega magnitudes to the AB system.

We imaged the field of GRB 140903A with the Gemini Multi-Object Spectrograph (GMOS; Hook et al. 2004) on the 8 m Gemini North telescope. We obtained a single 120 s i' image beginning at 05:24 UT on 2014 September 4 (Δt = 14.4 hr) and a dithered sequence of 10 × 60 s i' exposures at a mean epoch of Δt = 39.2 hr on 2014 September 5. Our last observation was performed on 2016 April 2 and used as a template for image subtraction. The images were reduced in the standard manner using the gemini IRAF package. We performed digital image subtraction on the GMOS images using the same analysis methods as was used for the DCT images (Section 2.3). In the subtracted frame transient emission is clearly detected at an offset of 96 ± 44 mas from the galaxy's center. At a redshift z = 0.351 this corresponds to a physical projected offset of 0.5 ± 0.2 kpc. For the transient component we infer $i^{\prime} =21.33\pm 0.05$ mag in our first epoch and $i^{\prime} =22.99\pm 0.13$ mag in the second epoch. This implies a steep temporal decay with slope α_o = 1.54 ± 0.15 between the two observations.

We obtained a series of spectra of the afterglow+galaxy with GMOS beginning at 05:34 UT on 2014 September 4 (Δt = 14.6 hr). GMOS was configured with the R400 grating and a central wavelength of 600 nm, providing coverage from λ ≈ 4000 to 8000 Å with a resolution of ≈1000. We restricted our analysis to λ > 5500 Å due to the poor signal-to-noise ratio of the spectrum at lower wavelengths.

The resulting spectrum is plotted in Figure 2. The strongest (non-telluric) feature is a broad (FWHM ≈ 15 Å) absorption line at λ ≈ 7963 Å, along with a weaker (but still broad, FWHM ≈ 10 Å) absorption line at λ ≈ 7915 Å. We interpret these features as corresponding to Na i with z ≈ 0.35. We also detect narrow emission lines at λ = 6569.6 ± 0.5 Å and λ = 6763.7 ± 0.6 Å, which correspond to Hβ and [O iii] at z = 0.351 ± 0.001, which we adopt for the redshift of the host.²⁰ Weak absorption features corresponding to Ca ii H + K are also visible at this redshift, though with marginal significance.

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Further optical spectroscopy of the host galaxy was performed using OSIRIS (Optical System for Imaging and low Resolution Integrated Spectroscopy; Cepa et al. 2000) at the 10.4 m GTC. Observations started on 2014 October 03, i.e., ∼30.2 days after the trigger, using the R1000B grism (2 × 600 s exposures) and R2500I VPH (3 × 600 s exposures). The spectra covered the 3600–7800 Å range at a resolution of ≈1000 and the 7300–10000 Å range at resolution ≈2500. The 10 slit was positioned on the location of the host galaxy, and 2 × 2 binning mode was used for data acquisition. The obtained spectra were reduced and calibrated following standard procedures using custom tools based in IRAF and Python. Spectra were flux-calibrated using the spectrophotometic standard star GD 248, which was observed during the same night with a 252 slit. In order to account for slit losses, we renormalized the flux of the source to match the DCT magnitudes shown in Table 1. Acquisition images were not usable due to the nearby saturated star.

Although close to a skyline, Hα is clearly detected in the red spectrum at λ = 8862.1 ± 0.8 Å, consistent with the redshift from GMOS (Section 2.6). No emission lines are visible in the blue grism spectrum. This may be due to the presence of dust, also suggested by a clear spectral curvature toward the short wavelengths.

GRB 140903A was observed with the Jansky Very Large Array (VLA) at both 6.1 GHz (C band) and 9.8 GHz (X band). Observations started ∼10 hr after the burst and periodically monitored the source for 18 days (Fong et al. 2015). Radio data were downloaded from the public NRAO archive and reduced using the Common Astronomy Software Applications (CASA) v. 4.5.2 package. After standard calibration and basic flagging, we visually inspected the data and applied further screening when needed. Galaxies 3C 286 and J1609+2641 were used as flux and phase calibrators, respectively. The log of radio observations is reported in Table 2. Our values are slightly higher, but largely consistent with those reported by Fong et al. (2015). A simple power-law fit to the data yields decay slopes ${\alpha }_{6\mathrm{GHz}}$ = ${0.63}_{-0.12}^{+0.14}$ and ${\alpha }_{9.8\mathrm{GHz}}\gt 0.5$ for t > 1 day. This does not take into account the possible effects of interstellar scintillations (ISSs), which we model in Section 4.2.

The prompt emission consists of a main Fast Rise Exponential Decay (FRED) pulse, with a duration of T₉₀ = 0.30 ± 0.03 s in the 15–350 keV band (Figure 3, left panel). The time-averaged spectrum, from T + 0.09 to T + 0.47, shows that the prompt emission is well described (χ² = 44 for 57 degrees of freedom) by a simple power law with Γ = 1.99 ± 0.08. According to this best-fit model, the burst fluence in the observed 15–150 keV energy band is (${1.35}_{-0.05}^{+0.07}$) $\,\times \,{10}^{-7}$ erg cm⁻², which, at a redshift z = 0.351, corresponds to an isotropic-equivalent energy of ${E}_{\gamma ,\mathrm{iso}}$ = (6.0 ± 0.3)$\,\times \,{10}^{49}$ erg. Due to the narrow BAT energy bandpass, this only places a lower limit to the bolometric energy release. However, for a typical GRB spectrum (Band et al. 1993), the measured soft photon index indicates that the spectral peak lies close to or within the BAT energy range (Sakamoto et al. 2009). In this case, the bulk of the emission mainly falls within the observed range, and the derived value of ${E}_{\gamma ,\mathrm{iso}}$ represents a good estimate of the total energy radiated in the prompt emission.

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Spectral lags were calculated by cross-correlating the light curves in the standard BAT channels: 1 (15–25 keV), 2 (25–50 keV), 3 (50–100 keV), 4 (100–350 keV). We followed the method outlined by Ukwatta et al. (2012) and, in order to increase the signal-to-noise ratio in the higher-energy channels, performed the analysis on non-mask-weighted light curves, each with a 4 ms time resolution. The derived lags are ${\tau }_{31}\,=\,{12}_{-7}^{+7}$ ms and τ₄₂ = $-{1}_{-7}^{+7}$ ms, where the quoted uncertainties were derived by Monte Carlo simulations. The results of our lag analysis are shown in Figure 3 (right panel).

We also searched for temporally extended emission following the main burst, but no significant signal was found. By assuming a power-law spectrum with photon index Γ = 2, we set a 3σ upper limit of 8 $\,\times \,{10}^{-10}$ erg cm⁻² s⁻¹ (15–50 keV) in the time interval 10–100 s. This is consistent with the MAXI upper limit of 8.4$\,\times \,{10}^{-10}$ erg cm⁻² s⁻¹ in the 4–10 keV energy band (Serino et al. 2014).

3.2.1. Spectral Analysis

3.2.2. Temporal Analysis

The X-ray light curve was binned to have a minimum of 15 counts in each temporal bin. The observed count rates were converted into flux units by using the ECFs derived in Section 3.2.1 and by propagating the relative uncertainties. We modeled the afterglow temporal decay with a series of power-law segments (${f}_{X}\propto {t}^{-{\alpha }_{i}}$) and minimized the χ² statistics to obtain the best fit to the data. The afterglow displays a shallow decay phase with temporal index α₁ ∼ 0.2, which steepens to α₂ ∼ 1.1 after ${t}_{{bk},1}\,\sim$ 7 ks. Our first Chandra/ACIS-S data point lies below the predictions based on the Swift/XRT data set, hinting at a second temporal break in the light curve. However, the combined XRT/ACIS-S data set could be reasonably well described by adopting a steeper temporal index α₂ ∼ 1.5 for the final power-law decay and no additional break. A second Chandra observation was therefore executed in order to distinguish between the two models. This last measurement confirms the presence of an additional break in the X-ray light curve at a time t_j ≈ 1 day and allows us to constrain the slope of the final decay to α₃ ∼ 2.1. The best-fit temporal models are summarized in Table 3. The X-ray light curve and our best-fit model are presented in Figure 4 and compared to the optical (Table 1) and radio measurements (Table 2) in order to highlight the achromatic nature of the last temporal break t_j, which we interpret as the jet-break time.

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Table 3.  Afterglow Light-curve Fit Parameters

Band	α1	${t}_{{bk},1}$	α2	${t}_{{bk},2}$	α3	χ2/dof
		(ks)		(ks)
X	0.20 ± 0.02	${7.3}_{-0.9}^{+0.6}$	${1.06}_{-0.11}^{+0.07}$	${69}_{-12}^{+17}$	${2.11}_{-0.07}^{+0.22}$	43/46
O	1.54 ± 0.15	...	...	...	...	...
X + O	0.21 ± 0.02	${7.9}_{-0.9}^{+1.0}$	${1.16}_{-0.03}^{+0.10}$	${89}_{-12}^{+11}$	${2.1}_{-0.2}^{+0.2}$	49/48
R (6.1 GHz)	−0.5a	${89}_{-12}^{+11}$	0.63 ± 0.14	...	...	...
R (9.8 GHz)	>0.5	...	...	...	...	...

Note.

^aThe temporal slope was held fixed at the value predicted by the standard fireball model for ν_sa < ν < ν_m.

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In order to study the spectral evolution across the temporal break t_j detected in X-rays, we extracted the afterglow spectral energy distribution (SED) at two different epochs, t₁ = 0.5 days (<t_j) and t₂ = 2.5 days (>t_j). These times were selected in order to maximize the simultaneous coverage at different wavelengths.

Optical fluxes were derived by the best-fit temporal model in Table 3 and corrected for Galactic extinction in the GRB direction (${E}_{B-V}\,\approx$ 0.03; Schlegel et al. 1998). A power-law fit (f_ν ∝ ${\nu }^{-\beta }$) to the optical and X-ray data yields spectral slopes β_OX = 0.72 ± 0.05 at t = t₁, β_OX = 0.76 ± 0.12 at t = t₂, significant intrinsic absorption N_H = (1.8 ± 0.4)$\,\times \,{10}^{21}$ cm⁻², and marginal evidence of dust extinction A_V = 0.47 ± 0.25. The simple power-law fit provides a good description of the data set (W-stat = 355 for 371 dof), suggesting that optical emission and X-ray emission belong to the same spectral segment (${\nu }_{m}\lt {\nu }_{\mathrm{opt}}\lt {\nu }_{X}\lt {\nu }_{c}$) of the synchrotron spectrum. The lack of significant spectral variation across the temporal break t_j is consistent with the properties of a jet break and excludes alternative interpretations (e.g., cooling frequency).

By extrapolating the observed spectrum to radio energies, the predicted flux at t = t₁ is ≈10 mJy, two orders of magnitude higher than the radio measurement. This implies a spectral break between the optical and radio band, and that the radio data belong to a different spectral segment (${\nu }_{r}\lt {\nu }_{m}$). By adopting the standard closure relations for GRB afterglows (Zhang & Mészáros 2004), we fixed the radio spectral index to β_r = 1/3 and fitted the broadband SED with a smoothly broken power law. We added to the model a systematic uncertainty in order to take into account the possible effects of interstellar scattering and scintillation at radio wavelengths. Although a proper estimate of the ISS fluctuations requires more complex modeling (see Section 4.2), at this stage we introduce an uncertainty of ≈30%. Our fit constrains the spectral peak to lie in the IR region at ν_pk ≈ 9.3 $\,\times \,{10}^{11}$ Hz at 0.5 days. At our second epoch, the radio measurements are only slightly lower than the extrapolation of the higher-energy spectrum, implying that the spectral peak moved close to the radio band. We estimate ν_pk ≈ 37 GHz at 2.5 days, above the VLA frequencies. This shows that the observed radio, optical, and X-ray emission remained in the same spectral regime; thus, the observed temporal break was not caused by spectral variations. Basic considerations on the spectral and temporal behavior of the afterglow disfavor a wind-like environment, which would cause a steeper decay (α_wind ≈ 1.5) of the pre-break X-ray afterglow. Our analysis also shows that the broadband spectrum evolved in time as ν_pk ∝ t⁻² and f_pk ∝ t^−0.3. As shown in Figure 5 (right panels), these decay rates are significantly steeper than the ones predicted by the spherical fireball model for a uniform medium, and are instead consistent with the spectral evolution of a collimated outflow. In particular, the slow decay of the peak flux strongly favors a narrow jet model seen slightly off-axis.

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GRB 140903A is located on top of a compact and red galaxy, suggestive of an old system. Based on the galaxy sky densities in the r band (Yasuda et al. 2001), we estimated a small probability of a chance association, P_ch ≈ 3 $\,\times \,{10}^{-4}$ (Bloom et al. 2002; Troja et al. 2008), and we therefore consider this galaxy as the GRB host. From our r-band measurement we derive a rest-frame absolute B-band magnitude M_B ≈ −20.9 mag, or ${L}_{B}\approx 0.8{L}_{* }$ when compared to the luminosity function of galaxies at a similar redshift 0.2 < z < 0.4 (Willmer et al. 2006). In order to characterize the galaxy's physical properties, we used the late-time (t > 3 days) optical and IR data to build the host galaxy SED, and we ran a photometric fit with a grid of spectral templates within LEPHARE v. 2.2 (Ilbert et al. 2006). The templates were created using the stellar population synthesis libraries of Bruzual & Charlot (2003) with the Padova 1994 evolutionary tracks, and assuming the initial mass function (IMF) from Chabrier (2003). We adopted an exponential star formation history with different e-folding times τ and included the contribution of emission lines following Kennicutt (1998).

Our results are shown in Figure 6. Our best-fit model (gray curve) well reproduces the optical and NIR continua. The best-fit parameters for the galaxy template are an intrinsic extinction ${E}_{B-V}$ = 0.25, solar metallicity, e-folding time τ = 500 Myr, stellar mass log(M/M_⊙) = 10.61 ± 0.15, an old stellar age t = ${4.1}_{-2.3}^{+3.9}$ Gyr, and a moderate star formation rate SFR = 1.0 ± 0.3 M_⊙ yr⁻¹, in agreement with the presence of nebular emission lines in our spectra.

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By using the extinction-corrected Hα line flux, we infer a comparable value of SFR = 0.38 ± 0.04 M_⊙ yr⁻¹ (Kennicutt 1998) for a Chabrier IMF and a specific SFR of 0.47 ± 0.05 ($L/{L}_{* }$) M_⊙ yr⁻¹. Based on the diagnostic F([O iii] λ5007)/$F({\rm{H}}\beta )\sim 0.48$ (Nagao et al. 2006), we estimate a supersolar metallicity 12 + log (O/H) ≈ 9.0 ± 0.2, not unprecedented among short GRB host galaxies (Perley et al. 2012).

The early X-ray afterglow of GRB 140903A is characterized by a period of fairly constant emission lasting ≈4 hr. The shallow decay slope α₁ ∼ 0.2 is not consistent with a standard forward shock origin, and this is often considered a sign of prolonged energy injection into the blast wave (Fan & Xu 2006; Zhang et al. 2006; Cannizzo et al. 2011). Indeed, it has been suggested that in a significant fraction of GRBs the X-ray plateaus originate from the internal dissipation of the engine-driven wind rather than from shocks at an external radius. In this scenario, known as "internal plateau" (Troja et al. 2007), the forward shock component is subdominant, and the observed X-ray emission is directly powered by the central engine. One of the most popular models invokes a newborn magnetar as the power source of the GRB and its afterglow: as the magnetar spins down, it injects energy into the jet, causing a period of nearly flat emission (the plateau), followed by a steeper temporal decline with slope α ≳ 2 (Zhang & Mészáros 2001). This rapid decay may mimic the presence of a jet break, complicating the interpretation of the observed X-ray emission.

In the case of GRB 140903A, the standard expression for magnetic dipolar radiation (Shapiro & Teukolsky 1983) provides an excellent description of the X-ray data set, as it can fully account for the two salient features of the observed light curve—a short-lived plateau and a final steep decay— with the advantage of only two free parameters. However, due to the small radius at which the internal dissipation occurs, a bright optical and radio counterpart is not expected in these cases. Indeed, a distinctive feature of "internal plateaus" is that they appear as achromatic bumps visible in X-rays, but not at lower energies (Troja et al. 2007; Lyons et al. 2010; Rowlinson et al. 2013). Our SED analysis showed instead that X-ray, optical, and radio data are consistent with being from the same emission component. In particular, by considering that the radio data lie above the self-absorption frequency ν_a, we can derive a rough estimate of the emitting radius R ≳ 4 $\,\times \,{10}^{16}$ cm at t = 0.5 days (Barniol Duran et al. 2013), consistent with an external shock origin. Moreover, the observed temporal and spectral indices (β_OX ≈ 0.7, α₂ ≈ 1.1) after the plateau phase are in agreement with the canonical closure relations for ν_m < ν_X < ν_c and p ≈ 2.4. Based on these considerations, we favor an external origin for the observed X-rays. In this scenario, the X-ray plateau is indirectly powered by the central engine via sustained energy injection into the forward shock, and after the cessation of energy injection is communicated to the shock front, the afterglow evolves in a standard fashion (van Eerten 2014). Therefore, the X-ray emission is not directly linked to the time history of the central engine; instead, it carries important information about the jet collimation, energetics, and surrounding environment.

We modeled the broadband data set (from radio to X-rays) by using the standard prescriptions for an expanding spherical fireball and the scaling relations for the post-jet-break evolution (Sari et al. 1999). We excluded from the fit the early-time data ($t\lt {t}_{{bk},1}$) as they are affected by persistent energy injection. In our fit we implemented a routine to calculate the expected ISS modulation for each set of input afterglow parameters. By adopting the "NE2001" model (Cordes & Lazio 2002), we derived a scattering measure SM = 1.3 $\,\times \,{10}^{-4}$ kpc/m^−20/3 and a transition frequency ν₀ = 8 GHz in the direction of GRB 140903A. Observations below this frequency could possibly be affected by strong scattering if the source size is smaller than the ISS angular scale, ${\theta }_{F0}\,\approx$ 1 μas. At the GRB redshift this corresponds to an apparent fireball size ${R}_{\perp }$ ≲ 2 $\,\times \,{10}^{16}$ cm, which is likely the case at the early timescales here considered. The derived ISS fluctuations were treated as a source of systematic uncertainty and added in quadrature to the statistical errors when evaluating the fit statistics.

We assumed a uniform circumburst medium with density n₀ and constant microphysical parameters _e and _B. Under these assumptions, we did not find an acceptable fit to the data (χ² = 65 for 43 dof), mainly because the model predicts a much faster decay of the peak flux and peak frequency after the jet break. We attempted to model this effect by leaving the microphysical parameters free to vary in time as ${\epsilon }_{e}\propto {t}^{e}$ and ${\epsilon }_{B}\propto {t}^{b}$. Although the fit formally improves for b ≈ 0.5 and e ≈ 0.2, it yields an unphysical solution _e > 1 and extreme values for the blast-wave kinetic energy and the jet opening angle. We considered this model an unrealistic description of the explosion and turned to a different interpretation to explain the observed properties.

As shown in Figure 5 (right panels), the temporal evolution of the broadband spectrum appears roughly consistent with a collimated fireball observed slightly off-axis. We therefore introduced in our model the effects of different viewing angles (van Eerten et al. 2010; van Eerten & MacFadyen 2013). This provides a better description of the observed data. The best-fit parameters are an isotropic-equivalent kinetic energy ${E}_{{\rm{K,iso}}}$ = ${4.3}_{-2.0}^{+1.2}$ $\,\times \,{10}^{52}$ erg, a circumburst density n₀ = ${0.032}_{-0.026}^{+0.14}$ cm⁻³, and shock parameters _B = ${2.1}_{-1.4}^{+3.6}$ $\,\times \,{10}^{-4}$, _e = ${0.14}_{-0.06}^{+0.19}$. We derived a jet opening angle of θ_j = 0.090 ± 0.012 rad and an observer's angle of θ_obs ≈ 0.055 rad. These values are similar to the opening angles inferred from other candidate jet breaks (Burrows et al. 2006; Coward et al. 2012; Fong et al. 2015).

The possibility of an optical/IR transient rising a few days after the short GRB explosion is the current focus of intense research (e.g., Barnes & Kasen 2013; Yu et al. 2013; Kasen et al. 2015). The detection and identification of such transients (e.g., Tanvir et al. 2013; Jin et al. 2015, 2016; Yang et al. 2015) would represent the smoking gun proof of short GRB progenitors and a powerful tool to search for electromagnetic counterparts of GW sources. We used our late-time observations to constrain some of the most promising models, as well as the presence of an emerging supernova (SN).

As shown in Figure 7 (left panel), our r-band upper limits at 2.5 and 4.5 days can constrain the presence of a fast-rising and rapidly decaying transient, peaking in the optical a few days after the burst. We considered two models: the classical Li & Paczyński (1998) macronova (or kilonova) powered by the radioactive decay of the ejecta (shaded area), and the more recent merger-nova (Yu et al. 2013) powered by a long-lived magnetar (shaded area). Recent theoretical (Barnes & Kasen 2013) and observational (Tanvir et al. 2013) results showed that the macronova emission is heavily suppressed at optical wavelengths due to the high opacity of the ejecta. Models for the late-time infrared emission (e.g., Barnes & Kasen 2013), although highly dependent on the input physics, generally predict a signal (H ≳ 23 mag at t ∼ 4 days) well below the sensitivity of our observations. However, exceptions may occur if a small amount of lanthanide-free material is ejected during the merger (Kasen et al. 2015) or if the ejecta are re-energized by the central engine (Yu et al. 2013). The resulting transient spans a wide range of luminosities depending on the details of the explosion, and our measurements can only constrain the bright end of the predicted values. For a Li & Paczyński (1998) macronova with a typical ejecta mass of M_ej = 0.01 M_⊙ (thin solid line) we can exclude only the extreme values of the f parameter (f > 2 $\,\times \,{10}^{-3}$), which measures the fraction of radioactive material converted into heat. Our limit is more interesting in the case of a larger ejecta mass of M_ej = 0.1 M_⊙, for which we can exclude f > ${10}^{-5}$ (thick solid line). This is consistent with the most recent calculations of the radioactive heating rate (Metzger et al. 2010; Lippuner & Roberts 2015).

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Yu et al. (2013) argued that, if the GRB central engine is a stable magnetar, the macronova luminosity could be boosted by several orders of magnitude. In this scenario, the main power source is the magnetar-driven wind rather than the radioactive decay energy. As shown in Figure 7, for a typical range of ejecta masses (M_ej ≲ ${10}^{-2}$ M_⊙) the predicted signal of a merger-nova (dashed line) could be consistent with our observations.

As mentioned in Section 2.3, we found marginal (≲3 σ) evidence of a signal in our observations 2.5 days post burst. The resulting magnitude, r = 23.11 ± 0.36, is above the predicted afterglow signal and, if real, would imply an optical rebrightening between our Gemini observations at 1.5 days and the DCT observations at 2.5 days. When compared with the macronova predictions, this signal would require either an extreme value of the f-parameter 5 $\,\times \,{10}^{-4}$ < f < ${10}^{-3}$ for M_ej = 0.01 M_⊙ or a large ejecta mass, M_ej = 0.1 M_⊙, and f ∼ ${10}^{-5}$, more typical of a neutron star (NS)–black hole (BH) merger (Foucart et al. 2014). The merger-nova predictions could instead reproduce the observed flux for ejecta masses M_ej ≈ ${10}^{-3}$ M_⊙, typical of NS–NS mergers (Bauswein et al. 2013).

Our last i-band observation, performed 3 weeks after the burst, is used to constrain the contribution of a possible SN. In Figure 7 (right panel) we compare our upper limit with the light curves of SN 1998bw and SN 2006aj, associated to nearby long GRBs. The templates were created by compiling data from literature (Galama et al. 1998; Ferrero et al. 2006) and then corrected for cosmological effects and extinction in a standard fashion. Our limit (M_V ≳ −19 mag, rest frame) is fainter than the emission expected from an SN 1998bw-like explosion. Although our photometric data set cannot exclude an event such as SN 2006aj, we also note that the spectroscopic observations do not show any evidence of broad absorption lines typical of GRB SNe.