Short GRB 160821B: A Reverse Shock, a Refreshed Shock, and a Well-sampled Kilonova

The Burst Alert Telescope (BAT) on board Swift triggered on sGRB 160821B on 2016 August 21 at 22:29 UT. The reported duration of the burst was T₉₀(15–350 keV) = 0.48 ± 0.07 s (Palmer et al. 2016). The burst was also detected by Fermi/GBM, from which a somewhat longer duration of ≈1 s was found (Stanbro & Meegan 2016). Lü et al. (2017) performed a joint fit to the Swift/BAT and Fermi/GBM data, finding the total fluence in the 8–10,000 keV band of (2.52 ± 0.19) × 10⁻⁶ erg cm⁻². This corresponds to an isotropic energy, assuming the redshift of z = 0.162, of ${E}_{\gamma ,\mathrm{iso}}\,=(2.1\pm 0.2)\times {10}^{50}$ erg, fairly typical of the population of short GRBs with measured redshifts (Berger 2014).

After slewing, the X-ray Telescope (XRT) on Swift detected a fading afterglow that provided a refined localization, and from the X-ray spectrum found no evidence for significant absorption beyond that expected due to foreground gas in our Galaxy (Sbarufatti et al. 2016). As described below, our early optical imaging identified the afterglow of the burst and a prominent nearby galaxy at a separation of about 57 (Xu et al.2016).

With a magnitude of r ≈ 19.4 (Section 2.3), the probability of the chance alignment of an unrelated galaxy of this brightness or brighter this close to the line of sight is P_chance ≈ 1.5% (using the formalism of Bloom et al. 2002) and although low, is not entirely negligible. However, the absence of any faint underlying quiescent emission in our final HST epochs (see Section 2.2), which might otherwise suggest a higher redshift host, adds support to our working hypothesis that this is the host galaxy of sGRB 160821B.

The NOT, located in the Canary Islands (Spain), began optical observations at 23:02 UT, only 33 minutes post-burst. These revealed an uncatalogued point source within the X-ray error region, presumed to be the optical afterglow (Xu et al. 2016). The best astrometry came from our HST images, and gave a position of R.A.(J2000) = 18:39:54.550, decl.(J2000) =+62:23:30.35 with an uncertainty of ≈003 in each coordinate, registered on the GAIA DR2 astrometric reference frame (Gaia Collaboration et al. 2016, 2018). Fong et al. (2016) reported a detection of the radio afterglow at 5 GHz with the VLA, which provided a burst location of R.A.(J2000) = 18:39:54.56, decl.(J2000) = +62:23:30.3 (reported error 03), consistent with our HST localization.

The position of the proposed host galaxy measured from our HST images is R.A.(J2000) = 18:39:53.968, decl.(J2000) =+62:23:34.35. We obtained spectroscopy of this galaxy with the WHT using the Auxiliary Port Camera (ACAM), in observations beginning on 2016 August 22 at 22:57 UT (Levan et al. 2016). The data were reduced using standard IRAF routines. The resulting 2D and 1D extracted spectra are shown in Figure 1, with emission lines of Hα, Hβ, [S ii], and [O iii] providing a redshift of z = 0.1616 ± 0.0002. The slit was aligned to cross both the nucleus of the main galaxy and a fainter blob of emission to the north, labeled "B" and "C," respectively, on Figure 2. The latter turned out to be a higher redshift galaxy²³ at z = 0.4985 ± 0.0002, the spectrum of which is also shown in Figure 1.

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At a redshift z = 0.162 the separation between afterglow and host corresponds to 16.4 kpc in projection, which is consistent with the offset distribution found for other sGRBs (Fong & Berger 2013; Tunnicliffe et al. 2014).

Morphologically, the host appears to be a face-on, disturbed spiral galaxy (Figure 2). The extended, warped appearance of the central bulge suggests an ongoing merger, and the nebular emission lines are consistent with active star formation. It is interesting to note, although most likely coincidental, that the hosts of both sGRB 130603B and GRB 170817A were also notably disturbed (Tanvir et al. 2013; Levan et al. 2017).

The foreground extinction corrected magnitude of the host from the HST imaging (with the flux from the z = 0.5 background galaxy subtracted) is r_606,0 = 19.4. This corresponds to an absolute magnitude of M_r = −20.0, which is ∼L*/3 with respect to the Loveday et al. (2015) "blue" (star-forming) galaxy population.

The r-band 25 mag arcsec⁻² isophote has a radius of ≈35, corresponding to a linear scale of ≈10 kpc. However, it is possible to trace lower surface brightness emission from the galaxy out to the GRB location, albeit at a faint surface brightness level of ≈27 r mag arcsec⁻².

sGRB 160821B is among the lowest redshift sGRBs found by Swift to date. This, combined with its comparatively low foreground Galactic extinction of A_V = 0.118 mag (Schlafly & Finkbeiner 2011), motivated an intensive follow-up monitoring campaign.

Further optical and near-IR imaging was obtained with the NOT, the GTC, and the WHT over the next several nights. These data were reduced using standard procedures, and calibrated photometrically using Pan-STARRS (optical) and 2MASS (near-IR) stars in the field.

Observations with the HST using the Wide Field Camera 3 (WFC3), were obtained in the F606W filter (a wide filter spanning approximately the V and r bands), the F110W filter (a wide YJ band), and the F160W filter (H band) from several days to several weeks post-burst (Troja et al. 2016). We adopted the standard photometric calibration for these bands,²⁴ and aperture corrections were determined using bright point sources on the frames.

In all cases, interactive aperture photometry was performed using the Gaia software.²⁵ Care was taken to obtain sky estimates close to the position of the transient, because the background was not entirely free of light from the host galaxy.

These observations revealed the counterpart to be initially steady in brightness during the observations made on the first night, but thereafter it faded monotonically in all bands. In the third HST visit, at ∼23 days, no emission is detected at the burst location, which was confirmed by a final visit at ≈100 days. A summary of the results of all our optical and near-IR photometry for the sGRB 160821B afterglow, together with selected magnitudes reported elsewhere, is presented in Table 1.

Table 1.  Optical and Near-IR Photometry of the sGRB 160821B Afterglow

Δt (day)	texp (s)	Telescope/Camera	Filter	AB0	Source of Photometry
0.95	14 × 300	TNG/DOLoRes	g	24.02 ± 0.16	This work
2.02	7 × 120	GTC/OSIRIS	g	25.56 ± 0.16	This work
3.98	10 × 120	GTC/OSIRIS	g	25.98 ± 0.15	This work
6.98	21 × 120	GTC/OSIRIS	g	26.90 ± 0.18	This work
0.05	6 × 300	NOT/AlFOSC	r	22.58 ± 0.09	This work
0.07	6 × 300	NOT/AlFOSC	r	22.52 ± 0.06	This work
0.08	3 × 90	GTC/OSIRIS	r	22.53 ± 0.03	This work
1.06	6 × 240	WHT/ACAM	r	23.82 ± 0.07	This work
1.95	9 × 300	NOT/AlFOSC	r	24.81 ± 0.07	This work
2.03	5 × 120	GTC/OSIRIS	r	24.80 ± 0.06	This work
3.64	4 × 621	HST/WFC3/UVIS	F606W	25.90 ± 0.06	This work
4.99	27 × 120	GTC/OSIRIS	r	26.12 ± 0.25	This work
10.40	4 × 621	HST/WFC3/UVIS	F606W	27.55 ± 0.11	This work
23.20	1350	HST/WFC3/UVIS	F606W	>27.34	This work
0.08	3 × 90	GTC/OSIRIS	i	22.37 ± 0.03	This work
2.04	5 × 90	GTC/OSIRIS	i	24.44 ± 0.10	This work
4.00	3 × 90	GTC/OSIRIS	i	25.70 ± 0.38	This work
9.97	18 × 90	GTC/OSIRIS	i	>25.59	This work
0.08	3 × 60	GTC/OSIRIS	z	22.39 ± 0.02	This work
1.08	6 × 240	WHT/ACAM	z	23.60 ± 0.15	This work
1.99	9 × 300	NOT/AlFOSC	z	23.90 ± 0.23	This work
2.04	7 × 60	GTC/OSIRIS	z	24.34 ± 0.24	This work
3.76	2397	HST/WFC3/IR	F110W	24.69 ± 0.02	This work
10.53	2397	HST/WFC3/IR	F110W	26.69 ± 0.15	This work
23.18	1498	HST/WFC3/IR	F110W	>27.34	This work
0.96	33 × 20	GTC/CIRCE	H	23.83 ± 0.35	This work
3.71	2397	HST/WFC3/IR	F160W	24.43 ± 0.03	This work
10.46	2397	HST/WFC3/IR	F160W	26.55 ± 0.23	This work
23.23	2098	HST/WFC3/IR	F160W	>27.21	This work
4.3	45 × 30.8	Keck/MOSFIRE	K	${24.04}_{-0.31}^{+0.44}$	Kasliwal et al. (2017a)

Note. Column (1): midtime of observation with respect to GRB trigger time. Magnitudes corrected for Galactic foreground extinction according to A_V = 0.118 from Schlafly & Finkbeiner (2011).

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Swift/XRT monitoring continued for 2.5 days, showing evidence for a significant break to a steeper rate of fading around 0.4 days. Our XMM-Newton observations comprised two visits at approximately 4 and 10 days post-burst. The first visit produced a very significant detection, and was above a simple extrapolation between the last Swift visits. This is discussed further in Section 3.

A summary of the X-ray observations is presented in Table 2.

Table 2.  Swift (Top) and XMM-Newton (Bottom) X-Ray Observations in the 0.3–10 keV Band, of the sGRB 160821B Afterglow after the First Hour

t	0.3–10 keV Flux
(day)	(10−14 erg cm−2 s−1)
${0.06}_{-0.01}^{+0.01}$	${59.6}_{-10.8}^{+10.8}$
${0.14}_{-0.02}^{+0.06}$	${45.8}_{-7.50}^{+7.50}$
${0.30}_{-0.03}^{+0.03}$	${32.1}_{-7.45}^{+9.46}$
${0.34}_{-0.01}^{+0.01}$	${28.0}_{-6.00}^{+7.42}$
${0.42}_{-0.02}^{+0.13}$	${13.1}_{-2.99}^{+3.74}$
${1.02}_{-0.30}^{+0.39}$	${3.44}_{-1.10}^{+1.49}$
${2.33}_{-0.67}^{+2.11}$	≤2.53
${3.91}_{-0.12}^{+0.12}$	${1.70}_{-0.21}^{+0.21}$
${9.95}_{-0.17}^{+0.17}$	${0.51}_{-0.20}^{+0.20}$

Note. Column (1): times of observation with respect to GRB trigger time, uncertainties represent the duration of the observation. Column (2): fluxes corrected for Galactic foreground absorption following the prescription of Willingale et al. (2013).

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The 5 GHz radio detection in 1 hr of observations at 3.6 hr after the burst had a reported flux density of ∼35 μJy; an additional observation with the same telescope at 26.5 hr post-burst returned a 3σ upper limit of 18 μJy (Fong et al. 2016).

Late-time radio observations of the GRB 160821B field were carried out with the VLA, at a central frequency of about 10 GHz and nominal bandwidth of 4 GHz. The first observation started on 2016 September 1 at 23:24:16 UT; the second observation started on 2016 September 8 at 00:10:33 UT. Data were calibrated using the automated VLA calibration pipeline available in the Common Astronomy Software Applications (CASA). After calibration, data were inspected for flagging, and then imaged using the CLEAN algorithm available in CASA. For each of the observations, we estimated the maximum flux density measured within a circular region centered around the position of GRB 160821B and with a radius of 06 (comparable to the nominal FWHM of the VLA synthesized beam in its B configuration at 10 GHz). If the maximum peak density found within this region is above 3× the image rms, then we report the measured flux density value and assign to it an error obtained by adding in quadrature the image rms and a 5% absolute flux calibration error. On the other hand, if the maximum flux density within the selected circular region does not exceed the 3× rms, we report an upper limit with a value equal to 3× the image rms. Radio data²⁶ are listed in Table 3.

A period of extended emission²⁷ (EE) follows the sGRB 160821B prompt emission for a duration of ∼200–300 s. Following the rapid decline of the EE, Swift/XRT, and XMM-Newton observations show a shallower decline between ∼0.01 and 10 days; as expected from an afterglow. However, this late-time X-ray flux deviates from the expected power-law decline of a simple afterglow model. The flux level drops below that expected from a power-law decay between ∼0.3 and 4 days. Rebinning the Swift/XRT data into photon bins with a lower minimum count, the behavior of the X-ray light curve is more clearly revealed; see Figure 3 where the gray markers show the data using the typical minimum photon count per bin and the black markers show the rebinned flux levels (a triangle indicates an upper limit). A photon index Γ = 1.7 is assumed, which is consistent with both Swift/XRT (${\rm{\Gamma }}={2.0}_{-0.6}^{+0.7}$) and XMM-Newton (${\rm{\Gamma }}={1.4}_{-0.4}^{+0.5}$). Horizontal error bars indicate the duration of the observations at each point. The rebinned data reveal a break in the X-ray light curve at ∼0.35 days, where the flux drops significantly for all the following data, and the flux level at 2–3 days is comparable to the XMM-Newton observed flux level at ∼4 days.

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Figure 4 shows the spectral energy distribution of all the optical data from Table 1, where we have averaged together points taken in the same filter at close to the same time. The color evolution of the transient exhibits a trend from blue in observations taken roughly one day after the burst to a much redder color in all subsequent detections. This is immediately indicative of an emerging kilonova component; which itself is evolving from blue to red on timescales of days (see, e.g., Perego et al. 2014; Tanaka et al. 2018; Wollaeger et al. 2018). r- and H-band data are shown in Figure 3 for comparison with a typical power-law decline extrapolated from the power law used to show the behavior at X-ray frequencies (see Section 3.1). The deviation from a power law with an excess in blue and then red is evident; the behavior at optical and near-IR is distinct from that at 1 keV.

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We note that while treating the F606W magnitudes as r-band in principle introduces a systematic error, the measured g-F606W color is flat (consistent with our interpretation below that the optical light is afterglow dominated at these times), indicating that color corrections would be smaller than the photometric errors. (Furthermore, even for our kilonova models, at the time of those epochs, the predicted difference between F606W and the r-band is ≲0.2 AB mag.)

Radio observations show a fading source between ∼0.1 and 1 day, but a detection at ∼10 days indicates continued radio afterglow emission as shown by the red contours in Figure 2 (note that the small apparent offset between the radio and optical positions is consistent with the effects of noise in the radio map, given the low S/N). The late afterglow is limited by a nondetection at ∼17 days.

A kilonova component is likely to peak in the optical within one to two days post-merger, leading us to expect the r-band flux to be dominated by afterglow at the early (∼0.1 days) and late (∼10 days) epochs. Inspection of the spectral energy distribution at ∼0.1 days between the X-ray (1 keV) and the r-band optical data reveals β = 0.66 ± 0.03, where F_ν ∝ ν^−β, and is consistent with β = 0.68 ± 0.07 at ∼10 days in agreement with this expectation (see Figure 3). Using the broader spectral index limits at ∼10 days, and assuming a temporal decline as F_ν ∝ t^−α, where α = 3(p − 1)/4, the power-law behavior for the limits on p from p = 2β + 1 is shown. A break in the light curve at t_j ∼ 7 days is required, where α = −p at t > t_j; this break will be achromatic. The X-ray light curve drops significantly below the lower limit (p = 2.23) power-law extrapolated to earlier times from ∼4 days.

The X-ray light curve exhibits an earlier break at t ∼ 0.35 days, and a late-time excess. Afterglow variability is discussed in Ioka et al. (2005), and such an excess is expected from either a refreshed shock where a slower shell catches up with the initial decelerating outflow (e.g., Panaitescu et al. 1998; Zhang & Mészáros 2002), or a structured jet with an angle-dependent energy and Lorentz factor distribution (e.g., Lamb & Kobayashi 2017). By assuming the jet structures used to model the afterglow to GRB 170817A in Lamb et al. (2019), where on axis the resultant GRB would have been consistent with the short GRB population (e.g., Salafia et al. 2019), then from the observed γ-ray energy of GRB 160821B we can estimate the system inclination following Ioka & Nakamura (2019). For a Gaussian structure with GRB 170817A-like core energy $[{\mathrm{log}}_{10}({E}_{c})={52.4}_{-0.5}^{+0.4}]$, then to reproduce the prompt γ-ray energy of GRB 160821B, the system should be inclined at ∼θ_c + (3 ± 2)° (see also Troja et al. 2019); for a two-component jet $[{\mathrm{log}}_{10}({E}_{c})={52.0}_{-0.9}^{+0.6}]$ then the opacity of the low-Γ second component must be considered (e.g., Lamb & Kobayashi 2016) and the expected inclination would be ∼θ_c + (1.5 ± 1.5)°. For a structured jet, however, a late-time rebrightening in the afterglow is only expected for some structure profiles and at higher inclinations, ∼(3–5) × θ_c²⁸ where bright γ-ray emission is not expected (see Lamb & Kobayashi 2017, 2018; Gill & Granot 2018; Beniamini & Nakar 2019; Matsumoto et al. 2019). Considering the bright GRB we assume that GRB 160821B is on axis or very close to on axis, where the resultant afterglow would behave similarly to the on-axis case regardless of the jet structure (see Lamb & Kobayashi 2017). For our working model we favor a refreshed shock scenario with two shells where Γ₁ > Γ₂, here the subscript indicates the shell order. If the jet breaks at t ∼ 0.35 days, then the apparent break at t > 4 days is indicative of a turnover in the light curve following a significant energy injection episode.

The extended emission at X-ray frequencies lasting until ∼200–300 s post sGRB 160821B supports continued engine activity beyond the timescale of the GRB. This X-ray emission is consistent with an outflow episode driven by fallback accretion onto a spinning black hole (Rosswog 2007; Metzger et al. 2008; Nakamura et al. 2014; Kisaka & Ioka 2015; Yu et al. 2015; Kisaka et al. 2017). A peak or break time of ∼4 days for the refreshed shock indicates that the bulk Lorentz factor of the outflow when the second shell catches the first should be low, with Γ(t) ∼ 10 and the second shell will have a Lorentz factor much lower than the value typically expected for a successful GRB, Γ₂ ≪ 100. Energy dissipated within a low-Γ outflow is not expected to be emitted at γ-ray energies; γ-rays injected into the outflow will be coupled to the plasma and these photons will adiabatically cool and thermalize due to scattering. The effect of these processes is to suppress any resulting emission, which will have a spectral peak at ∼X-ray frequencies. Photons that fail to escape from a low-Γ jet will be reabsorbed by the outflow and contribute to the jet kinetic energy driving the afterglow (Kobayashi & Sari 2001; Kobayashi et al. 2002; Lamb & Kobayashi 2016). The energy-loss by the photon distribution and reabsorption by the outflow will result in a very low value for the emission efficiency, η. This low-Γ X-ray extended emission producing shell follows the initial, high-Γ, GRB producing shell, which will decelerate as Γ₁(t) ∝ t^−3/8 as it sweeps-up the ambient medium. However, the second shell encounters very little material and will catch up with the forward shell when Γ₁(t) ∼ Γ₂/2 (Kumar & Piran 2000). The energy of the second shell refreshes the forward shock resulting in a rebrightening of the afterglow (e.g., Granot et al. 2003).

Although limited, the observations at radio frequencies place tight constraints on any possible afterglow, and the afterglow parameters will be constrained by the detection and upper limits at 1–10 days. The early radio detection at ∼0.1 days, brighter than the following upper limits and flux at ∼10 days, is likely the result of a reverse shock (e.g., Mészáros & Rees 1997; Sari & Piran 1999; Kobayashi 2000; Kobayashi & Sari 2001; Resmi & Zhang 2016; Lamb & Kobayashi 2019). Given the X-ray to optical spectral index β ∼ 0.66, the 5 GHz radio emission at ∼0.1 days is below the characteristic synchrotron frequency ν_m; if the ∼0.1 day radio emission at 5 GHz belongs to the forward shock, then as ${F}_{5\mathrm{GHz}}={F}_{\nu ,\max }{({\nu }_{{\rm{R}}}/{\nu }_{m})}^{1/3}$ and considering the flux at X-ray frequencies is ${F}_{{\rm{X}}}\,={F}_{\nu ,\max }{({\nu }_{{\rm{X}}}/{\nu }_{m})}^{-\beta }$, then ${\nu }_{m}\sim 6.4\times {10}^{14}{({F}_{{\rm{X}}}/{F}_{5\mathrm{GHz}})}^{\sim 1}$ Hz giving ν_m ∼ 10¹² Hz. As ν_m ∝ t^−3/2 and t⁻² for the afterglow before and after the jet break, the 5 GHz radio emission will brighten until a peak when ν_m = 5 GHz or the jet breaks; in either case, the upper limit of 18 μJy at ∼1 day post sGRB 160821B rules out the earlier detection being due to the forward shock. This is the first successfully modeled candidate of a reverse shock in an unambiguous sGRB afterglow and indicates that, in some cases, emission from the reverse shock can be bright despite previous nondetections (Lloyd-Ronning 2018; however, see Becerra et al. 2019 where a reverse shock was recently claimed for the candidate short GRB 180418A). Any afterglow model that can explain the behavior at X-ray frequencies and the early and late optical and near-IR should also be consistent with the detection and limits at radio frequencies.

The afterglow at both radio and X-ray frequencies can constrain the behavior at optical and near-IR. These observations indicate an excess in blue at early times followed by a reddening; this behavior is indicative of a kilonova. Previous studies of sGRB 160821B have been restricted to much smaller photometric data sets and consequently have only drawn weak conclusions about the possibility of a kilonova component and the nature of the afterglow (Kasliwal et al. 2017a; Gompertz et al. 2018; Jin et al. 2018). Here, we use the X-ray, early optical and radio constraints on the afterglow emission to interpret the kilonova contribution at optical and near-IR frequencies. We use the latest kilonova light-curve models based on numerical-relativity simulations to constrain the dynamical and post-merger ejecta masses (e.g., Kawaguchi et al. 2018).

We use the analytic solution for a relativistic blast wave from Pe'er (2012), and the method for generating afterglow light curves from Lamb et al. (2018) to estimate the broadband afterglow for a given set of parameters. We use the observed data to constrain several of the GRB afterglow parameters. As the optical flux at ∼10 days could still have some kilonova contribution, we use the 1 keV to r-band spectral slope at ∼0.05 days to estimate p, where β ∼ 0.66 giving p = 2.3. If we assume a prompt efficiency of η ∼ 0.1–0.15 (Fong et al. 2015), then the isotropic equivalent kinetic energy in the initial outflow is ${E}_{{\rm{k}},\mathrm{iso}}\sim (1\mbox{--}2)\times {10}^{51}$ erg. Throughout, we fix ε_B =0.01 for the forward shock, consistent with the range for short GRBs (Fong et al. 2015).

The optical flux is approximately flat between 0.05 and 0.07 days; this flatness combined with a likely reverse shock in the radio at the same time indicates that these points coincide with the deceleration timescale for the outflow. By fixing the ambient density to n = 10⁻⁴ cm⁻³, consistent with the location in the outskirts of the host galaxy (see Figure 2), the Lorentz factor of the GRB outflow can be estimated; ${{\rm{\Gamma }}}_{0}\sim 18\,{[{t}_{d}/(1+z)]}^{-3/8}$ ${({E}_{{\rm{k}},\mathrm{iso}}/{10}^{51}\mathrm{erg})}^{1/8}$ ${(n/{10}^{-4}{\mathrm{cm}}^{-3})}^{-1/8}\sim 55\mbox{--}60$, where t_d ∼0.06 days is the deceleration time. Similarly, the break at t_j ∼0.35 days can be used to estimate the jet half-opening angle, θ_j ∼ 0.05 [t_j/(1+z)]^3/8 (E_k,iso/10⁵¹ erg)^−1/8 (n/10⁻⁴ cm⁻³)^1/8 ∼ 0.033 rad, or ∼19. As the break time dominates the opening angle estimation, we can put weak limits on this value of ${1.9}_{-0.03}^{+0.10}$ degrees (these small errors are only the formal fit uncertainty given this choice of jet model and decomposition of the light curve; the systematic errors from uncertainties in the model assumptions are much greater, and poorly quantifiable), this narrow jet is consistent with the opening angle range for short GRBs (Jin et al. 2018).

The forward shock is refreshed at ∼1 day, peaking at ∼3 days and then declining as ∼t^−p. We assume that the second shell has the same half-opening angle as the first. As the jet has broken, sideways expansion could widen the initial blast wave and the second shell will only refresh the blast wave with an opening angle ≤θ_j. By assuming that the radius of the blast wave is roughly constant after the jet break²⁹ then the Lorentz factor of the second shell is

$$\begin{eqnarray}&&{{\rm{\Gamma }}}_{2}\gtrsim 47.4{\left(\displaystyle \frac{1+z}{{t}_{c}}\right)}^{1/2}{\left(\displaystyle \frac{{E}_{{\rm{k}},\mathrm{iso}}}{{10}^{51}\mathrm{erg}}\right)}^{1/6}{\left(\displaystyle \frac{n}{{10}^{-4}{\mathrm{cm}}^{-3}}\right)}^{-1/6}{\theta }_{j}^{1/3},\end{eqnarray} \tag{ 1 }$$

where Γ₂ ≳ 16 for an observed collision time t_c ∼ 1 day. The Lorentz factor of the forward shock at the collision is then Γ₁(t) ≳ 8.

We find that if the forward shock is refreshed when Γ₁(t) = 12 and the resulting blast wave has $12.5\times {E}_{{\rm{k}},\mathrm{iso}}$ of the initial outflow energy then the afterglow can account for the X-ray excess at ∼4 days. The radio afterglow at ∼10 days constrains the microphysical parameter ε_e ∼ 0.3, so as not to overproduce the radio flux. We assume throughout that the initial and final blast wave have identical microphysical parameters ε_B and ε_e, electron index p, and θ_j.

The early radio point at ∼0.1 days requires a significant reverse shock. For this point to be forward shock dominated the X-ray and optical data constrain the characteristic synchrotron frequency to ν_m ∼ 10¹² Hz, much lower than the model estimate of ν_m ∼ 3.5 × 10¹⁴ Hz. As ${\nu }_{m}\propto {{\rm{\Gamma }}}^{4}{\varepsilon }_{B}^{1/2}{n}^{1/2}{\varepsilon }_{e}^{2}$, then the parameters that can successfully explain the X-ray and optical afterglow would need significantly lower values. Such lowered parameter values result in an afterglow that is inconsistent with the other observations and unphysical parameters in many cases. Following Harrison & Kobayashi (2013), the characteristic synchrotron frequency ν_m and the maximum flux F_{ν, max} for the reverse shock can be found from the forward shock parameters. The reverse shock flux before and after the peak will scale following Kobayashi (2000); for the thin shell case and our parameters, the flux pre-peak will scale as F_ν ∝ t^5.7 and post peak F_ν ∝ t^−2.05. To accommodate the early radio detection, we need to use a magnetization parameter of R_B ∼ 8. The model light curve is shown in Figure 5, where we have taken an initial kinetic energy of ${E}_{{\rm{k}},\mathrm{iso}}=1.3\times {10}^{51}$ erg and θ_j = 0.033, with all other parameters as discussed.

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The kilonova appears as an excess in the optical above the afterglow. From Figure 5, where the optical afterglow is shown as dotted lines, it is clear that all bands are in excess at ∼1 day post-burst. The bluer bands (g, r, and i) follow the afterglow from ∼5 days while the redder bands (J, H, and K) remain in excess until ∼10 days post GRB.

Using two-component kilonova models from Kawaguchi et al. (2018), K-corrected to z = 0.16, we find the model parameters via a χ² minimization fit to the data for the kilonova plus model afterglow. The kilonova is best described³⁰ by a secular ejecta (or post-merger wind driven by viscous and neutrino heating) with a mass M_pm = 0.01 M_⊙, and a dynamic ejecta mass M_dyn = 0.001 M_⊙. The density profile for each ejecta component is given by

$$\begin{eqnarray}\rho (r,t)\propto \left\{\begin{array}{lr}{r}^{-3}\,{t}^{-3} & 0.025c\leqslant r/t\leqslant 0.15c,\\ {r}^{-6}\,\zeta (\theta )\,{t}^{-3} & 0.15c\leqslant r/t\leqslant 0.9c.\end{array}\right.\end{eqnarray} \tag{ 2 }$$

Here the top condition is for the secular ejecta, and the bottom condition for the dynamic ejecta. We find good fits for an upper limit for the secular ejecta velocity, and lower limits for the dynamic ejecta velocity, of 0.1–0.15c. The function ζ(θ) describes the angular distribution of the dynamic ejecta, and is given by

$$\begin{eqnarray}&&\zeta (\theta )=0.01+\displaystyle \frac{0.99}{1+{e}^{-20(\theta -\pi /4)}},\end{eqnarray} \tag{ 3 }$$

where θ is the angle from the central axis.

The element abundances for the ejecta are determined following the results of r-process nucleosynthesis calculations by Wanajo et al. (2014) and assuming that the secular and dynamic ejecta have initially flat electron fraction Y_e distributions ranging from 0.3 to 0.4 and from 0.1 to 0.4, respectively. Radiative transfer simulations were performed from 0.1 to 30 days resulting in a light curve with a statistical error in each band ∼0.1–0.2 mag.

The kilonova fit to the data depends on the afterglow subtraction, however, the precise details of the afterglow parameters are not crucial. As the optical afterglow is typically in the same spectral regime as the observed X-ray data for sGRBs, and supported by the similar spectral index between optical and X-rays at 0.1 and 10 days, then the optical afterglow will follow that at X-ray frequencies during the kilonova peak. The X-ray data extrapolated to the optical at ∼1–4 days post-burst indicates that the afterglow contributes ∼10%. The typical photometric uncertainty is ∼10%, and the kilonova model uncertainty is ∼10%. Combining these uncertainties, and using the analytic scaling for luminosity with mass L ∝ M^0.35 (e.g., Grossman et al. 2014), we can give limits on the mass estimates from the kilonova model fit of ∼±60%; however, we emphasize that both the masses and the uncertainties are model specific.