The Binary Neutron Star Event LIGO/Virgo GW170817 160 Days after Merger: Synchrotron Emission across the Electromagnetic Spectrum

We observed GW170817 with the Chandra X-ray Observatory (CXO) on 2017 August 19.71 UT, δt ≈ 2.3 days after the GW trigger (observation ID 18955; PI: Fong; Program 18400052), leading to a deep X-ray non-detection with L_x < 3.2 × 10³⁸ erg s⁻¹ (Margutti et al. 2017b) that sets GW170817 apart from all previous SGRBs seen on-axis (Fong et al. 2017). Further CXO observations obtained at δt ≈ 9 days (Troja et al. 2017b, observation ID 19294; PI: Troja; Program 18500489) and δt ≈ 15 days (Haggard et al. 2017b; Margutti et al. 2017b; Troja et al. 2017b, observation IDs 18988, 20728; PIs: Haggard, Troja; Programs 18400410,18508587) since the merger revealed X-ray emission at the location of GW170817 with rising temporal behavior.

We independently reanalyzed the CXO observations acquired δt ≈ 9 days post merger (ID 19294) and originally presented in Troja et al. (2017b). Chandra ACIS-S data have been reduced with the CIAO software package (v4.9) and relative calibration files, applying standard ACIS data filtering as in Margutti et al. (2017b). Using wavdetect we find that an X-ray source is clearly detected with significance of 5.8σ at the location of the optical counterpart of GW170817. The inferred count-rate in the 0.5–8 keV energy range is (2.9 ± 0.8) × 10⁻⁴ c s⁻¹ (exposure time of 49.4 ks), consistent with the results from Troja et al. (2017b). We employ Cash statistics to fit the spectrum. We adopt an absorbed power-law spectral model with index Γ and Galactic neutral hydrogen column density NH_mw = 0.0784 × 10²² cm⁻² (Kalberla et al. 2005) and use Markov Chain Monte Carlo (MCMC) sampling to constrain the spectral parameters. We find ${\rm{\Gamma }}={0.95}_{-0.19}^{+0.95}$. We find no statistical evidence for intrinsic neutral hydrogen absorption and place a limit NH_int < 7 × 10²² cm⁻² (3σ c.l.). For these parameters the 0.3–10 keV flux is (4.2–9.3) × 10⁻¹⁵ erg s⁻¹ cm⁻² (1σ c.l.), corresponding to an unabsorbed flux of (4.4–9.6) × 10⁻¹⁵ erg s⁻¹ cm⁻².

Comparison with the X-ray spectrum of GW170817 at δt ≈ 15 days (ID 20728) that we presented in Margutti et al. (2017b) indicates a possibly harder emission at early times (${\rm{\Gamma }}={0.95}_{-0.19}^{+0.95}$ at δt ≈ 9 days versus ${\rm{\Gamma }}={1.6}_{-0.1}^{+1.5}$ at δt ≈ 15 days). While we find this possibility intriguing, the limited number statistics of the two spectra does not allow us to draw conclusions as the two Γ values are statistically consistent. A joint spectral fit of the two epochs indicates ${\rm{\Gamma }}={1.4}_{-0.1}^{+0.9}$ (1σ c.l.) with a 3σ upper limit NH_int < 2.7 × 10²² cm⁻². The corresponding flux ranges are reported in Table 1. Our results from the joint fit are broadly consistent with the findings from Troja et al. (2017b).

Table 1.  X-Ray Spectral Parameters and Inferred Flux Ranges (1σ c.l.)

Obs ID	Time since Merger	Γ	Flux (0.3–10 keV)	Unabsorbed Flux (0.3–10 keV)
	(days)		(10−15 erg s−1 cm−2)	(10−15 erg s−1 cm−2)
18955	2.34	1.4	<1.8a	<1.9a
19294	9.21	${0.95}_{-0.19}^{+0.95}$	(4.2–9.3)b	(4.4–9.6)b
		${1.4}_{-0.1}^{+0.9}$	(2.7–6.8)c	(2.9–7.3)c
20728	15.39	${1.6}_{-0.1}^{+1.5}$	(3.0–5.6)d	(3.1–5.8)d
		${1.4}_{-0.1}^{+0.9}$	(3.7–7.3)c	(4.0–7.8)c
18988	15.94	1.4	(3.8–7.5)e	(4.1–8.0)e
20860/1	109.39	${1.62}_{-0.16}^{+0.16}$	(20.–25.)b	(22.–28.)b
20936/7/8/9-20945	158.50	${1.61}_{-0.17}^{+0.17}$	(22.–27.)b	(24.–29.)b

Notes. Upper limits are provided at the 3σ c.l.

^a0.5–8 keV count-rate upper limit of 1.2 × 10⁻⁴ cps from Margutti et al. (2017b), with updated flux calibration performed with an absorbed power-law model with Γ = 1.4 as inferred from our joint fit of the CXO observations with IDs 19294 and 20728. ^bThis work. ^cFrom a joint spectral fit of CXO observations, IDs 19294 and 20728. This work. ^dFrom Margutti et al. (2017b). ^eFlux from Haggard et al. (2017b) rescaled to the Γ = 1.4 spectrum. This work.

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Deep X-ray observations of GW170817 were obtained as soon as the source re-emerged from Sun constraint (PI: Wilkes, observation IDs 20860, 20861; Program 18408601; Haggard et al. 2017a; Margutti et al. 2017c, 2017a; Troja et al. 2017a). Observations are displayed in Figure 8. The CXO started observing GW170817 on 2017 December 3.07 UT (107.5 days since merger, ID 20860) for 74.1 ks. An X-ray source is clearly detected at the location of GW170817 with significance of 33.4σ and net count-rate (1.47 ± 0.14) × 10⁻³ c s⁻¹ (0.5–8 keV). The CXO observed the field for an additional 24.7 ks starting on 2017 December 6.45 UT (110.9 days since merger, ID 20861). The X-ray source is still detected with a significance of ∼15.0σ and net count-rate of (1.41 ± 0.24) × 10⁻³ (0.5–8 keV). The joint spectrum can be fit with an absorbed power-law spectral model with photon index Γ = 1.62 ± 0.16 (1 sigma c.l.), consistent with the results from Ruan et al. (2018). We find no evidence for intrinsic neutral hydrogen absorption and constrain NH_int < 0.7 × 10²² cm⁻² (3σ c.l.). These properties are consistent with the X-ray spectral properties of GW170817 at t ≤ 15 days. The 0.3–10 keV inferred flux range is (2.0–2.5) × 10⁻¹⁴ erg s⁻¹ cm⁻², (unabsorbed flux of (2.2–2.8) × 10⁻¹⁴ erg s⁻¹ cm⁻²). This result indicates substantial brightening of the X-ray source during the last ∼95 days with no measurable spectral evolution (Figure 1).

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Further CXO observations have been obtained between 2018 January 17 and 28, 153.4–163.8 days since merger (PI: Wilkes, observation IDs 20936, 20937, 20938, 20939, 20945; Program 19408607, total exposure time of 104.8 ks). GW170817 is detected with high confidence in each observation. The total source count-rate is 157.1 ± 12.7 (0.5–8 keV), corresponding to (1.50 ± 0.12) × 10⁻³ c s⁻¹. We do not find evidence for statistically significant spectral evolution during the entire observation. We also do not find evidence for statistically significant temporal variability of the source during the observation. The joint spectrum can be fit with an absorbed power-law spectral model with photon index Γ = 1.61 ± 0.17 and NH_int < 1.0 × 10²² cm⁻² (3σ c.l.). These results are broadly consistent with the preliminary analysis by Troja & Piro (2018) and Haggard et al. (2018). The corresponding 0.3–10 keV observed flux range is (2.2–2.7) × 10⁻¹⁴ erg s⁻¹ cm⁻², while the unabsorbed flux is (2.4–2.9) × 10⁻¹⁴ erg s⁻¹ cm⁻². This result indicates that the source did not experience significant temporal and spectral evolution between ∼100 and ∼150 days since merger. Our findings do not support the claim of declining emission from GW170817 by D'Avanzo et al. (2018), but suggest that the non-thermal emission from GW170817 is now close to its peak.

We obtained 1 orbit of Hubble Space Telescope (HST) observations of GW170817 on 2018 January 1 (137 days since merger) using the Advanced Camera for Surveys (ACS) with the F606W filter (PID: 15329; PI: Berger). We produced a drizzled image corrected for optical distortion using the astrodrizzle task in the drizzlepac software package provided by STScI. We detect a faint source at the location of the optical counterpart of GW170817, confirmed by relative astrometry with our ACS/F625W image from 2017 August 27 (Cowperthwaite et al. 2017). To measure the flux of the source we first subtract a model of the galaxy surface brightness profile determined using GALFIT v3.0.5 (Peng et al. 2010). Using aperture photometry and the ACS/F606W zeropoint provided by the HST team, we find an observed AB magnitude of 26.90 ± 0.25 mag. Correcting for Galactic extinction with E(B − V) = 0.105 mag (Schlafly & Finkbeiner 2011), the extinction corrected AB magnitude is 26.60 ± 0.25 mag. As a comparison, at 110 days since merger, Lyman et al. (2018) find m = 26.44 ± 0.14 mag.

Our radio observations of GW170817 from 0.5 to 39 days since merger have been reported in Alexander et al. (2017). We continued observing GW170817 with the Karl J. Jansky Very Large Array (VLA) under program 17A-231 (PI: Alexander), obtaining observations on 2017 November 5 (δt ∼ 80 days since merger) at a mean frequency of 6 GHz (C band), using a bandwidth of 4 GHz. These new observations were taken in the VLA's B configuration. We analyzed and imaged the VLA data using standard CASA routines (McMullin et al. 2007), using 3C286 as the flux calibrator and J1258−2219 as the phase calibrator. We fit the flux density and position of the emission using the imtool program within the pwkit package (Williams et al. 2017). We clearly detect the source with a flux density of 37 ± 4 μJy. The in-band spectral index is poorly constrained, but is clearly optically thin (Table 2).

We obtained further multi-frequency VLA observations under the same program on 2017 December 7 (C band) and under program 17B-425 (PI: Alexander) on 2010 December 10 (S, X, and Ku bands, spanning the frequency range 2–18 GHz). New observations spanning 2–18 GHz (S, C, X, and Ku bands) were obtained under program 17B-425 on 2018 January 27. We reduced the data using the same procedure outlined above and cross-checked our results against the automated CASA-based VLA pipeline. The flux densities obtained with each method are fully consistent to within the error bars at all frequencies; we choose to report the pipeline flux densities here because the images have slightly lower rms noise. GW170817 is clearly detected at all radio frequencies and has continued to brighten, enabling us to split the data into narrower frequency bandwidths for imaging. At S band, we divided the data into two 1 GHz sub-bands, although the effective bandwidth of each after flagging is closer to 750 MHz due to radio frequency interference (RFI). At higher frequencies, we split the data into 2 GHz bandwidth. We report the measured flux densities in Table 2. As before, uncertainties were calculated using the imtool package and represent the uncertainty on a point source fit. The December measurements clearly indicate an optically thin spectrum with spectral index β_R = 0.47 ± 0.08. This value is consistent with the X-ray spectral index β_X = 0.62 ± 0.16 (Γ = β + 1) obtained a few days before (Section 2.1). The latest VLA observations in January are also optically thin with β_R = 0.55 ± 0.10, in good agreement with the CXO spectral index β_X = 0.621 ± 0.17 around the same time.

A joint spectral fit of radio data obtained at δt ∼ 111–114 days and X-ray data obtained around δt ≈ 109 days with a simple power-law model ${F}_{\nu }\,\propto \,{\nu }^{-{\beta }_{{XR}}}$ constrains β_XR = 0.588 ± 0.005. This value is consistent with the spectral indices β_X and β_R derived from individual fits within the X-ray and radio bands (Section 2.1, 2.3), and shows that at t ≈ 110 days the broadband X-ray to radio emission from GW170817 originates from the same non-thermal spectral component.

To refine our measurement of the X-ray to radio spectral slope β_XR at ∼110 days we account for the (mild) temporal evolution of the afterglow flux adopting the iterative procedure that follows. We initially assume a fiducial spectral index value β_i = 0.60, which is used to construct a "master" radio light-curve of GW170817 at a given frequency using the entire set of radio observations available at all frequencies. Radio data have been compiled from Alexander et al. (2017), Hallinan et al. (2017), Kim et al. (2017), and Mooley et al. (2017). We fit the master radio light-curve with a power-law model F_ν ∝ t^α. The best-fitting α is then used to renormalize the flux densities measured at δt = 111–114 days to a common epoch of 109 days since merger (to match the time of CXO observations). Finally, we estimate β_f from a joint fit of the broadband radio-to-X-ray spectrum at 109 days. This procedure is repeated until convergence (i.e., β_f = β_f within error bars). We find β_XR = 0.585 ± 0.005 and α = 0.73 ± 0.04 (Figure 1). As a comparison, from the analysis of radio data alone at t < 93 days Mooley et al. (2017) inferred β_R = 0.61 ± 0.05, consistent with our results. Our measurement of the spectral slope benefits from the significantly larger baseline of eight orders of magnitude in frequency, and is consequently more precise. We plot in Figure 1 the HST measurement obtained by Lyman et al. (2018) at 110 days. This comparison shows a remarkable agreement with our best-fitting SED and demonstrates that at 110 days since merger the optical emission from GW170817 is of non-thermal origin and originates from the afterglow.

The X-ray and radio light-curves suggest that GW170817 might be now approaching its peak of non-thermal emission. From a fit of the radio-to-X-ray SED at ∼160 days we find β_XR = 0.584 ± 0.006, consistent with the value at 110 days.

We compile in Figure 1 the radio-to-X-ray SEDs of GW170817 at 15 and 9 days (orange and blue symbols). At these epochs the thermal emission from the radioactive decay of freshly synthesized heavy elements (i.e., the kilonova) dominates the UV-optical-NIR bands. Figure 1 shows that a rescaled version of the β_XR = 0.585 spectrum that best fits the 110 days epoch adequately reproduces the X-ray and radio emission from GW170817 at all times. Interestingly, the extrapolation of the X-ray flux density at 9 days with a ∝ν^−0.6 spectrum matches the 6 GHz measurement reported by Hallinan et al. (2017) as a potential—but possibly spurious—detection, suggesting that the 6 GHz measurement is in fact a real detection (and the earliest radio detection of GW170817).

Based on these results we conclude that the non-thermal emission from GW experienced negligible spectral evolution across the electromagnetic spectrum in the last ∼150 days, and that the radio and X-ray radiation from GW170817 continue to represent the same non-thermal emission component. This component of emission is now approaching its peak.

The simple power-law spectrum extending over eight orders of magnitude in frequency indicates that radio and X-ray radiation are part of the same non-thermal emission component, which we identify as synchrotron emission. At all times of our monitoring the synchrotron cooling frequency ν_c is above the X-ray band, ν_m is below the radio band, and the observed radio and X-ray emission is on the ${F}_{\nu }\,\propto \,{\nu }^{-(p-1)/2}$ spectral segment, where p is the index of the non-thermal electrons accelerated into a power-law distribution N_e(γ) ∝ γ^−p at the shock front. From our best-fitting β_XR, we infer p = 2.17 ± 0.01.

The precise measurement of the power-law slope p (ultimately enabled by the very simple spectral shape) allows us to test with unprecedented accuracy the predictions of the Fermi process for particle acceleration in relativistic shocks. The power-law index in trans-relativistic shocks will lie in between the value p = 2 expected at non-relativistic shock speeds (Bell 1978; Blandford & Ostriker 1978; Blandford & Eichler 1987) and p ≃ 2.22 at ultra-relativistic velocities (Kirk et al. 2000; Achterberg et al. 2001; Keshet & Waxman 2005; Sironi et al. 2013). From Keshet & Waxman (2005), we estimate that the measured p = 2.17 ± 0.01 implies a shock Lorentz factor of Γ ∼ 5 at 110 days (the 3σ c.l. is Γ ∼ 3–10). The straightforward implication is then that we are seeing electron acceleration in trans-relativistic shocks in action.¹⁰

As the non-thermal spectrum of GW170817 showed negligible evolution (Figure 1), a similar line of reasoning applies to the previous epochs at t ≤ 15 days, from which we conclude that the observed non-thermal radiation from GW170817 at t < 115 days is always dominated by emission from material with relatively small Γ ∼ 3–10.

These findings are consistent with the picture favored by Mooley et al. (2017; see also Hallinan et al. 2017; Kasliwal et al. 2017; Salafia et al. 2018; Nakar & Piran 2018) of emission from a quasi-isotropic mildly relativistic fireball with stratified ejecta and no surviving ultra-relativistic jet (i.e., their "choked-jet cocoon" scenario), but do not represent a unique prediction from this model as we detail below (see also Nakar & Piran 2018 for an independent study that reached a similar conclusion). A value Γ ∼ 3–10 is significantly smaller than the initial Γ ∼ a few 100 inferred for the luminous SGRBs, which are powered by ultra-relativistic jets seen on-axis (which have consistently larger inferred values of p Fong et al. 2015). However, one expects that even a blast wave with large energy E_k,iso ∼ 10⁵² erg propagating in a low-density medium with n ∼ 10⁻⁴–10⁻⁵ cm⁻³ will have decelerated to Γ ∼ 4–5 by ∼110 days since merger; i.e., the shock is mildly relativistic, in excellent agreement with the estimate above based on the physics of particle acceleration at shocks. Current observations are thus also consistent with a scenario where the BNS merger successfully launched an outflow with a collimated ultra-relativistic core (initially pointing away from our line of sight) and less-collimated mildly relativistic wings that dominate the early emission (i.e., the "successful structured jet" model of Section 3.3; Jin et al. 2017; Lamb & Kobayashi 2017; Lazzati et al. 2017c; Murguia-Berthier et al. 2017a; Troja et al. 2017b, 2018; D'Avanzo et al. 2018; Kathirgamaraju et al. 2018). In this latter scenario the emission that we observe is also always dominated by radiation from ejecta with relatively small Γ at all times.

We conclude that the observed optically thin non-thermal spectrum clearly identifies the nature of the emission as synchrotron radiation from a population of electrons accelerated at trans-relativistic shocks with Γ ∼ 3–10. This property, however, is common to both successful structured-jet scenarios and choked-jet scenarios and does not identify the nature of the relativistic ejecta.

The late onset of the X-ray and radio emission of GW170817 rules out relativistic jets with properties similar to those of SGRBs seen on-axis (Alexander et al. 2017; Fraija et al. 2017; Granot et al. 2017; Haggard et al. 2017b; Hallinan et al. 2017; Kasliwal et al. 2017; Margutti et al. 2017b; Mooley et al. 2017; Ruan et al. 2018; Troja et al. 2017b). Relativistic jets originally pointing away from our line of sight can instead produce rising X-ray and radio emission as they decelerate into the ambient medium (see e.g., Granot et al. 2002).

We first consider top-hat relativistic jets, i.e., jets characterized by a uniform angular distribution of the Lorentz factor within the jet Γ(θ). This is the simplest jet model and likely an oversimplification of real jets in BNS mergers (e.g., Aloy et al. 2005; Duffell et al. 2015; Lazzati et al. 2017b; Gottlieb et al. 2018; Kathirgamaraju et al. 2018). The simple top-hat jet model is expected to capture the overall behavior of the observed synchrotron emission from relativistic electrons at the shock fronts only after the core of the jet enters into our line of sight, leading to a peak of emission. Before peak, top-hat jets will underpredict the observed emission when compared to structured jets with similar core (Section 3.3), i.e., jets with with non-zero Γ(θ) in higher-latitude ejecta at θ > θ_j.

Figure 2 shows an update of our modeling of GW170817 with top-hat jets following the same procedure as in Alexander et al. (2017), Margutti et al. (2017b), Guidorzi et al. (2017) with BOXFIT (van Eerten et al. 2012). We show two representative models for two jet opening angles. Within the top-hat scenario, the most successful models share a preference for low densities n ∼ 10⁻⁴ cm³ and large energies E_k,iso ∼ 10⁵² erg, with off-axis angles θ_obs ∼ 15°–25°. As these plots demonstrate, top-hat jets viewed off-axis fail to reproduce the larger X-ray and radio luminosities of GW170817 at early times t ≲ 25 days and do not naturally account for the mild but steady rise of the non-thermal emission from GW170817. This is expected if the jet in GW170817 has similar core properties as the uniform jets that we are considering here, but with Γ(θ > θ_j) > 0 (i.e., a structured jet) and the core of the jet has yet to enter into our line of sight (Section 3.3). The X-rays suggest that GW170817 is reaching its peak of emission, which, in this scenario, would imply that the emission from the core of the jet is now close to entering our line of sight.

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In summary, the failure of the simple top-hat jets motivates the exploration of more realistic structured jet models in Section 3.3 and should not be interpreted as evidence to discard the notion that GW170817 harbored a fully relativistic outflow directed away from our line of sight.

Deviation from the simple top-hat jet picture is naturally expected as the relativistic jet has to propagate through the BNS merger immediate environment (e.g., Aloy et al. 2005; Murguia-Berthier et al. 2014; Duffell et al. 2015; Lazzati et al. 2017a; 2017b, Murguia-Berthier et al. 2017b; Gottlieb et al. 2018; Kathirgamaraju et al. 2018) polluted with ∼0.01 M_⊙ of neutron-rich material that was ejected during the merger (the same material produces the radioactively powered KN, e.g., Metzger 2017). Here we consider the scenario where the fully relativistic collimated outflow successfully survived the interaction with the BNS merger ejecta, and we refer to this model as successful off-axis relativistic structured jet. In this model the outflow has Γ ≡ Γ(θ) and E_k,iso ≡ E_k,iso (θ).

This scenario is clearly different from choked-jets, pure-cocoon models, and spherical models (favored by Gottlieb et al. 2017; Hallinan et al. 2017; Kasliwal et al. 2017; Mooley et al. 2017; Salafia et al. 2018; Nakar & Piran 2018) where no collimated ultra-relativistic outflow (even when there) survived the interaction with the BNS ejecta. This is clear from Figure 3, where we show the E_k structure of the two types of outflows. The two classes of models have important implications for the nature of GW170817. As the emission from the slower jet wings is subdominant at all times when seen on-axis, GW170817 would be consistent with being a canonical SGRB seen from the side, if indeed powered by a successful off-axis structured relativistic jet. GW170817 would be instead a subluminous event and intrinsically different from the population of known SGRBs in the choked-jets and pure-cocoon models. From Figure 3 it is also clear that quasi-spherical outflows require significantly larger amounts of energy coupled to slow material with Γ ∼ 1 (≳10⁵¹ erg for the "fast model" from Mooley et al. 2017). The quasi-spherical outflows in these models are powered by energy deposited by failed jets. However, observed successful jets in SGRBs have ≤3 × 10⁵⁰ erg (shaded region in Figure 3). The two notions can be reconciled only if the most energetic jets never manage to break out, which we find contrived.

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Structured off-axis jets have been specifically discussed in the context of GW170817 by Guidorzi et al. (2017), Kathirgamaraju et al. (2018), Lamb & Kobayashi (2017), Lazzati et al. (2017c), Murguia-Berthier et al. (2017a), Troja et al. (2017b), Lyman et al. (2018), D'Avanzo et al. (2018), Troja et al. (2018), Gottlieb et al. (2017), Hallinan et al. (2017), Kasliwal et al. (2017), Mooley et al. (2017), and Nakar & Piran (2018). These jets typically have large E_k,iso(θ) and Γ(θ) close to the axis of the jet that decrease for larger angles, resulting in a jet with a narrow, ultra-relativistic core and a wider, mildly relativistic sheath. For off-axis observers, the afterglow is initially dominated by the less-collimated emission from the mildly relativistic wings¹¹ (which would be also responsible for the detected γ-ray emission). As time progresses, the jet decelerates, beaming effects become less pronounced, and the observer will gradually see the more-luminous, initially ultra-relativistic jet core.

We use the moving-mesh relativistic hydrodynamics JET code (Duffell & MacFadyen 2013) to simulate the dynamics of explosive outflows launched in NS ejecta clouds using an engine model (Duffell et al. 2015) and density structure similar to Kasliwal et al. (2017) and Gottlieb et al. (2017). We then compute synchrotron light curves from the simulation data using standard synchrotron radiation models (Sari et al. 1998). We show in Figure 4 the results for two representative sets of jet-environment parameters that successfully account for current observations across the spectrum (a full description of the jet simulations will be presented in X. Xie et al. 2018, in preparation). Specifically, the jet has a narrow ultra-relativistic core of θ_c ∼ 9° with Γ ∼ 100 surrounded by a mildly relativistic sheath with Γ ∼ 10 at 10° ≲ θ ≲ 60° (see inset of Figure 4) and propagates in a low-density environment with n = 10⁻⁵–10⁻⁴ cm⁻³. At t ∼ 100 s, the energy in the ultra-relativistic core is ∼4.4 × 10⁵⁰ erg while the sheath carries ∼1.4 × 10⁵⁰ erg (see Xie et al. for details). The observer is located at θ_obs ∼ 17°–20° from the jet axis. We adopt _e = 0.02 (_e = 0.1), _B = 0.001 (_B = 0.0005) with p = 2.16, within the range of our inferred values (Section 3.1) for the n = 10⁻⁴ cm⁻³ (n = 10⁻⁵ cm⁻³) simulation.

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Our model predicts an observed broadband optically thin synchrotron spectrum that extends from the radio to the X-ray band on a ${F}_{\nu }\,\propto \,{\nu }^{-(p-1)/2}$ spectral segment, from the time of our first observations at t ∼ 10 days until now (at the low densities n ∼ 10⁻⁵–10⁻⁴ cm⁻³ favored by our modeling ν_c is not expected to cross the X-ray band at t < 10⁴ days, see Figure 4, upper panel). These findings are consistent with the independent results by Lazzati et al. (2017c) and Lyman et al. (2018), and demonstrate that the persistent optically thin non-thermal spectrum F_ν ∝ ν^−0.585 that characterizes GW170817 is not a unique prediction of choked-jets and/or pure-cocoon models. Instead, it is a natural expectation from fully relativistic structured outflows with properties similar to those of SGRBs but viewed from the side. Together with the very similar flux temporal evolution (see Figures 5–6), this makes these two classes of models virtually impossible to distinguish based on current observations.

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We compare the results from our simulations to those presented by Lazzati et al. (2017c) in Figures 5–6. The major difference is the flux evolution at t ≥ 200 days, with the Lazzati et al. (2017c) models steadily rising until t ∼ 600 days after merger. As the microphysics parameters (_B = 0.002, _e = 0.02, p = 2.13) and observing angle (θ_obs = 21°) are very similar to the values of one of our simulations, the different behavior can be ascribed to the combination of possibly different assumptions in the code and a narrower ultra-relativistic core, as shown in the inset of Figure 4 (which effectively places the observer more off-axis) more slowly decelerating into a lower density environment (n ∼ 10⁻⁵ cm⁻³ versus n ∼ 10⁻⁴ cm⁻³). In general, outflows with a fully relativistic core with isotropic energy ∼10⁵² erg, propagating into environments with n ≤ 10 ⁻⁵ cm⁻³ and viewed ∼20° off-axis will reach a peak at t_p ≥ 600 days (${t}_{p}\sim 2.1\,{E}_{k,\mathrm{iso},52}^{1/3}\,{n}^{-1/3}$ ((θ_obs − θ_j)/10°)^8/3 days, e.g., Granot & Sari 2002).

Gottlieb et al. (2017), Hallinan et al. (2017), Kasliwal et al. (2017), Mooley et al. (2017), and Nakar & Piran (2018) disfavor the structured off-axis model based on circumstantial evidence related to the energetics of the relativistic core needed to power GW170817 compared to SGRBs. We emphasize that these authors do not rule out structured off-axis jets in GW170817 but consider this possibility unlikely based on the large E_k,iso ≥ 10⁵² erg required. We show in Figure 3 the comparison of the kinetic energies in the different components of the outflow of GW170817 from our simulation with the values inferred for SGRBs from Fong et al. (2015). We conclude from this plot that the E_k in the ultra-relativistic ejecta of GW170817 is not unprecedented among SGRBs (shaded blue area, see also Fong et al. 2015, their Figure 7) and that GW170817 is consistent with having harbored a normal SGRB directed away from our line of sight. The shaded blue area cover the range of E_k for an assumed _B = 0.1. E_k would extend to larger values for smaller _B = 0.01 (e.g., Fong et al. 2015, their Figure 7), thus reinforcing our argument. In our model the ultra-relativistic component dominates the energetics of the outflow.

Some observational tests to distinguish between the successful structured jet scenario that we support here and the choked-jet/stratified ejecta scenarios have been proposed, including VLBI imaging and the acquisition of a larger sample of GW events with electromagnetic counterparts (Hallinan et al. 2017; Lazzati et al. 2017c; Mooley et al. 2017). Here we note that if a collimated outflow of fully relativistic material survived the interaction with the BNS ejecta, the observed light-curve will experience two temporal breaks in the future, which are apparent from Figure 4 (see also Figures 5–6): a peak when radiation from the jet core enters the line of sight at t_p (the flattening of the X-ray and radio light-curves is suggesting that GW170817 is approaching its peak of emission), and a jet-break when the far edge of the jet comes into view. In the case of collimated outflows a counter-jet signature is also expected when the jet transitions into the non-relativistic phase at t_NR ≈ 1100(E_k,iso,53/n)^1/3 days. For E_k,iso ≥ 10⁵² erg and n ≤ 10⁻⁴ cm⁻³ which are relevant here, t_NR ≥ 30 years and the appearance of the counter-jet will create a bump in the light-curve at a flux level below the sensitivity of current observing facilities.

Another source of potential X-ray emission is that originating directly from the central compact remnant, as discussed in detail in Murase et al. (2018). We first consider an accreting black hole. The ≈2.5 M_⊙ black hole created following the merger will still be accreting fall-back debris from the merger event (e.g., Rosswog 2007; Metzger et al. 2010). The accretion luminosity at the present epoch t can be estimated as

$$\begin{eqnarray}{L}_{{\rm{X}},\mathrm{fb}} & = & 0.1{\dot{M}}_{\mathrm{fb}}{c}^{2}\approx 3\\ & & \times {10}^{38}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\left(\displaystyle \frac{{\dot{M}}_{\mathrm{fb}}(t=1\,{\rm{s}})}{{10}^{-3}{M}_{\odot }\,{{\rm{s}}}^{-1}}\right){\left(\displaystyle \frac{t}{120\mathrm{days}}\right)}^{-5/3},\end{eqnarray} \tag{ 1 }$$

where we have assumed that the fall-back accretion rate follows a ∝t^−5/3 decay with a value at 1 s post merger normalized to 10⁻³ M_⊙ s⁻¹ (a characteristic value, which is however uncertain by at least an order of magnitude). The L_X,fb estimated above is thus close to the Eddington luminosity L_Edd ≈ 3 × 10³⁸ erg s⁻¹ of the black hole remnant.

The X-ray emission from the central engine is only visible if not absorbed by the kilonova ejecta along the line of sight. Given the estimated ejecta mass of ≳10⁻² M_⊙ and mean velocity v_ej ∼ 0.1–0.2 c (e.g., Villar et al. 2017 for an updated modeling), the optical depth through the ejecta of radius R ∼ v_ejt and density ρ ∼ M_ej/(4πR³/3) is approximately given by

$$\begin{eqnarray}{\tau }_{{\rm{X}}} & \simeq & \rho R{\kappa }_{{\rm{X}}}\\ & \approx & 1.2\left(\displaystyle \frac{{\kappa }_{{\rm{X}}}}{{10}^{3}\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}}\right)\left(\displaystyle \frac{{M}_{\mathrm{ej}}}{{10}^{-2}\,{M}_{\odot }}\right){\left(\displaystyle \frac{{v}_{\mathrm{ej}}}{0.2{\rm{c}}}\right)}^{-2}{\left(\displaystyle \frac{t}{120\mathrm{days}}\right)}^{-2}\end{eqnarray} \tag{ 2 }$$

where κ_X ∼ 10³ cm² g⁻¹ is the expected bound-free opacity of neutral or singly ionized heavy r-process nuclei at X-ray energies ∼a few keV (e.g., Metzger 2017). Thus, depending on the precise ejecta column along our line of sight, we could have τ_X ≲ 1 at the present epoch. Even in the case of negligible opacity to X-ray radiation at the present epoch, L_X,fb is ≪ than the observed X-ray luminosity ∼5 × 10³⁹ erg s⁻¹. The constant radio to X-ray flux ratio over 110 days provides an independent line of evidence against L_X,fb dominating the X-ray energy release at late times. Figure 6 shows that L_X,fb never dominates the X-ray emission from GW170817.

We now consider the spin-down luminosity from a magnetar remnant as potential source of X-ray radiation at late times. A long-lived magnetar remnant is already disfavored by the KN emission (e.g., Cowperthwaite et al. 2017; Drout et al. 2017; Kasliwal et al. 2017; Nicholl et al. 2017; Pian et al. 2017; Smartt et al. 2017; Tanvir et al. 2017; Villar et al. 2017), particularly the inferred presence of lanthanide-rich material created from very neutron-rich ejecta (neutrinos from a long-lived NS remnant would transform outflowing neutrons back into protons; see Metzger & Fernández 2014). Here we provide an independent argument against the long-lived magnetar scenario. Figure 7 shows the spin-down luminosity L_sd for a supramassive NS remnant (Equation (32)–(33) from Metzger 2017). At ∼10 days L_sd greatly exceeds the detected X-ray luminosity for any reasonable magnetic field strength B ≤ 10¹⁷ G. However, this argument alone cannot be used to rule out magnetar remnants because at this time τ_X ≫ 1, thus significantly suppressing the X-ray luminosity that can escape the system and reach the observer, as we showed in Margutti et al. (2017b; see also Equation (2) above). Pooley et al. (2017) reached the opposite conclusion, as they did not take into account the effects of bound-free opacity from the KN ejecta into their calculations (which, however, is significant). However, as we show in Figure 7, the same magnetar engines would produce luminous optical emission at early times (Metzger & Piro 2014) in excess to the observed bolometric luminosity from GW170817 and for this reason are ruled out. Finally, one can rule out the formation of a long-lived magnetar in GW170817 by the large rotational energy ≳10⁵² erg it would have injected into its environment, either into the GRB jet or the kilonova ejecta. As a comparison, in classical SGRBs, long-lived magnetars with rotational energy in the range ≳10⁵¹–10⁵⁴ erg are also ruled out (Fong et al. 2016; Margalit & Metzger 2017).

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We conclude that a central engine origin of the detected X-ray emission is disfavored at all times.