A year in the life of GW170817: the rise and fall of a structured jet from a binary neutron star merger

We present the results of our year-long afterglow monitoring of GW170817, the first binary neutron star (NS) merger detected by advanced LIGO and advanced Virgo. New observations with the Australian Telescope Compact Array (ATCA) and the Chandra X-ray Telescope were used to constrain its late-time behavior. The broadband emission, from radio to X-rays, is well-described by a simple power-law spectrum with index ~0.585 at all epochs. After an initial shallow rise ~t^0.9, the afterglow displayed a smooth turn-over, reaching a peak X-ray luminosity of ~5e39 erg/s at 160 d, and has now entered a phase of rapid decline ~t^(-2). The latest temporal trend challenges most models of choked jet/cocoon systems, and is instead consistent with the emergence of a relativistic structured jet seen at an angle of ~22 deg from its axis. Within such model, the properties of the explosion (such as its blastwave energy E_K~2E50 erg, jet width theta_c~4 deg, and ambient density n~3E-3 cm^(-3)) fit well within the range of properties of cosmological short GRBs.


INTRODUCTION
On August 17 th , 2017 the Advanced LIGO interferometers detected the first gravitational wave (GW) signal from a binary neutron star (NS) merger, GW170817, followed 1.7 s later by a short duration gamma-ray burst, GRB170817A (Abbott et al. 2017b). Located in the elliptical galaxy NGC4993 at a distance of ∼40 Mpc, GRB170817A was an atypical sub-luminous explosion. An X-ray afterglow was detected 9 days after the merger (Troja et al. 2017). A second set of observations, performed ∼15 days post-merger, revealed that the emission was not fading, as standard GRB afterglows, but was instead rising at a slow rate (Troja et al. 2017;Haggard et al. 2017). The radio afterglow, detected at 16 days (Hallinan et al. 2017), continued to rise in brightness (Mooley et al. 2018b), as later confirmed by X-ray and op-⋆ E-mail: eleonora.troja@nasa.gov tical observations (Troja et al. 2018b;D'Avanzo et al. 2018;Lyman et al. 2018).
The delayed afterglow onset and low-luminosity of the γ-ray signal could be explained if the explosion was observed at an angle (off-axis) of ≈15 • -30 • . Whereas a standard uniform jet viewed off-axis could account for the early afterglow emission, Troja et al. (2017) and Kasliwal et al. (2017) noted that it could not account for the observed gamma-ray signal and proposed two alternative models: a structured jet, i.e. a jet with an angular profile of Lorentz factors and energy (see also Abbott et al. 2017b;Kathirgamaraju et al. 2018), and a mildly-relativistic isotropic cocoon (see also Lazzati et al. 2017). In the latter model, the jet may never emerge from the merger ejecta (choked jet).
The subsequent temporal evolution ruled out both the uniform jet and the simple cocoon models, which predict a sharp afterglow rise. It was instead consistent with an off-axis structured jet and a cocoon with energy injec-tion (Mooley et al. 2018b), characterized by a radial profile of ejecta velocities. In Troja et al. (2018b) we developed semi-analytical models for both the structured jet and the quasi-spherical cocoon with energy injection, and showed that they describe the broadband afterglow evolution during the first six months (from the afterglow onset to its peak) equally well. This is confirmed by numerical simulations of jets (Lazzati et al. 2018;Xie et al. 2018) and cocoons (Nakar et al. 2018).
Several tests were discussed to distinguish between these two competing models (e.g. Gill & Granot 2018;Nakar et al. 2018). Corsi et al. (2018) used the afterglow polarization to probe the outflow geometry (collimated vs. nearly isotropic), but the results were not constraining. Ghirlanda et al. (2018) and Mooley et al. (2018a) used Very Long Baseline Interferometry (VLBI) to image the radio counterpart, and concluded that the compact source size ( 2 mas) and its apparent superluminal motion favor the emergence of a relativistic jet. A third and independent way to probe the outflow structure is to follow its latetime temporal evolution. In the case of a cocoon-dominated emission, the afterglow had been predicted to follow a shallow decay (t −α ) with α ∼1.0-1.2 (Troja et al. 2018b) for a quasi-spherical outflow, and α ∼1.35 for a wide-angled cocoon (Lamb et al. 2018). A relativistic jet is instead expected to resemble a standard on-axis explosion at latetimes, thus displaying a post-jet-break decay of α ∼ 2.5 (van Eerten & MacFadyen 2013).
Here, we present the results of our year-long observing campaign of GW170817, carried out with the Australian Telescope Compact Array (ATCA) in the radio, Hubble Space Telescope (HST) in the optical, the Chandra X-ray telescope and XMM-Newton in the X-rays. Our latest observations show no signs of spectral evolution (Sect. 2.1) and a rapid decline of the afterglow emission (Sect. 2.2), systematically faster than cocoon/choked jet models from the literature (Sect. 3.1). The rich broadband dataset allows us to tightly constrain the afterglow parameters, and to compare the explosion properties of GW170817 to canonical short GRBs (Sect. 3.2).

OBSERVATIONS AND DATA ANALYSIS
Our earlier observations have been presented in Troja et al. (2017), and Piro et al. (2018. To this we add a new series of observations tracking the post-peak afterglow evolution. Table 1 lists the latest unpublished data set, including our radio monitoring with ATCA (PI: Piro, Murphy) and X-ray observations with Chandra, carried out under our approved General Observer program (20500691; PI: Troja). Data were reduced and analyzed as detailed in Troja et al. (2018b). Additional data were taken from Resmi et al. (2018) and Alexander et al. (2018). We adopted a standard ΛCDM cosmology (Planck Collaboration et al. 2018). Unless otherwise stated, the quoted errors are at the 68% confidence level, and upper limits are at the 3 σ confidence level.

Spectral properties
The latest epoch of X-ray observations shows a simple power-law spectrum with index β=0.8±0.4, consistent with previous measurements, and with the spectral index 0.4±0.3 from the late time (t >220 d) radio data. Figure 1 shows that, at all epochs, the broadband spectrum can be fit with a simple power-law model with spectral index β=0.585±0.005 and no intrinsic absorption in addition to the Galactic value NH =7.6×10 20 cm −2 . The lack of any significant spectral variation on such long timescales is remarkable. In GRB afterglows, a steepening of the X-ray spectrum due to the gradual decrease of the cooling frequency νc is commonly detected within a few days. Since the cooling break is a smooth spectral feature, we used a curved afterglow spectrum (Granot & Sari 2002) to fit the data, and constrain its location. We derived νc 1 keV (90% confidence level) at 260 d after the merger and νc 0.1 keV (90% confidence level) at 360 d.
For a synchrotron spectrum with νm < ν obs < νc, the measured spectral index is related to the spectral index p of the emitting electrons as p = 2β +1 = 2.170 ± 0.010. Figure  2 compares this value with a sample of well-constrained short and long GRB spectra. It shows that, among short GRB spectra, GW170817/GRB170817A represents the most accurate measurement obtained so far. Such accuracy is rare, but not unprecedented among long GRB afterglows.
It is tempting to interpret the accurately determined value of p as an intermediate between relativistic and non-relativistic shock acceleration, based on theoretical considerations of plausible mechanisms (Kirk et al. 2000;Achterberg et al. 2001;Spitkovsky 2008), implying (Γ ≈2-10) for the emitting material (Margutti et al. 2018). On the other hand, various well constrained short GRB p-values lie outside this theoretical range (Fig. 2), the p-value distribution for the larger sample of (long) GRBs does not appear consistent with a universal value for p (Shen et al. 2006;Curran et al. 2010), nor is there generally any evidence for evolution of p from multi-epoch spectral energy distributions (SEDs) (Fig. 1, also e.g. Varela et al. 2016) or light curve slopes. In view of these features of the general sample of long and short GRBs (as well as other synchrotron sources, such as blazars), direct interpretation of p ≈ 2.17 in terms of shock-acceleration theory might be premature.

Temporal properties
We simultaneously fit the multi-color light curves by adopting a simple power-law function in the spectral domain, and a smoothly broken power-law in the temporal domain. The functional form is: F (ν, t) ∝ ν −β (t/tp) −sα 1 + (t/tp) sα 2 −1/s , where β is the spectral index, α1 and α2 are the rise and decay slopes, tp is the peak time, and s is the smoothness parameter.
We did not impose an achromatic behavior. Instead, the temporal properties were modeled as a hierarchy where the parameters for each wavelength have an independent value, sampled from a hyper distribution. All hyper- and smoothness parameter (s) for the radio (blue) and X-ray (red) light curves. The dashed line corresponds to α 2 = 1.35, the steepest value predicted by choked jet/cocoon models.
distributions are given weakly informative priors of appropriate scale. To fit the model, we employ the NUTS variant of Hamiltonian Monte Carlo via the Stan modeling language (Carpenter et al. 2017). The peak time and rise slope are well constrained to tp=164±12 d and α1=0.90±0.06. Whereas the optical afterglow is poorly sampled, the X-ray and radio light curves allow for better constraints on the decay slope ( Figure 3) and are both consistent with a rapid decline of the afterglow flux.

Modeling
We directly fit two semi-analytical models for structured outflows to the data, following the description in Troja et al. (2018b). The off-axis structured jet model assumes a Gaussian energy profile E ∝ exp −θ 2 /2θ 2 c up to a truncating angle θw. The jet is fully determined by a set of eight parameters Θjet = {E0, n, ǫe, ǫB p, θc, θw, θv}, where E0 is the on-axis isotropic-equivalent kinetic energy of the blast wave, n the circumburst density, ǫe the electron energy fraction, ǫB the magnetic energy fraction and θv the angle between the jet-axis and the observer's line of sight. Following Mooley et al. (2018b), we also fit a cocoon model with a velocity stratification of the ejecta to allow for a slower rise and late turnover. The total amount of energy in the slower ejecta above a particular four-velocity u is modelled as a power-law E(> u) = Einju −k . This model requires nine parameters Θcocoon = {Einj, n, p, ǫe, ǫB Mej, umax, umin, k}, where umax is the maximum ejecta four-velocity, umin the minimum ejecta four-velocity, and Mej the initial cocoon ejecta mass with speed umax.
As described in Troja et al. (2018b), our Bayesian fit procedure utilizes the emcee Markov-chain Monte Carlo package (Foreman-Mackey et al. 2013). For the structured jet we also include the GW constraints on the orientation ι of the system (Abbott et al. 2017a) in our prior for θv. Our best fit model is shown in Figure 4.

A rapid afterglow decline: constraints on the outflow structure
For jets that fail to break out ("choked jets"), the jet energy is dissipated into a surrounding cocoon of material. This scenario is therefore included in our group of 'cocoon' models (Troja et al. 2018b). The post-peak temporal slope is a shallow decay of α ≈ 1.0 up to at least 300 days for GRB 170817A, as can be inferred from semianalytical modeling of the evolution of a trans-relativistic shell (Troja et al. 2018b). Any remaining post-turnover impact due to continued energy injection from e.g. a complex velocity profile of the ejecta, would lead to an even shallower decay. Afterwards, the slope will eventually become that of an expanding non-relativistic (quasi-)spherical shell. As for the Sedov-Taylor solution of a point explosion in a homogeneous medium, this slope translates to α = (15p−21)/10 for νm < ν obs < νc, when combined with a standard synchrotron model for shock-accelerated electrons (Frail et al. 2000). The value p ≈ 2.17 implies α ≈ 1.155. If νm, νc < ν obs , α = (3p − 4)/2 ≈ 1.255 instead. If the cocoon choking the jet is not quasi-spherical, but merely wide-angled, some sideways spreading of the outflow may still occur. By definition for a non-relativistic flow velocity, this will not produce any observational features related to relativistic beaming, but the continuous increase in working surface will give rise to additional deceleration of the blast wave relative to the case of purely radial flow. As a result, the temporal slope could steepen slightly by another ∆α ≈ 0.15 − 0.2 (Lamb et al. 2018), before settling into the late quasi-spherical stage. For GW170817, this implies a maximum α ≈ 1.35 from a cocoon / choked jet model. By contrast, if the jet has a relativistically moving inner region (in terms of angular distribution of Lorentz factor), the post-peak temporal slope will be like that of an on-axis jet seen after the jet break: the entire surface of the jet has come into view and there is no longer a contribution to the light curve slope from a growing visible patch. At this point, the slope α ≈ p according to analytical models (Sari et al. 1999), and a somewhat steeper α ≈ 2.5 according to semi-analytical models (Troja et al. 2018b) and hydrodynamical simulations of jets (van Eerten & MacFadyen 2013, although the latter were done for jets starting from top-hat initial conditions).
As derived in section 2.2, the decay slope α2 of the empirical model exceeds the predictions of most choked jet models by a healthy margin. This is confirmed by the comparison of the late afterglow data, from radio to X-rays, with physical models of choked and structured jets (Figure 5). The observed decay is consistent with the turnover of a structured jet (solid line). While the observed α2 is not as steep as 2.5, this is not unexpected for a jetted flow as the transition of the light curve from rise to decay is spread out over time (and fully captured by the direct application of a structured jet model in section 2.3, see also Fig. 4).
The rapid decline of the afterglow therefore poses an additional challenge to the choked jet models, in support to the results of the high-resolution radio imaging (Mooley et al. 2018a;Ghirlanda et al. 2018). While growing evidence indicates that the merger remnant launched a successful relativistic jet, the presence of a cocoon cannot be excluded. There might well be an observable cocoon component present in the outflow even for successful jets (Nagakura et al. 2014;Murguia-Berthier et al. 2014). Indeed, the structured jet itself might be an indication of the presence of a cocoon (in case the structure is not imposed by the torus upon launching, Aloy et al. 2005). However, it would appear any such cocoon is not the dominant emission component at late times.

Afterglow properties: comparison to short GRBs
The results of the MCMC analysis are summarized in Table 2. For all models and priors, the posterior value of the electron power law slope lies around p = 2.170 ± 0.010, fully consistent with the value obtained by the spectral analysis (Section 2.1). The cocoon model requires a small amount of relativistic ejecta with a substantial Lorentz factor Γmax ∈ [6.1, 200] (all ranges with 68% percent confidence) followed by an energetic tail of slower ejecta with minimum Lorentz factor Γmin ∈ [1.9, 7.48]. The high Lorentz factors are in tension with a choked-jet scenario, where the ejecta achieve only Newtonian velocity. The total energy, assuming a spherical blast wave, is rather high, between 10 51 and 4 × 10 53 erg. The circumburst density and shock micro-physical parameters are very poorly constrained in this model.
The viewing angle derived from the electromagnetic observations alone is 0.52±0.16 rad (30 • ± 9 • ), consistent with the constraints from prompt emission (e.g Abbott et al. 2017b;Bégué et al. 2017). By adding the GW constraints on the binary inclination ι to our modeling, we obtain θv = 0.38±0.11 rad (22 • ± 6 • ), consistent with the LIGO estimates that informed the prior. The good agreement of the electromagnetic and GW constraints suggest that the relativistic jet was launched nearly perpendicularly to the orbital plane (θv ≈ ι).
The year-long monitoring of GW170817 significantly reduced the allowed parameter space of models, tightening the constraints on the afterglow properties. This allows for a comparison with other well-studied short GRB explosions, as presented in Figure 6. It is remarkable how the properties of GW170817 fit within the range of short GRB afterglows. The low circumburst densities n ≈0.01 cm −3 are typical of the interstellar medium, and consistent with the location of these bursts within their galaxy light. The electron energy fraction seems well constrained to ǫe 0.1, whereas ǫB tends to lower values 0.01. The narrow width of the Gaussian jet θc of GW170817 is comparable to the half-opening angle θj inferred from top-hat jet models of short GRBs, suggesting that these GRB jets had narrow cores of similar size. The isotropic-equivalent energy is also consistent with the measurements from other short GRBs, although we note that all the events in the sample lie above the median value of E k,iso (vertical band). This is not surprising as we selected the cases of well-sampled light curves with good afterglow constraints, thus creating a bias toward the brightest explosions.

CONCLUSIONS
The long-term afterglow monitoring of GW170817 supports the earlier suggestions of a relativistic jet emerging from the merger remnant, and challenges the alternative scenarios of a choked jet. Whereas emission at early times (<160 d) came from the slower and less energetic lateral wings, the rapid post-peak decline suggests that emission from the narrow jet core has finally entered our line of sight. The overall properties of the explosion, as derived from the afterglow modeling, are consistent with the range of properties observed in short GRBs at cosmological distances, and suggest that we detected its electromagnetic emission thanks to a combination  (Lamb et al. 2018), and our best fit models of quasi-spherical cocoon (dot-dashed line) and structured jet (solid line). Different symbols represent different wavelengths: X-rays (circles), optical (downward triangles; 3 σ upper limits), and radio (diamonds) from ATCA (filled) and VLA (empty).