GW170817A  a hundred days after merger

The Binary Neutron Star event LIGO/VIRGO GW170817 a hundred days after merger: synchrotron emission across the electromagnetic spectrum

R. Margutti11affiliation: Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208 , K. D. Alexander22affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA , X. Xie33affiliation: Center for Cosmology and Particle Physics, New York University, 726 Broadway, New York, NY 10003, USA , L. Sironi44affiliation: Columbia University, Pupin Hall, 550 West 120th Street, New York, NY 10027, USA , B. D. Metzger55affiliation: Department of Physics and Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA , A. Kathirgamaraju66affiliation: Department of Physics and Astronomy, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907, USA , W. Fong11affiliation: Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208 77affiliation: Hubble Fellow , P. K. Blanchard22affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA , E. Berger22affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA , A. MacFadyen33affiliation: Center for Cosmology and Particle Physics, New York University, 726 Broadway, New York, NY 10003, USA , D. Giannios66affiliation: Department of Physics and Astronomy, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907, USA , C. Guidorzi88affiliation: Department of Physics and Earth Science, University of Ferrara, via Saragat 1, I–44122, Ferrara, Italy , A. Hajela11affiliation: Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208 , R. Chornock99affiliation: Astrophysical Institute, Department of Physics and Astronomy, 251B Clippinger Lab, Ohio University, Athens, OH 45701, USA , P. S. Cowperthwaite22affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA , T. Eftekhari22affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA , M. Nicholl22affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA , V. A. Villar22affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA , P. K. G. Williams22affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA , J.  Zrake55affiliation: Department of Physics and Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA

We report deep Chandra, HST and VLA observations of the binary neutron star event GW170817 at d after merger. These observations show that GW170817 is steadily brightening with time and constrain the emission process as non-thermal synchrotron emission where the cooling frequency is above the X-ray band and the synchrotron frequency is below the radio band. The very simple power-law spectrum extending for eight orders of magnitude in frequency enables the most precise measurement of the index of the distribution of non-thermal relativistic electrons accelerated by a shock launched by a NS-NS merger to date. We find , which indicates that radiation from ejecta with dominates the observed emission. While constraining the nature of the emission process, these observations do not constrain the nature of the relativistic ejecta. We employ simulations of explosive outflows launched in NS ejecta clouds to show that the spectral and temporal evolution of the non-thermal emission from GW170817 at days is consistent with both emission from radially stratified quasi-spherical ejecta traveling at mildly relativistic speeds, and emission from off-axis collimated ejecta characterized by a narrow cone of ultra-relativistic material with slower wings extending to larger angles. In the latter scenario, GW170817 harbored a normal SGRB directed away from our line of sight. Observations at days are unlikely to settle the debate as in both scenarios the observed emission is effectively dominated by radiation from mildly relativistic material.

Subject headings:

1. Introduction

The joint discovery of gravitational waves (Abbott et al., 2017) and photons from the first binary neutron star (BNS) merger event GW170817 established that gravitational-wave detected BNS mergers can be accompanied by detectable emission across the electromagnetic spectrum, including -rays (Goldstein et al., 2017; Savchenko et al., 2017). During the first days the spectrum consisted of a combination of thermal emission powered by the radioactive decay of heavy elements freshly synthesized in the merger ejecta (i.e. the kilonova emission, KN; Metzger 2017; Chornock et al. 2017; Coulter et al. 2017; Cowperthwaite et al. 2017; Drout et al. 2017; Kasliwal et al. 2017; Nicholl et al. 2017; Pian et al. 2017; Smartt et al. 2017; Soares-Santos et al. 2017; Tanvir et al. 2017; Valenti et al. 2017; Villar et al. 2017) and non-thermal synchrotron emission dominating in the X-rays and radio bands (Alexander et al., 2017; Haggard et al., 2017; Hallinan et al., 2017; Margutti et al., 2017a; Troja et al., 2017b). The thermal component later subsided. After days of intense monitoring, the non-thermal emission is brightening with time (Mooley et al., 2017; Ruan et al., 2017; Margutti et al., 2017; Troja et al., 2017a) and the most pressing question regards the intrinsic nature of GW170817.

A first possibility is that GW170817 is an intrinsically sub-luminous event with total gamma-ray energy released . As a comparison, classical cosmological Short Gamma-Ray Bursts (SGRBs) typically have (Fong et al., 2015; Berger, 2014). In this scenario, GW170817 did not produce a successful collimated relativistic outflow (i.e. no observer in the Universe observed a classical SGRB in association with GW170817), the emission from GW170817 is quasi-spherical and powered by energy deposited by the interaction of the unsuccessful jet with the BNS ejecta (Gottlieb et al. 2017). The simplest incarnation of this model (i.e. the uniform fireball) fails to reproduce current observations, but a more complex version with highly stratified ejecta with energy (where in this context is the specific momentum of the outflow) successfully accounts for the observed properties of GW170817 (Gottlieb et al., 2018; Hallinan et al., 2017; Kasliwal et al., 2017; Mooley et al., 2017).

Here we present deep radio, optical and X-ray observations of GW170817 d after merger (Sec. 2) and offer an alternative interpretation. We employ hydrodynamical simulations of the jet interaction with the BNS ejecta to show that a core of ultra-relativistic material can successfully break through the closest environment and power a classical SGRB in association with GW170817, in agreement with the recent results by Lazzati et al. (2017a, c). We further demonstrate in Sec. 3 that the very simple power-law spectrum extending for eight orders of magnitude in frequency allows a precise measure of the properties of electrons accelerated at the shock front. In particular it enables inferences on the slope of the non-thermal tail of accelerated particles from which we derive robust constraints on the shock velocity which are independent from the morphology of the outflow (collimated vs. spherical). We demonstrate that all these properties are consistent with a SGRB-like outflow originally directed away from our line of sight (Sec. 3). In this scenario GW170817 is not intrinsically subluminous and its unusual observed properties result from a different viewing angle than classical SGRBs, which are viewed along the jet axis. We conclude in Sec. 4.

We assume that all electrons are shock accelerated to a power-law energy distribution , i.e. , which is the standard assumption in GRB studies. If only a fraction of electrons is accelerated into the non-thermal tail, the inferred density should be re-scaled as . We adopt the convention and , where is the spectral index and is the photon index. We assume a distance to NGC 4993 of 39.5 Mpc () as listed in the NASA Extragalactic Database. c.l. uncertainties are listed unless otherwise stated. In this manuscript we employ the notation .

2. Observations and data analysis

2.1. Chandra X-ray Observations

Obs ID Time since merger Flux (0.3-10 keV) Unabsorbed Flux (0.3-10 keV)
(days) () ()
18955 2.34 1.4
19294 9.21
20728 15.39
18988 15.94
20860/1 109.39

Note. – 0.5-8 keV count-rate upper limit of from Margutti et al. (2017a), with updated flux calibration performed with an absorbed power-law model with as inferred from our joint fit of the CXO observations with IDs 19294 and 20728. This work.
From Margutti et al. (2017a).
From a joint spectral fit of CXO observations, IDs 19294 and 20728. This work.
Flux from Haggard et al. (2017) re-scaled to the spectrum. This work.

Table 1X-ray Spectral Parameters and inferred flux ranges ( c.l.). Upper limits are provided at the c.l.

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

We independently re-analyzed the CXO observations acquired 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. 2017a. Using wavdetect we find that an X-ray source is clearly detected with significance of 5.8 at the location of the optical counterpart of GW170817. The inferred count-rate in the 0.5-8 keV energy range is (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 and Galactic neutral hydrogen column density (Kalberla et al. 2005) and use MCMC sampling to constrain the spectral parameters. We find . We find no statistical evidence for intrinsic neutral hydrogen absorption and place a limit ( c.l.). For these parameters the 0.3-10 keV flux is ( c.l.), corresponding to an unabsorbed flux of .

Comparison with the X-ray spectrum of GW170817 at (ID 20728) that we presented in Margutti et al. 2017a indicates a possibly harder emission at early times ( at vs. at ). While we find this possibility intriguing, the limited number statistics of the two spectra does not allow us to draw conclusions as the two values are statistically consistent. A joint spectral fit of the two epochs indicates ( c.l.) with a upper limit . 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).

Deep X-ray observations of GW170817 have been obtained as soon as the source re-emerged from Sun constraint (PI Wilkes, observation IDs 20860, 20861; Program 18408601; Margutti et al. 2017; Margutti et al. 2017b; Haggard et al. 2017; Troja et al. 2017a). The CXO started observing GW170817 on 2017 December 3.07UT ( d since merger, ID 20860) for 74.1 ks. An X-ray source is clearly detected at the location of GW170817 with significance of and net count-rate (0.5-8 keV). The CXO observed the field for an additional 24.7 ks starting on 2017 December 6.45UT ( d since merger, ID 20861). The X-ray source is still detected with a significance of and net count-rate of (0.5-8 keV). The joint spectrum can be fit with an absorbed power-law spectral model with photon index (1 sigma c.l.), consistent with the results from Ruan et al. (2017). We find no evidence for intrinsic neutral hydrogen absorption and constrain ( c.l.). These properties are consistent with the X-ray spectral properties of GW170817 at days. The 0.3-10 keV inferred flux range is , (unabsorbed flux of ). This result indicates substantial brightening of the X-ray source during the last d with no measurable spectral evolution (Fig. 1).

2.2. HST Observations

We obtained 1 orbit of Hubble Space Telescope (HST) observations of GW170817 on 1 January 2018 (137 d 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 27 August 2017 (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 AB magnitude of mag. As a comparison, at 110 d since merger, Lyman et al. (2018) find mag .

2.3. VLA Observations

Time since merger Mean Freq Freq Range On-source Flux Density
(days) (GHz) (GHz) Time (hr) ()
80.10 6.0
112.04 5.0
112.04 7.0
115.05 2.6
115.05 3.4
115.05 9.0
115.05 11.0
115.05 13.0
115.05 15.0
115.05 17.0
Table 2VLA observations of GW170817.

Our radio observations of GW170817 from d 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 5 November 2017 ( d 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 J12582219 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 Jy. 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 7 December 2017 (C band) and under program 17B-425 (PI: Alexander) on 10 December 2010 (S, X, and Ku bands, spanning the frequency range 2–18 GHz). 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 subbands, although the effective bandwidth of each after flagging is closer to 750 MHz due to 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. These measurements clearly indicate an optically thin spectrum with spectral index . This value is consistent with the X-ray spectral index () obtained a few days before (Sec. 2.1).

2.4. Joint X-Ray and Radio analysis

A joint spectral fit of radio data obtained at d and X-ray data obtained around d with a simple power-law model constrains . This value is consistent with the spectral indexes and derived from individual fits within the X-ray and radio bands (Sec. 2.1,2.3), and shows that at d the broad-band 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 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 , 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 . The best-fitting is then used to renormalize the flux densities measured at d to a common epoch of 109 d since merger (to match the time of CXO observations). Finally, we estimate from a joint fit of the broad-band radio-to-X-ray spectrum at 109 d. This procedure is repeated until convergence (i.e. within error bars). We find and (Fig. 1). As a comparison, from the analysis of radio data alone at d Mooley et al. 2017 infer , 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 Fig. 1 the HST measurement obtained by Lyman et al. (2018) at 110 d. This comparison shows a remarkable agreement with our bestfitting SED and demonstrates that at 110 d since merger the optical emission from GW170817 is of non-thermal origin and originates from the afterglow.

We compile in Fig. 1 the radio-to-X-ray SEDs of GW170817 at 15 d and 9 d (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. Fig. 1 shows that a re-scaled version of the spectrum that best-fits the 110 d 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 d with a 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 d, and that the radio and X-ray radiation from GW170817 continue to represent the same non-thermal emission component.

Figure 1.— Evolution of the broad-band radio-to-X-ray SED of GW170817 from 9 d until 110 d since merger. The radio and X-ray data are dominated by non-thermal synchrotron emission from the GW170817 afterglow at all times and consistently track each other on a spectral power-law segment. At early times d the optical-NIR is dominated by radioactively powered emission from the KN. By day 110 the KN component has faded away and the detected optical-NIR emission is dominated by the afterglow radiation. Filled circles: CXO data. Filled squares: VLA. Note that while Hallinan et al. (2017) consider their 6 GHz measurement at days only as a potential detection, here we show that it does naturally lie on the extrapolation of the X-ray data, which suggests that this is in fact a real detection (and the earliest radio detection of GW170817). Filled diamonds at 15 and 9 d: optical-NIR data from Villar et al. (2017). For day 9 we show the actual data from Tanvir et al. (2017); Soares-Santos et al. (2017); Cowperthwaite et al. (2017); Kasliwal et al. (2017), while for day 15 we show the extrapolated values from the best fitting model from Villar et al. (2017). Black dashed line: afterglow component with that best fits the observations at 110 d. Dashed red and blue lines: same afterglow model renormalized to match the observed flux level at 15 d and 9d. Dotted line: best fitting KN component. The SED at 15 d and 9 d have been rescaled for displaying purposes. The HST observations from Lyman et al. (2018) obtained at 110 d (filled diamonds) are shown here for comparison but have not been used in our fits.

3. Interpretation and discussion

3.1. A synchrotron spectrum from particles accelerated by shocks with

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 is above the X-ray band, is below the radio band and the observed radio and X-ray emission is on the spectral segment, where is the index of the non-thermal electrons accelerated into a power-law distribution at the shock front. From our best-fitting , we infer .

The precise measurement of the power-law slope (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 expected at non-relativistic shock speeds (Bell, 1978; Blandford & Ostriker, 1978; Blandford & Eichler, 1987) and 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 implies a shock Lorentz factor of at 110 d (the c.l. is ). The straightforward implication is then that we are seeing electron acceleration in trans-relativistic shocks in action.111We remark, though, that a power-law electron spectrum with slope might not necessarily result in the canonical radiation spectrum , if one of the following conditions are met: (i) the radiative signature has an appreciable contribution from electrons that cool in the precursor, i.e., upstream of the shock front, which has the effect of hardening the observed spectrum (Sironi & Spitkovsky, 2009; Zakine & Lemoine, 2017); or (ii) the magnetic field self-generated by the shock is not uniform in the post-shock region, but decays away from the shock (e.g., Spitkovsky, 2008; Chang et al., 2008; Keshet et al., 2009; Martins et al., 2009; Haugbølle, 2011; Sironi et al., 2013). In this case, the observed synchrotron spectrum encodes important information on the decay profile of the turbulent post-shock fields (Rossi & Rees, 2003; Lemoine, 2013; Lemoine et al., 2013).

As the non-thermal spectrum of GW170817 showed negligible evolution (Fig. 1), a similar line of reasoning applies to the previous epochs at d, from which we conclude that the observed non-thermal radiation from GW170817 at d is always dominated by emission from material with relatively small .

These findings are consistent with the picture proposed by Mooley et al. (2017) (see also Salafia et al. 2017; Kasliwal et al. 2017; Hallinan et al. 2017) 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. A value is significantly smaller than the initial a few inferred for the luminous SGRBs, which are powered by ultra-relativistic jets seen on axis (which have consistently larger inferred values of Fong et al. 2015). However, one expects that even a blast wave with large energy propagating in a low density medium with will have decelerated to by d 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 Sec. 3.3; Jin et al. 2017; Kathirgamaraju et al. 2018; Lamb & Kobayashi 2017; Lazzati et al. 2017c; Murguia-Berthier et al. 2017; Troja et al. 2017b). In this latter scenario the emission that we observe is also always dominated by radiation from ejecta with relatively small 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 . 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.

3.2. Off-Axis Relativistic Top-Hat Jets

Figure 2.— Best-fitting top-hat off-axis jet models with (upper panel) and (lower panel) for . These models fail to reproduce observations at early times and do not naturally account for the still-rising light-curve, which is a potential signature of structure in the jet, with an ultra-relativistic core still out of our line of sight. This is explored and quantified in Sec. 3.3.
Figure 3.— Kinetic energy structure of the ejecta of GW170817 for quasi-spherical outflows from Mooley et al. (2017) (grey lines) and for the structured jet that we present here (red line). Orange filled dots: kinetic energy of the red, purple and blue kilonova component associated to GW170817 as derived by Villar et al. (2017). Blue lines: SGRBs. For the SGRB slow ejecta we report a representative limit derived from the analysis of very late-time radio observations from Fong et al. (2016), while the shaded area mark the beaming-corrected of the jet component in SGRBs as derived by Fong et al. (2015). This plot highlights the difference between quasi-spherical outflows (which lack an ultra-relativistic component and require a large amount of energy to be coupled to slowly moving ejecta ) and structured ultra-relativistic outflows (which have properties consistent with SGRBs and are energetically less demanding).

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; Haggard et al. 2017; Hallinan et al. 2017; Kasliwal et al. 2017; Margutti et al. 2017a; Troja et al. 2017b; Mooley et al. 2017; Ruan et al. 2017; Granot et al. 2017; Fraija et al. 2017). 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 . This is the simplest jet model and likely an over simplification 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 (Sec. 3.3), i.e. jets with with non-zero in higher-latitude ejecta at .

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. (2017a); 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 and large energies , with off-axis angles . 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 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 (i.e. a structured jet) and the core of the jet has yet to enter into our line of sight (Sec. 3.3).

In summary, the failure of the simple top-hat jets motivates the exploration of more realistic structured jets models in Sec. 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.

3.3. Successful Off-Axis Relativistic Structured Jets

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; Duffell et al. 2015; Lazzati et al. 2017b, a; Kathirgamaraju et al. 2018; Gottlieb et al. 2018), polluted with 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 and .

This scenario is clearly different from choked-jets, pure-cocoon models and spherical models (Gottlieb et al., 2017; Hallinan et al., 2017; Kasliwal et al., 2017; Mooley et al., 2017; Salafia et al., 2017) where no collimated ultra-relativistic outflow (even when there) survived the interaction with the BNS ejecta. This is clear from Fig. 3, where we show the 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 Fig. 3 it is also clear that quasi-spherical outflows require significantly larger amounts of energy coupled to slow material with ( 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 erg (shaded region in Fig. 3). The two notions can be reconciled only if the most energetic jets never manage to break out, which we find contrived.

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. 2017; Troja et al. 2017b; Lyman et al. 2018. These jets typically have large and 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 wings222This component of emission is missing in top-hat jets, which, as a consequence, show a characteristic rise and underpredict the early time observations as shown in Fig. 2. (which would be also responsible for the detected -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.

Figure 4.— Results from our simulation of a successful off-axis relativistic jet with structure and displayed in the insets, propagating into a low-density environment with and viewed off-axis. We use and the microphysical parameters reported in the figure. These two representative models can adequately reproduce the current set of observations and predict an optically thin synchrotron spectrum at all times, in agreement with our observations (upper panel). Insets: and from our simulations (black solid lines) at s, compared to the jet structure from Lazzati et al. (2017c) (grey lines). The jet in our simulation has quasi-gaussian structure, with and , (red dashed line). Future observations will be able to constrain the jet-environment parameters.

Figure 5.— Comparison of models that fit current observations of GW170817 at radio frequencies (6 GHz). Red and orange lines: quasi-spherical stratified ejecta models from Mooley et al. (2017) and cocoon model from Gottlieb et al. (2017) where no ultra-relativistic jetted component survived the interaction with the BNS ejecta (i.e. no observer in the Universe observed a regular SGRB associated with GW170817). Blue lines: structured jet models from Lazzati et al. (2017c) (dark blue-line, their best-fitting model) and this work (light-blue lines) where an off-axis ultra-relativistic collimated component is present and contributes to the emission at some point (i.e. GW170817 is consistent with being an ordinary SGRB viewed off-axis). The parameters of our models are the same as in Fig. 4. At days all the models displayed predict an extremely similar flux evolution (and spectrum), with no hope for current data to distinguish between the two scenarios. All off-axis jet models have a similar and the different late-time evolution is a consequence of the different jet-environment parameters.

Figure 6.— Comparison of successful models at 1 keV. Same color coding as Fig. 5. For the spherical models by Mooley et al. (2017) and Gottlieb et al. (2017) we adopt the best fitting spectral index from Mooley et al. (2017) to convert their best fitting radio models into X-rays. These models underpredict the observed X-ray flux. This is a clear indication of a flatter spectral index as we find in Sec. 2.3. Using would bring the models to consistency with the observations. Thick gray line: expected flux from fall-back accretion onto the remnant black hole for the fiducial parameters of Sec. 3.4.

We use the moving-mesh relativistic hydrodynamics JET code (Duffell & MacFadyen, 2013) to simulate the dynamics of explosive outflows launched in neutron star ejecta clouds using an engine model (Duffell et al., 2015) and density structure similar to Kasliwal et al. (2017); 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 Fig. 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 Xie et al., in prep.). Specifically, the jet has a narrow ultra-relativistic core of with surrounded by a mildly relativistic sheath with at (see inset of Fig. 4) and propagates in a low-density environments with . At s, the energy in the ultra-relativistic core is erg while the sheath carries (see Xie at al for details). The observer is located at from the jet axis. We adopt (), () with , within the range of our inferred values (Sec. 3.1) for the () simulation.

Our model predicts an observed broad-band optically thin synchrotron spectrum that extends from the radio to the X-ray band on a spectral segment, from the time of our first observations at d until now (at the low densities favored by our modeling is not expected to cross the X-ray band at d, see Fig. 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 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 Fig. 5-6), this makes these two classes of models virtually impossible to distinguish based on current observations.

We compare the results from our simulations to those presented by Lazzati et al. (2017c) in Fig. 5-6. The major difference is the flux evolution at d, with the Lazzati et al. (2017c) models steadily rising until d after merger. As the microphysics parameters (, , ) and observing angle () are very similar to the values of one of our simulations, the different behavior can be ascribed to the combination of a narrower ultra-relativistic core, as shown in the inset of Fig. 4 (which effectively places the observer more off-axis) more slowly decelerating into a lower density environment ( vs. ). In general, outflows with a fully-relativistic core with isotropic energy , propagating into environments with and viewed off-axis will reach a peak at days ( days, e.g. Granot & Sari 2002).

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 Fig. 4 (see also Fig. 6-5): a peak when radiation from the jet core enters the line of sight at , 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  days. For and which are relevant here, yrs 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.

3.4. X-rays from the central compact remnant

Another source of potential X-ray emission is that originating directly from the central compact remnant. We first consider an accreting black hole. The 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 can be estimated as


where we have assumed that the fall-back accretion rate follows a decay with a value at 1 second post merger normalized to (a characteristic value, which is however uncertain by at least an order of magnitude). The estimated above is thus close to the Eddington luminosity erg s 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 and mean velocity c (e.g. Villar et al. 2017 for an updated modeling), the optical depth through the ejecta of radius and density is approximately given by


where cm g is the expected bound-free opacity of neutral or singly-ionized heavy -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 at the present epoch. Even in the case of negligible opacity to X-ray radiation at the present epoch, is than the observed X-ray luminosity . The constant radio to X-ray flux ratio over 110 d provides an independent line of evidence against dominating the X-ray energy release at late times. Figure 6 shows that never dominates the X-ray emission from GW170817.

Figure 7.— Red lines: spin-down luminosity for a supramassive NS remnant with magnetic field G. Black squares: GW170817 bolometric luminosity from Cowperthwaite et al. (2017). Blue filled circles: X-ray luminosity. The spin-down luminosity is always larger than the bolometric energy release from GW170817 at early times, which argues against a long-lived magnetar remnant.

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 neutron star remnant would transform outflowing neutrons back into protons; see Metzger & Fernández 2014). Here we provide an independent argument against the long-lived magnetar scenario. Fig. 7 shows the spin-down luminosity for a supramassive NS remnant (Eq. 32-33 from Metzger 2017). At d greatly exceeds the detected X-ray luminosity for any reasonable magnetic field strength . However, this argument alone cannot be used to rule out magnetar remnants because at this time , thus significantly suppressing the X-ray luminosity that can escape the system and reach the observer, as we showed in Margutti et al. (2017a) (see also Eq. 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 Fig. 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 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 erg are also ruled out (Fong et al., 2016; Margalit & Metzger, 2017).

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

4. Summary and Conclusions

Deep Chandra and VLA observations of the BNS event GW170817 d after merger show a steadily rising emission with across the electromagnetic spectrum. These findings rule out simple models of top-hat jets viewed off-axis (which predict before peak) and uniform spherical outflows (which predict ). We use the very simple power-law spectrum extending from the X-rays to the radio band to estimate that the emission is powered by mildly relativistic material with . This estimate is solely based on the theory of particle acceleration at shocks (and does not depend on other details of GW170817).

Models of GW170817 where no ultra-relativistic collimated component survives and the outflow is powered by mildly relativistic stratified ejecta (like those proposed by Mooley et al. 2017) successfully reproduce these observations. Here we offer an alternative interpretation. We employ simulations of the explosive outflows launched in NS ejecta clouds to show that a powerful relativistic core of material can survive the interaction with the BNS ejecta, producing a successful relativistic structured jet (Sec. 3.3). In this case, the observed emission is also effectively powered by mildly relativistic ejecta if the ultra-relativistic core is directed away from our line of sight. In this paper we showed one particular model (part of a family of successful models) that fits current observations. A detailed description of the jet simulations using the moving mesh relativistic hydrodynamics code JET (Duffell & MacFadyen, 2013) and light curves will be presented in Xie at al, in prep.

A key distinction between the two sets of models is that in the former scenario GW170817 would be intrinsically different from classical SGRBs and the first of a new class of transients. In the latter scenario GW170817 can be instead reconciled with an ordinary SGRB viewed from the side (in SGRBs we are not sensitive to the presence of lateral structure in the jet as the emission is always dominated by the brighter relativistic core). Distinguishing between these models is of paramount importance, as it has direct implications on the intrinsic nature of GW170817 and the potential existence of a new class of quasi-spherical transients powered by NS mergers. However, we show here that at the present time the two sets of models predict very similar flux temporal evolution and spectrum. Observations at days, able to track the evolution of (which evolves much faster in spherical models, e.g. Mooley et al. 2017) and to constrain the presence of temporal breaks in the flux evolution are the most promising to discriminate between the two scenarios.

We conclude that current observations do not distinguish the nature of the relativistic ejecta and cannot be used to rule out the presence of an off-axis originally ultra-relativistic core of collimated ejecta in the outflow of GW170817. The existence of a new class of BNS merger transients is not required by current observations and GW170817 is consistent with being a classical SGRB viewed off-axis.

Figure 8.— Evolution of the X-ray emission from GW170817 as seen by the CXO.

RM thanks the entire Chandra team for their work, time and dedication that made these observations possible. Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award Number DD7-18096A issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. WF acknowledges support for Program number HST-HF2-51390.001-A, provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. CG acknowledges University of Ferrara for use of the local HPC facility co-funded by the “Large-Scale Facilities 2010” project (grant 7746/2011). AM acknowledges support through NSF grant AST-1715356. We thank University of Ferrara and INFN–Ferrara for the access to the COKA GPU cluster. Development of the Boxfit code was supported in part by NASA through grant NNX10AF62G issued through the Astrophysics Theory Program and by the NSF through grant AST-1009863. The Berger Time-Domain Group at Harvard is supported in part by the NSF through grants AST-1411763 and AST-1714498, and by NASA through grants NNX15AE50G and NNX16AC22G. Simulations for BOXFITv2 have been carried out in part on the computing facilities of the Computational Center for Particle and Astrophysics of the research cooperation “Excellence Cluster Universe” in Garching, Germany. This research was supported in part through the computational resources and staff contributions provided for the Quest high performance computing facility at Northwestern University which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology. We gratefully acknowledge Piero Rosati for granting us usage of proprietary HPC facility. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.


  • Abbott et al. (2017) Abbott, B. P., et al. 2017, Physical Review Letters, 119, 161101
  • Achterberg et al. (2001) Achterberg, A., Gallant, Y. A., Kirk, J. G., & Guthmann, A. W. 2001, MNRAS, 328, 393
  • Alexander et al. (2017) Alexander, K. D., et al. 2017, ApJ, 848, L21
  • Aloy et al. (2005) Aloy, M. A., Janka, H.-T., & Müller, E. 2005, A&A, 436, 273
  • Bell (1978) Bell, A. R. 1978, MNRAS, 182, 147
  • Berger (2014) Berger, E. 2014, ARA&A, 52, 43
  • Blandford & Eichler (1987) Blandford, R., & Eichler, D. 1987, Phys. Rep., 154, 1
  • Blandford & Ostriker (1978) Blandford, R. D., & Ostriker, J. P. 1978, ApJ, 221, L29
  • Chang et al. (2008) Chang, P., Spitkovsky, A., & Arons, J. 2008, ApJ, 674, 378
  • Chornock et al. (2017) Chornock, R., et al. 2017, ApJ, 848, L19
  • Coulter et al. (2017) Coulter, D. A., et al. 2017, ArXiv e-prints, arXiv:1710.05452
  • Cowperthwaite et al. (2017) Cowperthwaite, P. S., et al. 2017, ApJ, 848, L17
  • Drout et al. (2017) Drout, M. R., et al. 2017, ArXiv e-prints, arXiv:1710.05443
  • Duffell & MacFadyen (2013) Duffell, P. C., & MacFadyen, A. I. 2013, ApJ, 775, 87
  • Duffell et al. (2015) Duffell, P. C., Quataert, E., & MacFadyen, A. I. 2015, ApJ, 813, 64
  • Fong et al. (2017) Fong, W., et al. 2017, ApJ, 848, L23
  • Fong et al. (2015) Fong, W., Berger, E., Margutti, R., & Zauderer, B. A. 2015, ApJ, 815, 102
  • Fong et al. (2016) Fong, W., Metzger, B. D., Berger, E., & Özel, F. 2016, ApJ, 831, 141
  • Fraija et al. (2017) Fraija, N., De Colle, F., Veres, P., Dichiara, S., Barniol Duran, R., & Galvan-Gamez, A. 2017, ArXiv e-prints, arXiv:1710.08514
  • Goldstein et al. (2017) Goldstein, A., et al. 2017, ApJ, 848, L14
  • Gottlieb et al. (2018) Gottlieb, O., Nakar, E., & Piran, T. 2018, MNRAS, 473, 576
  • Gottlieb et al. (2017) Gottlieb, O., Nakar, E., Piran, T., & Hotokezaka, K. 2017, ArXiv e-prints, arXiv:1710.05896
  • Granot et al. (2017) Granot, J., Gill, R., Guetta, D., & De Colle, F. 2017, ArXiv e-prints, arXiv:1710.06421
  • Granot et al. (2002) Granot, J., Panaitescu, A., Kumar, P., & Woosley, S. E. 2002, ApJ, 570, L61
  • Granot & Sari (2002) Granot, J., & Sari, R. 2002, ApJ, 568, 820
  • Guidorzi et al. (2017) Guidorzi, C., et al. 2017, ApJ, 851, L36
  • Haggard et al. (2017) Haggard, D., Nynka, M., Ruan, J. J., Kalogera, V., Cenko, S. B., Evans, P., & Kennea, J. A. 2017, ApJ, 848, L25
  • Haggard et al. (2017) Haggard et al. 2017, GRB Coordinates Network, 22206
  • Hallinan et al. (2017) Hallinan, G., et al. 2017, ArXiv e-prints, arXiv:1710.05435
  • Haugbølle (2011) Haugbølle, T. 2011, ApJ, 739, L42
  • Jin et al. (2017) Jin, Z.-P., et al. 2017, ArXiv e-prints, arXiv:1708.07008
  • Kalberla et al. (2005) Kalberla, P. M. W., Burton, W. B., Hartmann, D., Arnal, E. M., Bajaja, E., Morras, R., & Pöppel, W. G. L. 2005, A&A, 440, 775
  • Kasliwal et al. (2017) Kasliwal, M. M., et al. 2017, ArXiv e-prints, arXiv:1710.05436
  • Kathirgamaraju et al. (2018) Kathirgamaraju, A., Barniol Duran, R., & Giannios, D. 2018, MNRAS, 473, L121
  • Keshet et al. (2009) Keshet, U., Katz, B., Spitkovsky, A., & Waxman, E. 2009, ApJ, 693, L127
  • Keshet & Waxman (2005) Keshet, U., & Waxman, E. 2005, Physical Review Letters, 94, 111102
  • Kim et al. (2017) Kim, S., et al. 2017, ApJ, 850, L21
  • Kirk et al. (2000) Kirk, J. G., Guthmann, A. W., Gallant, Y. A., & Achterberg, A. 2000, ApJ, 542, 235
  • Lamb & Kobayashi (2017) Lamb, G. P., & Kobayashi, S. 2017, MNRAS, 472, 4953
  • Lazzati et al. (2017a) Lazzati, D., Deich, A., Morsony, B. J., & Workman, J. C. 2017a, MNRAS, 471, 1652
  • Lazzati et al. (2017b) Lazzati, D., López-Cámara, D., Cantiello, M., Morsony, B. J., Perna, R., & Workman, J. C. 2017b, ApJ, 848, L6
  • Lazzati et al. (2017c) Lazzati, D., Perna, R., Morsony, B. J., López-Cámara, D., Cantiello, M., & Workman, J. C. 2017c, ArXiv e-prints, arXiv:1712.03237
  • Lemoine (2013) Lemoine, M. 2013, MNRAS, 428, 845
  • Lemoine et al. (2013) Lemoine, M., Li, Z., & Wang, X.-Y. 2013, MNRAS, 435, 3009
  • Lyman et al. (2018) Lyman, J. D., et al. 2018, ArXiv e-prints
  • Margalit & Metzger (2017) Margalit, B., & Metzger, B. D. 2017, ApJ, 850, L19
  • Margutti et al. (2017a) Margutti, R., et al. 2017a, ApJ, 848, L20
  • Margutti et al. (2017b) Margutti, R., Fong, W., Eftekhari, T., Alexander, K., Berger, E., & Chornock, R. 2017b, The Astronomer’s Telegram, 11037
  • Margutti et al. (2017) Margutti et al. 2017, Atel, 11037
  • Martins et al. (2009) Martins, S. F., Fonseca, R. A., Silva, L. O., & Mori, W. B. 2009, ApJ, 695, L189
  • McMullin et al. (2007) McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 376, Astronomical Data Analysis Software and Systems XVI, ed. R. A. Shaw, F. Hill, & D. J. Bell, 127
  • Metzger (2017) Metzger, B. D. 2017, Living Reviews in Relativity, 20, 3
  • Metzger et al. (2010) Metzger, B. D., Arcones, A., Quataert, E., & Martínez-Pinedo, G. 2010, MNRAS, 402, 2771
  • Metzger & Fernández (2014) Metzger, B. D., & Fernández, R. 2014, MNRAS, 441, 3444
  • Metzger & Piro (2014) Metzger, B. D., & Piro, A. L. 2014, MNRAS, 439, 3916
  • Mooley et al. (2017) Mooley, K. P., et al. 2017, ArXiv e-prints, arXiv:1711.11573
  • Murguia-Berthier et al. (2017) Murguia-Berthier, A., et al. 2017, ApJ, 848, L34
  • Nicholl et al. (2017) Nicholl, M., et al. 2017, ApJ, 848, L18
  • Peng et al. (2010) Peng, C. Y., Ho, L. C., Impey, C. D., & Rix, H.-W. 2010, AJ, 139, 2097
  • Pian et al. (2017) Pian, E., et al. 2017, Nature, 551, 67
  • Pooley et al. (2017) Pooley, D., Kumar, P., & Wheeler, J. C. 2017, ArXiv e-prints, arXiv:1712.03240
  • Rossi & Rees (2003) Rossi, E., & Rees, M. J. 2003, MNRAS, 339, 881
  • Rosswog (2007) Rosswog, S. 2007, MNRAS, 376, L48
  • Ruan et al. (2017) Ruan, J. J., Nynka, M., Haggard, D., Kalogera, V., & Evans, P. 2017, ArXiv e-prints, arXiv:1712.02809
  • Salafia et al. (2017) Salafia, O. S., Ghisellini, G., Ghirlanda, G., & Colpi, M. 2017, ArXiv e-prints, arXiv:1711.03112
  • Sari et al. (1998) Sari, R., Piran, T., & Narayan, R. 1998, ApJ, 497, L17
  • Savchenko et al. (2017) Savchenko, V., et al. 2017, ApJ, 848, L15
  • Sironi & Spitkovsky (2009) Sironi, L., & Spitkovsky, A. 2009, ApJ, 707, L92
  • Sironi et al. (2013) Sironi, L., Spitkovsky, A., & Arons, J. 2013, ApJ, 771, 54
  • Smartt et al. (2017) Smartt, S. J., et al. 2017, Nature, 551, 75
  • Soares-Santos et al. (2017) Soares-Santos, M., et al. 2017, ApJ, 848, L16
  • Spitkovsky (2008) Spitkovsky, A. 2008, ApJ, 673, L39
  • Tanvir et al. (2017) Tanvir, N. R., et al. 2017, ApJ, 848, L27
  • Troja et al. (2017a) Troja, E., Piro, L., Ryan, G., van Eeerten, H., Sakamoto, T., & Cenko, S. B. 2017a, GCN, 22201
  • Troja et al. (2017b) Troja, E., et al. 2017b, Nature, 551, 71
  • Valenti et al. (2017) Valenti, S., et al. 2017, ApJ, 848, L24
  • van Eerten et al. (2012) van Eerten, H., van der Horst, A., & MacFadyen, A. 2012, ApJ, 749, 44
  • Villar et al. (2017) Villar, V. A., et al. 2017, ArXiv e-prints, arXiv:1710.11576
  • Williams et al. (2017) Williams, P. K. G., Clavel, M., Newton, E., & Ryzhkov, D. 2017, pwkit: Astronomical utilities in Python, Astrophysics Source Code Library, ascl:1704.001
  • Zakine & Lemoine (2017) Zakine, R., & Lemoine, M. 2017, A&A, 601, A64
Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
Add comment
Loading ...
This is a comment super asjknd jkasnjk adsnkj
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test description