Probing the Magnetic Field in the GW170817 Outflow Using H.E.S.S. Observations

The gravitational-wave (GW) event detected on 2017 August 17 by the advanced LIGO and Virgo detectors resulted from the merger of two neutron stars (NSs). The GW signal was followed after ∼2 s by a short, low-luminosity γがんま-ray burst (GRB) and seen by the Fermi-GBM (Goldstein et al. 2017) and International Gamma-Ray Astrophysics Laboratory-Space Platform Interferometry (Savchenko et al. 2017) instruments. Observations in the optical band later associated this GRB (GRB 170817A) as the counterpart of GW170817 and localized it to the host galaxy NGC 4993 (Coulter et al. 2017). The fading UV, optical, and infrared radiation was followed by a rising nonthermal radio and X-ray signal after ∼9 days (Troja et al. 2017). This behavior, as predicted by Takami et al. (2014), is indicative of efficient particle acceleration in the NS merger remnant and subsequent synchrotron emission of accelerated electrons in the ejecta's magnetic field.

After ∼160 days, the synchrotron radiation started to plateau and later fade (Figure 1). This is similar to the behavior of a young supernova remnant, and suggests that the ejecta is transitioning from the free expansion to the Sedov–Taylor phase when the ejected mass of the merger remnant equals the swept-up circumstellar material.

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Rodrigues et al. (2019) infer a total kinetic energy in the ejecta of 10⁵¹ erg, implying a total number of electrons in the remnant of 10⁵⁵. Accelerated electrons should also scatter off the intense radio and X-ray synchrotron radiation field and produce synchrotron self-Compton (SSC) emission. The expected peak energy of the SSC component depends on the maximum accelerated electron energy as probed by the X-rays. While the radio to X-ray emission probes the product of energy in electrons, u_e, and energy in magnetic fields, u_B, the SSC component is proportional to ${u}_{e}^{2}\cdot {u}_{B}$. As shown by Takami et al. (2014) and Rodrigues et al. (2019), observations in the γがんま-ray regime can break the ambiguity between u_B and u_e and provide crucial insight into the magnetic field in the ejecta as well as the maximum accelerated particle energy.

In this work, we present deep H.E.S.S. observations of GW170817/GRB 170817A covering the peak and onset of fading in the X-ray and radio lightcurves from 124 to 272 days after the merger. This measurement is accompanied by an improved analysis of the H.E.S.S. data taken on the early (up to 5 day) kilonova. In the next section we present the H.E.S.S. data set and results, followed by a discussion on the implied magnetic field strength in a non-relativistic kilonova scenario and a relativistic jet scenario. Throughout this work we adopt a distance to the host galaxy NGC 4993 of 41.0 Mpc, corresponding to a redshift of z = 0.009727 (Hjorth et al. 2017).⁴³

The data set was obtained from observations with the H.E.S.S. phase II array, including the upgraded 12 m diameter CT1-4 telescopes (Ashton et al. 2020) and the large 28 m diameter CT5 telescope. The analysis presented by Abdalla et al. (2017) used monoscopic data of the 28 m telescope obtained between 5.3 hr and 5.3 days after the binary neutron star (BNS) merger. Here we extend this analysis to also include data taken with CT1-4. Observations from 2017 December to 2018 May with telescopes pointing 05 offset from GW170817 were conducted allowing for simultaneous estimation of the background level in the signal region as discussed below. The different data sets are summarized in Table 1. A standard data quality selection is applied to the data (Aharonian et al. 2006; H.E.S.S. Collaboration et al. 2017). The events have been selected and their direction and energy reconstructed using a Monte Carlo, template-based, shower model technique (Parsons & Hinton 2014), requiring at least two telescope to see the same γがんま-ray event. With this method, an energy resolution of ∼10% and angular resolution (at 68% containment radius) of 008 above γがんま-ray energies of 200 GeV is achieved. The resulting energy threshold of data set III is E_th = 130 GeV. We define a circular region-of-interest centered on the optical position of GW170817 (Coulter et al. 2017) with a radius of 009 for data sets II and III—hereafter referred to as the ON region. Ten to twenty background control regions (OFF regions) are defined radially symmetric with respect to the telescope pointing position for each observation (Fomin et al. 1994). This technique assures that the γがんま-ray signal and background are estimated with the same acceptance and under the same observation conditions. No significant γがんま-ray excess above the expected background is detected from the direction of GW170817 in any data set. A second analysis using an independent event calibration and reconstruction (de Naurois & Rolland 2009) confirms the result. A search for significant emission on monthly timescales also does not reveal any signal. For the total data set, 95% confidence level (C.L.) upper limits on the photon flux are derived using the method described by Rolke et al. (2005) and assuming an underlying power-law spectral index of the γがんま-ray emission of αあるふぁ = −2.0 (see Rodrigues et al. 2019). Note that systematic errors are subdominant compared to statistical uncertainties when deriving upper limits, and are hence not considered here. All results are summarized in Table 1.

Table 1.  Properties of the H.E.S.S. Data Sets on GW170817/GRB 170817A and Analysis Results

Data Set	Configuration	T − T0	Exposure	Energy Range	F( > Eth)	$F(1\mbox{--}10\,\mathrm{TeV})$	Zenith Angle	Reference
		(days)	(hr)	(TeV)	(erg cm−2 s−1)	(erg cm−2 s−1)	(deg)
I	CT 5	0.22–5.23	3.2	0.27–8.55	<1.5 × 10−12	⋯	58	Abdalla et al. (2017)
II	CT 1–5	0.22–5.23	3.2	0.56–17.8	<4.7 × 10−12	<2.8 × 10−12	58	This work
III	CT 1–5	124–272	53.9	0.13–23.7	<1.6 × 10−12	<3.2 × 10−13	24	This work

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Figure 1 depicts the radio and X-ray flux measurements along with the inferred H.E.S.S. energy flux upper limits in the 1–10 TeV energy range for data sets II and III. Figure 2 shows the inferred energy flux upper limits at the 95% C.L. in the VHE γがんま-ray range from GRB 170817A for data set III, which has the best sensitivity at TeV energies. In the next section we discuss how the H.E.S.S. results constrain the magnetic field in the GW170817 ejecta in a jet and in a kilonova scenario.

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Recent detections of VHE emission from GRBs over minutes (Mirzoyan 2019) and hours (de Naurois 2019) motivate the search for very late time emission from GRB-related events, like the remnant of GW170817. The H.E.S.S. differential upper limits can be translated into an integral energy flux limit, for a given assumption on the spectrum of the radiating particles. In turn, this limit provides a constraint on the magnetic field strength under the assumption of one-zone synchrotron emission with corresponding inverse Compton (IC) emission.

Observational evidence suggests that at early times, the kilonova provides the dominant target radiation field in the remnant (Villar et al. 2017). However, the decay of this component, whose flux falls steeply with t^−2.3, results in a late-time dominance of the synchrotron radiation in the source. It is therefore naturally expected that at late times SSC will dominate the remnant's IC emission.

The measured X-ray flux of the source can be used to infer the X-ray luminosity emitted as synchrotron radiation, L_X. In order to consistently model the emission from this electron population, a geometry assumption is necessary. We consider two scenarios: one where the remnant expands isotropically and non-relativistically, and the other where a relativistic jet is launched.

In the isotropic scenario, we assume a volume-filled spherical emitter with radius R_iso = βべーたcΔでるたt, where Δでるたt = 110 days is the time since the merger.⁴⁴ Based on photospheric velocity measurements of the remnant (Piro & Kollmeier 2018), we consider a value of the expansion speed of βべーた = 0.2.

In the relativistic scenario, we consider a jet with speed βべーた = 0.94 (corresponding to a Lorentz factor of Γがんま = 3) at late times, and a jet opening angle⁴⁵ of ${\theta }_{\mathrm{jet}}^{{\prime} }=5^\circ$, observed at an angle of ${\theta }_{\mathrm{obs}}=20^\circ \approx 180^\circ /\pi {\rm{\Gamma }}$ from the jet axis; the source is therefore observed with a Doppler factor δでるた = Γがんま = 3. These parameter values are motivated by radio observations of superluminal motion of the source (Mooley et al. 2018). Furthermore, from a purely theoretical standpoint, this value of the Lorentz factor is expected at ∼100 day timescales, considering the energy transfer from the shock into a surrounding medium of constant density (Rees & Meszaros 1992). The emitting region is assumed to be a spherical blob at the front edge of the jet, whose radius is therefore given by ${R}_{\mathrm{blob}}^{{\prime} }\approx \delta \beta c{\rm{\Delta }}t{\theta }_{\mathrm{jet}}^{{\prime} }$.

The maximum energy of the emitted synchrotron radiation is fixed by X-ray observations, E_X ≈ 10 keV (Nynka et al. 2018). This is related to the magnetic field strength in the source, B', and the maximum electron energy of the emitting electrons, ${E}_{e}^{{\prime} }={\delta }^{-1}{E}_{e}$, through ${E}_{{\rm{X}}}^{{\prime} }\propto {E}_{e}^{{\prime} 2}{B}^{{\prime} }$. This means that in the relativistic scenario, for a given value of B', the maximum energy of the emitting electrons scales as ${E}_{e}^{{\prime} }\propto {\delta }^{-0.5}$. Furthermore, since the jet blob emits isotropically in its own rest frame, the X-ray luminosity, obtained assuming the observed emission is isotropic, ${L}_{X}^{\mathrm{iso}}$ deduced from flux measurements relates to the luminosity in the rest frame of the blob ${L}_{X}^{{\prime} }$ through ${L}_{{\rm{X}}}^{\mathrm{iso}}={\delta }^{4}{L}_{X}^{{\prime} }$. This luminosity relates to the total number of X-ray-emitting electrons, ${N}_{e}^{{\prime} }$, as well as ${E}_{e}^{{\prime} }$ and ${B}^{{\prime} }$, through ${L}_{{\rm{X}}}^{{\prime} }={N}_{e}^{{\prime} }{E}_{e}^{{\prime} }/{\tau }_{\mathrm{syn}}^{{\prime} }({E}_{e}^{{\prime} })\propto {N}_{e}^{{\prime} }{E}_{e}^{{\prime} 2}{B}^{{\prime} 2}$, where ${\tau }_{\mathrm{syn}}^{{\prime} }({E}_{e}^{{\prime} })$ is the synchrotron cooling timescale. Therefore, in the relativistic jet scenario, for a given value of B' and measured X-ray flux, the number of electrons scales as ${N}_{e}^{{\prime} }\propto {\delta }^{-3}$. This will affect the results of the SSC model, since for higher values of δでるた there will be fewer emitting electrons, and a lower density of synchrotron photons, thus reducing the expected γがんま-ray flux.

The γがんま-ray luminosity expected from SSC is given in the shock rest frame by ${L}_{\mathrm{IC}}^{{\prime} }={N}_{e}^{{\prime} }{E}_{e}^{{\prime} }/{\tau }_{\mathrm{IC}}^{{\prime} }({E}_{e}^{{\prime} })\propto {N}_{e}^{{\prime} }({L}_{{\rm{X}}}^{{\prime} }/(4\pi {R}^{{\prime} 2}c)){E}_{e}^{{\prime} 0.5}$, where ${\tau }_{\mathrm{IC}}^{{\prime} }({E}_{e}^{{\prime} })$ is the IC cooling timescale, and R^' is the size of the emitting region (either ${R}_{\mathrm{blob}}^{{\prime} }$ or ${R}_{\mathrm{iso}}^{{\prime} }$, defined above). The approximate scaling with ${E}_{e}^{{\prime} 0.5}$ is due to the fact that the IC cooling occurs deep in the Klein–Nishina regime (since the observed synchrotron spectrum peaks at X-ray energies and the Lorentz factor of the ejecta is mild). Putting together the scalings given previously, we obtain that for a given value of ${B}^{{\prime} }$, the IC emission for the relativistic jet scenario scales as ${L}_{{IC}}^{{\prime} }\,\propto {\theta }_{\mathrm{jet}}^{{\prime} -2}{(\beta {\rm{\Delta }}t)}^{-2}{\delta }^{-9.25}$ in the shock rest frame, which corresponds to a luminosity in the observer's frame of

$$\begin{eqnarray}&&{L}_{\mathrm{IC}}\approx {10}^{46}{\left(\displaystyle \frac{{\theta }_{\mathrm{jet}}^{{\prime} }}{5^\circ }\right)}^{-2}{\left(\displaystyle \frac{\beta {\rm{\Delta }}t}{0.94\times 110\mathrm{days}}\right)}^{-2}{\left(\displaystyle \frac{\delta }{3}\right)}^{-5.25}\,\mathrm{erg}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 1 }$$

Thus, a slower expansion of the emission region would lead to a more compact source and therefore a stronger constraint on the magnetic field strength (both in the jet-like and isotropic scenarios).

In Figure 2 we show the modeled synchrotron emission spectrum (black curves) and the respective SSC emission for both scenarios introduced above. These spectra were obtained with a numerical radiation model, introduced by Rodrigues et al. (2019). In this model, a population of electrons is considered to fill homogeneously the emission region, and to be continuously accelerated to a power-law spectrum, with a possible cutoff at the highest energies. As can be seen in Figure 2, these characteristics can explain radio (red points) and X-ray observations (blue points and blue shaded region). The parameters of the electron population have then been adjusted, and the magnetic field strength minimized, so that the predicted SSC emission does not exceed any of the 95% C.L. upper limits in the VHE γがんま-ray range derived from the H.E.S.S. observations (green). The solid versus dashed curves represent the two extreme cases consistent with the observed X-ray and radio fluxes. In the non-relativistic scenario, the H.E.S.S. limits can constrain the minimum magnetic field strength to ≳210 μみゅーG. In contrast, in more highly relativistic scenarios, the lower limit is weakened to the level of ≳24 μみゅーG. The reason is that the strong scaling of the SSC flux with the Doppler factor (Equation (1)) implies that for a more relativistic outflow, a higher electron number is necessary to reach the flux limits, which implies a lower magnetic field in order to maintain the X-ray flux.

As a point of comparison with the lower limit obtained through this analysis, the minimum magnetic field expected at late times downstream of the shock is of the order of $\sim 100({\rm{\Gamma }}/3)({B}_{\mathrm{ISM}}/10\,\mu {\rm{G}})\,\mu {\rm{G}}$ (Kumar et al. 2012), where B_ISM is the magnetic field strength in the interstellar medium (ISM). Furthermore, observations of the prompt emission of GRB 080916C by Fermi-LAT and 1 day afterglow emission in X-rays and optical wavelengths have provided evidence of magnetic fields in the shock that are at the level of the compressed surrounding medium (Kumar & Duran 2009), thus suggesting an ISM magnetic field of $\sim 10\,\mu {\rm{G}}$.

Very-high-energy γがんま-ray observations can provide a direct probe of the magnetic field in BNS merger remnants. While the radio and X-ray data constrain the synchrotron part of the nonthermal spectrum, a measurement of the IC component in γがんま-rays is needed to break the ambiguity between energy in electrons and magnetic fields. Interferometric radio observations and long-term X-ray observations are crucial for inferring the jet properties such as the opening angle, viewing angle, or the Doppler factor. Based on the GW170817/GRB 170817A characteristics, one other short GRB may have been seen off-axis (GRB 150101B; Troja et al. 2018). Long-term monitoring of BNS mergers in the radio, X-ray, and γがんま-ray domain is necessary to further constrain the source properties and bridge the gap between the early-time kilonova and nonthermal GRB emission on the one hand, and the long-term behavior and the interaction between the jet and the ISM on the other hand. Current-generation Imaging Atmospheric Cerenkov Telescopes such as H.E.S.S., MAGIC, or VERITAS can search for and study γがんま-ray counterparts on days-to-month timescales for BNS merger remnants seen under different viewing angles. Furthermore, the future Cerenkov Telescope Array (CTA) will be an order of magnitude more sensitive at around 1 TeV, allowing us to constrain the minimum magnetic field in events like GW170817/GRB 170817A to the mG regime. This will allow CTA to detect VHE γがんま-ray emission from events such as GW170817. As noted previously by Rodrigues et al. (2019), future observations may also be able to better constrain the nature of the nonthermal electrons. One possibility is that the observed radiation is dominated by "fresh" electrons picked up from the surroundings of the merger and accelerated at the shock front, allowing for hard photon spectra into the gamma-ray range. In a different scenario, the emission might originate in "old" electrons, continuously accelerated inside the volume of the ejecta, leading to cooling features at high energies.

The support of the Namibian authorities and of the University of Namibia in facilitating the construction and operation of H.E.S.S. is gratefully acknowledged, as is the support by the German Ministry for Education and Research (BMBF), the Max Planck Society, the German Research Foundation (DFG), the Helmholtz Association, the Alexander von Humboldt Foundation, the French Ministry of Higher Education, Research and Innovation, the Centre National de la Recherche Scientifique (CNRS/IN2P3 and CNRS/INSU), the Commissariat à l'Énergie atomique et aux Énergies alternatives (CEA), the U.K. Science and Technology Facilities Council (STFC), the Knut and Alice Wallenberg Foundation, the National Science Centre, Poland grant No. 2016/22/M/ST9/00382, the South African Department of Science and Technology and National Research Foundation, the University of Namibia, the National Commission on Research, Science & Technology of Namibia (NCRST), the Austrian Federal Ministry of Education, Science and Research and the Austrian Science Fund (FWF), the Australian Research Council (ARC), the Japan Society for the Promotion of Science and by the University of Amsterdam. We appreciate the excellent work of the technical support staff in Berlin, Zeuthen, Heidelberg, Palaiseau, Paris, Saclay, Tübingen, and in Namibia in the construction and operation of the equipment. This work benefited from services provided by the H.E.S.S. Virtual Organization, supported by the national resource providers of the EGI Federation. X.R. was supported by the Initiative and Networking Fund of the Helmholtz Association.