of 41
A mildly relativistic wide­angle outflow in the neutron star
merger GW170817
K. P. Mooley (1,2,3,19), E. Nakar (4), K. Hotokezaka (5), G. Hallinan (3), A. Corsi (6), D.A.
Frail (2), A. Horesh (7), T. Murphy (8,9), E. Lenc (8,9), D.L. Kaplan (10), K. De (3), D.
Dobie (8,9,11), P. Chandra (12,13), A. Deller (14), O. Gottlieb (4), M.M. Kasliwal (3), S. R.
Kulkarni (3), S.T. Myers (2), S. Nissanke (15), T. Piran (7), C. Lynch (8,9), V. Bhalerao
(16), S. Bourke (17), K.W. Bannister (11), L.P. Singer (18) (Affiliaitions: (1) Hintze Fellow.
Oxford, (2) NRAO, (3) Caltech, (4) Tel Aviv University, (5) Princeton University, (6) Texas
Tech University, (7) The Hebrew University of Jerusalem, (8) University of Sydney, (9)
CAASTRO, (10) University of Wisconsin ­ Milwaukee, (11) ATNF, CSIRO, (12) NCRA, (13)
Stockholm University, (14) Swinburne University of Technology, (15) Radboud University,
(16) IIT Bombay, (17) Chalmers University of Technology, (18) NASA GSFC, (19) Jansky
Fellow, NRAO/Caltech)
GW170817 is the first gravitational wave detection of a binary neutron star merger
1
.
It was accompanied by radiation across the electromagnetic spectrum and
localized
2
to the galaxy NGC 4993 at a distance of 40 Mpc. It has been proposed that
the observed gamma­ray, X­ray and radio emission is due to an ultra­relativistic jet
launched during the merger, directed away from our line of sight
3,4,5,6
. The presence
of such a jet is predicted from models positing neutron star mergers as the central
engines driving short­hard gamma­ray bursts
7,8
(SGRBs). Here we show that the
radio light curve of GW170817 has no direct signature of an off­axis jet afterglow.
While we cannot rule out the existence of a jet pointing elsewhere, the observed
gamma­rays could not have originated from such a jet. Instead, the radio data
requires a mildly relativistic wide­angle outflow moving towards us. This outflow
could be the high velocity tail of the neutron­rich material dynamically ejected
during the merger or a cocoon of material that breaks out when a jet transfers its
energy to the dynamical ejecta. The cocoon scenario can explain the radio light
curve of GW170817 as well as the gamma­rays and X­rays (possibly also ultraviolet
and optical emission)
9,10,11,12,13,14,15
, and hence is the model most consistent with the
observational data. Cocoons may be a ubiquitous phenomenon produced in
neutron star mergers, giving rise to a heretofore unidentified population of radio,
ultraviolet, X­ray and gamma­ray transients in the local universe.
The radio discovery
12
of GW170817, as well as observations within the first month post­
merger, were interpreted in the framework of classical off­axis jet, cocoon, and dynamical
ejecta. We continued to observe GW170817 with the Karl G. Jansky Very Large Array
(VLA), the Australia Telescope Compact Array (ATCA) and the upgraded Giant Metrewave
Radio Telescope (uGMRT), spanning the frequency range 0.6­18 GHz, whilst optical and
X­ray telescopes were constrained by proximity to the Sun. Our radio detections span up
to 107 days post­merger (Figure 1 and Methods). These data show a steady rise in the
radio light curve and a spectrum consistent with optically­thin synchrotron emission. A joint
temporal and spectral power­law fit to these data of the form S
∝ν
ɑ
t
δ
, is well­described by
a spectral index =­0.6 and a temporal index
ɑ
δ
=+0.8 (see Methods). On 2017 November
18 (93 days post­merger) the peak luminosity at 1.6 GHz was 2 x 10
27
erg s
­1
Hz
­1
, a
luminosity undetectable for even the nearest SGRB afterglow discovered to date
16
.
The (sub­luminous) gamma­ray emission detected immediately after the gravitational wave
detection
17
must have been emitted by a relativistic outflow
14
, but an on­axis jet (scenario A
in Figure 2) was ruled out by the late turn­on of the X­ray and radio emission
3,4,5,6,11,12,13
. If
GW170817 produced a regular (luminous) SGRB pointing away from us, then the
interaction of the jet with the circum­merger medium would have decelerated the jet, and
the afterglow emission would have eventually entered into our line of sight, thus producing
a so­called off­axis afterglow
18,19
. For this geometry, the light curve rises sharply and peaks
when the jet Lorentz factor ~ 1/(
ɣθ
obs
­
θ
j
), and then undergoes a power law decline (
θ
obs
is
the angle between the jet axis and the line of sight, and
θ
j
is the jet opening angle). This
behavior is clearly inconsistent with the full light curve shown in Figure 1. The rise is less
steep than an off­axis jet and it is consistent with a monotonic increase without either a
plateau or a subsequent decay. Initial off­axis models (based on available X­ray and radio
data at the time) predicted a radio flux density
3,4,5,12
of ~10
μ
Jy (between 3 GHz and 10
GHz) ~100 days post­merger, while our measured values are at least a factor of five
larger. The discrepancy with the off­axis jet model is further demonstrated in Figure 3
where various jet and medium parameters are considered, showing in all cases a similar
general light curve shape which cannot fit the data. We have considered a wide range in
the phase space of off­axis models, and can rule out an off­axis jet (scenario B in Figure 2)
as the origin of the radio afterglow of GW170817. We show below that even if we consider
a “structured jet”, in which the outflow has an angular dependence of the Lorentz factor
and energy (scenario E in Figure 2 represents one such configuration), the observed
radiation arises predominantly from a mildly relativistic outflow moving towards us (at an
angle less than 1/ ), and we do not detect the observational signature of a relativistic core
ɣ
within the structured jet.
With a highly collimated off­axis jet ruled out, we next consider spherical or quasi­spherical
ejecta components. A single spherical shell of expanding ejecta will produce a light curve
that rises as S ~ t
3
. The light curve of GW170817 immediately rules out such a simple
single­velocity ejecta model. The gradual but monotonic rise seen in our radio data (S
∝
t
0.8
; Figure 1
) points instead to
on­axis
emission from a mildly relativistic blast wave where
the energy is increasing with time (due to more mass residing in slower ejecta, which is
seen at later times). For example, using canonical microphysical parameters (
ε
B
=0.01,
ε
e
=0.1), a density of 10
­4
cm
­3
implies that between day 16 to day 107 the blast wave
decelerates from ~3.5 to ~2.5 and its isotropic equivalent energy increases from ~10
ɣɣ
49
erg to ~10
50
erg. On the other hand, a density of 0.01 cm
­3
implies a velocity range of 0.8c
to 0.65c and energy that rises from 10
48
erg to 10
49
erg. Figure 4 shows that a quasi­
spherical outflow with a velocity profile E(>
) (
)
βɣ∝βɣ
­5
provides an excellent fit to the data
(see Methods), and it is almost independent of the assumed circum­merger density and
microphysical parameters. The energy injection into the blast wave during the time span of
the observations (day 16 to day 107) increases its energy by a factor of ~10. The possible
origin of the outflow depends on its energy and velocity. A faster and more energetic
outflow, with ~2­3 and energy of 10
ɣ
49
­10
50
erg, is a natural outcome of the cocoon driven
by a wide­angle choked jet
9,11,14
(scenario C in Figure 2). This scenario explains many of
the puzzling characteristics of GW170817. First, the breakout of the cocoon from the
ejecta can produce the observed sub­luminous gamma­ray signal, including its peak
energy and spectral evolution
14
(see also Methods). Second, it provides a natural
explanation for the high velocities of the bulk of the ejecta (~0.3c) and for the early bright
UV and optical light
11,13,15
. On the other hand, a slower and less energetic outflow, with
0.8­0.6 ( ~1.67­1.25) and energy of 10
β≈ɣ
48
­10
49
erg can arise from the fast tail of the
merger ejecta
20,21,22
(scenario D in Figure 2), although we note that this component cannot
explain the gamma­ray signal (GRB 170817A) from GW170817. These two scenarios can
be easily distinguished by Very Long Baseline Interferometry or monitoring of the radio
evolution on ~years timescale.
A
hidden
jet, which does not contribute significantly to the observed afterglow, may still
exist (scenario E in Figure 2), but its properties are tightly constrained. First, its edge must
be far enough from the line­of­sight ( 10 degrees), which rules out off­axis gamma­ray
≳
emission as the source of GRB 170817A. Second, for every reasonable set of parameters,
an off­axis jet would have been brighter than the fast tail of the ejecta, implying that the
observed emission must be dominated by a ~2­3 outflow (i.e. a cocoon) for the jet to
ɣ
remain undetected. In addition, the jet energy should, most likely, be much lower than that
of the cocoon, which needs fine­tuning of the jet properties (see Methods). We therefore
conclude from the lack of a signature from an off­axis jet, that the jet was likely choked
(scenario C in Figure 2).
We compared the 3 GHz radio and X­ray
4,5,6
detections obtained on 2017 September 02­
03 (15­16 days post­merger). The measurements at these two disparate frequencies imply
a spectral index of ­0.6, consistent with our multi­epoch, multi­frequency, radio­only
measurements (see Methods and Extended Data Figure 4). It is therefore likely that the
radio and X­rays originate from the same (synchrotron) source, viz. a mildly relativistic
outflow. This common origin can be confirmed if the X­ray flux continues to rise in a similar
manner as the radio. We also highlight that, while at early times the cooling break will lie
well above the soft X­ray frequencies, beyond ~10
2
­10
3
days post­merger this break may
be seen moving downwards in frequency within the electromagnetic spectrum. If the
cooling break stays above 10
18
Hz, the common origin of the radio and X­rays implies that
the Chandra telescope will detect a brighter X­ray source (flux between 0.7x10
­14
and
5.2x10
­14
erg cm
­2
s
­1
in the 0.3­10 keV band
; see Methods) during its observation of
GW170817 on December 03­06 (
note: subsequent to the submission of this paper, the X­
ray observations took place and confirmed our prediction
). If a different spectral index is
derived from these X­ray observations relative to the in­band radio spectral index
presented here, or indeed at any time within ~1000 days of the merger, it will indicate that
the cooling break has already shifted below the X­ray band, which would favor the fast tail
of the merger ejecta as the common source of the X­ray and radio emission (see
Methods).
The confirmation of a wide­angle outflow in GW170817 bodes well for electromagnetic
counterpart searches of future gravitational wave events. Although on­axis (and slightly
off­axis;
θ
obs
<20 degrees) jets produce bright panchromatic afterglows, they represent only
a small fraction (~10%) of the gravitational wave events
(factoring in the larger detectable
distance for face­on events
23
). In contrast, the emission from wide­angle cocoons
9,10,11
will
be potentially seen in a much larger fraction of events, and at virtually all wavelengths,
thus increasing the probability of the detection of electromagnetic counterparts. The radio
emission from the cocoon, evolving on timescales of weeks to months, especially provides
a distinct signature (as opposed to the more common supernovae and AGN transients)
and diagnostics for observers. Specifically in the case of GW170817, continued monitoring
of the radio light curve will provide an independent constraint on the circum­merger density
and thereby the properties of the blast wave that dominated the early­time radio emission.
Our radio data support the hypothesis of a choked jet giving rise to a mildly relativistic
cocoon (scenario C in Figure 2), but this is only one of the possible outcomes of neutron
star merger events (see Figure 2). In some cases, the jet may break out after depositing a
fraction of its energy into the cocoon, thereby still successfully producing a SGRB
11
(scenario E in Figure 2). Indeed, a plateau in the distribution of SGRB durations has been
highlighted as evidence that SGRB jets often propagate through slower traveling ejecta
before breakout and at times it is choked
24
. The relative fractions of neutron star mergers
that successfully produce a SGRB or a choked jet can be directly probed via radio follow­
up of a sample of neutron star mergers in the upcoming LIGO­Virgo campaigns.
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Acknowledgements.
We would like to acknowledge the support and dedication of the
staff of the National Radio Astronomy Observatory and particularly thank the VLA Director,
Mark McKinnon, as well as Amy Mioduszewski and Heidi Medlin, for making the VLA
campaign possible. We thank Britt Griswold (NASA/GSFC) for beautiful graphic arts. SK
thanks Mike Shull for discussions. We thank the anonymous referees for their comments.
The National Radio Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc. We thank the
GMRT staff for scheduling our observations. The GMRT is run by the National Centre for
Radio Astrophysics of the Tata Institute of Fundamental Research. The Australia
Telescope Compact Array is part of the Australia Telescope National Facility which is
funded by the Australian Government for operation as a National Facility managed by
CSIRO. KM's research is supported by the Hintze Centre for Astrophysical Surveys which
is funded through the Hintze Family Charitable Foundation. EN acknowledges the support
of an ERC starting grant (GRB/SN) and an ISF grant (1277/13). GH acknowledges the
support of NSF award AST­1654815. AC acknowledges support from the National Science
Foundation CAREER award #1455090 titled “CAREER: Radio and gravitational­wave
emission from the largest explosions since the Big Bang”. AH acknowledges support by
the I­Core Program of the Planning and Budgeting Committee and the Israel Science
Foundation. TM acknowledges the support of the Australian Research Council through
grant FT150100099. Parts of this research were conducted by the Australian Research
Council Centre of Excellence for All­sky Astrophysics (CAASTRO), through project number
CE110001020. DK was supported by NSF grant AST­1412421. MK’s work was supported
by the GROWTH (Global Relay of Observatories Watching Transients Happen) project
funded by the National Science Foundation under PIRE Grant No 1545949. This work is
part of the research program Innovational Research Incentives Scheme
(Vernieuwingsimpuls), which is financed by the Netherlands Organization for Scientific
Research through the NWO VIDI Grant No. 639.042.612­Nissanke and NWO TOP Grant
No. 62002444­­Nissanke. PC acknowledges support from the Department of Science and
Technology via SwarnaJayanti Fellowship awards (DST/SJF/PSA­01/2014­15). TP
acknowledges the support of Advanced ERC grant TReX. VB acknowledges the support of
the Science and Engineering Research Board, Department of Science and Technology,
India, for the GROWTH­India project.
Author Contributions.
KM, EN, KH, GH and DF wrote the paper. AC compiled the
references. AC and AH compiled the methods section. DD and KD compiled the radio
measurements table. KM managed the VLA observing program and processed all the VLA
data. SM, AD and SB helped plan the VLA observations. EN, KH, DK and KM prepared
the figures. TM planned and managed ATCA observations and data analysis and
contributed to the manuscript text. DK helped propose for and plan the ATCA observations
and contributed to the manuscript text. EL, DD, CL and KB helped with ATCA observations
and data reduction. KD planned and managed GMRT observations and contributed to
manuscript text. KM and PC processed the GMRT data. VB helped in the GMRT
observations. OG and EN provided the cocoon simulation. KH provided the spherical
ejecta model. SN did the GW and cocoon rates analysis. SK, TP, MK and LS provided text
for the paper. All coauthors discussed the results and provided comments on the
manuscript.
Competing Interests.
The authors declare that they have no competing financial
interests.
Correspondence.
Correspondence and requests for materials should be addressed to
K.P.M. (email:
kunal@astro.caltech.edu
).
Figure 1. The radio light curve of GW170817.
Panel (a): The flux densities corresponding to the detections (markers with 1 error bars;
σ
some data points have errors smaller than the size of the marker) and upper limits
(markers with downward­pointing arrows) of GW170817 at frequencies ranging from 0.6­
15 GHz between day 16 and day 107 post­merger (ref. 12 and Extended Data Table 1).
Panel (b): Same as the panel (a) but with flux densities corrected for the spectral index =­
ɑ
0.61 (see Methods) and early­time, non­constraining, upper limits removed. The fit to the
light curve with the temporal index
δ
=0.78 (see Methods) is shown as a red line and the
uncertainty in
δ
(+/­0.05) as the red shaded region. Panel (c): Residual plot after correcting
for the spectral and temporal variations. The observing frequencies are color coded
according to the colorbar displayed at the right (black for
≤
1 GHz and yellow for
≥
10 GHz).
The marker shapes denote measurements from different telescopes.
Figure 2. Schematic illustration of the various possible jet and dynamical ejecta
scenarios in GW170817.
A) A jet seen on­axis, generating both the low­luminosity gamma­rays and the observed
radio afterglow. This scenario cannot explain the late rise of the radio emission. It is also
unable to explain
11
how a low­luminosity jet penetrates the ejecta. It is therefore ruled out.
B) A regular (luminous) SGRB jet seen off­axis, producing the gamma­rays and the radio.
The continuous moderate rise in the radio light curve rules out this scenario. C) A choked
jet giving rise to a mildly relativistic ( ~2­3) cocoon which generates the gamma­rays and
ɣ
the radio waves via on­axis emission. This is the model that is most consistent with the
observational data. It accounts for the observed gamma­rays, X­rays (possibly also the
ultraviolet and optical emission) and the radio emission, and provides a natural explanation
for the lack of an off­axis jet signature in the radio. D) The fast velocity tail ( ~0.8­0.6c, i.e.
β
~1.67­1.25) of the ejecta produces the radio emission. In this case, the jet must be
ɣ
choked (otherwise its off­axis emission should have been seen). While the radio emission
is fully consistent with this scenario, the energy deposited in faster ejecta ( ~2­3) must be
ɣ
very low. In this scenario, the source of the observed gamma­rays remains unclear. E) A
successful jet that drives a cocoon but does not have a clear signature in the radio. The
cocoon generates the gamma­rays and the radio emission, and outshines the jet at all
wavelengths. This scenario is less likely based on theoretical considerations, which
suggest that the jet and the cocoon should have comparable energies, in which case the
jet signature would have been observed in the radio band. This scenario can also be
visualized as a “structured” jet, having a relativistic narrow core surrounded by a mildly
relativistic wide­angle outflow, in which an off­axis observer does not see any signature of
the core. The relativistic core could have produced a regular SGRB for an observer
located along the axis of the jet. Such a jet, if it exists, could be too weak (made a sub­
dominant contribution to the radio light curve early on) or too strong (such that its radio and
X­ray signatures will be observed in the future; see Methods).
Figure 3. Off­axis jet models.
Synthetic light curves with a range of jet opening angles
θ
j
, isotropic­equivalent energy E
iso
,
and the ISM density n (see Methods) overplotted on the 3 GHz light curve (error bars are
1 ; ref. 12 and Extended Data Table 1). The overall shape of the light curve remains
σ
unchanged even after changing these parameters. We have considered a wide range of
parameters in the phase space of off­axis models (including unlikely scenarios like n=10
­6
cm
­3
; see Methods
); none of the models give a good fit to the observational data, and
hence we rule out the classical off­axis jet scenario as a viable explanation for the radio
afterglow. The dashed black and dotted red curves are calculated using the codes
described in the Methods. The dashed­dot blue curve is taken from figure 3 of ref. 4
(scaled to 3 GHz using =­0.6). All off­axis models assume
ɑθ
obs
= 26 deg,
ε
e
= 0.1,
ε
B
=
0.01 and p=2.2. (see main text and Methods).
Figure 4. Quasi­spherical ejecta models.
Radio light curves arising from quasi­spherical ejecta with velocity gradients, overplotted
on the 3 GHz data spanning days 16­93 post­merger (filled yellow circles; error bars are
1 ; ref. 12 and Extended Data Table 1). The solid red and dashed blue light curves
σ
represent power law models with maximum Lorentz factors =3.5 and =1.67 respectively
ɣɣ
(i.e. maximum =v/c=0.96 and 0.8 respectively). These curves approximately correspond
β
to the cocoon and dynamical ejecta, respectively. The shallow rise of the radio light curve
is consistent with a profile E(>
) (
)
βɣ∝βɣ
­5
. For n~0.03 cm
­3
, the observed radio emission
at 93 days is produced by an ejecta component with a velocity of ~0.6c and kinetic energy
of ~10
49
erg. For a lower ISM density, ~10
­4
cm
­3
, the radio emission at 93 days is produced
by a component with a velocity of 0.9c and energy 10
50
erg. Parameters
ε
e
=0.1 and p=2.2
are used for both models. Also shown for reference is the cocoon model light curve (dotted
black curve) taken from ref. 14, where parameter values n=1.3x10
­4
cm
­3
,
ε
B
=0.01,
ε
e
=0.1
and p=2.1 are used.
Methods
1. Radio Data Analysis.
VLA
. Radio observations of the GW170817 field were carried out with the Karl G. Jansky
Very Large Array in its B configuration, under a Director Discretionary Time (DDT)
program (VLA/17B­397; PI: K. Mooley). All observations were carried out with the
Wideband Interferometric Digital Architecture (WIDAR) correlator in multiple bands
including L­band (nominal center frequency of 1.5 GHz, with a bandwidth of 1 GHz), S­
band (nominal center frequency of 3 GHz, with a bandwidth of 2 GHz), and C­band
(nominal center frequency of 6 GHz, with a bandwidth of 4 GHz). We used QSO J1248­
1959 (L­band and S­band) and QSO J1258­2219 (C­band) as our phase calibrator
sources, and 3C 286 or 3C 147 as flux density and bandpass calibrators. The data were
calibrated and flagged for radio frequency interference (RFI) using the VLA automated
calibration pipeline which runs in the Common Astronomy Software Applications package
(CASA
25
). We manually removed further RFI, wherever necessary, after calibration.
Images of the observed field were formed using the CLEAN algorithm (with the “
psfmode”
parameter set to Hogbom
26
), which we ran in the interactive mode. The results of our VLA
follow­up campaign of GW170817 are reported in Extended Data Table 1, and the image
cutouts are shown in Extended Data Figure 1. The flux densities were measured at the
Gaia/HST position
27
. Flux density measurement uncertainties denote the local root­mean­
square (rms) noise. An additional 5% fractional error on the measured flux density is
expected due to inaccuracies in the flux density calibration. For non­detections, upper­
limits are calculated as three times the local rms noise in the image.
ATCA
. We observed GW170817 on 2017 November 01, November 18 and December 02
using the Australia Telescope Compact Array (ATCA) under a target of opportunity
program (CX391; PI: T. Murphy). During these observations the array was in
configurations 6A, 1.5C and 6C respectively. We observed using two 2 GHz frequency
bands with central frequencies of 5.5 and 9.0 GHz. For both epochs, the flux scale and
bandpass response were determined using the ATCA primary calibrator PKS B1934­638,
and observations of QSO B1245­197 were used to calibrate the complex gains. The
visibility data were reduced using the standard routines in the MIRIAD environment
28
. The
calibrated visibility data were split into the separate bands (5.5 GHz and 9.0 GHz),
averaged to 32 MHz channels, and imported into DIFMAP
29
. Bright field sources were
modeled separately for each band using the visibility data and a combination of point­
source and Gaussian components with power­law spectra. With the field sources modelled
and subtracted from the visibility data, the dominant emission in the residual image was
from GW170817. Restored images for each band were generated by convolving the model
components with the restoring beam, adding the residual map and then averaged to form
a wide­band image. Image­based Gaussian fitting for an unresolved source was
performed in the region of GW170817, leaving the flux density and source position
unconstrained. The source position from the fitting agrees with the Gaia/HST position
27
of
GW170817. The measured radio flux densities in the combined images are reported in the
Extended Data Table 1, and the image cutouts are shown in Extended Data Figure 1.
GMRT.
We carried out observations of the GW170817 field with the upgraded Giant
Meterewave Radio Telescope (uGMRT) at 700 MHz under a DDT program (DDTB288; PI:
K. De). All observations were carried out with 400 MHz bandwidth centered at 750 MHz
using the non­polar continuum interferometric mode of the GMRT Wideband Backend
(GWB
30
). Pointings were centered at the location of the optical transient. 3C 286 was used
as the absolute flux scale and bandpass calibrators, while phase calibration was done with
the sources J1248­199 (for the 2017 September 16 observation) and 3C 283 (for all other
observations). These data were calibrated and RFI flagged using a custom­developed
CASA pipeline. The data were then imaged interactively with the CASA task CLEAN,
incorporating a few iterations of phase­only self­calibration by
building a model for bright
sources in the field with each iteration
. The GMRT flux density measurements at the
Gaia/HST position
27
are reported in the Extended Data Table 1. The image cutouts are
shown in Extended Data Figure 1.
1.1 Radio Data Power­law Fit
We carried out a least­squares fit to the assembled radio data as a function of time and
frequency, using a two­dimensional power­law model:
S( ,t) = S
ν
0
( /
νν
0
)
ɑ
(t/t
0
)
δ
The fit results are shown in Extended Data Figure 2, where we find good results for =­
ɑ
0.61+/­0.05,
δ
=0.78+/­0.05, S
0
=13.1+/­0.4
μ
Jy,
ν
0
=3 GHz and
t
0
=10 d
. The fit has
χ
2
=42.3
for 44 degrees­of­freedom, although there are only 27 detections among the 47 data­
points.
1.2 Multi­epoch radio spectra
In Extended Data Figure 3 we show the radio continuum spectra obtained at different
epochs. All epochs are individually consistent with the spectral index =­0.61 within 1 .
ɑσ
2. Model Descriptions.
2.1 Off­axis afterglows.
The radio light curves were calculated using two independent semi­analytic codes
31,32
,
which are based on similar approximations. Both codes were compared to, and have been
found to be largely consistent with, the light curves produced by the BOXFIT code
33
. In
short, both codes approximate the jetted blast wave at any time in the source­frame as a
single zone emitting region which is a part of a sphere with an opening angle,
θ
j
. The
hydrodynamics includes the shock location and velocity, and the jet spreading. The
hydrodynamic variables in the emitting region are set to their values immediately behind
the shock. The emission from each location along the shock is calculated using standard
afterglow theory
34
, where the microphysics is parameterized by the fraction of internal
energy that goes to the electrons,
ε
e
, the fraction of internal energy that goes to the
magnetic field,
ε
B
, and the power­law index of the electron distribution. The code
calculates the rest frame emissivity at any time and any location along the shock and the
specific flux observed at a given viewing angle at a given time and frequency is then found
by integrating the contribution over equal­arrival­time surfaces, with a proper boost to the
observer frame.
2.2 Quasi­spherical ejecta.
Radio light curves arising from quasi­spherical outflows, e.g., a cocoon and the tail of the
dynamical ejecta, are approximately described by a model with a single one­dimensional
velocity profile: E(>
) (
)
βɣ∝βɣ
­k
, where is a velocity in units of the speed of light and is
βɣ
a Lorentz factor. The slope of the observed radio light curve is consistently explained with
k=5. The light curves are calculated using the same codes as in section 2.1. In Figure 4,
we show two cases: (1) a cocoon model, E(>
) = 2 x 10
βɣ
51
(
)
βɣ
­5
erg with a maximum
Lorentz factor of 3.5, n=8x10
­5
cm
­3
, and
ε
B
=0.01, and (2) a dynamical ejecta model,
E(>
) = 5 x 10
βɣ
50
(
/0.4)
βɣ
­5
erg with a maximum velocity of 0.8c, n=0.03 cm
­3
, and
ε
B
=0.003. This velocity profile of the dynamical ejecta contains a larger mass traveling
faster than 0.6c by a factor of ~5 compared with that found in general relativistic numerical
simulations
20,21,
. The small amount of mass ejected at these high velocities is plausible
since the simulations are affected by finite resolution and artificial atmosphere. In addition,
Figure 4 shows a prediction from the full 2D simulation of a choked jet and the resulting
cocoon presented in ref. 9. The light curve is taken from figure 4 of ref. 14 without any
attempt to fit the radio data that was added since it was published. A more detailed
publication reporting the full set of 2D simulations is in preparation. FInally, an upper limit
on the ISM density
12
of 0.04 cm
­3
suggests that the ejecta contains a fast moving
component with v 0.6c. For all the models shown in Figure 4, the mass of the ejecta that
≳
produces the radio signal up to 93 days is only ~10
­5
M
⊙
. This velocity is faster, and the
mass is much lower, than those inferred from the kilonova emission
35
. We note that
kilonova ejecta will produce observable radio signals on a timescale of years.
3. Hiding an off­axis jet
Hiding a luminous off­axis jet (of the type seen in regular SGRBs), given the radio data, is
not trivial. First, the jet emission peaks once its Lorentz factor drops to ~1/(
θ
obs
­
θ
j
), where
θ
obs
is the viewing angle with respect to the jet axis and
θ
j
is the jet opening angle. Thus,
emission from a jet that points only slightly away from us (<10 degrees), will peak when its
Lorentz factor is high ( 6). Since the flux in the radio at a given time is extremely sensitive
≳
to the blast wave Lorentz factor (roughly as
ɣ
10
) a jet at that angle will be much brighter
than any on­axis mildly relativistic outflow around the peak, even if the outflow carried
much more energy than the jet. Therefore, a hidden jet must be far away from the line­of
sight, namely
θ
obs
­
θ
j
≳
10 degrees. At such angle, any gamma­ray signal produced by a
relativistic jet will be too faint to explain the observed gamma­ray signal
11
. Thus, while our
previous radio observations strongly disfavored a regular SGRB seen off­axis as the origin
of the gamma­rays
12
(scenario B in Figure 2), the additional observations presented here
practically rule this out.
The extreme dependence of the radio flux density on the blast wave Lorentz factor also
implies that, for reasonable parameters also at
θ
obs
­
θ
j
≳
10 degrees, off­axis jet emission
will outshine a blast wave driven by material with ~0.8 ( ~1.67). Thus, the radio emission
βɣ
from an off­axis jet may remain undetected only if the observed emission is dominated by
an on­axis material with ~3, which is most likely a cocoon. In that case, a jet that is far
ɣ
from the line of sight may be hidden in two ways, either by being significantly less
energetic than the on­axis outflow or, surprisingly, by being significantly more energetic
(scenario E in Figure 2). In the latter case the jet emission will not appear in the radio data
available so far if it is so energetic that its Lorentz factor at day 93 is still significantly larger
than
θ
obs
­
θ
j
. For example, a 10 degree jet with an isotropic equivalent energy of 10
52
erg,
that propagates in circum­merger density of 10
­4
cm
­3
and observed at an angle of 30
degrees, peaks after 200 days and its brightness is comparable to the observed data only
around day 90 (
ε
B
=0.01,
ε
e
=0.1). While we cannot rule out this option, the extreme jet
energies make it unlikely, but if this is the case then we will see the jet contribution in the
future.
The other possibility, that the jet is less energetic than the on­axis outflow (again scenario
E in Figure 2), cannot be tested observationally. However, it is unlikely based on
theoretical considerations. The energy of the cocoon is distributed over a large range of
velocities. Thus, the energy of the mildly relativistic ejecta ( ~3) is expected to be only a
ɣ
small fraction of the total cocoon energy
9
. Moreover, observationally we see that the
energy carried by slower moving on­axis material is at least a factor of 10 larger than
energy carried by high velocity on­axis material. Now, the ratio between the total energy in
the cocoon and the energy in the jet depends on the ratio between the time spent by the
jet in the ejecta before it breaks out and the time over which the jet launching continues
after the breakout takes place. The engine that launches the jet is not affected by the
propagation of the jet though the ejecta and is causally disconnected from the jet head, if
and when it breaks out of the ejecta. Therefore, there is no reason for the engine to stop
upon breakout and without fine tuning. If the jet breaks out successfully the launching of
the jet is expected to continue over a time that is comparable to or larger than the time it
takes for the jet to cross the ejecta. As a result, the energy in the jet is expected to be
comparable or larger than that in the cocoon. Thus, it is highly unlikely that the jet is less
energetic than the fastest cocoon material, which as noted above carries only a small
fraction of the total cocoon energy.
We therefore conclude that there are no probable scenarios in which a jet successfully
breaks out, producing an SGRB seen by another (non­Earth) observer, and remains
undetected by our radio observations. We find the case in which the jet is choked as the
one that provides the best explanation to entire set of observations available to date.
4. The origin of the gamma­rays
Since a hidden jet cannot produce the observed gamma­rays and the rising radio emission
indicates a mildly relativistic wide­angle outflow moving towards us, we can expect that
this outflow is also the origin of the gamma­rays. We do not see any plausible scenario in
which the kilonova ejecta can produce the gamma­rays by itself. Compactness arguments
imply that this ejecta is too slow
11,14
and there is no natural dissipation process that can
convert the kinetic energy of the ejecta to gamma­rays. The cocoon, on the other hand,
can produce the gamma­rays. It has sufficient energy and its Lorentz factor is sufficiently
high to avoid compactness issues, so in the presence of a dissipation mechanism it can
produce the observed gamma­rays
9,10,,36,37
.
For example, a breakout of the shock driven by
the cocoon through the expanding ejecta can produce the observed signal, accounting for
its luminosity, duration, peak energy and spectral evolution
9
.
5. Lower limit to the circum­merger density
The mean cosmological baryon density is a function of the D/H ratio
38
, primordial Helium
density
39
, cosmographic parameters
40
and the fraction of diffuse baryons in the IGM (f
IGM
)
and is given
41
as,
n
H
~ (1.88 x 10
­7
cm
­3
)
f
IGM
(1+z)
3
.
We adopt
41
f
IGM
=0.7. At z~0, a density of 10
­6
cm
­3
corresponds to a baryon over density
Δ
b
=5. For the Lyman­alpha forest,
Δ
b
is in the range of 10­50, whereas that in condensed
halos
41
is 10
2
<
Δ
b
<10
4
. Thus, in the case of GW170817, a lower limit to the ambient density
is 2x10
­5
cm
­3
and a typical value
42
would be ~10
­4
cm
­3
.
6. Radio­X­ray comparison
The 3 GHz flux density measured
12
on 2017 September 03.9 is 15+/­4
μ
Jy. Scaling the X­
ray fluxes given in ref. 6 (reported in the energy range 0.3­8 keV) to the values reported in
ref. 5 (0.3­10 keV), we estimate the X­ray flux on 2017 September 02.2 as 5.5 x 10
­15
erg
cm
­2
s
­1
, with a 1 uncertainty of ~1.5 x 10
σ
­15
erg cm
­2
s
­1
. We use this information (X­ray
flux density is 0.23+/­0.06 nJy at a nominal center frequency of 4x10
17
Hz) to calculate the
spectral index between the radio and X­ray frequencies as ­0.60+/­0.03. This is consistent
with our estimated value of the radio­only spectral index, ­0.61+/­0.05, within 1 . Therefore
σ
the radio emission and X­rays likely originate from the same source, and the cooling
frequency ~16 days post­merger is well above the soft X­ray frequencies. Extended Data
Figure 4 shows a panchromatic spectrum between the radio and X­ray frequencies.
Ultraviolet and near­infrared data are also plotted for comparison. Although the early­time
emission in the ultraviolet, optical and infrared frequencies was dominated by thermal
emission, at late times there should be a significant synchrotron component. Using the
temporal and spectral indices estimated for the radio­only data (earlier in the Methods
section), and assuming the cooling break remains beyond 10
18
Hz, we can predict the X­
ray flux densities between 0.3­2.2 nJy (flux between 7x10
­15
to 52x10
­15
erg cm
­2
s
­1
in the
0.3­10 keV band
) on 2017 November 18 (and also for the Chandra observation on
December 03­06).
We note that, subsequent to the submission of this paper, the X­ray
observations took place and confirmed our prediction
. We estimate the synchrotron
cooling frequency as:
For >>1 (as expected for cocoon):
ɣ
For <<1 (i.e. ~1; as expected for the dynamical ejecta tail):
βɣ
We see that the cooling frequency at day ~16 post­merger is much larger than 10
18
Hz,
while beyond ~10
2
­10
3
days post­merger this break should be seen moving towards lower
frequencies within the electromagnetic spectrum.
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, 1430­1440 (2015)
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Data Availability.
All relevant data are available from the corresponding author on
request. Data presented in Figure 1 are included in the Extended Data Table 1.
Code Availability.
The codes used for generating the synthetic radio light curves are
currently being readied for public release (publication in preparation). Radio data
processing software: CASA, MIRIAD, DIFMAP.
Extended Data
Extended Data Table 1: Radio data for GW170817
UT Date
Δ
T
Telescope
ν
Bandwidth
S
ν
(d)
(GHz)
(GHz)
(
μ
Jy)
Sep 16.25
29.73
GMRT
0.68
0.2
< 246
Sep 17.84
31.32
VLA
3
2
34
±
3.6
Sep 21.86
35.34
VLA
1.5
1
44
±
10
Sep 25.86
39.34
VLA
15
4
<14.4
Oct 02.79
46.26
VLA
3
2
44
±
4
Oct 09.79
53.26
VLA
6
4
32
±
4
Oct 10.80
54.27
VLA
3
2
48
±
6
Oct 13.75
57.22
VLA
3
2
61
±
9
Oct 21.67
65.14
GMRT
0.61
0.4
117
±
42
Oct 23.69
67.16
VLA
6
4
42.6
±
4.1
Oct 28.73
72.20
VLA
4.5
0.5
54.6
±
5.5
Nov 01.02
75.49
ATCA
7.25
4
44.9
±
5.4
Nov 17.93
92.4
ATCA
7.25
4
39.6
±
7
Nov 18.60
93.07
VLA
1.6
1
98
±
14
Nov 18.66
93.13
VLA
3
2
70
±
5.7
Nov 18.72
93.19
VLA
15
4
18.6
±
3.1
Dec 02.89
107.36
ATCA
7.25
4
66.5
±
5.6
Table notes:
Δ
T represents the time post­merger. The Nov 17.93 ATCA observation was
affected by bad weather, and the uncertainty in the flux density is expected to be much
larger than the one reported here.
Extended Data Figure 1. GW170817 radio image cutouts.
Image cutouts (30” x 30”) from the upgraded GMRT, the VLA and the ATCA centred on
the NGC 4993. The position of GW170817 is marked by two black lines. Panels (a), (b)
and (c) show images from August­September 2017, using the data reported in ref. 12.
Panels (d), (e) and (f) show recent data, from October 2017. The flux density scale is
denoted by the colorbar in each column. The synthesized beam is shown as an ellipse in
the lower right corner of each image.
Extended Data Figure 2.
Confidence region for the radio spectral and temporal
indices.
Joint confidence contours for (the spectral power­law index) and (the temporal power­
ɑβ
law index). The contours are 1­, 2­, and 3­ confidence contours, and the location of the
σ
best­fit values, =­0.61+/­0.05,
ɑ
δ
=0.78+/­0.05,is indicated by the red “x” marker.