Optical measurement of superluminal motion in the neutron-star merger GW170817 Kunal P. Mooley12 Jay Anderson3 Wenbin Lu456

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Optical measurement of superluminal motion in the

neutron-star merger GW170817

Kunal P. Mooley1,2,∗, Jay Anderson3,∗, Wenbin Lu4,5,6,∗

1Caltech, 1200 E California Blvd, MC 249-17, Pasadena, CA 91125, USA

2National Radio Astronomy Observatory, Socorro, New Mexico, 87801, USA

3Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA

4Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA

5Departments of Astronomy and Theoretical Astrophysics Center, UC Berkeley, Berkeley, CA

94720, USA

6TAPIR, Walter Burke Institute for Theoretical Physics, Mail Code 350-17, Caltech, Pasadena, CA

91125, USA

∗These authors contributed equally to this work

The afterglow of the binary neutron star merger GW1708171gave evidence for a structured

relativistic jet2–6 and a link3, 7, 8 between such mergers and short gamma-ray bursts. Superlu-

minal motion, found using radio very long baseline interferometry3(VLBI), together with the

afterglow light curve provided constraints on the viewing angle (14–28 degrees), the opening

angle of the jet core (<5 degrees), and a modest limit on the initial Lorentz factor of the jet

core (Γi>4). Here we report on another superluminal motion measurement, at seven times

the speed of light, leveraging Hubble Space Telescope precision astrometry and previous ra-

arXiv:2210.06568v1 [astro-ph.HE] 12 Oct 2022

dio VLBI data of GW170817. We thereby obtain a unique measurement of the Lorentz factor

of the wing of the structured jet, as well as substantially improved constraints on the viewing

angle (19–25 degrees) and the initial Lorentz factor of the jet core (Γi>40).

We carried out precision astrometric measurements of GW170817 using Hubble Space Tele-

scope (HST) data obtained at mean epochs of 8 d and 159 d post-merger (each of the two mea-

surements utilizes HST exposures taken over a span of several days, see Methods). Our mea-

surement at 8 d, when the optical emission was dominated by the thermal emission due to r-

process nucleosynthesis (i.e. kilonova or macronova), indicates that the position of the neutron star

merger is RA=13:09:48.06847(2), Dec.=−23:22:53.3906(2) (1σuncertainties in the last digits

are given in parentheses). Our measurement at 159 d, when the optical emission was jet-dominated

(non-thermal emission), indicates that the position of the afterglow was RA=13:09:48.06809(89),

Dec.=−23:22:53.383(11). While the precision of the former measurement rivals radio VLBI,

the precision of the latter is coarse and would have beneﬁted from a deeper HST observation at

the peak of the afterglow light curve. Positions of the optical source at both epochs are shown in

Figure 1.

Astrometry tied to GAIA9, 10 enables us to analyze the optical and radio positions of GW170817

together. Comparison of the 8 d HST measurement with the High Sensitivity Array (HSA) radio

VLBI measurements3at 75 d and 230 d post-merger suggests offsets of 2.41 ±0.31 ±0.22 mas

and 5.07 ±0.33 ±0.22 mas (1σuncertainties; statistical and systematic, respectively; see Meth-

ods), implying mean apparent speeds of 7.6±1.3and 5.2±0.5respectively, in units of speed of

light. Here we have used the host galaxy distance of11 40.7±2.4Mpc (using the distance and

associated uncertainty from ref.12 does not change the apparent speeds to the speciﬁed signiﬁcant

digits). With respect to the global VLBI radio position4at 206 d, the HST position is offset by

4.09 ±0.35 ±0.23 mas, indicating motion at 4.7±0.6times the speed of light. Offset positions

of the optical and radio source along with the positional uncertainties are shown in Figure 1. In

comparison, the proper motion and the mean apparent speed measured with HSA3between 75 d

and 230 d is 2.7±0.3mas and 4.1±0.5times the speed of light respectively.

For obtaining precise constraints on geometry and jet parameters, we consider the HST–

HSA superluminal motion measurements. First, we use the point-source approximation and to

estimate the true speed of the emitting material (β, in units of speed of light) and its angle with

respect to the Earth line of sight (θ) from the apparent speed βapp. In such a case we have βapp =

βsin(θ)/(1 −βcos(θ)). Since βis less than unity, the inclinations of the emitting regions at

75 d and 230 d are <18 degrees and <24 degrees (1σupper limits) respectively. The material

along the axis of the jet comes into view only around the time when the afterglow light curve starts

declining steeply, occurring around13, 14 tc'175 days post-merger, when the core has decelerated

to a Lorentz factor of approximately the inverse viewing angle (i.e. Γ175d '1/θv, where θvis the

viewing angle — the angle between the jet axis and the Earth line of sight). While we do not know

the position of GW170817 around time tc, we can constrain the mean apparent speed between 0

d–175 d to be larger than 5.2−0.5 = 4.7(1σlower limit) times the speed of light, leading to a

conservative limit on the viewing angle of GW170817 of <24 degrees.

We now turn to estimating the orientation and Lorentz factor evolution of the jet wing. The

maximum value of the apparent speed, βapp = Γβ, is obtained for β= cos(θ)(i.e. for Γ1the

maximum βapp = Γ occurs when Γ=1/θ). Since we have measured the mean apparent speed

βapp,0d−75d '7(but not the instantaneous apparent speed), the initial Lorentz factor of the material

dominating the ﬂux at 75d must have been Γi,75d &7. Here we assume that the HST 8 d kilonova

position denotes the position of the merger, and hence use the subscript “0d–75d” for ¯

βapp. We

have denoted with the subscript “i” the initial Lorentz factor (before deceleration) and with “75d”

the material that is dominating the afterglow emission at 75 days post-merger. We can also estimate

the instantaneous Lorentz factor Γ75d of this jet wing material seen at 75 d in the observer’s frame.

The mean apparent speed is given by, ¯

βapp,0d−75d '8θ75dΓ2

75d/(4Γ2

75dθ2

75d + 1) (see Methods). For

simplicity we assume that the region satisfying Γ = 1/θ dominates the emission at any given time

prior to the peak of the afterglow light curve. Solving for the two parameters then we ﬁnd Γ75d ∼

4.5and θ75d ∼13 degrees. The HST–HSA measurement of superluminal motion therefore gives

us a unique constraint on the Lorentz factor of the wing of the structured jet located approximately

13 degrees from the Earth line of sight. This result disfavors alternative models such as top-hat jet

and refreshed shock15, 16 for the afterglow emission in GW170817.

We can use the above method to further estimate the viewing angle and the Lorentz factor

of the jet core at 230 d, since the afterglow emission at this time should be dominated by the

core (i.e. θ230d =θv). In order to simultaneously satisfy (a) Γ175d '1/θv, (b) ¯

βapp,0d−230d '

8θvΓ2

230d/(4Γ2

230dθ2

v+ 1) and (c) Γ∝t−3/8(the Blandford-McKee evolution17), the viewing angle

is inferred to be θv∼17 degrees, and correspondingly Γ230d ∼3.3. In reality, the emission at

a given time does not come from the region precisely satisfying18 Γθ= 1, so we calculate these

viewing angles and Lorentz factors in a more detailed semi-analytical point-source model taking

into account the likelihood distribution of Γθ(described in Methods §6). For the jet wing we

obtain Γ75d = 5.6+3.8

−1.7and θ75d = 12.8+2.5

−2.5degrees, and for the and jet core we ﬁnd θv=θ230d =

21.3+2.5

−2.3degrees and Γ230d = 4.7+3.1

−1.4(1σuncertainties). These results are shown graphically in

Figure 2 (panel a). A schematic diagram showing the derived geometry of the wing and core of the

structured jet in GW170817 can be found in Figure 3.

From the Lorentz factor of the emitting material at 230 d, we can also get a measurement

of the ratio between the isotropic equivalent energy for the jet core Eiso and the density of the

pre-shock medium nas Eiso/n = 1055.8±0.5erg cm3(see Methods). It is not possible to obtain a

robust constraint on Eiso/n based on the panchromatic afterglow light curves alone, because there

is an additional free parameter B(the fraction of thermal energy in magnetic ﬁelds) that cannot be

disentangled without measuring the characteristic synchrotron cooling frequency19.

For a robust veriﬁcation of the above results, we used the relativistic hydrodynamic code

Jedi20 to carry out about a million independent simulations of an axisymmetric, structured jet

interacting with the circum-stellar medium, including the effects of lateral expansion (see Meth-

ods). We parameterize the angular dependencies of the kinetic energy and Lorentz factor structures

of the jet using smoothed broken power-law functions. The free parameters of the structured jet

model are constrained based on the χ2-ﬁts to the complete proper motion and afterglow lightcurve

dataset of GW170817. The ﬁts to the observational data are shown in Figure 2 (panels b and c).

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Opticalmeasurementofsuperluminalmotionintheneutron-starmergerGW170817KunalP.Mooley1;2;,JayAnderson3;,WenbinLu4;5;6;1Caltech,1200ECaliforniaBlvd,MC249-17,Pasadena,CA91125,USA2NationalRadioAstronomyObservatory,Socorro,NewMexico,87801,USA3SpaceTelescopeScienceInstitute,3700SanMartinDrive,Baltimore,M...

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Optical measurement of superluminal motion in the neutron-star merger GW170817 Kunal P. Mooley12 Jay Anderson3 Wenbin Lu456

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