One of the key properties of any binary is its viewing angle (i.e., inclination), $θ_{\rm obs}$. In binary neutron star (BNS) mergers it is of special importance due to the role that it plays in the measurement of the Hubble constant, $H_0$. The opening angle of the jet that these mergers launch, $θ_j$, is also of special interest. Following the detection of the first BNS merger, GW170817, there were numerous attempts to estimate these angles using the afterglow light curve, finding a wide range of values. Here we provide a simple formula for the ratio $θ_{\rm obs}/θ_j$ based on the afterglow light curve and show that this is the only quantity that can be determined from the light curve alone. Namely, it is impossible to determine each of the angles separately without additional information. Our result explains the inconsistency of the values found by the various studies of GW170817 that were largely driven by the different priors taken in each study. Among the additional information that can be used to estimate $θ_{\rm obs}$ and $θ_j$, the most useful is a VLBI measurement of the afterglow image superluminal motion. An alternative is an identification of the afterglow transition to the sub-relativistic phase. These observations are possible only for mergers observed at small viewing angles, whose afterglow is significantly brighter than the detector's threshold. We discuss the implications of these results to measurements of $H_0$ using GW observations. We show that while the viewing angle will be measured only in a small fraction of future BNS mergers, it can significantly reduce the uncertainty in $H_0$ in each one of these events, possibly to a level of 4-5\%. A minority of the mergers with high precision measurements of this kind may dominate in the future the precision in which $H_0$ will be measured using this method.
Electromagnetic observations of the first binary Neutron Star (BNS) merger GW170817 has established that relativistic jets can be successfully launched in BNS mergers. Typically, such jets produce emission in two phases: $γ$-ray prompt emission and multi-wavelength afterglow. Due to relativistic de-boosting, the detectability of both these counterparts is dependent on the angle ($θ_v$) between the observer's line of sight and the jet axis. We compare the detectability of prompt and afterglow emission from off-axis jets, assuming standard detector thresholds. We find that for top-hat jets, afte…
VLBI and JVLA observations revealed that GW170817 involved a narrow jet ($ θ_j \approx 4^\circ $) that dominated the afterglow peak at our viewing angle, $ θ_{\rm obs} \approx 20^\circ $. This implies that at the time of the afterglow peak, the observed signal behaved like an afterglow of a top-hat jet seen at $ θ_{\rm obs} \gg θ_j $, and it can be modeled by analytic expressions that describe such jets. We use a set of numerical simulations to calibrate these analytic relations and obtain generic equations for the peak time and flux of such an afterglow as seen from various observing angles. …
Constraining gamma-ray burst viewing angles with Swift/XRT afterglow light curves
Qufu Normal University（曲阜师范大学）；Huazhong University of Science and Technology（华中科技大学）；Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；University of Science and Technology of China（中国科学技术大学）；Nanjing University（南京大学）
The multi-messenger data of neutron star merger events are promising for constraining the Hubble constant. So far, GW170817 is still the unique gravitational wave event with multi-wavelength electromagnetic counterparts. In particular, its radio and X-ray emission have been measured in the past $\sim 3-5$ years. In this work, we fit the long-lasting X-ray, optical, and radio afterglow light curves of GW170817/GRB 170817A, including the forward shock radiation from both the decelerating relativistic GRB outflow and the sub-relativistic kilonova outflow (though whether the second component contr…
Following the historical observation of GW170817 and its electromagnetic follow-up, new neutron star merger afterglows are expected to be observed as counterparts to gravitational wave signals during the next science runs of the gravitational interferometer network. The diversity of the observed population of afterglows of these future events is subject to various factors, which are (i) intrinsic, such as the energy of the ejecta, (ii) environmental, such as the ambient medium density or (iii) observational, such as the viewing angle and distance of the source. Through prescribing a population…
In the numerical modeling of the GRB afterglow, some approximations have been made for simplicity, and different groups developed their codes. A robust test of these models/approaches is challenging because of the lack of directly measured physical parameters. Fortunately, the viewing angle inferred from the afterglow modeling is widely anticipated to be the same as the inclination angle of the binary neutron star (BNS) mergers that can be evaluated with the gravitational wave (GW) data. Therefore in the future, it is possible to calibrate the afterglow modeling with the GW inclination angle m…
GW170817, the first neutron star merger event detected by advanced LIGO/Virgo detectors, was associated with an underluminous short duration GRB 170817A. In this work we compare the forward shock afterglow emission of GW170817/GRB 170817A to other luminous short GRBs (sGRBs) with both a known redshift and an afterglow emission lasting at least one day after the burst. In the rapid decay phase, the afterglow emission of the bright sGRBs and GW170817/GRB 170817A form a natural and continuous sequence, though separated by an observation time gap. If viewed on-axis, the forward shock afterglow emi…
The independent measurement of Hubble constant with gravitational-wave standard sirens will potentially shed light on the tension between the local distance ladders and Planck experiments. Therefore, thorough understanding of the sources of systematic uncertainty for the standard siren method is crucial. In this paper, we focus on two scenarios that will potentially dominate the systematic uncertainty of standard sirens. First, simulations of electromagnetic counterparts of binary neutron star mergers suggest aspherical emissions, so the binaries available for the standard siren method can be …
In the first work of this series, we adopt a GW170817-like, viewing-angle-dependent kilonova model and the standard afterglow model with the lightcurve distribution based on the properties of cosmological short gamma-ray bursts afterglows to simulate the luminosity functions and color evolution of both kilonovae and optical afterglow emissions from binary neutron star (BNS) mergers. {We find that $\sim10\%$ afterglows are brighter than the associated kilonovae at the peak time, most of which are on-axis or nearly-on-axis. These kilonovae would be significantly polluted by the associated afterg…
The joint detection of gravitational waves (GWs) and electromagnetic (EM) radiation from the binary neutron star merger GW170817 ushered in a new era of multi-messenger astronomy. Joint GW-EM observations can be used to measure the parameters of the binary with better precision than either observation alone. Here, we use joint GW-EM observations to measure the viewing angle of GW170817, the angle between the binary's angular momentum and the line of sight. We combine a direct measurement of the distance to the host galaxy of GW170817 (NGC 4993) of $40.7\pm 2.36$ Mpc with the Laser Interferomet…
Assuming all binary Neutron Star mergers produce Short Gamma Ray Bursts (SGRBs), we combine the merger rates of binary Neutron Stars (BNS) from population synthesis studies, the sensitivities of advanced Gravitational Wave (GW) interferometer networks, and of the electromagnetic (EM) facilities in various wave bands, to compute the detection rate of associated afterglows in these bands. Using the inclination angle measured from GWs as a proxy for the viewing angle and assuming a uniform distribution of jet opening angle between 3 to 30 degrees, we generate light curves of the counterparts usin…
The ultra-relativistic outflows powering gamma-ray bursts (GRBs) acquire angular structure through their interaction with external material. They are often characterized by a compact, nearly uniform narrow core (with half-opening angle $θ_{c,\{ε,Γ\}}$) surrounded by material with energy per unit solid angle ($ε=ε_cΘ_ε^{-a}$, where $Θ_{\{ε,Γ\}}=[1+θ^2/θ_{c,\{ε,Γ\}}^2]^{1/2}$) and initial specific kinetic energy ($Γ_0-1=[Γ_c-1]Θ_Γ^{-b}$) declining as power laws. Multi-wavelength afterglow lightcurves of off-axis jets (with viewing angle $θ_{\rm obs} > θ_c$) offer robust ways to constrain $a$, $b…
We present Hubble Space Telescope (HST) observations of the exceptionally bright and luminous Swift gamma-ray burst, GRB 130427A. At z=0.34 this burst affords an excellent opportunity to study the supernova and host galaxy associated with an intrinsically extremely luminous burst ($E_{iso} >10^{54}$ erg): more luminous than any previous GRB with a spectroscopically associated supernova. We use the combination of the image quality, UV capability and and invariant PSF of HST to provide the best possible separation of the afterglow, host and supernova contributions to the observed light ~17 rest-…
Using the resultant profiles from 3D hydrodynamic simulations of relativistic jets interacting with neutron star merger wind ejecta, we show how the inhomogeneity of energy and velocity {across the jet surface profile} can alter the observed afterglow lightcurve. We find that the peak afterglow flux depends sensitively on the observer's line-of-sight, not only via the jet inclination but also through the jet rotation: for an observer viewing the afterglow within the GRB-bright jet core, we find a peak flux variability on the order $<0.5$ dex through rotational orientation and $<1.3$ dex for th…
The electromagnetic radiation that followed the neutron star merger event GW170817 revealed that gamma-ray burst afterglows from jets misaligned with our line of sight exhibit a light curve with slowly rising flux. The slope of the rising light curve depends sensitively on the angle of the observer with respect to the jet axis, which is likely to be perpendicular to the merger plane of the neutron star binary. Therefore, the afterglow emission can be used to constrain the inclination of the merging system. Here, we calculate the gamma-ray burst afterglow emission based on the realistic jet str…
We verified the off-axis jet model of X-ray flashes (XRFs) and examined a discovery of off-axis orphan gamma-ray burst (GRBs) afterglows. The XRF sample was selected on the basis of the following three factors: (1) a constraint on the lower peak energy of the prompt spectrum $E^{src}_{obs}$, (2) redshift measurements, and (3) multi-color observations of an earlier (or brightening) phase. XRF020903 was the only sample selected basis of these criteria. A complete optical multi-color afterglow light curve of XRF020903 obtained from archived data and photometric results in literature showed an ach…
Following the historical observations of GW170817 and its multi-wavelength afterglow, more radio afterglows from neutron star mergers are expected in the future as counterparts to gravitational wave inspiral signals. We wish to describe these events using our current knowledge of the population of neutron star mergers coming from gamma-ray burst science, and taking into account the sensitivities of current and future gravitational wave and radio detectors. We combine analytical models for the merger gravitational wave and radio afterglow signals to a population model prescribing the energetics…
We present observations of the optical afterglow of GRB\,170817A, made by the {\it Hubble Space Telescope}, between February and August 2018, up to one year after the neutron star merger, GW170817. The afterglow shows a rapid decline beyond $170$~days, and confirms the jet origin for the observed outflow, in contrast to more slowly declining expectations for `failed-jet' scenarios. We show here that the broadband (radio, optical, X-ray) afterglow is consistent with a structured outflow where an ultra-relativistic jet, with Lorentz factor $Γ\gtrsim100$, forms a narrow core ($\sim5^\circ$) and i…
Binary neutron star (BNS) mergers are one of the proposed origins for both repeating and non-repeating fast radio bursts (FRBs), which associates FRBs with gravitational waves and short gamma-ray bursts (GRBs). In this work, we explore detectability of radio afterglows from BNS mergers and compare it to the observed radio limits on FRB afterglows. We calculate the afterglow flux powered by the two components: a relativistic jet and a slower isotropic ejecta, and quantify the detection probability as a function of the source redshift, observing time, and flux sensitivity. The model parameter di…
Binary neutron star mergers offer a new and independent means of measuring the Hubble constant $H_0$ by combining the gravitational-wave inferred source luminosity distance with its redshift obtained from electromagnetic follow-up. This method is limited by intrinsic degeneracy between the system distance and orbital inclination in the gravitational-wave signal. Observing the afterglow counterpart to a merger can further constrain the inclination angle, allowing this degeneracy to be partially lifted and improving the measurement of $H_0$. In the case of the binary neutron star merger GW170817…
Linear polarization measurements in the optical band show polarization degrees of a few percent at late times. Recently, polarization at sub-percent level was also detected in radio by ALMA, opening the window for multi-wavelength polarimetry and stressing the importance of properly modeling polarization in GRB afterglows across the EM spectrum. We introduce a numerical tool that can calculate the polarization from relativistically moving surfaces by discretizing them to small patches of uniform magnetic field, calculating the polarized emission from each cell assuming synchrotron radiation an…
In the second work of this series, we explore the optimal search strategy for serendipitous and gravitational-wave-triggered target-of-opportunity (ToO) observations of kilonovae and optical short-duration gamma-ray burst (sGRB) afterglows from binary neutron star (BNS) mergers, assuming that cosmological kilonovae are AT2017gfo-like (but with viewing-angle dependence) and that the properties of afterglows are consistent with those of cosmological sGRB afterglows. A one-day cadence serendipitous search strategy with an exposure time of $\sim30\,$s can always achieve an optimal search strategy …
In this paper, we present a numerical method to study the predicted lightcurves as a function of viewing angle. We extrapolate the fitting formulae for the mass and velocity of tidal dynamical ejecta across a wide range of mass ratio validated with 66 simulations and use them in the calculations of the kilonova lightcurves. The calculated peak luminosity of a BH-NS merger kilonova is typically about a few times $10^{41}\ {\rm erg\ s^{-1}}$, which is always $\lesssim4.5\times10^{41}\ {\rm erg\ s^{-1}}$. This corresponds to the AB absolute magnitudes fainter than $\sim -15\ {\rm mag}$ in optical…
CDF-S XT1 is a fast-rising non-thermal X-ray transient detected by \textit{Chandra} in the Deep-Field South Survey. Although various hypotheses have been suggested, the origin of this transient remains unclear. Here, we show that the observations of CDF-S XT1 are well explained as the X-ray afterglow produced by a relativistic structured jet viewed off-axis. We measure properties of the jet, showing that they are similar to those of GRB170817A, albeit at cosmological distances. We measure the observers viewing angle to be $θ_{\textrm{obs}} = 10^{\circ}\pm3^{\circ}$ and the core of the ultra-re…
The joint detection of the gravitational wave (GW) GW170817 and its electromagnetic (EM) counterparts GRB170817A and kilonova AT 2017gfo has triggered extensive study of the EM emission of binary neutron star mergers. A parameter which is common to and plays a key role in both the GW and the EM analyses is the viewing angle of the binary's orbit. If a binary is viewed from different angles, the amount of GW energy changes (implying that orientation and distance are correlated) and the EM signatures can vary, depending on the structure of the emission. Information about the viewing angle of the…
The afterglow of the binary neutron star merger GW170817 gave evidence for a structured relativistic jet and a link between such mergers and short gamma-ray bursts. Superluminal motion, found using radio very long baseline interferometry (VLBI), together with the afterglow light curve provided constraints on the viewing angle (14-28 degrees), the opening angle of the jet core (less than about 5 degrees), and a modest limit on the initial Lorentz factor of the jet core (more than 4). Here we report on another superluminal motion measurement, at seven times the speed of light, leveraging Hubble …
In addition to producing a strong gravitational signal, a short gamma-ray burst (GRB), and a compact remnant, neutron star mergers eject significant masses at significant kinetic energies. This mass ejection takes place via dynamical mass ejection and a GRB jet but other processes have also been suggested: a shock-breakout material, a cocoon resulting from the interaction of the jet with other ejecta, and viscous and neutrino driven winds from the central remnant or the accretion disk. The different components of the ejected masses include up to a few percent of a solar mass, some of which is …
Near infrared (NIR) flare/rebrightening in the afterglow of the short hard gamma ray burst (SHB) 130603B measured with the Hubble Space Telescope (HST) and an alleged late-time X-ray excess were interpreted as possible evidence of a neutron-star merger origin of this SHB. However, the X-ray afterglow that was measured with the Swift-XRT and Newton XMM have the canonical behaviour of a synchrotron afterglow produced by a highly relativistic jet. The H-band flux observed with HST 9.41 days after burst is that expected from the measured late-time X-ray afterglow. A late-time flare/re-brightening …
The afterglow of GRB$\,$170817A/GW$\,$170817 was very unusual, slowly rising as $F_ν\propto{}t_{\rm{}obs}^{0.8}ν^{-0.6}$, peaking at $t_{\rm{obs,pk}}\sim\,150\;$days, and sharply decaying as $\sim{}t_{\rm{}obs}^{-2.2}$. VLBI observations revealed an unresolved radio afterglow image whose flux centroid moved superluminally with $v_{\rm{app}}\approx4c$, clearly indicating that the afterglow was dominated by a relativistic jet's compact core. Different jet angular structures explained the afterglow lightcurves: Gaussian and steep power-law profiles with narrow core angles $θ_c\lesssim5^\circ$ and…
GRB 170817A/GW 170817 is the first GRB clearly viewed far from the GRB jet's symmetry axis. Its afterglow was densely monitored over a wide range of frequencies and times. It has been modeled extensively, primarily numerically, and although this endeavour was very fruitful, many of the underlying model parameters remain undetermined. We provide analytic modelling of GRB afterglows observed off-axis, considering jets with a narrow core (of half-opening angle $θ_{\rm c}$) and power-law wings in energy per unit solid angle ($ε=ε_cΘ^{-a}$ where $Θ=[1+(θ/θ_{\rm c})^2]^{1/2}$) and initial specific k…
We present detailed simulations of black hole-neutron star (BH-NS) mergers kilonova and gamma-ray burst (GRB) afterglow and kilonova luminosity function, and discuss the detectability of electromagnetic (EM) counterpart in connection with gravitational wave (GW) detections, GW-triggered target-of-opportunity observations, and time-domain blind searches. The predicted absolute magnitude of the BH-NS kilonovae at $0.5\,{\rm days}$ after the merger falls in $[-10,-15.5]$. The simulated luminosity function contains the potential viewing-angle distribution information of the anisotropic kilonova em…
During the in-spiral stage of a compact binary, a wind bubble could be blown into interstellar medium, if the electromagnetic radiation due to the binary orbital motion is strong enough. Therefore, short gamma-ray bursts (SGRBs) due to double neutron star mergers would in principle happen in a wind bubble environment, which can influence the propagation of the SGRB jet and the consequent afterglow emission. By calculating the dynamics and synchrotron radiation of the jet-driven external shock, we reveal that an abrupt jump could appear in the afterglow light curves of SGRBs and the observation…
There is a strong degeneracy between the luminosity distance ($D_L$) and the observer viewing angle ($θ_{\rm obs}$; hereafter viewing angle) of the gravitational wave (GW) source with an electromagnetic counterpart, GW170817. Here, for the first time, we present independent constraints on $θ_{\rm obs} = 32.5 ^{\circ +11.7}_{-9.7}$ from broad-band photometry of the kilonova (kN) AT2017gfo associated with GW170817. These constraints are consistent with independent results presented in the literature using the associated gamma ray burst GRB170817A. Combining the constraints on $θ_{\rm obs}$ with …
We present the complete set of {\it Hubble Space Telescope} imaging of the binary neutron star merger GW170817 and its optical counterpart AT 2017gfo. Including deep template imaging in F814W, F110W, F140W, and F160W at 3.4 years post-merger, we re-analyze the full light curve of AT 2017gfo across 12 bands from 5--1273 rest-frame days after merger. We obtain four new detections of the short $γ$-ray burst (GRB) 170817A afterglow from 109--170 rest-frame days post-merger. These detections are consistent with the previously observed $β=-0.6$ spectral index in the afterglow light curve with no evi…
We combine the gravitational-wave measurement of the effective distance to the binary neutron star merger GW170817, the redshift of its host galaxy NGC 4993, and the latest Hubble constant measurement from the Dark Energy Survey to constrain the inclination between the orbital angular momentum of the binary and the line of sight to $18 \pm 8$ degrees (less than 28 degrees at 90% confidence). This provides a complementary constraint on models of potential afterglow observations.
GRB afterglow jets have been notoriously difficult to resolve numerically using 2D hydrodynamical simulations due to high outflow Lorentz factors. By performing simulations in a boosted frame, it is possible to calculate light curves from numerically computed flows in sufficient detail to accurately quantify the shape of the jet break and the post-break steepening of the light curve. We study jet breaks for jets with opening angles of theta_0 = 0.05, 0.1 and 0.2 radians decelerating in a constant density medium, observed at angles (theta_obs) ranging from on-axis to the jet edge. We present a …
The Hubble constant ($H_0$) measures the current expansion rate of the Universe, and plays a fundamental role in cosmology. Tremendous effort has been dedicated over the past decades to measure $H_0$. Notably, Planck cosmic microwave background (CMB) and the local Cepheid-supernovae distance ladder measurements determine $H_0$ with a precision of $\sim 1\%$ and $\sim 2\%$ respectively. A $3$-$σ$ level of discrepancy exists between the two measurements, for reasons that have yet to be understood. Gravitational wave (GW) sources accompanied by electromagnetic (EM) counterparts offer a completely…
We use the correlation relation between the energy emitted by the GRBs in their prompt phases and the X-ray afterglow fluxes, in an effort to constrain cosmological parameters and aiming to construct a Hubble diagram at high redshifts, i.e. beyond those found with Type Ia supernovae. We use a sample of 126 \textit{Swift} GRBs, that we have selected among more than 800 long bursts observed until April 2015. The selection is based on a few observational constraints: GRB flux higher than 0.4 $photons/cm^2/s$ in the band 15-150 keV, spectrum fitted with simple power law, redshift accurately known …
The short-duration ($\lesssim2\;$s) GRB 170817A in the nearby ($D=40\;$Mpc) elliptical galaxy NGC 4993 is the first electromagnetic counterpart of the first gravitational wave (GW) detection of a binary neutron-star (NS-NS) merger. It was followed by optical, IR, and UV emission from half a day up to weeks after the event, as well as late time X-ray and radio emission. The early UV, optical, and IR emission showed a quasi-thermal spectrum suggestive of radioactive-decay powered kilonova-like emission. Comparison to kilonova models favors the formation of a short-lived ($\sim1\;$s) hypermassive…
Gravitational waves from a merger of two neutron stars (NSs) were discovered for the first time in GW170817, together with diverse electromagnetic (EM) counterparts. To make constraints on a relativistic jet from the NS merger, we calculate the EM signals in (1) the short gamma-ray burst sGRB 170817A from an off-axis jet, (2) the optical-infrared macronova (or kilonova), especially the blue macronova, from a jet-powered cocoon, and (3) the X-ray and radio afterglows from the interaction between the jet and interstellar medium. We find that a typical sGRB jet is consistent with these observatio…
We present realistic expectations for the number and properties of neutron star binary mergers to be detected as multi-messenger sources during the upcoming fourth observing run (O4) of the LIGO-Virgo-KAGRA gravitational wave (GW) detectors, with the aim of providing guidance for the optimization of observing strategies. Our predictions are based on a population synthesis model which includes the GW signal-to-noise ratio, the kilonova (KN) optical and near-infrared light curves, the relativistic jet gamma-ray burst (GRB) prompt emission peak photon flux, and the afterglow light curves in radio…
We present the full panchromatic afterglow light curve data of GW170817, including new radio data as well as archival optical and X-ray data, between 0.5 and 940 days post-merger. By compiling all archival data, and reprocessing a subset of it, we have evaluated the impact of differences in data processing or flux determination methods used by different groups, and attempted to mitigate these differences to provide a more uniform dataset. Simple power-law fits to the uniform afterglow light curve indicate a $t^{0.86\pm0.04}$ rise, a $t^{-1.92\pm0.12}$ decline, and a peak occurring at $155\pm4$…
We present full-time-domain, moving-mesh, relativistic hydrodynamic simulations of jets launched from the center of a massive progenitor star and compute the resulting synchrotron light curves for observers at a range of viewing angles. We follow jet evolution from ignition inside the stellar center, propagation in the stellar envelope and breakout from the stellar surface, then through the coasting and deceleration phases. The jet compresses into a thin shell, sweeps up the circumstellar medium, and eventually enters the Newtonian phase. The jets naturally develop angular and radial structure…
We present a revised and complete optical afterglow light curve of the binary neutron star merger GW170817, enabled by deep Hubble Space Telescope (HST) F606W observations at $\approx\!584$ days post-merger, which provide a robust optical template. The light curve spans $\approx 110-362$ days, and is fully consistent with emission from a relativistic structured jet viewed off-axis, as previously indicated by radio and X-ray data. Combined with contemporaneous radio and X-ray observations, we find no spectral evolution, with a weighted average spectral index of $\langle β\rangle = -0.583 \pm 0.…
We report our observation of the short GRB 170817A, associated to the binary neutron star merger event GW 170817, perfomed in the X-ray band with XMM-Newton 135 d after the event (on the 29th December 2017). We find evidence for a flattening of the X-ray light curve with respect to the previously observed brightening. This is also supported by a nearly simultaneous optical Hubble Space Telescope and successive X-ray Chandra and low-frequency radio observations recently reported in the literature. Since the optical-to-X-ray spectral slope did not change with respect to previous observations, we…
Very long base interferometry (VLBI) radio images recently proved to be essential in breaking the degeneracy in the ejecta model for the neutron star merger GW170817. We discuss the properties of synthetic radio images of merger jet afterglows by using semi-analytic models of laterally spreading or non-spreading jets. The image centroid initially moves away from the explosion point in the sky with apparent superlumianal velocity. After reaching a maximum displacement its motion is reversed. This behavior is in line with that found in full hydrodynamics simulations. We show that the evolution o…
Revisiting GW170817 at milliarcsecond scale: high-precision constraints on jet geometry and $H_0$
CSIRO, Space and Astronomy（CSIRO空间与天文）；Centre for Astrophysics and Supercomputing, Swinburne University of Technology（斯威本科技大学天体物理与超级计算中心）；ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav)（ARC引力波发现卓越中心（OzGrav））；School of Physics and Astronomy, Tel Aviv University（特拉维夫大学物理与天文学学院）；School of Mathematics and Physics, University of Queensland（昆士兰大学数学与物理学院）；Indian Institute Of Technology Kanpur（坎普尔印度理工学院）；Caltech（加州理工学院）
