arXiv subjects

Jonathan Granot

Publications and source records attributed to Jonathan Granot.

At least 37 records · Page 2Linked to original sources

arXiv2025

Extragalactic Magnetar Giant Flares: Population Implications, Rates and Prospects for Gamma-Rays, Gravitational Waves and Neutrinos

Magnetar Giant Flares (MGFs) are the most energetic non-catastrophic transients known to originate from stellar objects. The first discovered events were nearby. In recent years, several extragalactic events have been identified, implying an extremely high volumetric rate. We show that future instruments with a sensitivity $\lesssim 5\times 10^{-9}$ erg cm$^{-2}$ at $\sim 1$ MeV will be dominated by extragalactic MGFs over short gamma-ray bursts (sGRBs). Clear discrimination of MGFs requires intrinsic GRB localization capability to identify host galaxies. As MGFs involve a release of a sizable fraction of the neutron star's magnetic free energy reservoir in a single event, they provide us with invaluable tools for better understanding magnetar birth properties and the evolution of their magnetic fields. A major obstacle is to identify a (currently) small sub-population of MGFs in a larger sample of more energetic and distant sGRBs. We develop the tools to analyze the properties of detected events and their occurrence rate relative to sGRBs. Even with the current (limited) number of events, we can constrain the initial internal magnetic field of a typical magnetar at formation to be $B_0\approx 4\times 10^{14}-2\times 10^{15}$\,G. Larger samples will constrain the distribution of birth fields. We also estimate the contribution of MGFs to the gravitational wave (GW) stochastic background. Depending on the acceleration time of baryon-loaded ejecta involved in MGFs, their GW emission may reach beyond 10~kHz and, if so, will likely dominate over other conventional astrophysical sources in that frequency range.

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arXiv2024

Afterglow Linear Polarization Signatures from Shallow GRB Jets: Implications for Energetic GRBs

Gamma-ray bursts (GRBs) are powered by ultra-relativistic jets. The launching sites of these jets are surrounded by dense media, which the jets must cross before they can accelerate and release the high energy emission. Interaction with the medium leads to the formation of a mildly relativistic sheath around the jet resulting in an angular structures in the jet's asymptotic Lorentz factor and energy per solid angle, which modifies the afterglow emission. We build a semi-analytical tool to analyze the afterglow light curve and polarization signatures of jets observed from a wide range of viewing angles, and focus on ones with slowly declining energy profiles known as shallow jets. We find overall lower polarization compared to the classical top-hat jet model. We provide an analytical expression for the peak polarization degree as a function of the energy profile power-law index, magnetic field configuration and viewing angle, and show that it occurs near the light curve break time for all viewers. When applying our tool to GRB 221009A, suspected to originate from a shallow jet, we find that the suggested jet structures for this event agree with the upper limits placed on the afterglow polarization in the optical and X-ray bands. We also find that at early times the polarization levels may be significantly higher, allowing for a potential distinction between different jet structure models and possibly constraining the magnetization in both forward and reverse shocks at that stage.

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arXiv2023

Prompt GRB Polarization from Non-Axisymmetric Jets

Time-resolved linear polarization ($Π$) measurements of the prompt gamma-ray burst emission can reveal its dominant radiation mechanism. A widely considered mechanism is synchrotron radiation, for which linear polarization can be used to probe the jet's magnetic-field structure, and in turn its composition. In axisymmetric jet models the polarization angle (PA) can only change by $90^\circ$, as $Π$ temporarily vanishes. However, some time-resolved measurements find a continuously changing PA, which requires the flow to be non-axisymmetric in at least one out of its emissivity, bulk Lorentz factor or magnetic field. Here we consider synchrotron emission in non-axisymmetric jets, from an ultrarelativistic thin shell, comprising multiple radially-expanding mini-jets (MJs) or emissivity patches within the global jet, that yield a continuously changing PA. We explore a wide variety of possibilities with emission consisting of a single pulse or multiple overlapping pulses, presenting time-resolved and integrated polarization from different magnetic field configurations and jet angular structures. We find that emission from multiple incoherent MJs/patches reduces the net polarization due to partial cancellation in the Stokes plane. When these contain a large-scale ordered field in the plane transverse to the radial direction, $Π$ always starts near maximal and then declines over the single pulse or shows multiple highly polarized peaks due to multiple pulses. Observing $Π\lesssim40\%$ ($15\%$) integrated over one (several) pulse(s) will instead favor a shock-produced small-scale field either ordered in the radial direction or tangled in the plane transverse to it.

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arXiv2023

Internal Shocks Hydrodynamics: the Collision of Two Cold Shells in Detail

Emission in many astrophysical transients originates from a shocked fluid. A central engine typically produces an outflow with varying speeds, leading to internal collisions within the outflow at finite distances from the source. Each such collision produces a pair of forward and reverse shocks with the two shocked regions separated by a contact discontinuity (CD). As a useful approximation, we consider the head-on collision between two cold and uniform shells (a slower leading shell and a faster trailing shell) of finite radial width, and study the dynamics of shock propagation in planar geometry. We find significant differences between the forward and reverse shocks, in terms of their strength, internal energy production efficiency, and the time it takes for the shocks to sweep through the respective shells. We consider the subsequent propagation of rarefaction waves in the shocked regions and explore the cases where these waves can catch up with the shock fronts and thereby limit the internal energy dissipation. We demonstrate the importance of energy transfer from the trailing to leading shell through $pdV$ work across the CD. We outline the parameter space regions relevant for models of different transients,e.g., Gamma-ray burst (GRB) internal shock model, fast radio burst (FRB) blastwave model, Giant flare due to magnetars, and superluminous supernovae (SLSN) ejecta. We find that the reverse shock likely dominates the internal energy production for many astrophysical transients.

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arXiv2023

Prompt Gamma-Ray Burst Emission from Internal Shocks -- New Insights

Internal shocks are a leading candidate for the dissipation mechanism that powers the prompt $γ$-ray emission in gamma-ray bursts (GRBs). In this scenario a compact central source produces an ultra-relativistic outflow with varying speeds, causing faster parts or shells to collide with slower ones. Each collision produces a pair of shocks -- a forward shock (FS) propagating into the slower leading shell and a reverse shock (RS) propagating into the faster trailing shell. The RS's lab-frame speed is always smaller, while the RS is typically stronger than the FS, leading to different conditions in the two shocked regions that both contribute to the observed emission. We show that optically-thin synchrotron emission from both (weaker FS + stronger RS) can naturally explain key features of prompt GRB emission such as the pulse shapes, time-evolution of the $νF_ν$ peak flux and photon-energy, and the spectrum. Particularly, it can account for two features commonly observed in GRB spectra: (i) a sub-dominant low-energy spectral component (often interpreted as ``photospheric''-like), or (ii) a doubly-broken power-law spectrum with the low-energy spectral slope approaching the slow cooling limit. Both features can be obtained while maintaining high overall radiative efficiency without any fine-tuning of the physical conditions.

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arXiv2023

Gamma rays from a reverse shock with turbulent magnetic fields in GRB 180720B

Gamma-ray bursts (GRBs) are the most electromagnetically luminous cosmic explosions. They are powered by collimated streams of plasma (jets) ejected by a newborn stellar-mass black hole or neutron star at relativistic velocities (near the speed of light). Their short-lived (typically tens of seconds) prompt $γ$-ray emission from within the ejecta is followed by long-lived multi-wavelength afterglow emission from the ultra-relativistic forward shock. This shock is driven into the circumburst medium by the GRB ejecta that are in turn decelerated by a mildly-relativistic reverse shock. Forward shock emission was recently detected up to teraelectronvolt-energy $γ$-rays, and such very-high-energy emission was also predicted from the reverse shock. Here we report the detection of optical and gigaelectronvolt-energy $γ$-ray emission from GRB 180720B during the first few hundred seconds, which is explained by synchrotron and inverse-Compton emission from the reverse shock propagating into the ejecta, implying a low-magnetization ejecta. Our optical measurements show a clear transition from the reverse shock to the forward shock driven into the circumburst medium, accompanied by a 90-degree change in the mean polarization angle and fluctuations in the polarization degree and angle. This indicates turbulence with large-scale toroidal and radially-stretched magnetic field structures in the reverse and forward shocks, respectively, which tightly couple to the physics of relativistic shocks and GRB jets -- launching, composition, dissipation and particle acceleration.

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arXiv2023

A Numerical Study of Relativistic Oblique Shock Reflection

Shocks are ubiquitous in astrophysical sources, many of which involve relativistic bulk motions, leading to the formation of relativistic shocks. Such relativistic shocks have so far been studied mainly in one dimension, for simplicity, but the complex nature of the relevant astrophysical flows often requires higher dimensional studies. Here we study the two-dimensional problem of the reflection of a planer shock off of a wall for a general incidence angle and a cold unshocked medium. We use primarily relativistic hydrodynamic numerical simulations, and elaborately compare the results to an analytic treatment. The simulations are performed both in the rest frame S of the unshocked fluid, where the dimensionless proper speed of the singly shocked fluid is $u_1=Γ_1β_1$ and the shock incidence angle is $α_1$, and in the rest frame S$^\prime$ of the point P of intersection of the incident shock and the wall for regular reflection (RR). Good agreement is obtained between the simulations in these two frames and with the analytic solution. The establishment of a steady flow in frame S$^\prime$ is explored, along with the transition between the strong and weak shock RR solutions. The transition line between RR and Mach reflection (MR) is studied numerically in the $u_1$-$α_1$ plane and found to coincide with the analytic detachment/sonic line. The flow properties along the sonic line are investigated in detail focusing on how they vary between the Newtonian and relativistic limits.

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arXiv2023

Relativistic Shock Reflection using Integral Conservation Laws

Shock wave reflection from a rigid wall has been thoroughly studied in the Newtonian limit, simplifying the problem by analyzing it in a steady-state frame, $S'$, where the point $P$ of the shock's intersection with the wall is at rest. However, a "super-luminal" regime emerges when the velocity of point $P$ ($v_p$) exceeds the speed of light ($v_p>c$), where no steady-state frame $S'$ exists. It occurs predominantly in the relativistic regime, relevant in astrophysics, where it encompasses nearly all of the shock incidence angles. To study this regime, we introduce a new approach. We formulate integral conservation laws in the lab frame $S$ (where the unshocked fluid is at rest) for regular reflection (RR), using two methods: a. fixed volume analysis and b. fixed fluid analysis. We show the equivalence between the two methods, and also to the steady-state oblique shock jump conditions in frame $S'$ in the sub-luminal regime ($v_p<c$). Applying this framework, we find that both the weak and strong shock RR solutions are bounded in the parameter space by the detachment line on the higher incidence angles side. The strong shock solution is also bounded by the luminal line on the lower incidence angles side, and exists only between these two critical lines, in the sub-luminal attachment region.

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arXiv2023

GRB 221009A Afterglow from a Shallow Angular Structured Jet

Exceptionally bright gamma-ray burst (GRB) afterglows can reveal the angular structure of their jets. GRB jets appear to have a narrow core (of half-opening angle $θ_c$), beyond which their kinetic energy drops as a power-law with angle $θ$ from the jet's symmetry axis, $E_{k,\rm iso}(θ)\propto[1+(θ/θ_c)^2]^{-a/2}$. The power-law index $a$ reflects the amount of mixing between the shocked jet and confining medium, which depends on the jet's initial magnetization. Weakly magnetized jets undergo significant mixing, leading to shallow ($a\lesssim2$) angular profiles. We use the exquisite multi-waveband afterglow observations of GRB 221009A to constrain the jet angular structure using a dynamical model that accounts for both the forward and reverse shocks, for a power-law external density profile, $n_{\rm{}ext}\propto{}R^{-k}$. Both the forward-shock emission, that dominates the optical and X-ray flux, and the reverse-shock emission, that produces the radio afterglow, require a jet with a narrow core ($θ_c\approx0.021$) and a shallow angular structure ($a\approx0.8$) expanding into a stellar wind ($k\approx2$). Moreover, these data appear to favor a small fraction ($ξ_e\approx10^{-2}$) of shock-heated electrons forming a power-law energy distribution in both shocks.

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arXiv2022

Robust Features of Off-Axis Gamma-Ray Burst Afterglow Lightcurves

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 $a$, $b$ and the external density radial profile ($ρ\propto R^{-k}$), even while other burst parameters may remain highly degenerate. We extend our previous work on such afterglows to include more realistic angular structure profiles derived from three-dimensional hydrodynamic simulations of both long and short GRBs (addressing also jets with shallow angular energy profiles, whose emission exhibits unique evolution). We present afterglow lightcurves based on our parameterized power-law jet angular profiles for different viewing angles $θ_{\rm obs}$ and $k=\{0,1,2\}$. We identify a unique evolutionary power-law phase of the characteristic synchrotron frequencies ($ν_m$ and $ν_c$) that manifests when the lightcurve is dominated by emission sensitive to the angular structure of the outflow. We calculate the criterion for obtaining single or double peaked light-curves in the general case when $θ_{c,Γ}\neqθ_{c,ε}$. We emphasize how the shape of the lightcurve and the temporal evolution of $ν_m$ and $ν_c$ can be used to constrain the outflow structure and potentially distinguish between magnetic and hydrodynamic jets.

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arXiv2022

Gamma-Ray Bursts at TeV Energies: Theoretical Considerations

Gamma-ray bursts (GRBs) are the most luminous explosions in the Universe and are powered by ultra-relativistic jets. Their prompt $γ$-ray emission briefly outshines the rest of the $γ$-ray sky making them detectable from cosmological distances. It is followed by, and sometimes partially overlaps with, a similarly energetic but very broadband and longer-lasting afterglow emission. While most GRBs are detected below a few MeV, over a hundred were detected at high ($\gtrsim0.1\;$GeV) energies and several have now been observed up to tens of GeV with the \textit{Fermi} Large Area Telescope (LAT). A new electromagnetic window in the very high energy (VHE) domain ($\gtrsim0.1\;$TeV) was recently opened with the detection of afterglow emission in the $(0.1$\textendash$1)\,$TeV energy band by ground-based imaging atmospheric Cherenkov telescopes. The emission mechanism for the VHE spectral component is not fully understood, and its detection offers important constraints for GRB physics. This review provides a brief overview of the different leptonic and hadronic mechanisms capable of producing VHE emission in GRBs. The same mechanisms possibly give rise to the high-energy spectral component seen during the prompt emission of many \textit{Fermi}-LAT GRBs. Possible origins of its delayed onset and long duration, well into the afterglow phase, with implications for the emission region and relativistic collisionless shock physics are discussed. Key results for using GRBs as ideal probes for constraining models of extra-galactic background light and intergalactic magnetic fields, as well as for testing Lorentz invariance violation, are presented.

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arXiv2021

GRB Polarization: A Unique Probe of GRB Physics

Over half a century from the discovery of gamma-ray bursts (GRBs), the dominant radiation mechanism responsible for their bright and highly variable prompt emission remains poorly understood. Spectral information alone has proven insufficient for understanding the composition and main energy dissipation mechanism in GRB jets. High-sensitivity polarimetric observations from upcoming instruments in this decade may help answer such key questions in GRB physics. This article reviews the current status of prompt GRB polarization measurements and provides comprehensive predictions from theoretical models. A concise overview of the fundamental questions in prompt GRB physics is provided. Important developments in gamma-ray polarimetry including a critical overview of different past instruments are presented. Theoretical predictions for different radiation mechanisms and jet structures are confronted with time-integrated and time-resolved measurements. The current status and capabilities of upcoming instruments regarding the prompt emission are presented. The very complimentary information that can be obtained from polarimetry of X-ray flares as well as reverse-shock and early to late forward-shock (afterglow) emission is highlighted. Finally, promising directions for overcoming the inherent difficulties in obtaining statistically significant prompt-GRB polarization measurements are discussed, along with prospects for improvements in the theoretical modeling, which may lead to significant advances in the field.

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arXiv2021

Temporal Evolution of Prompt GRB Polarization

The dominant radiation mechanism that produces the prompt emission in gamma-ray bursts (GRBs) remains a major open question. Spectral information alone has proven insufficient in elucidating its nature. Time-resolved linear polarization has the potential to distinguish between popular emission mechanisms, e.g., synchrotron radiation from electrons with a power-law energy distribution or inverse Compton scattering of soft seed thermal photons, which can yield the typical GRB spectrum but produce different levels of polarization. Furthermore, it can be used to learn about the outflow's composition (i.e. whether it is kinetic-energy-dominated or Poynting-flux-dominated) and angular structure. For synchrotron emission it is a powerful probe of the magnetic field geometry. Here we consider synchrotron emission from a thin ultrarelativistic outflow, with bulk Lorentz factor $Γ(R)=Γ_0(R/R_0)^{-m/2}\gg1$, that radiates a Band-function spectrum in a single (multiple) pulse(s) over a range of radii, $R_0\leq R\leq R_0+ΔR$. Pulse profiles and polarization evolution at a given energy are presented for a coasting ($m=0$) and accelerating ($m=-2/3$) thin spherical shell and for an off-axis top-hat jet with sharp as well as smooth edges in emissivity. Four different magnetic field configurations are considered, such as a locally ordered field coherent over angular scales $θ_B\gtrsim1/Γ$, a tangled field ($B_\perp$) in the plane transverse to the radial direction, an ordered field ($B_\parallel$) aligned in the radial direction, and a globally ordered toroidal field ($B_{\rm tor}$). All field configurations produce distinct polarization evolution with single (for $B_\perp$ and $B_\parallel$) and double (for $B_{\rm tor}$) $90^\circ$ changes in the polarization position angle.

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arXiv2020

Modelling the prompt optical emission of GRB 180325A: the evolution of a spike from the optical to gamma-rays

The transition from prompt to the afterglow emission is one of the most exciting and least understood phases in gamma-ray bursts (GRBs). Correlations among optical, X-ray and gamma-ray emission in GRBs have been explored, to attempt to answer whether the earliest optical emission comes from internal and/or external shocks. We present optical photometric observations of GRB 180325A collected with the TAROT and RATIR ground-based telescopes. These observations show two strong optical flashes with separate peaks at $\sim50\;$s and $\sim120\;$s, followed by a temporally extended optical emission. We also present X-rays and gamma-ray observations of GRB 180325A, detected by the Burst Alert Telescope (BAT) and X-ray Telescope (XRT), on the Neil Gehrels Swift observatory, which both observed a narrow flash at $\sim80\;$s. We show that the prompt gamma- and X-ray early emission shares similar temporal and spectral features consistent with internal dissipation within the relativistic outflow (e.g. by internal shocks or magnetic reconnection), while the early optical flashes are likely generated by the reverse shock that decelerates the ejecta as it sweeps up the external medium.

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arXiv2020

GRB Spectrum from Gradual Dissipation in a Magnetized Outflow

Modeling of gamma-ray burst (GRB) prompt emission spectra sometimes requires a (quasi-) thermal spectral component in addition to the Band function. In photospheric emission models, a prominent thermal component broadened by sub-photospheric dissipation is expected to be released at the photospheric radius, $r_{\rm ph}\sim10^{12}\,$cm. We consider an ultra-relativistic strongly magnetized outflow with a striped-wind magnetic-field structure undergoing gradual and continuous magnetic energy dissipation at $r<r_s$ that heats and accelerates the flow, leading to a bulk Lorentz factor $Γ(r)=Γ_\infty\min[1,(r/r_s)^{1/3}]$, where typically $r_{\rm ph}<r_s$. Similar dynamics and energy dissipation rates are also expected in highly-variable magnetized outflows without stripes/field-reversals. Two modes of particle energy injection are considered: (a) power-law electrons, e.g. accelerated by magnetic reconnection, and (b) continuous distributed heating of all electrons (and $e^\pm$-pairs), e.g. due to MHD instabilities. Time-resolved energy spectra are obtained using a numerical code that evolves coupled kinetic equations for a photon-electron-positron plasma. We find that (i) the thermal component peaks at $(1+z)E_{\rm pk}\sim0.2-1\,$MeV, for a source at redshift $z$, and becomes subdominant if the total injected energy density exceeds the thermal one, (ii) power-law electrons cool mainly by synchrotron emission whereas mildly relativistic and almost monoenergetic electrons in the distributed heating scenario cool by Comptonization on thermal peak photons, (iii) both scenarios can yield a low-energy break at $E_{\rm br}\approx E_{\rm th}$, and (iv) the $0.5(1+z)^{-1}\,$keV X-ray emission is suppressed in the power-law injection case, but it is expected for the distributed heating scenario. Energy-dependent linear polarization can differentiate between the two energy injection cases.

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arXiv2020

Spectral Modification of Magnetar Flares by Resonant Cyclotron Scattering

Spectral modification of energetic magnetar flares by resonant cyclotron scattering (RCS) is considered. During energetic flares, photons emitted from the magnetically-trapped fireball near the stellar surface should resonantly interact with magnetospheric electrons or positrons. We show by a simple thought experiment that such scattering particles are expected to move at mildly relativistic speeds along closed magnetic field lines, which would slightly shift the incident photon energy due to the Doppler effect. We develop a toy model for the spectral modification by a single RCS that incorporates both a realistic seed photon spectrum from the trapped fireball and the velocity field of particles, which is unique to the flaring magnetosphere. We show that our spectral model can be effectively characterized by a single parameter; the effective temperature of the fireball, which enables us to fit observed spectra with low computational cost. We demonstrate that our single scattering model is in remarkable agreement with Swift/BAT data of intermediate flares from SGR 1900+14, corresponding to effective fireball temperatures of $T_{\rm eff}=6$-$7$ keV, whereas BeppoSAX/GRBM data of giant flares from the same source may need more elaborate models including the effect of multiple scatterings. Nevertheless, since there is no standard physically-motivated model for magnetar flare spectra, our model could be a useful tool to study magnetar bursts, shedding light on the hidden properties of the flaring magnetosphere.

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arXiv2020

Afterglow Lightcurves from Misaligned Structured Jets

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 kinetic energy ($Γ_0-1=[Γ_{\rm c,0}-1]Θ^{-b}$), as well as briefly discuss Gaussian jets. Our study reveals qualitatively different types of lightcurves that can be viewed in future off-axis GRBs, with either single or double peaks, depending on the jet structure and the viewing angle. Considering the lightcurve shape rather than the absolute normalizations of times and / or fluxes, removes the dependence of the lightcurve on many of the highly degenerate burst parameters. This study can be easily used to determine the underlying jet structure, significantly reduce the effective parameter space for numerical fitting attempts and provide physical insights. As an illustration, we show that for GRB 170817A, there is a strong correlation between the allowed values of $Γ_{\rm c,0}$ and $b$, leading to a narrow strip of allowed solutions in the $Γ_{\rm c,0}$-$b$ plane above some minimal values $Γ_{\rm c,0}\gtrsim 40, b\gtrsim1.2$. Furthermore, the Lorentz factor of the material dominating the early lightcurve can be constrained by three independent techniques to be $Γ_{0}(θ_{\rm min,0})\approx5-7$.

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arXiv2019

ALMA Detection of a Linearly Polarized Reverse Shock in GRB 190114C

We present ALMA 97.5 GHz total intensity and linear polarization observations of the mm-band afterglow of GRB 190114C spanning 2.2 to 5.2 hours after the burst. We detect linear polarization at the $\approx 5\,σ$ level, decreasing from $Π=(0.87\pm0.13)\%$ to $(0.60\pm0.19)\%$, and evolving in polarization position angle from $(10\pm5)^\circ$ to $(-44\pm12)^\circ$ during the course of the observations. This represents the first detection of polarized millimeter emission in a $γ$-ray burst. We show that the optical and X-ray observations between $0.03$ days and $\sim0.3$ days are consistent with a fast cooling forward shock expanding into a wind environment. However, the optical observations at $\lesssim0.03$ days, as well as the radio and millimeter observations arise from a separate component, which we interpret as emission from the reverse-shocked ejecta. Using the measured linear polarization, we constrain the coherence scale of tangled magnetic fields in the ejecta to an angular size of $θ_{\rm B} \approx10^{-3}$ radian, while the rotation of the polarization angle rules out the presence of large scale, ordered axisymmetric magnetic fields, and in particular a large scale toroidal field, in the jet.

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