Relativistic oblique shocks with ordered or random magnetic fields: tangential field governs

Ma, Jing-Ze; Zhang, Bing

doi:10.1093/mnras/stac060

Cited by 3 publications

(1 citation statement)

References 79 publications

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“…In reality, many GRBs should be observed for finite values of θ v . The shock jump condition would make the magnetic field anisotropic in the downstream region even if it is isotropic in the upstream region (Ma & Zhang 2022). The nonlinear dynamics of MHD turbulence also show anisotropic magnetic energy spectrum (Goldreich & Sridhar 1995;Lazarian & Vishniac 1999).…”

Section: Future Workmentioning

confidence: 99%

Synchrotron Polarization of Gamma-Ray Burst Afterglow Shocks with Hydrodynamic-scale Turbulent Magnetic Field

Kuwata

Toma

Kimura

et al. 2023

ApJ

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Afterglows of gamma-ray bursts (GRBs) are emitted from expanding forward shocks, which are expected to have magnetic fields much stronger than the interstellar field, although the origin of the field is a long-standing problem. Two field amplification mechanisms, plasma kinetic instabilities and magnetohydrodynamic instabilities, have been discussed so far. The coherence-length scales of the fields amplified by these two processes are different by 7–10 orders of magnitude, and the polarimetric observations may distinguish them. We construct a semi-analytic model of the forward-shock afterglow polarization under the assumption of hydrodynamic-scale turbulent magnetic field. We perform numerical calculations of synchrotron polarization for the isotropic turbulence and the zero viewing angle. We find that the polarization degrees are ∼1% when the field coherence-length scale in the fluid co-moving frame is of the order of the thickness of the shocked regions. This range of polarization degree is comparable to that of the observed late-phase optical afterglows. Our model also shows that the radio polarization degrees are comparable to the optical ones on average but can be higher than the optical ones at some time intervals. The polarization angles are shown to vary randomly and continuously. These polarimetric properties are clearly different from the case of plasma kinetic instability. Simultaneous polarimetric observations of GRB afterglows at the radio and optical bands have recently started, which will help us constrain the magnetic field amplification mechanism.

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Section: Future Workmentioning

confidence: 99%

Synchrotron Polarization of Gamma-Ray Burst Afterglow Shocks with Hydrodynamic-scale Turbulent Magnetic Field

Kuwata

Toma

Kimura

et al. 2023

ApJ

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A numerical study of relativistic oblique shock reflection

Bera,

Granot,

Rabinovich

et al. 2024

Physics of Fluids

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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 u1=Γ1β1 and the shock incidence angle is α1, and in the rest frame S′ 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′ is explored, along with the transition between the strong and weak shock RR solutions. The transition line between RR and Mach reflection is studied numerically in the u1 − α1 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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Reverse shock forming condition for magnetized relativistic outflows: reconciling theories and simulations

Zhang

2022

Monthly Notices of the Royal Astronomical Society

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Reverse shock (RS) emission can be used to probe the properties of the relativistic ejecta, especially the degree of magnetization σ, in gamma-ray burst (GRB) afterglows. However, there has been confusion in the literature regarding the physical condition for the RS formation, and the role of magnetic fields in the RS dynamics in the Poynting-flux-dominated regime is not fully understood. Exploiting the shock jump conditions, we characterize the properties of a magnetized RS. We compare the RS dynamics and forming conditions from different theories and numerical simulations, and reconcile the discrepancies among them. The strict RS forming condition is found to be $\sigma < \sigma _\mathrm{cr}=(8/3)\gamma _4^2(n_1/n_4)$, where n4 and n1 are the rest-frame number densities of the ejecta and the ambient medium, respectively, γ4 is the bulk Lorentz factor, and σcr is the critical magnetization. Contrary to previous claims, we prove that this condition agrees with other theoretical and simulated results, which can be further applied to the setup and consistency check of future numerical simulations. Using this condition, we propose a characteristic radius for RS formation, and categorize the magnetized shell into three regimes: ‘thick shell’ (relativistic RS), ‘thin shell’ (trans-relativistic RS), and ‘no RS’ regimes. The critical magnetization σcr is generally below unity for thin shells, but can potentially reaches ∼100 − 1000 in the ‘thick shell’ regime. Our results could be applied to the dynamical evolution of Poynting-flux-dominated ejecta, with potential applications to self-consistent lightcurve modelling of magnetized relativistic outflows.

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Relativistic oblique shocks with ordered or random magnetic fields: tangential field governs

Cited by 3 publications

References 79 publications

Synchrotron Polarization of Gamma-Ray Burst Afterglow Shocks with Hydrodynamic-scale Turbulent Magnetic Field

Synchrotron Polarization of Gamma-Ray Burst Afterglow Shocks with Hydrodynamic-scale Turbulent Magnetic Field

A numerical study of relativistic oblique shock reflection

Reverse shock forming condition for magnetized relativistic outflows: reconciling theories and simulations

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