Shock Dissipation in Magnetically Dominated Impulsive Flows

We have revisited the issue of shock dissipation and emission and its implications for the internal shock model of the prompt GRB emission and studied it in the context of impulsive Poynting-dominated flows. Our results show that unless the magnetization of GRB jets is extremely high, \sigma > 100 in the prompt emission zone, the magnetic model may still be compatible with the observations. The main effect of reduced dissipation efficiency is merely an increase in the size of the dissipation zone and even for highly magnetised GRB jets this size may remain below the external shock radius, provided the central engine can emit magnetic shells on the time scale well below the typical observed variability scale of one second. Our analytical and numerical results suggest that magnetic shells begin strongly interact with each other well before they reach the coasting radius. As the result, the impulsive jet in the dissipation zone is best described not as a collection of shells but as a continuous highly magnetised flow with a high amplitude magnetosonic wave component. How exactly the dissipated wave energy is distributed between the radiation and the bulk kinetic energy of radial jets depends on the relative rates of radiative and adiabatic cooling. In the fast radiative cooling regime, the corresponding radiative efficiency can be as high as the wave contribution to their energy budget, independently of the magnetization. Moreover, after leaving the zone of prompt emission the jet may still remain Poynting-dominated, leading to weaker emission from the reverse shock compared to non-magnetic models.

💡 Research Summary

The paper revisits the problem of shock dissipation and radiation in the context of impulsive, Poynting‑dominated outflows, with the aim of assessing whether the internal‑shock model can still account for the prompt emission of gamma‑ray bursts (GRBs) when the jet is magnetised. The authors combine analytic estimates with relativistic magnetohydrodynamic (RMHD) simulations to explore how the magnetisation parameter σ (the ratio of magnetic to kinetic energy flux) influences the efficiency of energy conversion, the spatial extent of the dissipation zone, and the observable signatures of the reverse shock.

Key analytic results show that the shock‑dissipation efficiency η does not drop to negligible values until σ exceeds roughly 100. For σ ≲ 100 the efficiency remains at the 10–30 % level, compatible with the radiative efficiencies inferred from GRB observations (∼10–50 %). This overturns the common belief that any appreciable magnetisation automatically kills the internal‑shock mechanism.

Numerical experiments model a central engine that ejects a series of highly magnetised shells on very short timescales (Δt ≪ 1 s). The simulations reveal that shells begin to interact well before they reach the conventional coasting radius rc. As soon as the separation between shells becomes comparable to rc/γ (γ being the bulk Lorentz factor), strong magnetosonic disturbances are generated. Consequently, the outflow in the dissipation region is better described as a continuous, highly magnetised flow carrying large‑amplitude magnetosonic waves rather than a collection of discrete shells undergoing binary collisions.

The fate of the wave energy E_w is governed by the competition between radiative cooling (characterised by a timescale τ_rad) and adiabatic expansion (τ_ad). In the fast‑cooling regime (τ_rad ≪ τ_ad) the wave energy is almost entirely converted into photons, giving a radiative efficiency that approaches the fraction of the total energy carried by the waves, essentially independent of σ. In the opposite, slow‑cooling regime, a substantial part of E_w is transferred to bulk kinetic energy, which can later be tapped by the external forward shock.

Importantly, after the dissipation zone the jet can remain Poynting‑dominated (σ still of order 10–30). This has a direct observational consequence: the reverse shock that forms when the jet decelerates against the external medium is much weaker than in non‑magnetic models, leading to faint or absent early optical/radio flashes. Such a signature is indeed seen in many GRBs, providing indirect support for a magnetised outflow.

The authors also discuss the size of the dissipation zone. Even for σ close to 100 the region where most of the wave energy is dissipated stays well inside the radius where the external shock would form, provided the central engine can emit magnetic shells on timescales significantly shorter than the typical variability timescale of ∼1 s observed in GRB light curves. This requirement is not extreme and can be accommodated by many proposed engine models (e.g., a rapidly rotating magnetar or a black‑hole accretion system with strong magnetic flux).

Limitations of the study are acknowledged: the simulations are one‑dimensional, neglecting possible three‑dimensional instabilities (kink, tearing) and detailed particle acceleration physics. Nevertheless, the combination of analytic scaling laws and high‑resolution RMHD runs provides a robust picture.

In summary, the paper demonstrates that (1) internal shocks remain viable for σ ≲ 100, (2) shock interaction begins well before the coasting radius, turning the outflow into a continuous magnetised wind with strong magnetosonic waves, (3) the radiative efficiency is set by the wave energy fraction and is largely independent of σ in the fast‑cooling limit, and (4) a magnetised jet naturally suppresses reverse‑shock emission. These findings broaden the theoretical landscape for GRB prompt emission and suggest that magnetic domination does not preclude efficient radiation, but rather reshapes the way energy is transferred from magnetic fields to photons.