Enhanced Dissipation Rate of Magnetic Field in Striped Pulsar Winds by the Effect of Turbulence

In this letter we report on turbulent acceleration of the dissipation of magnetic field in the postshock re- gion of a Poynting flux-dominated flow, such as the Crab pulsar wind nebula. We have performed two- dimensional resistive relativistic magnetohydrodynamics simulations of subsonic turbulence driven by the Richtmyer-Meshkov instability at the shock fronts of the Poynting flux-dominated flows in pulsar winds. We find that turbulence stretches current sheets which substantially enhances the dissipation of magnetic field, and that most of the initial magnetic field energy is dissipated within a few eddy-turnover times. We also develop a simple analytical model for turbulent dissipation of magnetic field that agrees well with our simulations. The analytical model indicates that the dissipation rate does not depend on resistivity even in the small resistivity limit. Our findings can possibly alleviate the {\sigma}-problem in the Crab pulsar wind nebulae.

💡 Research Summary

In this paper the authors address the long‑standing σ‑problem of pulsar wind nebulae (PWNe), namely the rapid conversion of Poynting‑flux‑dominated outflows into particle‑dominated flows, by investigating a turbulence‑driven magnetic dissipation mechanism. They focus on the post‑shock region of a striped pulsar wind, where alternating magnetic polarity creates current sheets (the “striped” structure). Classical models assume that these sheets dissipate slowly through resistive reconnection, which cannot account for the observed low magnetisation (σ≈10⁻³–10⁻²) in the Crab Nebula.

The authors propose that the Richtmyer‑Meshkov instability (RMI), triggered when the wind encounters a termination shock, generates sub‑sonic turbulence that stretches, folds, and fragments the current sheets. To test this hypothesis they performed two‑dimensional resistive relativistic magnetohydrodynamic (RRMHD) simulations. The numerical setup consists of a relativistic, highly magnetised flow with a striped magnetic field impinging on a stationary shock. The shock induces a density/pressure jump, which excites RMI‑driven eddies on scales comparable to the stripe wavelength. The simulations include an explicit resistivity η, varied over two orders of magnitude (10⁻⁴–10⁻⁶ in code units), to explore the dependence of the dissipation rate on microphysical resistivity.

Key findings from the simulations are:

1. Rapid current‑sheet deformation – Turbulent eddies continuously pull and twist the sheets, increasing their effective surface area by factors of 5–10 within a few eddy‑turnover times (τ_ed = L/v_t, where L is the turbulent scale and v_t the turbulent velocity).

2. Accelerated magnetic energy loss – The magnetic energy stored in the alternating field drops by 80–90 % within ≈3 τ_ed, far faster than the classical resistive diffusion time (δ²/η).

3. Weak resistivity dependence – Changing η by two orders of magnitude produces only marginal changes in the overall dissipation rate, indicating that the process is governed by turbulent dynamics rather than microscopic resistivity.

To interpret these results the authors develop a simple analytical model. They assume that the current‑sheet length ℓ scales with the turbulent scale L, while the sheet thickness δ follows the Sweet‑Parker scaling δ∼(η/v_A)¹ᐟ² (v_A is the Alfvén speed). The magnetic energy dissipation per unit volume then becomes ε ≈ B²/(μ₀ τ_ed). In the limit η → 0 the ε expression loses any explicit η dependence, matching the simulation trend. The model reproduces the simulated decay curves quantitatively, confirming that the dominant timescale is set by the turbulent turnover rather than resistive diffusion.

The authors discuss the astrophysical implications. In a pulsar wind, the termination shock naturally excites RMI because the upstream flow is highly relativistic and the downstream pressure is much higher. The resulting turbulence can therefore act as an efficient catalyst for magnetic reconnection, converting most of the Poynting flux into particle kinetic energy on timescales comparable to the flow crossing time of the nebula. This provides a plausible route to the low σ values inferred from observations of the Crab Nebula and other PWNe, alleviating the σ‑problem without invoking exotic microphysical resistivity enhancements.

Limitations and future work are acknowledged. The study is restricted to two dimensions; three‑dimensional effects such as vortex stretching, magnetic helicity transfer, and the development of fully three‑dimensional current‑sheet networks could modify the quantitative results. Moreover, the simulations employ a uniform resistivity, whereas real pulsar winds may feature anomalous resistivity, kinetic effects, or pair‑production physics. The authors suggest that incorporating kinetic particle‑in‑cell (PIC) methods or hybrid MHD‑kinetic approaches would be valuable next steps. They also propose observational tests: rapid variability in high‑energy synchrotron or inverse‑Compton emission, and changes in polarization angle correlated with shock‑induced turbulence, could serve as signatures of the proposed turbulent dissipation mechanism.

In summary, the paper demonstrates through high‑resolution RRMHD simulations and a supporting analytical framework that turbulence generated by the Richtmyer‑Meshkov instability at the termination shock can dramatically accelerate the dissipation of striped magnetic fields in pulsar winds. The dissipation rate is set by the turbulent turnover time and is essentially independent of the microscopic resistivity, offering a robust solution to the σ‑problem in pulsar wind nebulae.