Origin of Pulsed Radio Emission from Magnetars

TL;DR

This paper addresses the origin of pulsed radio emission from magnetars by presenting first-principles kinetic simulations of a radiatively locked, current-carrying flow in a closed twisted magnetosphere. Using a relativistic Vlasov-Maxwell solver with discontinuous Galerkin methods, the authors show that radiative drag on the $e^+-e^-$ flow sustains a two-stream instability, driving turbulence that traps particles and seeds low-frequency electromagnetic waves. In 2D, a portion of this turbulence feeds a superluminal electromagnetic mode that can escape the magnetar environment, and a global radiative model places the radio-emitting region on inner closed field lines at radii of 15–50 stellar radii, predicting luminosities around $L_{EM}\sim 10^{30}$ erg s$^{-1}$ and spectra extending to tens of GHz and up to ~100 GHz after Doppler boosting. The model naturally explains the post-outburst emergence, wide pulse profiles, and polarization patterns observed in magnetar radio emission, and it provides concrete predictions for spectra and polarization that can be tested with future multi-frequency observations and more comprehensive global kinetic simulations.

Abstract

Extended periods of radio pulsations have been observed for six magnetars, displaying characteristics different from those of ordinary pulsars. In this Letter, we argue that radio emission is generated in a closed, twisted magnetic flux bundle originating near the magnetic pole and extending beyond 100 km from the magnetar. The electron-positron flow in the twisted bundle has to carry electric current and, at the same time, experiences a strong drag by the radiation field of the magnetar. This combination forces the plasma into a ``radiatively locked'' state with a sustained two-stream instability, generating radio emission. We demonstrate this mechanism using novel first-principles simulations that follow the plasma behavior by solving the relativistic Vlasov equation with the discontinuous Galerkin method. First, using one-dimensional simulations, we demonstrate how radiative drag induces the two-stream instability, sustaining turbulent electric fields. When extended to two dimensions, the system produces electromagnetic waves, including superluminal modes capable of escaping the magnetosphere. We measure their frequency and emitted power, and incorporate the local simulation results into a global magnetospheric model. The model explains key features of observed radio emission from magnetars: its appearance after an X-ray outburst, wide pulse profiles, luminosities $\sim 10^{30}{\rm{erg/s}}$, and a broad range of frequencies extending up to $\sim 100\, \mathrm{GHz}$.

Figures (8)

• Figure 1: Two-fluid model of the plasma flow in the magnetar magnetosphere. Panels (a) and (b) show Lorentz factors of positrons, $\gamma_+$, and electrons, $\gamma_-$. In this example, we have assumed that the $e^\pm$ outflow is injected at $r=2R_\star$ with a fixed multiplicity ${\cal M}=100$ (which remains constant along the outflow). The particles move along the magnetic field lines (thick dashed green and white lines) and resonantly scatter thermal photons streaming from the surface of the magnetar. Radiation exerts a drag force on both electrons and positrons. Its local strength is characterized by the value of $D_\pm$ calculated in the model; the contours of $D_\pm=1,10,100$ are indicated by the red curves. In panel (c), we show $\gamma_\pm$ as well as $\gamma_\star$ along the thick dashed green field line, which has $R_{\rm max} = 900R_*$. The evolution of $\gamma_\pm$, when only the radiative force is considered, is shown with dashed lines. We also show velocities of electrons ($v_{d, -}'$) and positrons ($v_{d, +}'$) in the "radiatively locked frame". The orange and blue shaded regions have $D_+\geq3$ and $D_-\geq 3$, respectively.
• Figure 2: Results of the 1X1V simulations. Panels (a) and (b) show snapshots of the electric field and distribution functions in the phase space, $f(x,p_x)$, at the end of the simulation with $v_d/c=0.5$ and $\omega_p t_{\rm cool}=3000$, measured at $t = 5t_{\rm cool}$. Panel (c) shows the distribution functions, $f(p_x)$ at the beginning of the simulation, just before the onset of the instability, and at the saturation. Panel (d) shows the evolution of electric field energy density normalized to kinetic energy density, $\epsilon_E$, for different cooling times, $t_{\rm cool}$. The vertical dotted line marks $t=0.4 t_{\rm cool}$, which corresponds to the moment just before the onset of the instability. The saturated turbulence level is consistent with $\epsilon_E\approx 2(\omega_p t_{\rm cool})^{-1}$ (indicated by the horizontal dashed lines) for all three simulations with different $t_{\rm cool}$.
• Figure 3: Snapshot during the quasi-steady state of the 2X1V simulation for $v_d/c=0.5$, $\omega_pt_{\rm cool}=3000$. Panels (a)-(c) show the snapshots of plasma density, $n_{+}+n_{-}$, and electric field components, $E_x$, $E_y$, displaying the excitation of turbulence in the current-carrying zone, as well as the production and propagation of electromagnetic waves. In panel (a), different zones are indicated with dashed boxes and labeled as follows: z0 is the vacuum zone, z1 is the density transition zone, z2 is the current transition zone, and z3 is the current zone. The inset (d) shows density fluctuations in the current-carrying zone, and insets (e)-(f) show electromagnetic waves escaping through the absorbing layers.
• Figure 4: Dispersion of the plasma modes in 2X1V simulation for $v_d/c=0.5$, $\omega_pt_{\rm cool}=3000$. Intensities in the Fourier space, $(\omega-k)$, are shown for electric, $E_x$, panels (b)-(d), and magnetic, $B_z$, field components, (f)-(h), for different angles of propagation, $\theta_k=0, \pi/6, \pi/3$. The red and green dashed lines correspond to the dispersion relations of the superluminal and Alfven modes, respectively. The white lines mark the vacuum light wave dispersion, $\omega = kc$. For reference, panels (a) and (b) show corresponding Fourier intensities in the 1X1V simulation with same parameters.
• Figure 5: Dependence of the normalized Poynting vector, $S_{\rm EM}$, of electromagnetic radiation escaping through the $y$-boundaries of 2X1V simulations on the cooling strength (panel (a), for a fixed $v_d/c=0.5$), and the drift speed (panel b). Blue, orange and green data points in both panels correspond to simulations with cooling times $\omega_p t_{\rm cool}=300,1000,3000$. The values represented by the dashed lines in panel (a) and the points in panel (b) are calculated from the data taken over the last $0.5 t_{\rm cool}$ of each simulation. Errorbars represent fluctuations of the measured Poynting flux.