Relativistic Magnetohydrodynamic Simulations of Giant Magnetar Bursts

TL;DR

The paper investigates magnetar giant flares by performing the first relativistic MHD simulation of a surface shear–driven eruption, capturing reconnection heating, relativistic ejecta, and a stratified fireball confined to the inner magnetosphere. Using a hybrid force-free/MHD framework on a high‑resolution grid, it quantifies energy partition between the giant plasmoid ejecta and the trapped fireball, linking reconnection dynamics to the observed two‑phase flare structure. The results show that about $0.22$ of the dipole energy can be injected as twist to trigger eruption, with roughly $0.175$ of the dipole energy carried by the ejecta (split into electromagnetic and thermal components) and a trapped fireball of $≈0.015$ energy; the ejecta tail is highly relativistic with $oldsymbol{alpha} $ and beamed into a narrow cone, while Alfvén and fast waves carry negligible energy. This work provides a self‑consistent physical framework for magnetar flare energetics, beaming, and potential FRB production, highlighting the roles of reconnection heating and magnetospheric fireballs in interpreting observations and guiding future 3D studies.

Abstract

Gradual crustal deformation can generate strongly twisted magnetic fields around magnetars, potentially triggering giant flares with total energies exceeding $10^{44}\,\mathrm{erg}$. In this Letter, we present the first relativistic magnetohydrodynamic simulation of a surface shear-driven magnetar eruption, capturing reconnection-driven plasma heating, the ejection of relativistically hot plasma, and the formation of a hot fireball confined within the inner magnetosphere. We find that magnetic reconnection in the equatorial current sheet launches a hot trailing outflow capable of powering the initial spike observed in giant flares, while simultaneously leaving behind a thermally stratified fireball with sufficient thermal energy to produce the pulsating, decaying tail. Together, these features provide a self-consistent physical framework for understanding the observed energetics of magnetar giant flares. The eruption also expels a magnetically dominated giant plasmoid carrying up to $\sim 9\%$ of the magnetosphere's total magnetic energy. Furthermore, our simulation demonstrates how the plasmoid drives the formation of a blast wave -- an important ingredient in models linking magnetar eruptions to fast radio bursts.

Figures (7)

• Figure 1: Onset and evolution of the eruption. Top row (a–d): Evolution of the inner magnetosphere ($r \leq 30\,r_{\star}$) during a flare, showing the toroidal-to-poloidal magnetic energy ratio and the total magnetic energy. The magnetosphere initially inflates as the rotating stellar surface twists the magnetic field lines (a–b). Following magnetic reconnection in the equatorial plane (c), the magnetosphere relaxes toward a nearly dipolar configuration, retaining only a small residual toroidal field (d). Bottom row (e–g): Time evolution of the plasma internal energy, $U$, in the inner magnetosphere, illustrating the formation of a hot, magnetized fireball. The internal energy is normalized to the magnetic energy density $U_{\rm B_*}=B_*^2/8\pi$ corresponding to the stellar magnetic field $B_*$ (Eq. \ref{['eqn:edip']}); the magenta line marks the reconnecting field line. The hot magnetization $\sigma_{\rm hot}$ (panel h) remains above unity within the fireball, indicating that the magnetosphere remains magnetically dominated.
• Figure 2: Flare energetics. (a) Inner magnetosphere: electromagnetic energy, $\mathcal{E}_{\rm EM}$; thermal energy, $\mathcal{E}_{\rm U}$; and the time-integrated ejected energy, $\int \dot{\mathcal{E}}_{\rm ej}dt$, together with its individual components. We find that nearly $17\%$ of the dipolar magnetic energy, $\mathcal{E}_{\rm dip}$, is released as ejecta, powering the flare, while a substantial amount of hot plasma remains trapped in the inner magnetosphere. The horizontal dashed line denotes the twist energy stored in the inner magnetosphere at the onset of reconnection, and the vertical dashed lines mark the times of inflation and reconnection onset, respectively. (b) Decomposition of the electromagnetic energy in the inner magnetosphere (solid curves) and outside the inner region ($r > 30r_*$; dotted curves). Shown are the energies of the total and poloidal components of the magnetic field, $\mathcal{E}_{\rm B}$ and $\mathcal{E}_{\rm B}^{\rm pol}$, as well as the poloidal and toroidal electric field components, $\mathcal{E}_{\rm E}^{\rm pol}$ and $\mathcal{E}_{\rm E}^{\rm tor}$. In each case, we plot the fractional change $\delta \tilde{\mathcal{E}} \equiv (\mathcal{E} - \mathcal{E}_{t=0}) / \mathcal{E}_{\rm dip}$. The dashed curved line indicates an exponential fit to the decay of $\mathcal{E}_{\rm B}^{\rm pol}$ due to reconnection. The inset shows a zoomed-in view at late times.
• Figure 3: Time evolution of the plasma internal energy, $U$, and its connection to the history of reconnection. (a) Time evolution of $U$ as a function of the poloidal flux function, $\Psi$, both evaluated at a fixed radius of $2\,r_{\star}$. At late times, $U \propto \Psi^6$, as expected for a nearly dipolar magnetic field at the reconnection radius (see Sec. \ref{['sec:fireball']}). $U$ is normalized by $U_{\rm B_*}$ (see Fig. \ref{['fig:inner']}), and $\Psi$ is normalized by the total stellar magnetic flux, $\Psi_*$. (b) Internal energy, $U$, as a function of the flux function evaluated at the reconnection radius, $\Psi_{\rm rec}$, demonstrating $U \propto \Psi^6$, consistent with the nearly dipolar magnetic field at the reconnection radius and with panel (a). (c) Temporal evolution of the reconnection radius, $r_{\rm rec}$ (black curve), which migrates outward over time. Its evolution closely tracks that of $1/\Psi_{\rm rec}$ (orange curve). A simple fit-by-eye to $r_{\rm rec}(t)$ is overplotted, providing an estimate of the reconnection rate (see Sec. \ref{['sec:fireball']}).
• Figure 4: Structure of the flare ejecta at $532r_*/c$. Three distinct regions emerge: (i) the magnetic pulse, a relativistically moving, near-spherical envelope of compressed outer magnetospheric field lines filled with cold plasma and containing negligible toroidal field; (ii) the piston, a relativistically moving ejecta head containing cold plasma and significant toroidal magnetic fields; and (iii) the ejecta tail, filled with relativistically hot plasma moving at high Lorentz factor, which can produce the initial hard X-ray spike observed in magnetar giant flares. (a) Ratio of toroidal to poloidal magnetic field components, highlighting the dominance of $B_{\varphi}$ in the piston. (b) Internal energy, $U$, normalized by the stellar magnetic energy density $U_{\rm B_*}$, showing the hot plasma in the ejecta tail. (c) Lorentz factor, $\gamma$, of the different ejecta components.
• Figure 5: Production of Alfvén and fast waves during the eruption. We show electric field components shortly after the onset of reconnection (top) and in the post-flare state (bottom). The poloidal component, $E_{\rm pol}$, traces Alfvén waves, while the toroidal component, $E_{\varphi}$, tracks fast magnetosonic waves. As the field lines in the inner magnetosphere close following the eruption, fast waves gradually escape the magnetosphere, whereas Alfvén waves remain confined to the inner region. The electric fields are normalized by the stellar magnetic field strength $B_*$.