Relativistic jets from millisecond proto-magnetars

TL;DR

Millisecond proto-magnetars formed in core-collapse, neutron star mergers, and white-dwarf AIC are viable engines for short GRBs and kilonovae, but early neutrino winds load baryons and limit jet acceleration. The authors perform 3D GRMHD simulations with M0 neutrino transport to capture the multidimensional wind structure and find that centrifugal effects boost equatorial mass loss while polar magnetic flux remains relatively clean, yielding high magnetization $\sigma$ and $\Gamma_{\infty}$ along the axis. This angular stratification yields an ultra-relativistic jet with $\Gamma_{\infty} \sim 100$ and a substantial sub-relativistic wind, broadly matching the energy partition inferred from GRB and SN/kilonova observations. The work demonstrates that jets can form within seconds of magnetar birth, supporting millisecond proto-magnetars as plausible engines for short GRBs and related transients, and underscores the value of three-dimensional, neutrino-radiation GRMHD simulations for early post-collapse dynamics.

Abstract

Rapidly rotating, strongly magnetized neutron stars (``millisecond proto-magnetars'') formed in stellar core-collapse, neutron star mergers, and white dwarf accretion-induced collapse have long been proposed as central engines of gamma-ray bursts (GRB) and accompanying supernovae/kilonovae. However, during the first few seconds after birth, neutrino heating drives baryon-rich winds from the neutron star surface, potentially limiting the magnetization and achievable Lorentz factors of the outflow and casting doubt on whether proto-magnetars can launch ultra-relativistic jets at early times, as needed to power short-duration GRB. We present 3D general-relativistic magnetohydrodynamic simulations of neutrino-heated proto-magnetar winds that incorporate M0 neutrino transport. While the global wind properties broadly agree with previous analytic estimates calibrated to one-dimensional models, our simulations reveal essential multidimensional effects. For rapidly rotating models with spin periods P = 1 ms, centrifugal forces strongly enhance mass loss near the rotational equator, producing a dense, sub-relativistic outflow ( ~0.1c). This equatorial wind naturally confines and collimates less baryon-loaded outflows emerging from higher latitudes, leading to the formation of a structured bipolar jet with a peak magnetization up to ~ 30-100 along the pole, sufficient to reach bulk Lorentz factors ~ 100 on larger scales. The resulting angular stratification of the outflow energy into ultra-relativistic polar and sub-relativistic equatorial components is broadly consistent with the observed partition between beaming-corrected GRB energies and supernova/kilonova ejecta. Our results demonstrate that millisecond proto-magnetars can launch relativistic jets within seconds of formation and highlight their potential role in powering the diverse electromagnetic counterparts of compact-object explosions.

Figures (6)

• Figure 1: Volume rendering of a rapidly rotating proto-magnetar launching powerful equatorial winds and a magnetized jet as simulated in our B3P1 model. Density isosurfaces are represented in light red ($\rho\approx 10^{14}\,{\rm g}{\,\rm cm}^{-3}$) and blue ($\rho\approx 10^{9}\,{\rm g}{\,\rm cm}^{-3}$), whereas magnetization is represented in red ($\sigma\approx 1$) and yellow ($\sigma\approx 100$) contours. White lines show polar magnetic field lines.
• Figure 2: We show 2D cross-sections of the $y=0$ plane time-averaged over $\approx 5$ ms for our most strongly magnetized models with $B_{\rm P} =3\times 10^{15}$ G, for three different spin periods (left to right) $P=18$ ms, $P=1.8$ ms, and $P=1$ ms. Top row: Rest-mass density $\rho$ ($z>0$) and net neutrino heating rate $\dot q_{\rm net} \equiv \dot q_+ - \dot q_-$ ($z<0$). White shading represents regions of net cooling, and red contours denote the electron anti-neutrino sphere ($\tau_{ \bar{\nu}_e}\simeq 2/3$). Bottom row: Radial 3-velocity $v^r$ ($z>0$) and magnetization $\sigma = b^2/4\pi\rho$ ($z<0$). The blue (outer) contour denotes the Alfvén surface (where the radial Alfvén velocity $v_A^r=v^r$), whereas the brown (inner) contour denotes the slow magnetosonic surface.
• Figure 3: Profiles of (from top to bottom) radial 3-velocity $v^r$, isotropic-equivalent mass outflow rate $\dot M_{\rm iso}$, magnetization $\sigma$, and isotropic-equivalent electromagnetic power $\dot E_{\rm EM}$ in the magnetar outflow as a function of polar angle $\theta$, as determined through a sphere of radius $r=500$ km from 2D slices time-averaged over an interval $\sim5$ ms after the wind has achieved a quasi steady-state.
• Figure 4: Left: Meridional cross sections showing steady-state properties (averaged over $\approx 5$ ms) of the wind models B3P1 (left) and B3P1.8 (right). The top three rows (from top to bottom) show the fractional contributions of the specific kinetic energy ($\approx -u_t-1$ at large distances), magnetic energy ($-u_tb^2/4\pi\rho$), and thermal enthalpy ($-u_t(\epsilon +P/\rho)$), to the total specific wind energy $\mathcal{B}$ (defined in Eq. \ref{['eq:bern']}). The bottom row shows the ratio of electromagnetic $\dot E_{\rm EM}$ to kinetic $\dot E_{\rm K} \equiv (W-1) \dot M_{\rm iso}$ power. The top row shows fluid velocity field lines, whereas the bottom three rows show the magnetic field lines. Right: Angle-averaged radial profiles of isotropic-equivalent luminosities along the $y=0$ plane for three models: B3P1 (solid, $0^\circ \le \theta \le 30^\circ$), B.6P1 (dashed, $0^\circ \le \theta \le 30^\circ$), B3P1.8 (dotted, $0^\circ \le \theta \le 90^\circ$). We show separately the Poynting luminosity (blue), kinetic luminosity (green), thermal luminosity (red), and their sum (black).
• Figure 5: Left: Cumulative distribution of wind luminosity $\dot E$ in material above a given value of $\Gamma_\infty \simeq \sigma$ (Eq. \ref{['eq:gamma_inf']}), for the most rapidly spinning, highly magnetized model (B3P1). The Poynting ($\dot E_{\rm EM}$, blue), thermal ($\dot E_{\rm therm}$ red), and kinetic ($\dot E_{\rm K}$, green) luminosity of the wind are measured at a spherical shell of radius $r\simeq 236$ km, between $t\simeq 155-166$ ms after magnetic field initialization. Right: Total isotropic-equivalent energy carried by the outflow over a duration $\Delta t=2\,\mathrm{s}$, in material with asymptotic Lorentz factor $\Gamma_\infty > 10$ ($\Gamma_\infty > 30$) shown with blue (red) points, vs. total isotropic-equivalent kinetic energy of the outflow $E_K (\Delta t=2~\rm s)$, as measured from cumulative distributions shown in the left panel. Most of the energy in fluid with $\Gamma_\infty\lesssim10$ resides in sub or moderately-relativistic wind components that would likely couple to the surrounding supernova or kilonova ejecta. Black points show inferred isotropic-equivalent energies of gamma-ray emission $E_{\gamma,\rm iso}$ and associated kilonovae $E_K$ from short GRBs compiled by rastinejad_kn_grb_2025, rescaled to a common duration of $2\,\mathrm{s}$ and assuming a jet half-opening angle $\theta_{j,\rm col} \simeq 8^\circ$ to match those found from the strongly magnetized, rapidly spinning wind models.