Simulating the quasi-ballistic regime of a short Gamma-Ray Burst jet

TL;DR

The study tackles how a short GRB jet propagates through the dense, asymmetric post-merger environment and approaches a quasi-ballistic regime. It extends a prior 3D MHD jet simulation by evolving to ~10 s using a Cartesian grid after an initial spherical phase, with jet parameters $\Theta_j=10^\circ$, $\Gamma_j=3$, $\Gamma_\infty=300$, $L_j=3\times10^{51}$ erg s$^{-1}$ and 8% magnetic energy. Key findings include a breakout at $t_{\rm BO} \approx 350$ ms and $r_{\rm BO} \approx 5\times10^{4}$ km, with about 98% of the jet energy converted into kinetic form and the angular structure stabilizing into a quasi-ballistic profile, albeit with non-axisymmetric, environment-imprinted features. These results provide robust inputs for afterglow modeling and demonstrate a general, ready-to-apply method for simulating jets in BNS merger contexts.

Abstract

This study extends the 3D magnetohydrodynamic (MHD) simulation of a jet emerging from a binary neutron star (BNS) merger presented in Pavan et al. (2023), in which an incipient jet was manually injected into the realistic environment imported from a previous general-relativistic MHD simulation of a merging BNS system. The jet evolution is followed up to almost 10 seconds without loss of resolution. Our results reveal that the jet faces challenges in penetrating the dense surroundings, leading to a barely successful outflow that exhibits structural asymmetries and low Lorentz factors. By the end of the extended simulation, 98% of the jet energy is converted to kinetic form and its angular structure is stabilized. The physical quantities inferred thus provide reliable inputs for afterglow emission calculations. This work demonstrates a method for simulating jets in 3D up to nearly ballistic regimes that is general and ready to be applied to any jet in a BNS merger context.

Figures (3)

• Figure 1: Meridional view of Lorentz factor, rest-mass density, total pressure, and magnetic field strength (left to right) of the simulation at three different times after jet injection (top to bottom): $\approx\!3$ s (beginning of the evolution on the new Cartesian grid), $\approx\!6.5$ s, and $\approx\!9.5$ s.
• Figure 2: Upper panel: time evolution of the different energy components in the whole computational domain: kinetic ($E_\mathrm{kin}$), internal ($E_\mathrm{int}$) and magnetic ($E_\mathrm{mag}$). The dashed (continuous) lines refer to the evolution employing the original spherical (Cartesian) grids. The vertical line represents the breakout time (see text). Lower panel: evolution of the fraction of $E_\mathrm{kin}/E_\mathrm{sum}$ (see text) within the simulation time in the spherical and Cartesian grids (in blue), further extrapolated to later times via a polynomial fit (orange line). Time is represented in logarithmic scale.
• Figure 3: 2D front-view angular distribution of the isotropic equivalent energy (top) and the radially averaged Lorentz factor (bottom) of the jet head at the times (after jet launching) $t_{BO}$, $t_1$, $t_2$ and $t_3$ specified at the top