AthenaK Simulations of Magnetized Binary Neutron Star Mergers

TL;DR

We address modeling of magnetized binary neutron star mergers with a finite-temperature equation of state using the GPU-accelerated AthenaK code. The method combines six-level adaptive mesh refinement, a dipolar magnetic field of $B_0=10^{16}~\mathrm{G}$, and a temperature- and composition-dependent EOS to evolve the system from inspiral through about ${\sim}30$ ms post-merger, comparing results across three resolutions. The simulations show the formation of a magnetized funnel and a long-lived remnant neutron star, with a post-merger gravitational-wave peak near $f \approx 3~\mathrm{kHz}$ and cross-resolution agreement of $\Delta f \lesssim 82~\mathrm{Hz}$. However, due to significant baryon loading, no magnetically dominated outflow or relativistic jet is launched, though higher resolution and improved physics (e.g., Riemann solvers, neutrino transport) could change this outcome. The work demonstrates AthenaK's capability for accurate inspiral modeling and post-merger dynamics, with implications for multimessenger predictions and future enhancements.

Abstract

We present new numerical-relativity simulations of a magnetized binary neutron star merger performed with AthenaK. The simulations employ a temperature- and composition-dependent tabulated nuclear equation of state, with initially dipolar fields with a maximum initial strength of ${\sim}10^{16}\ {\rm G}$ which extend outside the stars. We employ adaptive mesh refinement and consider three grid resolutions, with grid spacing down to $Δx_{\rm min} \simeq 92\ {\rm m}$ in the most refined region. When comparing the two highest resolution simulations, we find orbital dephasing of over 7 orbits until merger of only $0.06$ radians. The magnetic field is amplified during the merger and we observe the formation of a magnetized funnel in the polar region of the remnant. Simulations are continued until about $30$ milliseconds after merger. However, due to significant baryonic pollution, the binary fails to produce a magnetically-dominated outflow. Finally, we discuss possible numerical and physical effects that might alter this outcome.

Figures (3)

• Figure 1: (Left) The power spectrum of the real part of the $(\ell=2,m=2)$ mode of the gravitational-wave strain for each resolution. The dashed vertical lines mark $f_2$, the peak frequency of the post-merger phase. (Right) The phase difference of the LR and MR runs measured relative to the HR run. The dashed vertical lines mark the merger time for each run using the same colors as the left plot. The waveform is extracted at a radius of $r=400~G\mathrm{M}_\odot/c^2\approx591~\mathrm{km}$ from the origin.
• Figure 2: A slice plot of the magnetization $\sigma=b^2/\rho$ and temperature in the $xy$ plane of the HR run at various times relative to merger. The cyan, yellow, green, blue, and black contours correspond to rest-mass densities of $10^{11}$, $10^{12}$, $10^{13}$, $10^{14}$, and $10^{15}~\mathrm{g}/\mathrm{cm}^{3}$, respectively.
• Figure 3: Slice plots of the magnetization $\sigma=b^2/\rho$ in the $xz$ plane for the LR, MR, and HR runs at $t-t_\mathrm{merg}\approx30~\mathrm{ms}$. The cyan, yellow, green, blue, and black contours correspond to rest-mass densities of $10^7$, $10^8$, $10^9$, $10^{10}$, and $10^{11}~\mathrm{g}/\mathrm{cm}^3$.