The initial spin matters: the impact of rapid rotation on magnetic-field amplification at merger

TL;DR

The paper tackles how the initial spin of merging binary neutron stars affects KHI-driven magnetic-field amplification during the merger. Using a novel hybrid GRMHD approach that pairs a full GR evolution with a high-resolution post-merger xCFC-GWRR scheme at $35\,\rm m$ resolution, the authors simulate four spin configurations (IR, UU, DD, DU) with $\chi = 0.35$ in equal-mass binaries governed by the TNTYST EOS. They find that anti-aligned spins produce the strongest magnetic-field amplification via KHI, while aligned spins yield the weakest, with mixed spins displaying intermediate behavior; despite different initial growth rates, all cases converge to a topological partition where $E_{\rm EM}^{\rm pol} \approx 2\,E_{\rm EM}^{\rm tor}$ and $E_{\rm EM}^{z} \approx E_{\rm EM}^{\rm tor}$. This quasi-universal equipartition emerges only at high resolution and has implications for the EM emission at merger and the spun state of the merger remnant, suggesting that spin leaves a lasting imprint on post-merger magnetization. The work demonstrates that spin is a critical factor in magnetic-field amplification and provides a framework to explore longer evolutions, different mass ratios, and EOSs relevant for multi-messenger observations.

Abstract

A couple of milliseconds after the merger of a binary system of neutron stars can play a fundamental role in amplifying the comparatively low initial magnetic fields into magnetar strengths. The basic mechanism responsible for this amplification is the Kelvin-Helmholtz instability (KHI) and we here report the first systematic study of the impact of rapid rotation on the KHI-amplification process exploiting general-relativistic magnetohydrodynamic simulations at very high-resolutions of $35\,{\rm m}$. Concentrating on four different spinning configurations, we find that aligned, anti-aligned, and mixed (aligned/anti-aligned) spin configurations lead to markedly different growth rates of the electromagnetic (EM) energy, field topologies, and vortex properties when compared to the irrotational case. These differences arise from intrinsic variations in the system dynamics, such as tidal deformation, collision strength, and contact surface area, with the anti-aligned configuration producing the largest vorticity and growth in EM energy. Importantly, while different spin configurations lead to significantly different initial growth rates of the poloidal/toroidal components, all systems converge to a specific topological partition. Our simulations are confined to a short window in time, but the different EM energies produced as a result of spin will imprint the EM emission at merger and provide information on the spinning state at merger.

Figures (6)

• Figure 1: Top panel: evolution of the total EM for the four binaries considered, star symbols indicating when the KHI can be considered to be globally quenched ($t = t_{\rm sh, 1/2}$). Second panel: evolutions of the EM energy in the poloidal (solid lines) and toroidal components (dashed lines). Third panel: Evolutions of the KHI growth rate $\gamma := \dot{E}_{_{\rm EM}}/E_{_{\rm EM}}$. Bottom panel: evolutions of the KHI growth rates in the poloidal (solid lines) and toroidal components (dashed lines). In all panels, the vertical dashed lines mark the merger time $t_{\rm mer}$ for each binary.
• Figure 2: Distributions of the magnetic-field strength $|B|$ on $z=0$-plane for all cases considered (different rows) at times $t = t_{\rm sh}$, $t_{\rm sh, 1/2}$, and $t-t_{\rm sh}=2\,{\rm ms}$ (different columns). Note that all figures have been rotated so that the maxima of the rest-mass density of the two NSs at $t = t_{\rm sh}$ are on the $y=0$ line (for the DU binary, only the density maximum of aligned-spinning star is on $y=0$ line.). Each panel reports data covered by the finest resolution box with $\Delta x \simeq 35\,{\rm m}$. The arrows in first column indicate the spin-alignment of each star.
• Figure 3: Distributions of the Lorentz factor $W$ for all cases considered (different columns) at time $t = t_{\rm mer}$. As in Fig. \ref{['fig:fig2']}, the distributions are rotates so that the stellar centres are on a $y=0$ line. Dashed and solid lines correspond to the rest-mass density contours of $4\times 10^{14}$ and $6\times 10^{14}\,{\rm g~cm^{-3}}$, respectively.
• Figure 4: Top panel: evolution of the ratio of the EM energy in the poloidal and toroidal components (solid lines) for all binaries considered; note that at late times the ratio converges to a constant value of $\simeq 2$. Bottom panel: as in the top but relative to the ratio between the $z$- and the toroidal components; note that at late times the ratio converges to a constant value of $\simeq 1$. Shown with dashed lines are the same quantities when employing a coarser resolution of $300\,{\rm m}$ and yielding to significantly different values.
• Figure 5: Absolute values of density-weighted kinematic vorticity $\left|\rho \omega_{\perp}^{ij}\right|$ for all cases at the time when the growth rate of poloidal EM energy reach their peaks. The top and bottom rows show the distributions of $\left|\rho \omega_{\perp}^{xz}\right|$ and $\left|\rho \omega_{\perp}^{xy}\right|$ on the $(x,z)$ and $(x,y)$ planes, respectively. The different columns refer to the four binaries considered and at four representative times. The distributions are rotated so as to highlight the different distributions of vorticity.