Subgrid modelling of MRI-driven turbulence in differentially rotating neutron stars

TL;DR

The paper tackles MRI-driven turbulence in differentially rotating neutron stars by implementing the MInIT subgrid model in global Newtonian MHD simulations. It evolves two turbulent energy densities, $e_{ m MRI}$ and $e_{ m PI}$, to close the turbulent stresses that mediate angular-momentum transport, linking them to resolved quantities via calibrated closures. The results show outward transport of angular momentum, flattening of the inner rotation profile, and a turbulence decay as rotation becomes more rigid, with transport strength depending on the initial rotation rate, magnetic-field strength, and initial turbulence. The study demonstrates the feasibility of LES closures like MInIT for MRI in astrophysical remnants and highlights the need for fully relativistic, 3D extensions to capture the MRI comprehensively in BNS merger remnants and related phenomena.

Abstract

Following a binary neutron star (BNS) merger, the transient remnant is often a fast-spinning, differentially rotating, magnetised hypermassive neutron star (HMNS). This object is prone to the magnetorotational instability (MRI) which drives magnetohydrodynamic turbulence that significantly influences the HMNS global dynamics. A key consequence of turbulence is the outward transport of angular momentum which impacts the remnant's stability and lifetime. Most numerical simulations of BNS mergers are unable to resolve the MRI due to its inherently small wavelength. To overcome this limitation, subgrid models have been proposed to capture the effects of unresolved small-scale physics in terms of large-scale quantities. We present the first implementation of our MHD-Instability-Induced Turbulence (MInIT) model in global Newtonian simulations of MRI-sensitive, differentially rotating, magnetised neutron stars. Here, we show that by adding the corresponding turbulent stress tensors to the momentum equation, MInIT successfully reproduces the angular momentum transport in neutron stars driven by small-scale turbulence.

Figures (11)

• Figure 1: Radial equatorial profile of the initial mass density with (blue) and without (red) the exponential decay at low values. The profiles are identical for density values above $\rho_{\rm thresh, atm}$.
• Figure 2: Time evolution of the turbulent energy densities, $e_{\rm MRI}$ (solid lines) and $e_{\rm PI}$ (dashed lines), averaged over a radius of $r = 4$ km. Different colours represent different central initial rotation frequencies, $\Omega_i$.
• Figure 3: Radial equatorial profiles of the angular frequency, $\Omega$, for several initial central values, $\Omega_i$. Each colour represents different times, indicated in the top legend. The solid curves correspond to simulations incorporating the MInIT model while the dashed ones for simulations without it. For $t = 1$ ms, both solid and dashed curves overlap, because the MRI is still developing.
• Figure 4: Contour plot of the turbulent kinetic energy density of the MRI, $e_{\rm MRI}$. Each panel stands for different times $t = \{2.5,7.5,25,75\}$ ms. After a rapid growth during the first $\sim 10$ ms through all the stellar domain, the energy density starts decaying at the inner region of the star, due to the transport of angular momentum from the centre. The blue dashed line stands for the isocontour of the mass density $\rho$ at 10$\%$ of its central value.
• Figure 5: Radial equatorial profiles of the shear parameter at different times, corresponding to the simulation labelled with $\Omega_3$. Due to angular momentum transport, $q$ tends to 0 (dashed grey line) as time increases.