Turbulent magnetic-field amplification in the first 10 milliseconds after a binary neutron star merger: Comparing high-resolution and large-eddy simulations

Abstract

The detection of binary neutron star mergers represents one of the most important and complex astrophysical discoveries of the recent years. One of the unclear aspects of the problem is the turbulent magnetic field amplification, initially triggered by the Kelvin-Helmholtz instability at much smaller scales than any reachable numerical resolution nowadays. Here we present numerical simulations of the first 10 milliseconds of a binary neutron star merger. First, we confirm in detail how the simulated amplification depends on the numerical resolution and is distributed on a broad range of scales, as expected from turbulent magnetohydrodynamics theory. We find that an initial large-scale magnetic field of 10 11 G inside each star is amplified in the remnant to root-mean-square values above 10 16 G within the first 5 milliseconds for our highest-resolution run. Then, we run large eddy simulations, exploring the performance of the subgrid-scale gradient model, already tested successfully in previous turbulent box simulations. We show that the addition of this model is especially important in the induction equation, since it leads to an amplification of the magnetic field comparable to a higher-resolution run, but with a greatly reduced computational cost. In the first 10 milliseconds, there is no clear hint for an ordered, large-scale magnetic field, which should indeed occur in longer timescales through magnetic winding and the magnetorotational instability.

Turbulent magnetic field amplification in binary neutron star mergers

“…The pressure p is obtained from the EoS as detailed in Sec. II C. The full set of evolution equations, including the hyperbolic divergence cleaning via damping of a new field φ [65] and all the gradient SGS terms, can be found in [58,59]. Following our previous studies, we include only the SGS term appearing on the induction equation,…”

“…Although the pre-coefficient C M is meant to be of order one for a numerical scheme having a mathematically ideal Gaussian filter kernel and neglecting higher-order corrections, the value that best mimics the feedback of small scales onto the large scales in a LES can differ depending partially on the numerical methods employed and on the specific problem, as discussed in [56][57][58][59]. In this work, we will set C M = 8, which has been shown to reproduce the magnetic field amplification more accurately for our numerical schemes [59]. Note that less dissipative numerical schemes would need smaller values of C M .…”

“…Each SGS term has a free normalization of order unity, which needs to be magnified to compensate for the numerical dissipation of the employed numerical scheme. In our scheme, enhancing such normalization for the induction equation SGS term, allows to improve the convergence of the magnetic amplification excited by the KHI, both in box simulations [57,58] and in binary neutron star mergers [59].…”

Universality of the turbulent magnetic field in hypermassive neutron stars produced by binary mergers

“…We evolve the GRMHD equations using the same formalism and numerical methods presented in [38,39]: in particular, with the addition of an explicit SGS term in the induction equation, which is able to provide a more convergent amplified field. We employ the same hybrid EoS as in [39] for the evolution, with a cold contribution given by a tabulated polytrope fit to the APR4 zerotemperature EoS [45], and thermal effects modeled by the ideal gas EoS with adiabatic index Γ th = 1.8 [46].…”

“…Following this line, we have recently extended and implemented the so-called gradient SGS model used in non-relativistic fluid dynamics [33,34] to the non-relativistic [35], special [36] and general relativistic [37] MHD with excellent results on capturing the small scale effects of turbulent flow induced by the KHI. We have performed LES of BNS coalescence [38], and found that the average magnetic field in the remnant is amplified with much less computational resources than the higher-resolution simulations leading to comparable results. In an accompanying paper [39], we show that high-resolution LES provide an amplification of the average magnetic field from 10 11 G to 10 16 G. More importantly, for the first time the magnetic field strength and its energy spectral distribution are converging to the same saturated level.…”