Magnetorotational Instability Research Articles

Angular-momentum Transport in Proto-neutron Stars and the Fate of Neutron Star Merger Remnants

Both the core collapse of rotating massive stars, and the coalescence of neutron star (NS) binaries result in the formation of a hot, differentially rotating NS remnant. The timescales over which differential rotation is removed by internal angular-momentum transport processes (viscosity) have key implications for the remnant’s long-term stability and the NS equation of state (EOS). Guided by a nonrotating model of a cooling proto-NS, we estimate the dominant sources of viscosity using an externally imposed angular-velocity profile Ω(r). Although the magneto-rotational instability provides the dominant source of effective viscosity at large radii, convection and/or the Tayler–Spruit dynamo dominate in the core of merger remnants where dΩ/dr ≥ 0. Furthermore, the viscous timescale in the remnant core is sufficiently short that solid-body rotation will be enforced faster than matter is accreted from rotationally supported outer layers. Guided by these results, we develop a toy model for how the merger remnant core grows in mass and angular momentum due to accretion. We find that merger remnants with sufficiently massive and slowly rotating initial cores may collapse to black holes via envelope accretion, even when the total remnant mass is less than the usually considered threshold ≈1.2 M TOV for forming a stable solid-body rotating NS remnant (where M TOV is the maximum nonrotating NS mass supported by the EOS). This qualitatively new picture of the post-merger remnant evolution and stability criterion has important implications for the expected electromagnetic counterparts from binary NS mergers and for multimessenger constraints on the NS EOS.

The Role of Strong Magnetic Fields in Stabilizing Highly Luminous Thin Disks

We present and analyze a set of three-dimensional, global, general relativistic radiation magnetohydrodynamic simulations of thin, radiation-pressure-dominated accretion disks surrounding a nonrotating, stellar-mass black hole. The simulations are initialized using the Shakura–Sunyaev model with a mass accretion rate of (corresponding to L = 0.17L Edd). Our previous work demonstrated that such disks are thermally unstable when accretion is driven by an α-viscosity. In the present work, we test the hypothesis that strong magnetic fields can both drive accretion through magnetorotational instability and restore stability to such disks. We test four initial magnetic field configurations: (1) a zero-net-flux case with a single, radially extended set of magnetic field loops (dipole), (2) a zero-net-flux case with two radially extended sets of magnetic field loops of opposite polarity stacked vertically (quadrupole), (3) a zero-net-flux case with multiple radially concentric rings of alternating polarity (multiloop), and (4) a net-flux, vertical magnetic field configuration (vertical). In all cases, the fields are initially weak, with a gas-to-magnetic pressure ratio ≳100. Based on the results of these simulations, we find that the dipole and multiloop configurations remain thermally unstable like their α-viscosity counterpart, in our case collapsing vertically on the local thermal timescale and never fully recovering. The vertical case, on the other hand, stabilizes and remains so for the duration of our tests (many thermal timescales). The quadrupole case is intermediate, showing signs of both stability and instability. The key stabilizing factor is the ability of specific field configurations to build up and sustain strong, P mag ≳ 0.5P tot, toroidal fields near the midplane of the disk. We discuss the reasons why certain configurations are able to do this effectively and others are not. We then compare our stable simulations to the standard Shakura–Sunyaev disk.

Simulating the magnetorotational instability on a moving mesh with the shearing box approximation

ABSTRACT The magnetorotational instability (MRI) is an important process in sufficiently ionized accretion discs, as it can create turbulence that acts as an effective viscosity, mediating angular momentum transport. Due to its local nature, it is often analysed in the shearing box approximation with Eulerian methods, which otherwise would suffer from large advection errors in global disc simulations. In this work, we report on an extensive study that applies the quasi-Lagrangian, moving-mesh code arepo, combined with the Dedner cleaning scheme to control deviations from $\nabla \cdot \boldsymbol B=0$, to the problem of magnetized flows in shearing boxes. We find that we can resolve the analytical linear growth rate of the MRI with mean background magnetic field well. In the zero net flux case, there is a threshold value for the strength of the divergence cleaning above which the turbulence eventually dies out, and in contrast to previous Eulerian simulations, the strength of the MRI does not decrease with increasing resolution. In boxes with larger vertical aspect ratio we find a mean-field dynamo, as well as an active shear current effect that can sustain MRI turbulence for at least 200 orbits. In stratified simulations, we obtain an active αω dynamo and the characteristic butterfly diagram. Our results compare well with previous results obtained with static grid codes such as athena. We thus conclude that arepo represents an attractive approach for global disc simulations due to its quasi-Lagrangian nature, and for shearing box simulations with large density variations due to its continuously adaptive resolution.

Assessment of a new sub-grid model for magnetohydrodynamical turbulence. I. Magnetorotational instability

ABSTRACT Insufficient numerical resolution of grid-based, direct numerical simulations (DNS) hampers the development of instability-driven turbulence at small (unresolved) scales. As an alternative to DNS, sub-grid models can potentially reproduce the effects of turbulence at small scales in terms of the resolved scales, and hence can capture physical effects with less computational resources. We present a new sub-grid model, the MHD-instability-induced-turbulence (MInIT) mean-field model. MInIT is a physically motivated model based on the evolution of the turbulent (Maxwell, Reynolds, and Faraday) stress tensors and their relation with the turbulent energy densities of the magnetorotational (MRI) and parasitic instabilities, modelled with two partial differential evolution equations with stiff source terms. Their solution allows obtaining the turbulent stress tensors through the constant coefficients that link them to the energy densities. The model is assessed using data from MRI in-box DNS and applying a filtering operation to compare the filtered data with that from the model. Using the L2-norm as the metric for the comparison, we find less than one order-of-magnitude difference between the two sets of data. No dependence on filter size or length scale of unresolved scales is found, as opposed to results using the gradient model (which we also use to contrast our model) in which the L2-norm of some of the stresses increases with filter size. We conclude that MInIT can help DNS by properly capturing small-scale turbulent stresses which has potential implications on the dynamics of highly magnetized rotating compact objects, such as those formed during binary neutron star mergers.

Fully Kinetic Shearing-box Simulations of Magnetorotational Turbulence in 2D and 3D. I. Pair Plasmas

The magnetorotational instability (MRI) is a fundamental mechanism determining the macroscopic dynamics of astrophysical accretion disks. In collisionless accretion flows around supermassive black holes, MRI-driven plasma turbulence cascading to microscopic (i.e., kinetic) scales can result in enhanced angular-momentum transport and redistribution, nonthermal particle acceleration, and a two-temperature state where electrons and ions are heated unequally. However, this microscopic physics cannot be captured with standard magnetohydrodynamic (MHD) approaches typically employed to study the MRI. In this work, we explore the nonlinear development of MRI turbulence in a pair plasma, employing fully kinetic particle-in-cell (PIC) simulations in two and three dimensions. First, we thoroughly study the axisymmetric MRI with 2D simulations, explaining how and why the 2D geometry produces results that differ substantially from 3D MHD expectations. We then perform the largest (to date) 3D simulations, for which we employ a novel shearing-box approach, demonstrating that 3D PIC models can reproduce the mesoscale (i.e., MHD) MRI dynamics in sufficiently large runs. With our fully kinetic simulations, we are able to describe the nonthermal particle acceleration and angular-momentum transport driven by the collisionless MRI. Since these microscopic processes ultimately lead to the emission of potentially measurable radiation in accreting plasmas, our work is of prime importance to understand current and future observations from first principles, beyond the limitations imposed by fluid (MHD) models. While in this first study we focus on pair plasmas for simplicity, our results represent an essential step toward designing more realistic electron–ion simulations, on which we will focus in future work.

Trapping (sub-)Neptunes similar to TOI-216b at the inner disk rim

Context. The occurrence rate of observed sub-Neptunes has a break at 0.1 au, which is often attributed to a migration trap at the inner rim of protoplanetary disks where a positive co-rotation torque prevents inward migration. Aims. We argue that conditions in inner disk regions are such that sub-Neptunes are likely to open gaps, lose the support of the co-rotation torque as their co-rotation regions become depleted, and the trapping efficiency then becomes uncertain. We study what it takes to trap such gap-opening planets at the inner disk rim. Methods. We performed 2D locally isothermal and non-isothermal hydrodynamic simulations of planet migration. A viscosity transition was introduced in the disk to (i) create a density drop and (ii) mimic the viscosity increase as the planet migrated from a dead zone towards a region with active magneto-rotational instability (MRI). We chose TOI-216b as a Neptune-like upper-limit test case, but we also explored different planetary masses, both on fixed and evolving orbits. Results. For planet-to-star mass ratios q ≃ (4–8) × 10−5, the density drop at the disk rim becomes reshaped due to a gap opening and is often replaced with a small density bump centred on the planet's co-rotation. Trapping is possible only if the bump retains enough gas mass and if the co-rotation region becomes azimuthally asymmetric, with an island of librating streamlines that accumulate a gas overdensity ahead of the planet. The overdensity exerts a positive torque that can counteract the negative torque of spiral arms. Under suitable conditions, the overdensity turns into a Rossby vortex. In our model, efficient trapping depends on the a viscosity and its contrast across the viscosity transition. In order to trap TOI-216b, αDZ = 10−3 in the dead zone requires αMRI ≳ 5 × 10−2 in the MRI-active zone. If αDZ = 5 × 10−4, αMRI ≳ 7.5 × 10−2 is needed. Conclusions. We describe a new regime of a migration trap relevant for massive (sub-)Neptunes that puts valuable constraints on the levels of turbulent stress in the inner part of their natal disks.

Cosmic-Ray Ionization Rate in Protoplanetary Disks with Sheared Magnetic Fields

We investigate the effects of magnetic-field configurations on the ionization rate by cosmic rays in protoplanetary disks. First, we consider cosmic-ray propagation from the interstellar medium (ISM) to the protoplanetary disks and showed that the cosmic-ray density around the disk should be 2 times lower than the ISM value. Then, we compute the attenuation of cosmic rays in protoplanetary disks. The magnetic fields in the disk are stretched to the azimuthal directions, and cosmic rays need to detour while propagating to the midplane. Our results show that the detouring effectively enhances the column density by about two orders of magnitude. We employ a typical ionization rate by cosmic rays in diffuse ISM, which is considered too high to be consistent with observations of protoplanetary disks, and find that the cosmic rays are significantly shielded at the midplane. In the case of the disk around IM Lup, the midplane ionization rate is very low for r ≲ 100 au, while the value is as large as a diffuse ISM in the outer radii. Our results are consistent with the recent Atacama Large Millimeter/submillimeter Array observation that indicates the radial gradient in the cosmic-ray ionization rate. The high ionization rate in the outer radii of disks may activate the magnetorotational instability that was thought to be suppressed due to ambipolar diffusion. These results will have a strong influence on the dynamical and chemical evolutions of protoplanetary disks.

MRI turbulence in accretion discs at large magnetic Prandtl numbers

ABSTRACT The effect of large magnetic Prandtl number Pm (the ratio of viscosity to resistivity) on the turbulent transport and energetics of the magnetorotational instability (MRI) is poorly understood, despite the realization of this regime in astrophysical environments as disparate as discs from binary neutron star (BNS) mergers, the inner regions of low-mass X-ray binaries and active galactic nuclei, and the interiors of protoneutron stars. We investigate the MRI dynamo and associated turbulence in the regime Pm > 1 by carrying out fully compressible, 3D MHD-shearing box simulations using the finite-volume code pluto, focusing mostly on the case of Keplerian shear relevant to accretion discs. We find that when the magnetic Reynolds number is kept fixed, the turbulent transport (as parameterized by α, the ratio of stress to thermal pressure) scales with the magnetic Prandtl number as α ∼ Pmδ, with δ ∼ 0.5−0.7 up to Pm ∼ 128. However, this scaling weakens as the magnetic Reynolds number is increased. Importantly, compared to previous studies, we find a new effect at very large Pm – the turbulent energy and stress begin to plateau, no longer depending on Pm. To understand these results we have carried out a detailed analysis of the turbulent dynamics in Fourier space, focusing on the effect of increasing Pm on the transverse cascade – a key non-linear process induced by the disc shear flow that is responsible for the sustenance of MRI turbulence. Finally, we find that α–Pm scaling is sensitive to the box vertical-to-radial aspect ratio, as well as to the background shear.

MRI-driven dynamo at very high magnetic Prandtl numbers

ABSTRACT The dynamo driven by the magnetorotational instability (MRI) is believed to play an important role in the dynamics of accretion discs and may also explain the origin of the extreme magnetic fields present in magnetars. Its saturation level is an important open question known to be particularly sensitive to the diffusive processes through the magnetic Prandtl number Pm (the ratio of viscosity to resistivity). Despite its relevance to proto-neutron stars and neutron star merger remnants, the numerically challenging regime of high Pm is still largely unknown. Using zero-net flux shearing box simulations in the incompressible approximation, we studied MRI-driven dynamos at unprecedentedly high values of Pm reaching 256. The simulations show that the stress and turbulent energies are proportional to Pm up to moderately high values (Pm ∼ 50). At higher Pm, they transition to a new regime consistent with a plateau independent of Pm for $\rm Pm \gtrsim 100$. This trend is independent of the Reynolds number, which may suggest an asymptotic regime where the energy injection and dissipation are independent of the diffusive processes. Interestingly, large values of Pm not only lead to intense small-scale magnetic fields but also to a more efficient dynamo at the largest scales of the box.

Turbulence in outer protoplanetary discs: MRI or VSI?

ABSTRACT The outer protoplanetary discs (PPDs) can be subject to the magnetorotational instability (MRI) and the vertical shear instability (VSI). While both processes can drive turbulence in the disc, existing numerical simulations have studied them separately. In this paper, we conduct global 3D non-ideal magnetohydrodynamic (MHD) simulations for outer PPDs, with ambipolar diffusion and instantaneous cooling, and hence conductive to both instabilities. Given the range of ambipolar Elsässer numbers (Am) explored, it is found that the VSI turbulence dominates over the MRI when ambipolar diffusion is strong (Am = 0.1); the VSI and MRI can co-exist for Am = 1; and the VSI is overwhelmed by the MRI when ambipolar diffusion is weak (Am = 10). Angular momentum transport process is primarily driven by MHD winds, while viscous accretion due to MRI and/or VSI turbulence makes a moderate contribution in most cases. Spontaneous magnetic flux concentration and formation of annular substructures remain robust in strong ambipolar diffusion-dominated discs (Am ≤ 1) with the presence of the VSI. Ambipolar diffusion is the major contributor to the magnetic flux concentration phenomenon rather than advection.

GRMHD simulations of accreting neutron stars I: Non-rotating dipoles

ABSTRACT We study the general-relativistic dynamics of matter being accreted on to and ejected by a magnetized and non-rotating neutron star. The dynamics is followed in the framework of fully general relativistic magnetohydrodynamics (GRMHD) within the ideal-MHD limit and in two spatial dimensions. More specifically, making use of the numerical code BHAC, we follow the evolution of a geometrically thick matter torus driven into accretion by the development of a magnetorotational instability. By making use of a number of simulations in which we vary the strength of the stellar dipolar magnetic field, we can determine self-consistently the location of the magnetospheric (or Alfvén) radius rmsph and study how it depends on the magnetic moment μ and on the accretion rate. Overall, we recover the analytic Newtonian scaling relation, i.e. rmsph ∝ B4/7, but also find that the dependence on the accretion rate is very weak. Furthermore, we find that the material torque correlates linearly with the mass-accretion rate, although both of them exhibit rapid fluctuations. Interestingly, the total torque fluctuates drastically in strong magnetic field simulations and these unsteady torques observed in the simulations could be associated with the spin fluctuations observed in X-ray pulsars.

Primordial dusty rings and episodic outbursts in protoplanetary discs

ABSTRACT We investigate the formation and evolution of ‘primordial’ dusty rings occurring in the inner regions of protoplanetary discs, with the help of long-term, coupled dust-gas, magnetohydrodynamic simulations. The simulations are global and start from the collapse phase of the parent cloud core, while the dead zone is calculated via an adaptive α formulation by taking into account the local ionization balance. The evolution of the dusty component includes its growth and back reaction on to the gas. Previously, using simulations with only a gas component, we showed that dynamical rings form at the inner edge of the dead zone. We find that when dust evolution, as well as magnetic field evolution in the flux-freezing limit are included, the dusty rings formed are more numerous and span a larger radial extent in the inner disc, while the dead zone is more robust and persists for a much longer time. We show that these dynamical rings concentrate enough dust mass to become streaming unstable, which should result in a rapid planetesimal formation even in the embedded phases of the system. The episodic outbursts caused by the magnetorotational instability have a significant impact on the evolution of the rings. The outbursts drain the inner disc of grown dust, however, the period between bursts is sufficiently long for the planetesimal growth via streaming instability. The dust mass contained within the rings is large enough to ultimately produce planetary systems with the core accretion scenario. The low-mass systems rarely undergo outbursts, and, thus, the conditions around such stars can be especially conducive for planet formation.

Observation of Axisymmetric Standard Magnetorotational Instability in the Laboratory.

We report the first direct evidence for the axisymmetric standard magnetorotational instability (SMRI) from a combined experimental and numerical study of a magnetized liquid-metal shear flow in a Taylor-Couette cell with independently rotating and electrically conducting end caps. When a uniform vertical magnetic field B_{i} is applied along the rotation axis, the measured radial magnetic field B_{r} on the inner cylinder increases linearly with a small magnetic Reynolds number Rm due to the magnetization of the residue Ekman circulation. Onset of the axisymmetric SMRI is identified from the nonlinear increase of B_{r} beyond a critical Rm in both experiments and nonlinear numerical simulations. The axisymmetric SMRI exists only at sufficiently large Rm and intermediate B_{i}, a feature consistent with theoretical predictions. Our simulations further show that the axisymmetric SMRI causes the velocity and magnetic fields to contribute an outward flux of axial angular momentum in the bulk region, just as it should in accretion disks.

Meshless methods for magnetohydrodynamics with vector potential

We present a meshless method for magnetohydrodynamics by evolving the vector potential of magnetic fields. A novel scheme and numerical techniques are developed to restrict the divergence of magnetic field, based on the Meshless Finite Mass/Volume with HLLD Riemann solver for conservative flux calculation. We found the magnetic field could be stabilized by a proper smoothing process and so the long-term evolution becomes available. To verify the new scheme, we perform the Brio-Wu shock tube, 2D and 3D Orszag-Tang vortex and Magnetorotational Instability test problems. The results suggest that our method is robust and has better precision on central offset, amplitude and detailed pattern than an existing meshless code–GIZMO.

The magneto-rotational instability in massive stars

Context. The magneto-rotational instability (MRI) has been proposed as a mechanism to transport angular momentum (AM) and chemical elements in theoretical stellar models. Aims. Using as a prototype a massive star of 15 M⊙ with solar metallicity, we explore the effects of the MRI on the evolution of massive stars. Methods. We used the Geneva Stellar Evolution Code to simulate the evolution of various models, up to the end of oxygen burning, including the MRI through effective, one-dimensional, diffusion coefficients. We consider different trigger conditions (depending on the weighting of chemical gradients through an arbitrary but commonly used factor) and different treatments of meridional circulation as either advective or diffusive. We also compare the MRI with the Tayler-Spruit (TS) dynamo in models that included both instabilities. Results. The MRI triggers throughout stellar evolution. Its activation is highly sensitive to the treatment of meridional circulation and the existence of chemical gradients. The MRI is very efficient at transporting both matter and AM, leading to noticeable differences in rotation rates and chemical structure, which may be observable in young main sequence stars. While the TS dynamo is the dominant mechanism for transferring AM, the MRI remains relevant in models where both instabilities are included. Extrapolation of our results suggests that models that include the MRI tend to develop more compact cores, which likely produce failed explosions and black holes, than models where only the TS dynamo is included (where explosions and neutron stars may be more frequent). Conclusions. The MRI can be an important factor in massive star evolution but is very sensitive to the implementation of other processes in the model. The transport of AM and chemical elements due to the MRI alters the rotation rates and the chemical makeup of the star from the core to the surface and may change the explodability properties of massive stars.

A Nonlocal Magneto-curvature Instability in a Differentially Rotating Disk

A global mode is shown to be unstable to nonaxisymmetric perturbations in a differentially rotating Keplerian disk containing either vertical or azimuthal magnetic fields. In an unstratified cylindrical disk model, using both global eigenvalue stability analysis and linear global initial-value simulations, it is demonstrated that this instability dominates at strong magnetic fields where local standard magnetorotational instability (MRI) becomes stable. Unlike the standard MRI mode, which is concentrated in the high flow shear region, these distinct global modes (with low azimuthal mode numbers) are extended in the global domain and are Alfvén-continuum-driven unstable modes. As its mode structure and relative dominance over MRI are inherently determined by the global spatial curvature as well as the flow shear in the presence of a magnetic field, we call it the magneto-curvature (magneto-spatial-curvature) instability. Consistent with the linear analysis, as the field strength is increased in the nonlinear simulations, a transition from MRI-driven turbulence to a state dominated by global nonaxisymmetric modes is obtained. This global instability could therefore be a source of nonlinear transport in accretion disks at a higher magnetic field than predicted by local models.

Turbulent Dust-trapping Rings as Efficient Sites for Planetesimal Formation

Recent observations of protoplanetary disks (PPDs) at submillimeter wavelengths have revealed the ubiquity of annular substructures that are indicative of pebble-sized dust particles trapped in turbulent ringlike gas pressure bumps. This major paradigm shift also challenges the leading theory of planetesimal formation from such pebbles by means of the streaming instability, which operates in a pressure gradient and can be suppressed by turbulence. Here, we conduct 3D local shearing box nonideal magnetohydrodynamic simulations of dust trapping in enforced gas pressure bumps, including dust backreaction. Under a moderate level of turbulence generated by the magnetorotational instability with ambipolar diffusion, which is suitable for outer disk conditions, we achieve quasi-steady states of dust trapping balanced by turbulent diffusion. We find strong dust clumping in all simulations near the gas pressure maxima, reaching a maximum density well above the threshold for triggering gravitational collapse to form planetesimals. A strong pressure bump concentrates dust particles toward the bump’s center. With a weak pressure bump, dust can also concentrate in secondary filaments off the bump’s center, due to dust backreaction, but strong clumping still occurs mainly in the primary ring around the bump’s center. Our results reveal dust-trapping rings to be robust locations for planetesimal formation in outer PPDs, while they may possess diverse observational properties.

Discovery of Line Pressure Broadening and Direct Constraint on Gas Surface Density in a Protoplanetary Disk

The gas surface density profile of protoplanetary disks is one of the most fundamental physical properties to understanding planet formation. However, it is challenging to determine the surface density profile observationally, because the H2 emission cannot be observed in low-temperature regions. We analyzed the Atacama Large Millimeter/submillimeter Array (ALMA) archival data of the 12CO J = 3 − 2 line toward the protoplanetary disk around TW Hya and discovered extremely broad line wings due to the pressure broadening. In conjunction with a previously reported optically thin CO isotopologue line, the pressure broadened line wings enabled us to directly determine the midplane gas density for the first time. The gas surface density at ∼5 au from the central star reaches ∼103 g cm−2, which suggests that the inner region of the disk has enough mass to form a Jupiter-mass planet. Additionally, the gas surface density drops at the inner cavity by ∼2 orders of magnitude compared to outside the cavity. We also found a low CO abundance of ∼10−6 with respect to H2, even inside the CO snow line, which suggests conversion of CO to less volatile species. Combining our results with previous studies, the gas surface density jumps at r ∼ 20 au, suggesting that the inner region (3 < r < 20 au) might be the magnetorotational instability dead zone. This study sheds light on the direct gas surface density constraint without assuming the CO/H2 ratio using ALMA.

Identification of a non-axisymmetric mode in laboratory experiments searching for standard magnetorotational instability

The standard magnetorotational instability (SMRI) is a promising mechanism for turbulence and rapid accretion in astrophysical disks. It is a magnetohydrodynamic (MHD) instability that destabilizes otherwise hydrodynamically stable disk flow. Due to its microscopic nature at astronomical distances and stringent requirements in laboratory experiments, SMRI has remained unconfirmed since its proposal, despite its astrophysical importance. Here we report a nonaxisymmetric MHD instability in a modified Taylor-Couette experiment. To search for SMRI, a uniform magnetic field is imposed along the rotation axis of a swirling liquid-metal flow. The instability initially grows exponentially, becoming prominent only for sufficient flow shear and moderate magnetic field. These conditions for instability are qualitatively consistent with SMRI, but at magnetic Reynolds numbers below the predictions of linear analyses with periodic axial boundaries. Three-dimensional numerical simulations, however, reproduce the observed instability, indicating that it grows linearly from the primary axisymmetric flow modified by the applied magnetic field.

Turbulent magnetic field amplification in binary neutron star mergers

Magnetic fields are expected to play a key role in the dynamics and the ejection mechanisms that accompany the merger of two neutron stars. General relativistic magnetohydrodynamic (MHD) simulations offer a unique opportunity to unravel the details of the ongoing physical processes. Nevertheless, current numerical studies are severely limited by the fact that any affordable resolution remains insufficient to fully capture the small-scale dynamo, initially triggered by the Kelvin-Helmholtz instability, and later sourced by several MHD processes involving differential rotation. Here, we alleviate this limitation by using explicit large-eddy simulations, a technique where the unresolved dynamics occurring at the subgrid scales (SGS) is modeled by extra terms, which are functions of the resolved fields and their derivatives. The combination of high-order numerical schemes, high resolutions, and the gradient SGS model allow us to capture the small-scale dynamos produced during the binary neutron star mergers, as shown in previous works. Here, we follow the first 50 milliseconds after the merger and, for the first time, we find numerical convergence on the magnetic field amplification, in terms of integrated energy and spectral distribution over spatial scales. Among other results, we find that the average intensity of the magnetic field in the remnant saturates at $\ensuremath{\sim}{10}^{16}\text{ }\text{ }\mathrm{G}$ around 5 ms after the merger. After 20--30 ms, both toroidal and poloidal magnetic field components grow continuously, fed by the winding mechanism that provides a slow inverse cascade, i.e., gradually transferring kinetic into magnetic energy. We find no clear hints for magnetorotational instabilities and no significant impact of the magnetic field on the redistribution of angular momentum in the remnant in our simulations, probably due to the very turbulent and dynamical topology of the magnetic field at all stages, with small-scale components largely dominating over the large-scale ones. Although the magnetic field grows near the rotation axis of the remnant, longer large-eddy simulations are necessary to further investigate the formation of large-scale, helical structures close to the rotational axis, which could be associated to jet formation.