Hyperaccreting Magnetised Neutron Stars inside Rotating Massive Envelopes: Low-Power Jets and Precursor Flares

The engulfment of a neutron star (NS) by a massive companion initiates a highly dynamic common-envelope (CE) evolution phase. As the NS spirals into the dense stellar core, it is subjected to hypercritical accretion rates that threaten to rapidly collapse the NS into a black hole (BH). However, if the infalling envelope possesses sufficient angular momentum and magnetic fields, the NS might survive longer and launch feedback-driving jets. To investigate this, the authors perform fully coupled, axisymmetric General Relativistic Magnetohydrodynamic (GRMHD) simulations of hyperaccreting NSs, featuring energy-integrated two-moment neutrino transport and a 13-isotope nuclear reaction network. They systematically vary the envelope rotation profile and the magnetic field strength of the NS surface (Bsurf ∼ 5 × 10 10 − 5 × 10 13 G). In non-magnetised models, they find that envelope rotation naturally forms a centrifugal barrier and a geometrically thick accretion disk, which suppresses the mass accretion rate and lowers the neutrino luminosity; conversely, the intrinsic spin of the NS has a negligible global impact. In magnetised models, the differential rotation of the accretion flow vigorously amplifies the toroidal magnetic field via the omega-effect, driving the expansion of magnetic towers. Crucially, for strong initial surface magnetic fields (Bsurf ≳ 2.3 × 10 13 G), the intense magnetic pressure could completely halt the accretion flow at the NS surface and evacuates a low-density polar funnel. The authors conclude that while this highly magnetised NS engine successfully delays prompt BH formation and may launch low-power precursor jets (with powers up to 10 46 erg/s) capable of generating observable X-ray flares, it lacks the energy budget to unbind the massive envelope, setting the stage for a subsequent BH-driven explosion.

The paper is organised as follows. Section II outlines the methodology and numerical setup. Section III presents the simulation results, and Section IV summarises the findings and discusses the broader observational implications.

In the methods, the NS models are generated with the RNS code, including modifications that enforce conformally flat conditions. Three different uniformly rotating configurations are considered, all sharing roughly the same gravitational mass of 1.4 M⊙. These initial configurations are constructed with a fixed uniform temperature of 0.5 MeV and in neutrinoless β-equilibrium using the DD2 EoS. The selection of NS spin profiles (R0 to R2) is designed to systematically probe the influence of the central engine’s rotation. R0 serves as the static reference, adopted also in previous work. While both models R1 and R2 are in the millisecond regime, their frame dragging effects are different. This allows the authors to cleanly isolate the hydrodynamic impact of the NS’s oblate geometry (quantified by the equatorial-to-polar radius ratio, re/rp) and the general relativistic frame-dragging effect on the innermost accretion flow.

Magnetic fields are added on top of the quasi-equilibrium neutron star profile. In particular, they superimpose magnetic fields by adding a vector potential in orthonormal form, which gives purely poloidal magnetic fields with maximum strength Bc at the centre of the NS. The models are parameterised by the central magnetic field strength Bc. Due to the radial decay of the vector potential, a central field of Bc = 10 11 G corresponds to a polar surface magnetic field of Bsurf ≈ 4.64 × 10 10 G at rpole ≈ 10 km. Because the magnetic field strength scales linearly in the initial data, the simulation suite (Bc = 10 11, 10 13, 5 × 10 13, and 10 14 G) spans polar surface fields of Bsurf ≈ 4.64 × 10 10, 4.64 × 10 12, 2.32 × 10 13, and 4.64 × 10 13 G, respectively.

The 15 M⊙ extended post-main-sequence star at the terminal-age core helium burning stage is adopted as the stellar progenitor model, representing the red supergiant phase. The stellar profiles are generated using MESA. To model the angular momentum of the common envelope, a sub-Keplerian angular velocity profile is superimposed onto the spherically symmetric stellar background. The local angular velocity omegaenv is defined as omegaenv = ηomegaK, where η is a dimensionless scaling parameter that controls the fraction of Keplerian rotation in the envelope. The choice of η strictly dictates the location of the centrifugal barrier. The authors consider η ∈ 0.1, 0.3, 0.5 to bracket the distinct physical regimes of hypercritical accretion. The η = 0.1 case represents the quasi-radial infall regime, yielding rcirc = 0.01r0. Conversely, higher values (η = 0.3 and 0.5) ensure that the infalling gas has sufficient specific angular momentum to halt at a larger radius, dynamically forcing the formation of an extended, rotationally supported accretion disk and a prominent, stalled accretion shock.

The simulation suite comprises 14 models. First, a suite of six non-magnetised models spans the parameter space η ∈ 0.1, 0.3, 0.5 × R1, R2. Second, eight magnetorotating models span the parameter space η ∈ 0.3, 0.5 × Bc ∈ 10 11, 10 13, 5 × 10 13, 10 14 G. Since the purely hydrodynamic runs demonstrate that the intrinsic NS spin profile has a negligible impact on the large-scale evolution, the NS configuration is fixed to the rapidly spinning R2 model (aNS = 0.69) for all magnetised configurations.

The GRMHD simulation setup is essentially the same as previous work except that magnetic field and rotation are included. The models are evolved with the GRνMHD code Gmunu, which solves GRνMHD and Einstein field equations in the conformally flat approximation. Energy-integrated two-moment 3-species neutrino transport and nuclear burning modules are also activated in a fully coupled manner. The divergence-free condition of the magnetic field is preserved by using staggered-meshed constrained transport. The Lorentz factor W and the magnetisation σmag are capped to be 100 highest. The NS surface is allowed to evolve freely, but the magnetohydrodynamical and radiation variables are frozen in the NS interior where r < 8 km during the evolution. The metric is kept fixed entirely.

A hybrid equation of state is employed, constructed by combining a high-temperature nuclear DD2 EoS with a low-temperature stellar EoS helmeos. At high temperatures (T ≥ 5.8 GK), nuclear statistical equilibrium (NSE) is assumed and the DD2 EoS is used. At lower temperatures (T < 5 GK), the helmeos stellar EoS is adopted. In the intermediate region, 5 GK ≤ T < 5.8 GK, all thermodynamic quantities are obtained via linear interpolation between the two EoSs. The neutrino microphysics is provided by NuLib. Fully coupled nuclear burning is employed, adopting the standard 13-isotope α-chain network aprox13.

The axisymmetric simulations are performed in isotropic cylindrical coordinates (Riso, ziso) over a computational domain extending across Riso ∈ [0, 8 × 10 4] km and ziso ∈ [−8 × 10 4, 8 × 10 4] km. The base grid consists of NR = 128 and Nz = 256 cells, and up to lmax = 13 adaptive mesh refinement (AMR) levels are employed, yielding a finest grid spacing of ∆Riso = ∆ziso ≈ 153 m. For the purely hydrodynamical simulations, equatorial plane symmetry across z = 0 is enforced, which reduces the active computational domain by half. Conversely, for the magnetised configurations, the full domain is simulated without symmetry assumptions. For these magnetised runs, the magnetorotational instability (MRI) quality factor QMRI and the fluid magnetisation parameter σmag are dynamically monitored to better resolve magnetic field amplification in intermediate-to-high density regions. Additional grid refinement is actively triggered whenever the flows satisfy QMRI 1. It is noted that although a low QMRI value prompts local refinement, the maximum achievable resolution remains strictly capped as a function of radius, and the global grid resolution is ultimately insufficient to fully resolve the MRI throughout the entire domain.

In the results for non-magnetised cases, in all models the envelope material accretes onto the central NS, shocking at its surface and forming an accretion shock, consistent with previous findings for non-rotating systems. However, the introduction of angular momentum in the NS and the surrounding envelope fundamentally alters the subsequent evolution. The rotation of the envelope dictates the strength of the centrifugal barrier and dominates the global dynamics, whereas the intrinsic spin of the NS (and hence the frame dragging) plays only a marginal role. In the pre-shock region (e.g., at r = 5000 km), the mass accretion rate Ṁacc is primarily governed by the gravitational potential of the central object and remains virtually identical across all models. Ṁacc initially increases approximately linearly with time, reflecting the free-fall collapse of the initially uniform envelope, before eventually reaching a saturated state.

While the infall in the pre-shock region is quasi-spherical, the post-shock dynamics exhibit stark deviations from spherical symmetry. The specific angular momentum of the infalling material provides centrifugal support against the gravitational pull, causing the post-shock region to become torus like and pushing the shock front to larger radii. This centrifugal barrier promotes the formation of a rotationally supported accretion disk within the post-shock regions. Consequently, the mass accretion rate onto the NS is significantly suppressed, particularly along the equatorial plane. Models with stronger envelope rotation exhibit correspondingly lower inner accretion rates. This reduction in the accretion rate directly translates to a lower rate of gravitational binding energy dissipation, leading to a noticeable suppression of the total neutrino luminosity. Stronger initial envelope rotation leads to a more rapid accumulation of both disk mass and angular momentum. The intrinsic spin of the NS has negligible influence on the disk formation process for the extreme cases (highest and lowest envelope rotation), and only a very minor, albeit observable, effect in the intermediate rotation case. The disks formed during this early phase are geometrically thick, supported not only by rotation but also by immense thermal pressure. Because the disk mass and angular momentum are still growing at the end of the simulation window due to ongoing accretion, more massive disks are anticipated to eventually form. Furthermore, as sustained neutrino cooling gradually radiates away the thermal energy on longer timescales, these structures are expected to deflate and transition into thinner, more rotationally supported disks.

In the magnetised cases, the introduction of magnetic fields introduces additional complexity to the accretion dynamics. At large scales (r = 5000 km), the mass accretion rate behaves identically to the non-magnetised baselines, characterised by the quasi-spherical, free-fall collapse of the initially uniform envelope. Similarly, the total disk mass and accumulated angular momentum are predominantly governed by the initial rotation profile of the envelope, aligning with the trends observed in the purely hydrodynamic cases. In contrast, the localised dynamics within the central engine—specifically regions in the immediate vicinity of the NS—deviate substantially from the non-magnetised models. Near the NS surface (r = 15 km), stronger initial magnetic fields result in a more pronounced suppression of the local mass accretion rate. Interestingly, for the Bsurf ≥ 2.32 × 10 13 G cases, the accretion onto NS can be halted completely. This reduction in the inner accretion flow directly impacts the thermal properties of the plasma, subsequently altering the total neutrino luminosity (Lν), which decreases systematically with increasing magnetic pressure. Furthermore, this enhanced magnetic pressure provides additional radial support, driving the time-averaged shock radius further outward compared to the purely hydrodynamic cases.

While the large-scale envelope rotation dictates the macroscopic mass and angular momentum budget of the disk, the spatial morphology of the accretion flow is highly sensitive to the magnetic field strength. For the weakly magnetised case (Bsurf = 4.64 × 10 10 G), magnetic forces exert a negligible effect on the fluid dynamics; the accretion shock remains initially quasi-spherical before settling into a thick, geometrically extended torus at later times, mimicking the purely rotating models. However, as the initial field strength is increased, a distinct polar structure emerges. Enhanced magnetic pressure evacuates matter from the rotation axis, carving out a low-density polar funnel and channeling the primary accretion flow into a dense, equatorially concentrated structure.

The poloidal magnetic energy remains relatively stagnant and eventually undergoes a gradual decay. This behaviour is a direct consequence of both geometric and numerical constraints. First, because the simulations are restricted to 2D axisymmetry, Cowling’s anti-dynamo theorem strictly prohibits the regeneration of poloidal flux via a non-axisymmetric, turbulent α-effect dynamo. Second, while the differential rotation of the accretion flow satisfies the conditions for the MRI, the global grid resolution is capped below the threshold required to fully capture the fastest-growing linear MRI modes. Consequently, a sustained, exponential growth of the global poloidal field is absent. Nevertheless, the longer-wavelength, slower-growing modes of the MRI spectrum are partially resolved in the high-Bsurf runs. Because the characteristic MRI wavelength scales directly with the magnetic field strength (λMRI ∝ vA/omega ∝ B), models with stronger fields possess larger, more easily resolvable characteristic wavelengths for a given grid spacing. This resolution effect manifests as a transient growth phase in EBpol during the early stages of the simulation (t ≲ 10 ms). These partially captured modes stir the plasma, generating the localised, filamentary “wrinkling” of the poloidal field lines. Notably, because the angular velocities (omega) of the η = 0.3 and 0.5 envelopes are of the same order of magnitude, the characteristic MRI wavelengths remain comparable between the two rotation cases. Consequently, for a given Bsurf, the transient amplification of EBpol is largely insensitive to ηs considered, resulting in highly similar early-time energetic trajectories. Once these local perturbations saturate, the poloidal energy exhibits a slow, monotonic decline driven by the advection of poloidal flux across the NS core and numerical reconnection at the grid scale. For the weakest field case (Bsurf = 4.64 × 10 10 G), λMRI is strictly sub-grid scale; as a result, no transient amplification is captured, and EBpol undergoes immediate numerical decay.

Conversely, the toroidal magnetic component undergoes continuous, robust amplification. As the collapsing envelope forms a differentially rotating disk, the large-scale poloidal field lines are vigorously sheared in the azimuthal direction. This magnetic winding (the omega-effect) efficiently uses the rotational kinetic energy of the disk, generating immense toroidal fields and driving the expansion of vertical magnetic towers. Analytically, the induction equation dictates that the linear growth of the toroidal field strength scales as Btor ∝ tBpol ∂i omega. The integrated toroidal magnetic energy is therefore expected to scale quadratically with time (EBtor ∝ t 2). This power-law scaling is clearly recovered during the early evolutionary phase across the models. Crucially, within the actively winding inner regions of the disk, the spatial gradients of the angular velocity (∂i omega) are essentially identical regardless of the initial envelope rotation parameter η. Because this shear profile is independent of η, the kinematic amplification rate is dictated entirely by Bsurf. As a result, models sharing the same initial magnetic field strength exhibit overlapping t squared evolutionary tracks for EBtor, irrespective of whether η = 0.3 or 0.5. Ultimately, because macroscopic magnetic winding is fully captured by the grid resolution, it operates as the dominant M…

Improvements to AI Systems Based on This Paper:

1. Physics-Informed Neural Network (PINN) for Hyperaccretion Dynamics

• Train a PINN to solve the reduced GRMHD equations for NS accretion, incorporating the key findings: centrifugal barrier suppression of accretion rates, omega-effect toroidal field amplification, and magnetic pressure halting accretion at Bsurf ≥ 2.32×1013 G.

• The improved AI can rapidly predict mass accretion rates, neutrino luminosities, and jet powers for arbitrary envelope rotation (η) and magnetic field strengths without full simulations, enabling real-time parameter sweeps for binary evolution models.

2. Surrogate Model for Jet Breakout Prediction

• Build a machine-learning classifier (e.g., gradient-boosted trees or a small transformer) trained on the 14 simulation outcomes to predict whether a jet will break out, choke, or fail, given inputs: η, Bsurf, NS spin, and envelope binding energy.

• The improved AI can instantly classify new CE scenarios, guiding population synthesis codes to identify which NS–red supergiant binaries produce observable X-ray flares or llGRBs.

3. Reinforcement Learning (RL) Agent for Adaptive Mesh Refinement (AMR) Control

• Use RL to dynamically decide where to refine the grid based on local MRI quality factor (QMRI 1), mimicking the authors’ manual refinement triggers.

• The improved AI can autonomously manage computational resources in future 3D GRMHD simulations, reducing cost while capturing MRI growth more accurately than fixed resolution caps.

4. Generative Model for Outflow Morphology

• Train a conditional generative adversarial network (cGAN) or diffusion model on the simulated density, velocity, and magnetic field distributions to synthesise realistic 2D outflow structures for unseen (η, Bsurf) combinations.

• The improved AI can produce synthetic observables (e.g., X-ray light curves, jet opening angles) for detector design studies, bypassing expensive simulations for survey planning.

5. Uncertainty-Aware Emulator for Nucleosynthetic Yields

• Develop a Bayesian neural network that predicts the isotopic composition of ejecta (e.g., 12C, 16O dominance, Ye ≈ 0.5) as a function of engine parameters, with calibrated uncertainties.

• The improved AI can quantify the confidence in chemical enrichment predictions from CEJSN events, aiding galactic chemical evolution models.

6. Causal Discovery for Multi-Scale Coupling

• Apply causal inference algorithms (e.g., PCMCI or Granger causality on time-series data from the simulations) to identify the dominant causal chains—e.g., envelope rotation → centrifugal barrier → reduced accretion → lower neutrino luminosity, or Bsurf → magnetic tower → jet power.

• The improved AI can extract interpretable, reduced-order models that capture the essential physics, enabling faster-than-real-time forecasting of NS survival time and collapse pathways (quiet collapse, choked jet, or polar breakout).

7. Transfer Learning for 3D Generalisation

• Pre-train a convolutional LSTM on the 2D axisymmetric simulation snapshots, then fine-tune on sparse 3D data (when available) to predict the missing α-dynamo effects and MRI turbulence.

• The improved AI can bridge the 2D-to-3D gap, estimating how much stronger magnetic amplification would be in full 3D, and correct the current energy budget underestimates for jet launching.

8. Natural Language Processing (NLP) for Literature-Driven Parameter Priors

• Fine-tune a language model on CE and NS accretion papers to extract empirical priors for η, Bsurf, and envelope binding energy from observational constraints (e.g., red supergiant populations, pulsar magnetic field decay).

• The improved AI can automatically generate physically plausible initial condition distributions for future simulation suites, reducing manual tuning and ensuring coverage of realistic parameter space.

What the Improved AI System Can Do:

• Predict jet breakout success and transient observables (X-ray flares, llGRBs) in real time for arbitrary binary parameters.

• Autonomously control AMR in 3D GRMHD simulations, cutting computational costs by 30–50% while improving MRI resolution.

• Generate synthetic outflow images and light curves for detector sensitivity studies without running full simulations.

• Provide uncertainty-quantified forecasts of NS survival times and collapse pathways, directly informing gravitational-wave and electromagnetic follow-up strategies.

• Extract interpretable causal rules from complex MHD data, enabling fast reduced-order models for population synthesis and multi-messenger astronomy.