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 MHD mechanism in the simulations, driving the toroidal magnetic energy to values orders of magnitude greater than its poloidal counterpart.

A low-density, highly magnetised polar funnel—driven by sufficiently rapid rotation and strong magnetic fields—is an essential prerequisite for launching relativistic jets. In the Bsurf = 4.64 × 10 12 G model, while the magnetic pressure initially rivals the gas pressure (βmag 1) in the post-shock region near the poles, the gas pressure eventually overwhelms the magnetic field almost everywhere at later times. Notably, regions where βmag 1 persist around the equatorial surface of the NS, providing additional magnetic support that suppresses equatorial accretion, but this magnetic dominance fails to establish itself along the polar axis. In models with stronger initial magnetisation, a magnetically dominated funnel successfully forms along the poles following the initial transient phase. For the Bsurf = 2.32 × 10 13 G model, this jet-like structure reaches peak magnetic dominance around t 80 ms, though it weakens at later times. Conversely, the Bsurf = 4.64 × 10 13 G model sustains a much wider and more robust magnetically dominated funnel.

The temporal evolution of the jet power extracted at r = 500 km for the high-B models across all values of η is examined. Low-B models are not shown because they fail to form funnels with sufficient magnetisation (σmag > 1) at the extraction radius to drive an outflow. For the most strongly magnetised cases (Bsurf = 4.64 × 10 13 G), regardless of η, a jet successfully breaks out past the extraction radius, sustaining a jet power on the order of O(10 46) erg/s. In contrast, the jets in the Bsurf = 2.32 × 10 13 G models struggle to overcome the ram pressure of the infalling envelope, exhibiting ‘choked’ or stuttering behaviours. For both η values, an initial short burst occurs at t 0.03 s, lasting less than 0.02 s before falling back. At t 0.08 s, a secondary burst arises. In the η = 0.3 case, this secondary burst is again extremely short-lived, quickly collapsing with no further breakouts (i.e. Ljet ≳ 2 × 10 45 erg/s) recorded at this radius during the simulated time. However, in the η = 0.5 case, the jet successfully revives from this secondary burst, resulting in a more sustained outflow with a power slightly below 10 46 erg/s. The divergent fates of the jets in the Bsurf = 2.32 × 10 13 G models highlight the critical role of the envelope’s rotation. A faster-rotating envelope (η = 0.5) carries greater specific angular momentum, subjecting the infalling gas to a stronger centrifugal barrier. This enhanced centrifugal force naturally evacuates gas from the rotational axis, resulting in a polar funnel that is less baryon-loaded. The η = 0.5 case exhibits a stronger initial burst at the poles and carves out a substantially wider magnetically dominated funnel than its η = 0.3 counterpart. By mitigating the ram pressure of the infalling baryons, the rapid rotation provides the ideal environmental conditions necessary for the jet to break out and survive at late times.

To evaluate the potential for a coincident optical transient, the total unbound mass and diagnostic explosion energy within the shocked region are estimated. Sustained growth of the unbound mass and energy is only achieved when the initial magnetic field is sufficiently strong (Bsurf ≥ 2.32 × 10 13 G). While the Bsurf = 4.64 × 10 12 G model exhibits a brief period where a fraction of the mass is unbound, this material is eventually recaptured and becomes gravitationally bound again at later times due to the continuously intensifying accretion flow. In the most strongly magnetised cases, the unbound mass and energy saturate at approximately O(10-6) M⊙ and O(10 46) erg, respectively. These quantities are calculated instantaneously and locally within the post-shock region; their late-time evolution may deviate from these values, particularly as the macroscopic mass accretion continues to strengthen. By the end of the simulations at t 0.35 s, the forward shock of the outflow has propagated to a radius of approximately r 2,000 km. Because this is still deep within the stellar interior (well below typical stripped-envelope radii of 10 5 km), the outflow properties derived here strictly represent the early-time, engine-driven injection phase prior to jet breakout.

The velocity and angular distributions of the outflow are captured. Overall, the outflow exhibits a clear bipolar structure, with almost no unbound matter found along the equatorial plane. The vast majority of the unbound mass resides at low velocities (v∞ ≲ 0.2c), which is expected to later expand as a massive, sub-relativistic wind or cocoon. In the cases where a jet is successfully launched, a highly energetic polar component is present despite its extremely low rest-mass density. These polar jets are mildly to highly relativistic (reaching v∞ ≳ 0.8c) and remain tightly collimated along a narrow opening angle.

To assess whether the engine-driven outflows can successfully escape the progenitor star, the angle-dependent diagnostic explosion energy ∆Eexp(θ) is compared with the total pre-shock envelope binding energy Ebind(θ). While a global, spherical unbinding of the 15 M⊙ stellar envelope would require an integrated energy budget of Ebind,total 10 51 erg, a collimated polar outflow does not need to lift the entire star. Instead, it only needs to overcome the gravitational overburden sitting directly within its narrow polar opening cone (θ ≲ 10°), with a breakout threshold of Ebind,cone ≈ 10 49 erg. The profiles are evaluated at t = 100 ms, when the central engine has only just begun operating. As hypercritical accretion continues over long physical timescales (1–2 s), continuous energy injection could build up cumulative integrated energy at the shock front. Therefore, while the wide-angle wind (θ ≳ 30°) likely remains choked within the dense envelope, the highly energetic polar jet is very likely to drill through the polar overburden and achieve successful shock breakout. Furthermore, the unperturbed 1D stellar progenitor structure used in the setup represents a strict upper bound on the stellar overburden. In a realistic CEE, orbital energy dissipation during the inspiral phase ejects a major fraction (50%–90%) of the envelope mass prior to central engine ignition. This pre-ejection reduces the remaining envelope binding energy down to Ebind 10 47 – 10 49 erg, drastically lowering the physical threshold for successful jet breakout.

The time evolution of the nucleosynthetic yields for the high-Bsurf models shows that the isotopes 12C and 16O strictly dominate the composition of the unbound material. This directly reflects the dominant initial composition of the stellar envelope. While the shocked region is substantially hotter and denser than the unshocked envelope, a massive amount of pristine stellar material is rapidly swept up and accreted into this region at a rate of Ṁ 10-3 M⊙/s. Crucially, the dynamical expansion timescale of this magnetohydrodynamically driven outflow is extremely short compared to the nuclear burning timescale. Consequently, the outflow is mechanically accelerated before explosive nucleosynthesis can take place, leaving the composition largely unchanged from the progenitor profile. Furthermore, the electron fraction Ye of the ejecta remains firmly around 0.5. This behaves distinctly differently from cases involving the formation of a strongly magnetised proto-neutron star. In these models, the central NS is uniformly rotating, which limits the efficacy of internal MHD processes compared to standard core-collapse supernovae or binary neutron star mergers, where the engine is highly differentially rotating. Consequently, there is limited angular momentum transport acting to dredge up neutron-rich material from deep within the NS. Because the stellar envelope natively begins with Ye = 0.5, and the combination of mass accretion and neutrino irradiation is not perfectly tuned to drive massive neutronization within the polar funnel, the ejected outflow simply retains the pristine electron fraction of the progenitor star.

In the discussion, the authors note that from a dynamical perspective, the rotation of the envelope and the magnetic fields provide vital support against the infalling material. Driven by the differentially rotating envelope and the initial poloidal magnetic fields, all magnetised models experience sustained toroidal magnetic field amplification. This continuous winding forms a classical “magnetic tower” structure, which provides the necessary magnetic pressure gradient to launch outflows. Crucially, the simulations reveal that strong magnetisation fundamentally alters the boundary conditions of the central engine. For models with Bsurf ≥ 2.32 × 10 13 G, the accumulated magnetic pressure, aided by the centrifugal barrier, becomes so intense that accretion onto the NS surface is completely halted. Mass flowing inward from the envelope is temporarily trapped in a highly magnetised, turbulent reservoir just outside the magnetosphere, functionally decoupling the NS from the immediate infall and delaying its eventual collapse.

In the most highly magnetised configurations (Bsurf = 4.64 × 10 13 G), a structured, magnetically driven polar outflow—an incipient jet—is successfully launched, accompanied by unbound material. The measured jet power is O(10 46) erg/s. While this power falls short of the 10 50 erg/s required for a canonical long Gamma-Ray Burst (GRB), it represents a viable mechanism for powering a low-luminosity, engine-driven transient. From an astronomical and evolutionary perspective, it is crucial to emphasise that a true primordial magnetar-level field (Bsurf ≳ 10 14 G) is not a prerequisite for launching these precursor outflows. By the time a binary companion evolves into a red supergiant and engulfs the NS to initiate the common envelope phase, the NS is typically a canonical, ordinary pulsar with a surface magnetic field of Bsurf ≲ 10 12 G. The simulation results demonstrate that for a successful jet breakout, the surface field only needs to reach Bsurf 2.32 × 10 13 G, provided the infalling envelope is rotating rapidly (e.g., the η = 0.5 models). Transitioning from a standard pulsar field (Bsurf 10 12 G) to this jet-launching threshold requires an amplification factor of only 10. Such a modest increase can be easily and rapidly achieved via the α-omega dynamo or continuous magnetic winding, fueled by the immense reservoir of differential rotation brought inward by the common envelope itself. Conversely, exploratory test runs initialised with extreme primordial fields (e.g., Bsurf ≳ 5 × 10 14 G) were unable to establish a stable accretion state. In these cases, the overwhelming magnetic pressure violently disrupted the initial equilibrium of the inner envelope, leading to severe numerical instabilities before a steady flow could form. This physical and numerical constraint strongly implies that the transient engine relies on a completely ordinary pulsar that dynamically scales up its field to a critical threshold via the accretion flow, rather than a pre-existing magnetar remnant.

A central takeaway is that the diagnostic explosion energy injected by the strongest magnetised NS engine (Eexp O(10 45) erg) and the associated unbound mass (O(10-6) M⊙) are fundamentally insufficient to unbind the massive envelope of a red supergiant. Therefore, rather than driving the primary supernova, this hyperaccreting NS phase must be viewed strictly as a transient precursor stage. Because the system is fueled by an effectively infinite mass reservoir, the NS will eventually exceed its maximum mass limit and collapse into a BH. The ultimate observational signature of the transient depends on how this NS precursor phase modifies the stellar interior before BH formation. Based on the outflow dynamics observed in the data, three evolutionary pathways are anticipated:

a. Weakly Magnetised Engine: Quiet Collapse. In models with weak initial magnetic fields (e.g., Bsurf ≤ 4.64 × 10 12 G) or insufficient rotation, the central engine fails to launch an outflow or establish a magnetic barrier. The mass falls freely onto the NS, which is rapidly overwhelmed by the accretion flow. In this scenario, the system undergoes a prompt, quiet collapse into a BH. Observationally, this manifests as a “failed supernova”; surveys would observe the sudden disappearance of a red supergiant, accompanied only by a thermal neutrino burst and a faint, long-wavelength transient as the envelope is consumed. While the initial collapse itself remains quiet due to weak early field strengths, late-time accretion onto the newly formed black hole provides a secondary channel for activity. Continued fallback accretion can progressively amplify magnetic fields in the inner disk via shear and flux accumulation, potentially launching delayed, late-time outflows long after the prompt NS phase has ended.

b. Moderately Magnetised Engine: Choked Jets. In moderately magnetised models with insufficient rotation (e.g., Bsurf = 2.32 × 10 13 G and η = 0.3), the magnetic field is strong enough to halt accretion at the surface, but the resulting jet struggles to overcome the ram pressure of the infalling envelope and ultimately stutters or chokes. The 10 45 erg of energy does not break out; instead, it is dumped into the stellar core, inflating a hot, pressurised cocoon. Because the accretion is temporarily halted, the NS survives longer in a suspended state. When the magnetic barrier eventually breaks and the NS collapses, the newly formed BH engine inherits this lower-density, high-entropy cocoon environment, which will drastically alter the dynamics of the subsequent primary explosion.

c. Highly Magnetised Engine: Potential Polar Breakouts. In the most optimal models (Bsurf = 4.64 × 10 13 G), the accretion is successfully halted, and a stable O(10 46) erg/s jet successfully breaks out of the extraction region. Observationally, because the energy budget is too low to unbind the star, this will not present as a canonical supernova. Instead, observers aligned with the jet axis would detect a low-luminosity GRB (llGRB) or an extended X-ray precursor. Crucially, this weak jet acts as a hydrodynamic drill, clearing a low-density polar funnel through the massive envelope. When the NS subsequently collapses, the vastly more powerful BH-disk engine will launch its outflow directly into this pre-cleared channel, providing a highly efficient, virtually drag-free pathway for powering a classical long GRB. These strongly magnetised models produce a fast, low-mass outflow propagating at 0.1 c along the polar axis, phenomenologically resembling the polar CEJSN scenario proposed by Soker et al. However, due to this sub-relativistic jet head velocity, a successful breakout within the engine’s lifetime strictly requires a compact envelope. Such conditions could be met if the neutron star merges with a heavily stripped massive star, or if a significant fraction of the extended envelope was already unbound by orbital drag during the prior inspiral phase.

Regarding observational implications of a choked engine, the authors note that the jet power generated by the central engine (10 46 erg/s) is generally overwhelmed by the massive common envelope, making a choked jet the most likely physical outcome. Even if the outflow is insufficient to completely unbind the star, it is often energetic enough to drive a shock through the envelope, contributing additional expansion energy. The orbital energy loss from the binary inspiral already unbinds much of the stellar envelope, and this expansion can power a transient. The choked explosion sends a shock through the star and, when it breaks out of the photosphere, this shock-heated material can produce blackbody emission in the UV and X-rays. Using a simple model that parameterizes the properties of the ejecta by employing a distribution of ejecta velocities and emitting areas, the X-ray luminosity is estimated. The peak luminosity (especially above 0.3 keV) is fairly low, but such X-ray flares could be detected by current detectors, although it is likely that the rate is 100 times lower than normal supernovae. The additional optical/IR emission from this explosion is minimal. Ultimately, these choked engine models will produce X-ray flares without bright optical or IR emission beyond the baseline luminous red nova. This specific scenario occurs in compact object common envelope systems and should account for only a small fraction of all observed luminous red novae.

Regarding limitations and future work, the results highlight the difficulty of powering the most energetic CEJSN directly from a hyperaccreting NS. Within the 2D GRMHD framework, the crushing accretion rates and intense neutrino cooling overwhelmingly favour choked jets capped at Lj 10 46 erg/s. This severe energy deficit presents two distinct possibilities. On one hand, it suggests that the initial NS phase may serve merely as a transient precursor; generating the 10 50 erg outflows invoked by macroscopic models may strictly require the subsequent collapse into a BH, where a magnetically arrested disk can efficiently extract spin energy. On the other hand, because 2D axisymmetry inherently suppresses the turbulent α-dynamo, the NS engine cannot be definitively ruled out. It remains an open question whether fully 3D magnetic field amplification could generate sufficient magnetic pressure to halt the hypercritical accretion and launch a successful jet before collapse occurs. A primary limitation of the current work is the assumption of 2D axisymmetry, which inherently suppresses the α-dynamo and limits the fully turbulent development of the MRI, thereby artificially restricting long-term magnetic field amplification. Future work will include incorporating phenomenological dynamo prescriptions or employing full 3D, high-resolution GRMHD configurations to better capture the complete α-omega dynamo and accurately track turbulent angular momentum transport. Furthermore, strong magnetisation can temporarily decouple the infalling envelope from the NS surface, creating a stalled magnetospheric reservoir. Predicting the exact timescale for the breakdown of this barrier, whether via magnetic interchange instabilities or direct gravitational crushing, is highly non-trivial. Capturing the episodic drainage of this reservoir and determining the true survival time of the NS before BH collapse will require extended, seconds-long or even minutes-long 3D simulations. Finally, the initial conditions governing the envelope rotation profile dictate the strength of the centrifugal barrier and the efficiency of the jet launching. The idealised setups used in this study must eventually be replaced by initial conditions extracted directly from 3D CE evolution models, bridging the physical gap between the binary inspiral phase and the final core collapse.

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.