Production of Jets before Neutron Star Mergers

Maxim Lyutikov; Maxim V. Barkov; Praveen Sharma; Slava G. Turyshev

REVIEW 2 major objections 5 minor 2 cited by

Production of Jets before Neutron Star Mergers

T0 review · 2 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read Merging neutron stars drive dual Alfvén-wing current jets that beam radio and high-energy precursor emission before the gravitational-wave burst.

desk verdict Solid 3D RMHD demonstration of Alfvén-wing currents in the relativistic sub-Alfvénic regime; the observable-precursor claim rests on an unmodeled 'emission follows current' step and needs a charge-carrier check or a softer wording. read the letter →

arxiv 2602.14300 v2 pith:M7Q5HX4S submitted 2026-02-15 astro-ph.HE

Praveen Sharma , Slava G. Turyshev , Maxim V. Barkov , Maxim Lyutikov This is my paper · ORCID

classification astro-ph.HE

keywords neutronstarmergersAlfvénwingsrelativisticMHDprecursoremissionunipolarinductorradiotransientsmagnetohydrodynamicscompactbinarystars

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish how two neutron stars approaching a merger interact electromagnetically before they touch. It shows, through 3D relativistic MHD simulations, that when one conducting, unmagnetized star moves through the magnetized plasma of its companion, the interaction creates two coherent Alfvén-wing current channels—jet-like outflows of field-aligned electric current—rather than a simple bow shock. Because the interaction is relativistic yet sub-Alfvénic, these wings carry roughly 3×10^43 erg/s of electromagnetic power and beam it into narrow directions. The consequence is that a merging binary may emit a focused, pulsar-like radio and high-energy precursor seconds to minutes before the gravitational-wave signal peaks, giving telescopes an early warning.

What carries the argument

The central mechanism is the Alfvén-wing unipolar inductor: a perfectly conducting obstacle moving across a magnetized plasma generates a motional EMF, and the resulting current closes through two stationary Alfvén-wave channels that attach to the body like wings, angled as tan θ ≈ M_A. The paper uses 3D relativistic ideal MHD simulations to resolve the draping layer near the star and to measure the integrated field-aligned current in the wings, linking the computed current topology to the proposed emission.

What would settle it

A targeted radio search in the seconds to minutes before a gravitational-wave-detected neutron star merger: if no coherent pulse with the predicted dispersive delay and beamed flux is seen across several detections, the 'emission follows the current' conversion is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that a conducting, unmagnetized neutron star moving through a strongly magnetized, sub-Alfvénic relativistic plasma acts as a unipolar inductor: the motional electric field generates currents that are channeled into two oppositely directed, field-aligned Alfvén wings extending along the ambient magnetic field. The simulations quantify the wing current, finding a non-relativistic scaling I ∝ v0^0.96 B0^0.06 and a relativistic scaling roughly I ∝ v0 Γ², which explains why late-inspiral velocities substantially boost the current. The paper argues that this beamed power, combined with a pulsar-like 'emission follows the current' paradigm, makes observable precursor r

Load-bearing premise

The observable-precursor conclusion rests on the assumption that the large-scale field-aligned currents computed in ideal MHD will dissipate into coherent radio and high-energy emission, pulsar-style; if the currents instead thermalize or radiate incoherently, the predicted precursor would not occur even though the Alfvén-wing channels exist.

Editorial extensions

If this is right

If the wing currents convert to electromagnetic radiation, neutron star mergers should produce beamed radio and high-energy precursors seconds to minutes before the main gravitational-wave burst.
Beaming focuses the otherwise modest ~3×10^43 erg/s power into narrow cones, making detection plausible with existing radio and X-ray monitors rather than requiring isotropic sensitivity.
The predicted dispersive delay of roughly 14 seconds at 1 GHz for a source at 200 parsecs provides a clear timing signature to distinguish a precursor from post-merger emission.
The Mach-number-controlled sequence from coherent wings (sub-Alfvénic) to turbulent, shock-dominated interaction (trans-Alfvénic) predicts an evolutionary change in precursor character as the inspiral progresses.
Black hole–neutron star mergers should also form Alfvén wings through the same unipolar-inductor physics, extending the precursor phenomenon to a broader class of binary mergers.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the wing currents are as robust as computed, the same geometry implies a characteristic linear polarization for the precursor set by the background magnetic field direction—an observational signature the paper does not discuss but which is testable with polarimetric radio observations.
The computed weak dependence of wing current on background field strength suggests that even modestly magnetized binaries could generate substantial wing currents, potentially raising the expected precursor rate above estimates based on B0² scalings alone.
A direct test of the mechanism would be kinetic particle-in-cell simulations of the draping layer to determine whether the field-aligned currents break into coherent-emitting bunches rather than simply heating the plasma; the paper explicitly leaves this conversion step to future work.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The one thing to know: this paper delivers the first 3D RMHD simulations of a perfectly conducting sphere moving through a relativistic, sub-Alfvénic magnetized plasma, and the core result—coherent, bipolar Alfvén-wing current channels that persist across the non-relativistic to mildly relativistic regime—is well supported. The stronger headline claim, that these currents make observable precursor emission likely, is not supported by the simulations as they stand.

What is actually new: the full 3D current topology, the B1→B2→B3 transition from coherent wings to turbulent wings to shock-dominated loops, and the comparison to independent analytic scalings (Neubauer, Mottez & Heyvaerts). The setup is careful: PLUTO v4.3, stretched grids, divergence error below 1e-3, and a convergence study showing integrated quantities stable between 113^3 and 190^3. The wing-current scaling I ∝ v0^0.96 B0^0.06 is consistent with the analytic I ∝ v0 once the B0 dependence of vA is folded in, and the B2/B1 current ratio (~1.8) matches the predicted v0Γ² ratio (~2.0). They also correctly emphasize in §4.1 that these are Alfvén wings, not mass-loaded jets, even though the title says jets—that mismatch is a problem.

Where it gets soft is the step from simulated currents to observable emission. Section 6 explicitly says they do not address the emission mechanism and instead invoke the pulsar-like paradigm of 'emission follows the current.' That is a legitimate heuristic, but the paper never checks whether the simulated current density can be supported by the available charge carriers in a magnetically dominated NS magnetosphere. The stress-test note is right: a quick J∥/(e n_GJ c) estimate would tell you whether the circuit closes in ideal MHD or whether you are in a charge-starved, gap-like regime. Without that, the abstract's 'likely to lead to observable precursor emission' is a hope, not a result.

Also, the relativistic runs use β=0.16–0.8, not the β≪1 regime they argue is physically relevant; they acknowledge lower-β runs are numerically unstable, which is honest, but it means the simulations do not actually land in the target parameter space. Minor issue: Fig. 6's caption gives A2 as MA≈2.2, β=0.1, while Table 1 and the text say MA=0.63, β=0.01. That needs fixing.

Bottom line: this is a solid simulation paper for the NS-merger-precursor community, worth serious refereeing. The main result stands; the observable-emission extrapolation needs either a quantitative charge-carrier check or a clearly softened claim. I'd send it to peer review, not desk reject.

Referee Report

2 major / 5 minor

Summary. The paper uses 3D ideal (R)MHD simulations (PLUTO v4.3) to model an unmagnetized, perfectly conducting sphere moving through a magnetized plasma, as a proxy for the interaction of one neutron star with the magnetosphere of its companion before merger (the 1M-DNS case). Non-relativistic runs from deeply sub-Alfvénic to super-Alfvénic regimes show that coherent Alfvén-wing current channels form for M_A<1 and disappear for M_A>1, with a fitted scaling I_wings ∝ v0^0.96 B0^0.06. Mildly relativistic sub-Alfvénic runs (v0/c=0.3–0.5, Γ=1.05–1.15) produce bipolar field-aligned current channels reminiscent of planetary Alfvén wings; the ratio of wing currents between runs B2 and B1 is ≈1.8, consistent with the analytic I∝v0Γ² expectation (≈2.0). The paper concludes that these current outflows are beamed and ‘likely to lead to observable precursor emission’ before the gravitational-wave peak.

Significance. If the central MHD result holds, the paper usefully extends the well-established planetary Alfvén-wing/unipolar-inductor paradigm into the relativistic, sub-Alfvénic regime relevant to neutron-star mergers, and it provides a concrete mechanism for coherent electromagnetic structures that could precede the merger. The simulations are carefully set up and documented: PLUTO v4.3, stretched grids, divergence control (≤10⁻³), a convergence study in Appendix A.3, and an explicit comparison with the analytic scalings of Neubauer (1980) and Mottez & Heyvaerts (2011). The B2/B1 current-ratio test is a genuinely quantitative check. The main gap is that the leap from simulated current channels to observable radio/high-energy emission rests on an unevaluated heuristic, not on any radiative or kinetic calculation. With that gap addressed or the claim appropriately softened, the paper would be a solid contribution; as it stands, the observable-precursor conclusion is premature.

major comments (2)

[§6, §6.2, Abstract] The abstract’s final claim that the interaction is ‘likely to lead to observable precursor emission’ is not established by the simulations. Section 6 explicitly states ‘We do not address the emission mechanism per se’ and §6.2 concedes that dissipation is purely numerical. The invoked ‘emission follows the current’ paradigm requires that the field-aligned currents, I∼4R E0 ΣA (Eq. 12), are actually carried by a plasma that can radiate. The paper never computes J∥/(e n_GJ c) for the simulated or neutron-star parameters, nor checks whether the current density exceeds the Goldreich–Julian value needed for charge starvation or current-driven instabilities. Without such a quantitative check, the connection from simulated Alfvén-wing channels to coherent radio/high-energy emission is an assumption, not a result. I recommend either adding a quantitative estimate of the available charge-carrier
[§3.1, Appendix A.1] The numerical treatment of the ‘perfectly conducting sphere’ is underspecified. The initial conditions (Eqs. A2–A3) impose the vacuum superconductor solution with B=0 inside the star, but no immersed-boundary condition or mask is described that keeps B_r=0 at r=R⋆ and v=0 inside the sphere during the evolution. In ideal MHD, unless the interior velocity is artificially held at zero and the normal field is explicitly reset, numerical diffusion and Lorentz forces can allow magnetic flux to penetrate and the obstacle to move. Since the entire unipolar-inductor model depends on flux exclusion, please specify the boundary treatment and report the time evolution of the radial magnetic field at the stellar surface and the total magnetic flux through the sphere. This is central to the interpretation of the computed current topology.

minor comments (5)

[Figure 6 caption] The caption says ‘Moderate sub-Alfvénic run A2 (MA ≈2.2, β=0.1)’, but Table 1 and §4.2 give A2 as MA≈0.63, β=0.01. The caption values correspond more closely to run A3; please correct.
[Table 3] The convergence discussion in §A.3 focuses on v_max but not on I_wings, whose relative change is −10.7% at N=113 and +3.4% at N=190. Please state whether the I_wings variation is considered acceptable and why.
[Eq. (11)] The notation ‘I_wings ∝ v0^0.96 B0^0.06 ∝ M_A^0.96 B0^1.02’ is confusing on first reading. Since M_A = v0/v_A and v_A ∝ B0 at fixed density, the second proportionality follows, but this should be stated explicitly so the reader does not interpret the two forms as independent scalings.
[§5.2] The sentence ‘even modest increases in Γ should lead to significantly Alfvén wing currents’ overstates the effect: between B1 and B2, Γ² increases by only about 20%, while the observed factor ≈2 is dominated by the increase in v0. Rephrase to reflect the combined v0Γ² scaling.
[Title/Abstract] The title and abstract use ‘jets’, but §4.1 correctly notes that these are Alfvén-wing current channels, not mass-loaded relativistic jets. Consider using ‘current outflows’ or ‘Alfvén-wing outflows’ in the title to avoid overstatement.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: Alfvén-wing currents and the MA-dependent sequence emerge from the RMHD runs; the precursor-emission step is an explicitly flagged heuristic, not a derived prediction.

full rationale

The derivation chain is self-contained at the level of the central numerical claim. The PLUTO runs solve the ideal (R)MHD equations with no free parameters fitted to the Alfvén-wing outcome; the bipolar current-channel topology and the MA-controlled transition (A1→A2→A3, B1→B2→B3) appear from time evolution. The wing-current scaling in Eq. (11) is explicitly labeled an empirical log-log fit over the explored runs ('should be interpreted as an empirical fit over the explored parameter range rather than as independent scaling'), so it is not a fitted input disguised as a prediction. The relativistic comparison in §5.2 uses an independent analytic estimate I∼4R⋆E0ΣA and predicts a B2/B1 ratio of ≈2.0 against the measured ≈1.8; no parameter is adjusted to force agreement. The initial conditions (Eqs. A2–A3, from Lyutikov 2023) are the potential-flow and dipolar-draping fields around a perfectly conducting sphere, i.e., they contain no volume Alfvén-wing currents; the wings develop dynamically. The only load-bearing external assumption is the observable-precursor step: §6 states 'We do not address the emission mechanism per se. Instead, we invoke a pulsar-like paradigm of “emission follows the current”', and §6.2 concedes that no explicit resistivity, radiation reaction, or kinetic physics is included. That is a genuine, self-flagged physical limitation (the MHD currents may not convert to radio/high-energy photons), but it is not a circular reduction: the existence and geometry of the current channels are computed independently of the emission heuristic. The paper also does not check whether the computed J∥ is charge-starved relative to the Goldreich–Julian density, so the emission step remains incomplete, but this is an unvalidated extrapolation, not a circularity. The self-citations (Lyutikov 2019, 2023, 2024) supply power normalizations and initial-condition profiles, but the core result does not reduce to them and they are not used to rule out alternatives. Score 2 reflects the presence of minor self-citations without load-bearing circularity.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central simulation results rest on few postulates beyond ideal MHD and the conducting-obstacle idealization. The most consequential assumption is the 'emission follows the current' heuristic linking simulated currents to observable precursors—that step is not derived in this paper. The relativistic runs use β values an order of magnitude above the expected NS-magnetosphere value, chosen for numerical stability rather than physical fidelity.

free parameters (2)

Power-law exponents in Iwings fit = a = 0.96±0.05, b = 0.06±0.08
Exponents fitted by log-log regression to 7 non-relativistic sub-Alfvénic simulation runs (Fig. 8, Eq. 11).
Plasma beta in relativistic runs = β = 0.16, 0.40, 0.80
Chosen for numerical stability, not from the physical low-β NS magnetosphere (Sec. 3.3).

assumptions (4)

domain assumption Ideal (R)MHD with no explicit resistivity; dissipation is numerical
Stated in Sec. 3 and Limitations; current dissipation and emission are not modeled.
domain assumption Neutron star is an unmagnetized, non-rotating, perfectly conducting sphere; external field is uniform
Used throughout; 1M-DNS case only, uniform B0 valid for R* << orbital separation; spin and intrinsic dipole neglected (Sec. 3.1, Sec. 6.2).
ad hoc to paper 'Emission follows the current' heuristic connects simulated currents to observable radio/high-energy emission
Invoked in Sec. 6; not derived in this paper.
standard math Initial velocity and magnetic fields set by the potential-flow solution around a conducting sphere (Eq. B4, Eq. A3 from Lyutikov 2023)
Used as initial conditions; steady state is expected to be independent of the initial transient.

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Cite this review

Pith. "Pith review of Production of Jets before Neutron Star Mergers." pith.science (2026). https://pith.science/paper/M7Q5HX4S

@misc{pith2026260214300,
  author       = {Pith},
  title        = {Pith review of: Production of Jets before Neutron Star Mergers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M7Q5HX4S}},
  note         = {Machine review of arXiv:2602.14300}
}

read the original abstract

We demonstrate that magnetospheric interactions between merging neutron stars (NSs) generate dual-jetted current outflows, analogous to the Alfv\'{e}n wings observed during planetary interactions in the Solar System. Using 3D relativistic MHD simulations, we model the interaction as a conducting sphere moving through a highly magnetized plasma of the companion's magnetosphere. Unusually, the interaction operates in a regime that is relativistic yet sub-Alfv\'{e}nic. Electromagnetic draping amplifies magnetic fields in a narrow layer near the stellar surface, leading to the generation of electric currents along the local magnetic field. The generation of beamed outflows enhances the instantaneous power of the pulsar-like radio and high-energy emission, produces spin/orbital modulations, and is likely to lead to observable precursor emission preceding the main gravitational wave event.

Figures

Figures reproduced from arXiv: 2602.14300 by the authors.

**Figure 1.** Non-relativistic Sub-Alfvénic run A1. Top row: xy-plane slices of flow velocity (v), density (ρ), ram pressure (pram), and fast magnetosonic Mach number (Mf). Bottom row: corresponding xz-plane slices. All quantities, except Mf , are normalized by the upstream values. Velocity Streamlines and magnetic field lines are overlaid where applicable. The green contour in fast Mach plots marks the boundary Mf = 1. Current S… view at source ↗

**Figure 2.** Non-relativistic Sub-Alfvénic run A1. 3D contour plot of the magnetic pressure B2 /8π at the steady state viewed along the x-axis. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Alfvén wing structure in illustrative run A1c. (a) Isosurface of current density magnitude |J| showing bipolar field-aligned current channel (purple) extending from the neutron star surface. The green and red arrows on the wings indicate upward (+z) and downward (-z) directed currents, respectively, forming the bipolar Alfvén wing current system. (b) Current streamlines colored by Jz component, revealing the field-a… view at source ↗

Figures from the paper (13 more)

**Figure 4.** Figure 4: Non-relativistic Sub-Alfvénic run A1. We show 3D streamlines of the current colored by Jz for flow past a perfectly conducting sphere. Left: View along +z direction. The upstream hemisphere (x > 0) hosts an antisymmetric pair of organized current sheets wrapping around…

**Figure 5.** Figure 5: Non-relativistic Sub-Alfvénic run A1. Here we show 2D slices of parallel current Jz along x = 0, and y = 0.5. In the left panel, we observe currents with alternating directions, while an upstream-downstream asymmetry is clearly visible in the right image. 4.2. Moderate…

**Figure 6.** Figure 6: Moderate sub-Alfvénic run A2 (MA ≈ 2.2, β = 0.1). The details are the same as in [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: Moderate sub-Alfvénic run A2. 3D streamlines plot of current density at the steady state as viewed across +z axis (left panel) and +x axis (right panel) [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: Scaling of the integrated field-aligned current through the z0 = 1.5R⋆ transverse plane (Iwings) as a function of the inflow velocity v0 and background magnetic field strength B0. A log-log regression over selected 7 sub-Alfvénic runs ( [PITH_FULL_IMAGE:figures/full_f…

**Figure 9.** Figure 9: Super-Alfvénic run A3. The details are the same as in [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

**Figure 10.** Figure 10: Super-Alfvénic run A3. 3D streamlines plot of current density at the steady state as viewed across various planes, with the viewing direction labeled in the plots. 5.1. Relativistic Sub-Alfvénic Flow Run B1 explores the mildly relativistic strongly sub-Alfvénic regime…

**Figure 11.** Figure 11: Relativistic Sub-Alfvénic run B1. The details are similar to those in [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]

**Figure 12.** Figure 12: Relativistic Sub-Alfvénic run B1. We show 3D current density streamlines colored by Jz for relativistic flow past a conducting sphere. Left: z = 0 equatorial view. Right: x = 0 meridional view. Compared to the smooth, strongly sub-Alfvénic flow (B1), the velocity fiel…

**Figure 13.** Figure 13: Relativistic moderate sub-Alfvénic run B2. Details are similar to [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]

**Figure 14.** Figure 14: Moderately relativistic sub-Alfvénic run B2. 3D streamlines of current density at the steady state, viewed across various planes, with the viewing direction labeled in the plots. The rest of the details are the same as in [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]

**Figure 15.** Figure 15: shows the relevant plots. The flow deflects smoothly around the obstacle in a largely hydrodynamic manner, without the sharp channeling or well-defined Alfvén wings seen in B1 and B2. The density distribution shows a clear bow shock with a well-defined shock cone and …

**Figure 16.** Figure 16: Relativistic super-Alfvénic run B3. 3D streamlines plot of current density at the steady state as viewed across various planes, with the viewing direction labeled in the plots. The rest of the details are the same as in [PITH_FULL_IMAGE:figures/full_fig_p016_16.png]

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Reference graph

Works this paper leans on

4 extracted references · 1 canonical work pages · cited by 2 Pith papers

[1]

J., Breivik, K., Pankow, C., D‚ÄôOrazio, D

Andrews, J. J., Breivik, K., Pankow, C., D‚ÄôOrazio, D. J., & Safarzadeh, M. 2020, The Astrophysical Journal Letters, 892, L9, doi: 10.3847/2041-8213/ab5b9a Bagenal, F., & Dols, V. 2020, Journal of Geophysical Research (Space Physics), 125, e27485, doi: 10.1029/2019JA027485 Bai, X.-N., & Spitkovsky, A. 2010, ApJ, 715, 1282, doi: 10.1088/0004-637X/715/2/12...

work page doi:10.48550/arxiv.2511.14932 2020
[2]

Far from the sphere (r≫R⋆), the plasma flows with velocityv=−v 0ˆxfrom right (upstream) to left (downstream)

We work in the star’s rest frame so that the neutron star remains fixed in space. Far from the sphere (r≫R⋆), the plasma flows with velocityv=−v 0ˆxfrom right (upstream) to left (downstream). We initialize the velocity field following Eq. B4 of Lyutikov (2023): v= 0 r≤R ⋆ vr =−v 0 1− R3⋆ r3 sinθcosφr > R ⋆ vθ =−v 0 1+ R3⋆ 2r3 cosθcosφr > R ⋆ vφ = v0 1+ R3...

2023
[3]

Error A1 120 Eight-Wave 1.8×10 −3 A2 120 Eight-Wave 2.6×10 −3 A3 120 Eight-Wave 3.3×10 −3 B1 170 Hyp

Method Normalized Div. Error A1 120 Eight-Wave 1.8×10 −3 A2 120 Eight-Wave 2.6×10 −3 A3 120 Eight-Wave 3.3×10 −3 B1 170 Hyp. Div. Clean. 4.4×10 −4 B2 170 Hyp. Div. Clean. 6.4×10 −4 B3 170 Hyp. Div. Clean. 1.2×10 −3 Table 4.Volume-averaged normalized divergence errors for all runs, demonstrating robust constraint enforcement. B.PLUTO CODE We perform both n...

2007
[60]

A.4.Divergence Control The divergence-free constraint∇ ·B= 0 is enforced differently for relativistic and non-relativistic runs

The stabilization of all quantities at high resolution indicates the solution has converged. A.4.Divergence Control The divergence-free constraint∇ ·B= 0 is enforced differently for relativistic and non-relativistic runs. For the relativistic B-series, we employ the hyperbolic divergence cleaning method (Dedner et al. 2002; Mignone et al. 2010), which int...

2002

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [1]

J., Breivik, K., Pankow, C., D‚ÄôOrazio, D

Andrews, J. J., Breivik, K., Pankow, C., D‚ÄôOrazio, D. J., & Safarzadeh, M. 2020, The Astrophysical Journal Letters, 892, L9, doi: 10.3847/2041-8213/ab5b9a Bagenal, F., & Dols, V. 2020, Journal of Geophysical Research (Space Physics), 125, e27485, doi: 10.1029/2019JA027485 Bai, X.-N., & Spitkovsky, A. 2010, ApJ, 715, 1282, doi: 10.1088/0004-637X/715/2/12...

work page doi:10.48550/arxiv.2511.14932 2020

[2] [2]

Far from the sphere (r≫R⋆), the plasma flows with velocityv=−v 0ˆxfrom right (upstream) to left (downstream)

We work in the star’s rest frame so that the neutron star remains fixed in space. Far from the sphere (r≫R⋆), the plasma flows with velocityv=−v 0ˆxfrom right (upstream) to left (downstream). We initialize the velocity field following Eq. B4 of Lyutikov (2023): v= 0 r≤R ⋆ vr =−v 0 1− R3⋆ r3 sinθcosφr > R ⋆ vθ =−v 0 1+ R3⋆ 2r3 cosθcosφr > R ⋆ vφ = v0 1+ R3...

2023

[3] [3]

Error A1 120 Eight-Wave 1.8×10 −3 A2 120 Eight-Wave 2.6×10 −3 A3 120 Eight-Wave 3.3×10 −3 B1 170 Hyp

Method Normalized Div. Error A1 120 Eight-Wave 1.8×10 −3 A2 120 Eight-Wave 2.6×10 −3 A3 120 Eight-Wave 3.3×10 −3 B1 170 Hyp. Div. Clean. 4.4×10 −4 B2 170 Hyp. Div. Clean. 6.4×10 −4 B3 170 Hyp. Div. Clean. 1.2×10 −3 Table 4.Volume-averaged normalized divergence errors for all runs, demonstrating robust constraint enforcement. B.PLUTO CODE We perform both n...

2007

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A.4.Divergence Control The divergence-free constraint∇ ·B= 0 is enforced differently for relativistic and non-relativistic runs

The stabilization of all quantities at high resolution indicates the solution has converged. A.4.Divergence Control The divergence-free constraint∇ ·B= 0 is enforced differently for relativistic and non-relativistic runs. For the relativistic B-series, we employ the hyperbolic divergence cleaning method (Dedner et al. 2002; Mignone et al. 2010), which int...

2002