The stakes are enormous. Since the landmark detection of GW170817 in 2017, gravitational-wave observatories have confirmed two likely binary neutron star mergers and at least two neutron star-black hole collisions. These events are cosmic alchemists: the neutron-rich matter they eject undergoes rapid neutron capture nucleosynthesis, forging many of the heavy elements in the periodic table, from iodine to gold to uranium. The radioactive decay of these freshly minted nuclei powers a kilonova, an optical and infrared glow that fades over days to weeks. Whether an outflow produces heavy elements or lighter ones hinges on a single crucial quantity, the electron fraction, which measures the balance of protons to neutrons in the fluid. And that balance is dictated almost entirely by how many electron neutrinos and antineutrinos the matter absorbs on its way out of the merger wreckage. Get the neutrino physics wrong, and predictions for the color, brightness, and duration of kilonovae collapse.

The fundamental difficulty is that neutrinos in a merger remnant live in two radically different regimes simultaneously. Deep inside the hot, dense remnant, neutrinos are trapped, scattering constantly off nucleons and reaching thermal equilibrium with the fluid, diffusing outward only slowly. Far away, in the tenuous ejecta streaming into space, they fly freely along geodesics of the curved spacetime, barely noticing the matter around them. In between lies a treacherous semi-transparent zone where neutrino-matter interactions profoundly alter the temperature and composition of the gas, yet the particles cannot be assumed to be in equilibrium with anything. A perfect simulation would solve the general relativistic Boltzmann equation, tracking the full six-dimensional distribution function of neutrinos coupled to Einstein’s equations and relativistic magnetohydrodynamics. No code on Earth can do that at acceptable cost, so every merger simulation to date relies on approximations whose errors are difficult to quantify.

Foucart’s review organizes the field’s approaches into three families. The simplest are leakage schemes, which do not transport neutrinos at all. Instead, they compute local emission rates for each grid cell, estimate an optical depth along the path of least resistance to the simulation boundary, and interpolate between free emission in transparent regions and slow diffusion in opaque ones. First developed in the 1990s and early 2000s, these schemes cost essentially nothing and capture the broad strokes of remnant cooling. But they cannot follow where emitted neutrinos go, so they miss the absorption of neutrinos in outflows, the very process that raises the electron fraction of hot ejecta from a neutron-rich value below 0.1 up to the 0.2 to 0.4 range that determines the nucleosynthesis outcome. More sophisticated variants now track trapped neutrino energy densities and propagate emission along rays to approximate reabsorption, but their accuracy is calibrated on symmetric test problems and degrades in the genuinely asymmetric geometry of a merger.

The workhorses of modern general relativistic merger simulations are moment schemes, which evolve angular moments of the neutrino distribution function, typically the energy density and energy flux, using equations formally similar to those of relativistic fluid dynamics. Because these equations can be cast in conservative form, they mesh naturally with the shock-capturing methods used for the fluid, and they automatically include emission, propagation, and reabsorption of neutrinos. The catch is closure: evolving only the lowest moments leaves the pressure tensor and higher moments unknown, forcing analysts to adopt approximate analytical prescriptions, most commonly the maximum-entropy closure of Minerbo, that interpolate between an isotropic diffusion limit and a free-streaming limit. In the optically thin regime this closure is simply wrong for realistic radiation fields, producing artificial collisions where crossing neutrino beams should pass through one another and inflating neutrino energy densities in the polar regions by factors of roughly two compared with more exact calculations.

Grey, energy-integrated moment schemes introduce a second, subtler problem. Neutrino cross-sections scale with the square of the neutrino energy, so estimating absorption and scattering opacities requires knowing the neutrino spectrum, which an energy-integrated scheme does not evolve. Assuming neutrinos sit in thermal equilibrium with the fluid can badly underestimate opacities in outflows, where escaping neutrinos carry energies of 10 to 20 megaelectronvolts while the gas has cooled to around one megaelectronvolt. Recent work addresses this by evolving the neutrino number density alongside the energy density, extracting an average energy from their ratio, and rescaling opacities accordingly, while also guaranteeing exact conservation of lepton number. Handling the diffusion of trapped neutrinos through dense regions poses yet another numerical trap: the dissipative terms in shock-capturing fluxes can overwhelm the physical diffusion rate, and the latest implementations switch to non-dissipative high-order fluxes precisely where the optical depth across a grid cell exceeds unity.

The newest entrant is Monte Carlo transport, which represents the neutrino distribution with packets, or superparticles, that propagate along null geodesics and interact with the fluid probabilistically. Because each packet carries a full energy and direction, Monte Carlo schemes sidestep the closure and spectral assumptions that plague moment methods, and comparisons show they agree with moment simulations on global quantities such as neutrino luminosities and ejecta masses to within roughly 10 to 20 percent. Their Achilles heel is the optically thick interior, where a single packet would undergo enormous numbers of interactions per time step. Practical codes borrow tricks from implicit Monte Carlo methods, transforming emission and absorption rates so that equilibration happens over a few time steps rather than within one, and treating scattering-dominated regions as a random walk advected with the fluid. These approximations achieve sub-percent accuracy in neutrino luminosities on test problems, but they remain poorly tested, and the sparse packet populations in low-density regions make it impossible to reconstruct the instantaneous neutrino distribution function, which is exactly what would be needed to model fast neutrino flavor oscillations.

Indeed, the review emphasizes that algorithmic uncertainty is only half the story. Several physically important processes are absent from essentially all merger simulations. Neutrino-antineutrino pair annihilation above the remnant’s poles may deposit enough energy to help clear baryons from the jet funnel of short gamma-ray bursts, yet it is a nonlinear process coupling neutrino and antineutrino distributions that grey schemes can only treat at the order-of-magnitude level. Inelastic scattering, which thermalizes neutrinos as they diffuse out, is omitted entirely, likely affecting the energies of heavy-lepton neutrinos. And neutrino flavor oscillations, including the fast flavor instability that can transform flavors on nanosecond timescales wherever the net lepton flux changes sign between directions, could plausibly reshape the composition of outflows, but quantum kinetic equations are not yet coupled to any general relativistic merger code.

What emerges from a decade of increasingly sophisticated simulations is a coherent physical picture with quantified uncertainties. Neutrino emission peaks at a staggering 10^53 to 10^54 ergs per second in the first milliseconds, then settles to 10^52 to 10^53 ergs per second sustained for hundreds of milliseconds, with a long-lived neutron star remnant outshining its accretion disk. Hot ejecta from the collision interface and the disk corona are whipped up to electron fractions of 0.2 to 0.4 by neutrino absorption, while cold tidal tails remain neutron-rich below 0.05, guaranteeing a two-component kilonova, one red and infrared, one blue and optical, exactly the pattern observed after GW170817. Moment schemes, despite their known flaws, remain the best available source of quantitative predictions, while Monte Carlo methods are rapidly maturing into the field’s benchmark and error-estimation tool. The next frontier, the review concludes, lies in energy-dependent transport, better treatments of pair processes and inelastic scattering, and ultimately a self-consistent marriage of radiation transport with the magnetic turbulence that may launch the universe’s brightest explosions.

Subject of Research: Neutrino transport methods in general relativistic simulations of neutron star mergers

Article Title: Neutrino transport in general relativistic neutron star merger simulations

Article References: Neutrino transport in general relativistic neutron star merger simulations. (n.d.). https://doi.org/10.1007/s41115-023-00016-y

Image Credits: AI Generated

DOI: 10.1007/s41115-023-00016-y

Keywords: neutrino transport, neutron star mergers, general relativity, kilonova, r-process nucleosynthesis, gravitational waves, numerical simulations, Monte Carlo radiation transport, moment schemes, leakage schemes, accretion disks, gamma-ray bursts

The problem begins with the sheer range of scales involved. In the final orbit before two neutron stars merge, the stellar cores slam into one another at a substantial fraction of the speed of light, generating a shear layer roughly a kilometer wide that becomes Kelvin-Helmholtz unstable. This instability, the same mechanism that shapes wind-blown clouds on Earth, shreds the interface between the stars into vortices that fragment into ever smaller eddies, producing a turbulent cascade that spans from kilometer scales down to about a nanometer, where viscosity finally converts kinetic energy into heat. The Reynolds number of this flow, a measure of the ratio of inertial to viscous forces, is a staggering ten to the power of sixteen. Simulating every eddy directly, the approach known as direct numerical simulation, would require computational resources that scale as the Reynolds number cubed, making it utterly impossible for the foreseeable future.

Turbulence is not confined to the moment of contact. Once the stars have merged, the remnant, whether a massive neutron star or a newly formed black hole, is typically encircled by a hot, dense accretion disk. There, the magnetorotational instability stirs the plasma, redistributing angular momentum and governing how matter spirals inward or is flung outward. The way turbulence transports angular momentum determines whether the remnant neutron star collapses promptly to a black hole or survives as a long-lived object, and it controls the mass ejection that powers the kilonova flashes and the nucleosynthesis of r-process elements. It may also amplify magnetic fields to magnetar levels, potentially launching the relativistic jets that produce short gamma-ray bursts. In short, nearly every observable signature of a neutron star merger is touched by turbulence somewhere along the way.

The mathematical machinery for handling unresolved turbulence has a long history in Newtonian fluid dynamics. The classic approach, Reynolds averaging, splits the flow into a mean component and fluctuations, yielding equations for the mean motion that contain an extra term, the Reynolds stress, which encapsulates the momentum carried by the unresolved eddies. A more practical alternative for simulations is large-eddy simulation, or LES, in which the equations are filtered over a length scale comparable to the numerical grid. The filtered equations resemble the original ones but include subgrid-scale stresses that must be modeled. The central difficulty, known as the closure problem, is that these stresses depend on information about the small scales that the simulation does not compute, so modelers must supply approximate relations, or closures, that capture the net effect of the missing physics using only the resolved quantities.

Extending this framework to general relativity introduces subtleties that have no Newtonian counterpart. Radice and Hawke review how averaging or filtering the equations of relativistic hydrodynamics produces effective stresses even when the underlying fluid is ideal, and how the nonlinear structure of the fluxes demands additional closure relations, including one for turbulent mass diffusion. More troubling still is the question of covariance: the averaging operations used in practice are tied to a particular slicing of spacetime, which breaks the four-dimensional symmetry of Einstein’s theory. Recent work has explored building the averaging procedure around a physical observer rather than a coordinate slice, showing that the coarse-grained equations then take the form of a non-ideal relativistic fluid, complete with bulk viscosity, shear stresses, and heat transport terms that arise purely from the turbulence. Even the equation of state, the relation linking pressure, density, and energy, is modified by averaging, since fluctuations in density generate corrections that behave like an additional pressure.

In practice, most published neutron star merger simulations to date have used the simplest possible strategy: implicit large-eddy simulation, which sets the subgrid stresses to zero and relies on the intrinsic numerical dissipation of shock-capturing schemes to mimic the effect of unresolved turbulence. This approach has been remarkably successful in other fields, but the review is blunt about its limitations in this context. The modified equation analysis shows that numerical dissipation can indeed act like an effective viscosity, but implicit methods require a significant fraction of the inertial range to be resolved before results converge, and no neutron star merger simulation has yet been demonstrated to be in that regime. The alternative is explicit modeling. Radice’s own general-relativistic large-eddy simulations employ a relativistic version of the Smagorinsky closure, in which the turbulent viscosity is estimated from a mixing length set by the local scale of the flow and the speed of sound. A third family of methods, gradient or approximate-deconvolution models, reconstructs the effect of the filter algebraically and has the advantage of introducing no tunable parameters beyond the filter width itself.

The payoff of these techniques is already visible in the study of magnetic field amplification. Early Newtonian simulations suggested that the Kelvin-Helmholtz instability could amplify even weak seed fields to magnetar strengths of around ten to the fifteenth gauss, but general-relativistic calculations initially failed to reproduce this, simply because their grids were too coarse. Later, extraordinarily high-resolution simulations by Kenta Kiuchi and collaborators showed that the saturated field strength kept climbing with resolution, with no sign of convergence, precisely because the magnetic back-reaction only halts the cascade at centimeter scales, far below anything a global simulation can resolve. When subgrid models were introduced, the picture changed dramatically. Gradient-model simulations by Ricard Aguilera-Miret, Carlos Palenzuela, and colleagues achieved converged results, confirming that weak fields are indeed amplified to ten to the sixteenth gauss and that the statistical properties of the resulting turbulence are remarkably insensitive to the unknown initial magnetic configuration inside the stars, a reassuring result for predictive modeling.

The same simulations revealed tantalizing evidence of an inverse cascade, in which the characteristic scale of the magnetic field grows from roughly half a kilometer immediately after merger to several kilometers a hundred milliseconds later, as turbulent resistivity rearranges field lines into larger structures. Meanwhile, measurements of the effective viscosity generated by magnetic stresses suggest it remains modest in the dense core of the remnant, implying that turbulence is unlikely to distort the post-merger gravitational-wave signal enough to compromise plans to probe the equation of state of nuclear matter with next-generation detectors such as the Einstein Telescope and Cosmic Explorer. On the other hand, turbulence and dynamo action are expected to leave a significant imprint on the long-term evolution of the remnant, its mass ejection, and its multi-messenger emission, from kilonova light curves to the engines of short gamma-ray bursts.

Much remains to be done. The review highlights open questions about whether angular momentum transport accelerates or delays the collapse of the remnant neutron star, about the topology of the amplified magnetic fields and whether tangled configurations better explain the energetics of gamma-ray bursts, and about the formidable challenge of uncertainty quantification in a parameter space already crowded with uncertain inputs. Validation is particularly thorny: unlike wind tunnels, neutron stars offer no laboratory tests, so models must be calibrated against resolved simulations whose own fidelity is uncertain, and tuned to observables, such as gravitational waves and neutrino signals, that differ from the statistical quantities conventionally used in closure validation. The authors anticipate rapid progress on three fronts: simulations that combine sophisticated microphysics, magnetohydrodynamics, and large-eddy closures; improved phenomenological subgrid models tested in local calculations; and data-driven, machine-learned closures that learn the missing physics directly from high-resolution data. As gravitational-wave astronomy enters its next generation, taming turbulence may prove the key to turning collisions of dead stars into precision measurements of matter at its densest.

Subject of Research: Turbulence modelling in general-relativistic simulations of binary neutron star mergers

Article Title: Turbulence modelling in neutron star merger simulations

Article References: Radice, D., & Hawke, I. (2024). Turbulence modelling in neutron star merger simulations. Living Reviews in Computational Astrophysics, 10(1), Article 1. https://doi.org/10.1007/s41115-023-00019-9

Image Credits: AI Generated

DOI: 10.1007/s41115-023-00019-9

Keywords: neutron star mergers, turbulence, large-eddy simulation, gravitational waves, magnetohydrodynamics, Kelvin-Helmholtz instability, magnetic field amplification, subgrid models, numerical relativity, accretion disks, r-process nucleosynthesis, equation of state

The question of universality has been difficult to answer because of the sheer disparity of timescales involved. Stellar-mass black holes, which weigh in at a few to a few dozen times the mass of the sun, evolve quickly: their accretion disks brighten and fade over weeks and months, and astronomers have watched them undergo state transitions many times. During these outbursts, the accretion flow switches between a hot, radiatively inefficient mode and a cooler, geometrically thin disk, and it is precisely at these transitions that jets are switched on or off. Decades of monitoring have pinned down the critical accretion rate at which this happens with considerable precision.

Supermassive black holes, by contrast, are far less cooperative. The accretion flows that power active galactic nuclei evolve over thousands of years, which means that no single observer—or even several generations of observers—can watch one system cross the critical threshold where jets are born. As a result, whether the well-established rules of stellar-mass black holes apply to their supermassive cousins remained an open and contested question, one with profound implications for how galaxies grow and how black holes shape their cosmic environments.

Goodwin and Mummery realized that tidal disruption events offered a way around this bottleneck. When a star wanders too close to a supermassive black hole, tidal forces rip it apart, and its debris forms a glowing accretion disk around the hole. Unlike ordinary active galactic nuclei, these newly formed disks evolve dramatically on timescales of just years, blazing bright at super-Eddington accretion rates before fading steadily. That means a single tidal disruption event can carry a black hole through the entire range of accretion rates where jets are expected to appear, all within a human lifetime.

The researchers assembled multiwavelength data for a sample of tidal disruption events, combining radio observations—which trace outflows launched by the black hole—with detailed modeling of the evolving accretion disk using publicly available fitting tools. The disk modeling allowed them to reconstruct the accretion rate of each system at any moment in its evolution, while the radio data, interpreted through synchrotron spectral fitting, revealed when outflows were launched and how fast they were moving. By cross-referencing the two, they could determine the accretion rate at the precise moment each outflow was ejected.

The results were striking. Every tidal disruption event in the sample launched an early outflow while accreting at super-Eddington rates, consistent with the powerful disk winds expected when radiation pressure overwhelms gravity. But many systems also produced a second, physically distinct outflow later in their evolution, and these delayed ejections occurred when the disk accretion rate had fallen to a critical value of roughly two percent of the Eddington luminosity—the same threshold, scaled by mass, at which stellar-mass black holes are known to undergo their hard-to-soft state transitions and launch their characteristic compact jets. In one well-studied event, ASASSN-14li, the accretion rate at the time of outflow launch could be constrained with particular precision, and it matched the universal value.

This convergence is remarkable because the two classes of systems differ by factors of a million or more in black hole mass. The Eddington rate itself scales with mass, so expressing the accretion rate as a fraction of the Eddington value is the natural way to compare systems across cosmic scales. That the critical fraction comes out the same—about two percent—for both stellar-mass black holes and supermassive black holes strongly suggests that the physical mechanism responsible for jet launching does not care about scale. The processes are thought to involve the geometry of the inner accretion flow, where a hot, tenuous, magnetized plasma can collimate magnetic fields into a jet, and the new results indicate that the conditions for this configuration arise at the same fractional accretion rate regardless of the black hole’s mass.

The framework also resolves a puzzle that has dogged tidal disruption observers for years: why some events show prompt radio emission, why others flare in radio years after the optical outburst, and why surveys now routinely detect late-time radio re-brightenings that earlier models struggled to explain. In the new picture, the prompt outflows are super-Eddington winds ejected when the disk first forms, while delayed radio flares mark the launch of a second, jet-like outflow as the fading disk crosses the universal critical threshold. The timing of the delayed flares should then depend on how quickly each disk evolves from its super-Eddington peak down to two percent of Eddington, a prediction the authors tested with a modeled population of tidal disruption disks and found consistent with the observed distribution of outflow launch times.

Beyond tidally disrupted stars, the findings extend naturally to the broader population of accreting black holes. The critical threshold provides a predictive tool: given a black hole’s mass and its current accretion rate, astronomers can now estimate whether jets should be on or off, and when a fading system will cross the line. For active galactic nuclei, whose long-term evolution is normally inaccessible, this offers a way to infer jet activity from snapshot measurements of accretion rate. It also connects to long-standing empirical relations, such as the fundamental plane of black hole activity that links radio and X-ray luminosities across mass scales, which hinted at scale-invariant physics but lacked the direct observational anchor that tidal disruption events now supply.

The implications reach beyond pure astrophysics. Jets launched by supermassive black holes inject enormous amounts of energy into their host galaxies, heating gas, suppressing star formation, and shaping the largest structures in the universe. Understanding exactly when and why these jets switch on is therefore essential for modeling galaxy evolution itself. If a single scale-invariant threshold controls jet formation everywhere, simulations of galaxy feedback can be anchored to a universal rule rather than calibrated separately for each mass regime. And with new time-domain surveys set to discover tidal disruption events by the thousands in the coming years, the framework developed by Goodwin and Mummery promises a growing catalog of natural experiments—each a black hole caught mid-transformation, its jet poised to switch on at the same universal moment.

Subject of Research: The universal critical accretion rate governing jet formation in black holes across mass scales, probed through tidal disruption events

Article Title: A universal critical accretion rate for black hole jet formation

Article References: A universal critical accretion rate for black hole jet formation. (n.d.). https://doi.org/10.1038/s41550-026-02951-1

Image Credits: AI Generated

DOI: 10.1038/s41550-026-02951-1

Keywords: black holes, jets, tidal disruption events, accretion, supermassive black holes, Eddington limit, radio astronomy, active galactic nuclei, outflows, state transitions, accretion disks, Nature Astronomy