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DOE OSTI2020

Local measurements of the spatial magnetic field distribution in a z-pinch plasma during and near stagnation using polarization spectroscopy

We present here the detailed measurements of radial distribution of the magnetic field in a gas-puff z-pinch plasma at the final stages of the implosion phase and at stagnation. While the measurements are chordal, the radial distribution of different charge states was utilized to measure the magnetic field locally for certain radii, so that unlike chordal measurements in general, the magnetic field radial distribution was obtained with no need for the Abel inversion of the data. The distribution was measured using the Zeeman effect via a novel spectroscopic technique, at several axial locations, and demonstrates striking features such as the peak field remaining at a radius much larger than the stagnation radius at all times. Furthermore, while the distribution observed is sometimes monotonic with respect to the radius, it is often not, a behavior that can be linked to 2D features in the plasma column resulting from the Rayleigh–Taylor instability. The current flowing through the stagnating plasma was found to be a small fraction of the total current, resulting in clearly insufficient magnetic pressure to balance the plasma pressure at stagnation. The magnetic field data, taken over several axial positions, are used to obtain the true inductance in the imploding plasma for the first time; it is found that the data cannot explain the current turnover at stagnation. A simulation with the MACH2-Tabular Collisional-Radiative Equilibrium magnetohydrodynamics code in the r–z plane shows that the peak of the magnetic field pinches to a much smaller radius than is observed in the spectroscopic data. Furthermore, the depth of the computed current turnover at stagnation is smaller than the measured one. The two observed features of a radially extended magnetic field at stagnation together with a deep current turnover are a challenge to match in simulations. Various calculations and estimates of the inductive and resistive load voltages are examined to ascertain if they are responsible for the observed current notch. Lastly, the results demonstrate that the knowledge of the true inductance in the driven load requires such magnetic-field-distribution measurements and that imaging data or electrical measurements are insufficient.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Radiatively cooled magnetic reconnection experiments driven by pulsed power

We present evidence for strong radiative cooling in a pulsed-power-driven magnetic reconnection experiment. Two aluminum exploding wire arrays, driven by a 20 MA peak current, 300 ns rise time pulse from the Z machine (Sandia National Laboratories), generate strongly driven plasma flows (MA≈7) with anti-parallel magnetic fields, which form a reconnection layer (SL≈120) at the mid-plane. The net cooling rate far exceeds the Alfvénic transit rate (τcool−1/τA−1≫1), leading to strong cooling of the reconnection layer. We determine the advected magnetic field and flow velocity using inductive probes positioned in the inflow to the layer, and inflow ion density and temperature from analysis of visible emission spectroscopy. A sharp decrease in x-ray emission from the reconnection layer, measured using filtered diodes and time-gated x-ray imaging, provides evidence for strong cooling of the reconnection layer after its initial formation. X-ray images also show localized hotspots, regions of strong x-ray emission, with velocities comparable to the expected outflow velocity from the reconnection layer. These hotspots are consistent with plasmoids observed in 3D radiative resistive magnetohydrodynamic simulations of the experiment. X-ray spectroscopy further indicates that the hotspots have a temperature (170 eV) much higher than the bulk layer (≤75 eV) and inflow temperatures (about 2 eV) and that these hotspots generate the majority of the high-energy (>1 keV) emission.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Resolution Study of Thermonuclear Initiation in White Dwarf Tidal Disruption Events

Abstract We study the initiation of thermonuclear detonations in tidally disrupted white dwarf stars by intermediate-mass (10 3 M ⊙ ) black holes. The length scales required to resolve the initiation mechanism are not easily reached in 3D, so instead we have devised 2D proxy models, which, together with a logarithmic gridding strategy, can adequately capture detonation wave fronts as material undergoes simultaneous compression and stretching from tidal forces. We consider 0.15 and 0.6 M ⊙ white dwarf stars parameterized by tidal strengths in the range β = 4–23. High spatial resolution elucidates the manner and conditions leading to thermonuclear detonation, linking the initiation sequence to stellar composition and tidal strength. All of our models suffer sustained detonations triggered by a combination of adiabatic compression, mild thermonuclear preconditioning, and collisional heating, in degrees depending primarily on tidal strength. We find that many diagnostics, such as temperature, total released energy, and iron-group products, are fairly well converged (better than 10%) at resolutions below 10 km along the scale height of the orbital plane. The exceptions are intermediate-mass transients like calcium, which remain uncertain up to factors of 2, even at 1 km resolution.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Planet Formation by Gas-assisted Accretion of Small Solids

We compute the accretion efficiency of small solids, with radii 1 cm ≤ R s ≤ 10 m, on planets embedded in gaseous disks. Planets have masses 3 ≤ M p ≤ 20 Earth masses (M ⊕ ) and orbit within 10 au of a solar mass star. Disk thermodynamics is modeled via 3D radiation-hydrodynamics calculations that typically resolve the planetary envelopes. Both icy and rocky solids are considered, explicitly modeling their thermodynamic evolution. The maximum efficiencies of 1 ≤ R s ≤ 100 cm particles are generally ≲10%, whereas 10 m solids tend to accrete efficiently or be segregated beyond the planet’s orbit. A simplified approach is applied to compute the accretion efficiency of small cores, with masses M p ≤ 1 M ⊕ and without envelopes, for which efficiencies are approximately proportional to $M^{2/3}_{p}$. The mass flux of solids, estimated from unperturbed drag-induced drift velocities, provides typical accretion rates dM p /dt ≲ 10 -5 M ⊕ yr -1 . In representative disk models with an initial gas-to-dust mass ratio of 70–100 and total mass of 0.05–0.06 M ⊙ , the solids’ accretion falls below 10 -6 M ⊕ yr -1 after 1–1.5 Myr. The derived accretion rates, as functions of time and planet mass, are applied to formation calculations that compute dust opacity self-consistently with the delivery of solids to the envelope. Assuming dust-to-solid coagulation times of ≈0.3 Myr and disk lifetimes of ≈3.5 Myr, heavy-element inventories in the range 3–7 M ⊕ require that ≈90–150 M ⊕ of solids cross the planet’s orbit. The formation calculations encompass a variety of outcomes, from planets a few times M ⊕ , predominantly composed of heavy elements, to giant planets. The peak luminosities during the epoch of the solids’ accretion range from ≈10 -7 to ≈10 -6 L ⊙ .

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

On the Stability Analysis of Astrophysical Cooling Functions

To model the temperature evolution of optically thin astrophysical environments at MHD scales, radiative and collisional cooling rates are typically either pretabulated or fit into a functional form and then input into MHD codes as a radiative loss function. Thermal balance requires estimates of the analogous heating rates, which are harder to calculate, and due to uncertainties in the underlying dissipative heating processes these rates are often simply parameterized. The resulting net cooling function defines an equilibrium curve that varies with density and temperature. Such cooling functions can make the gas prone to thermal instability (TI), which will cause departures from equilibrium. There has been no systematic study of thermally unstable parameter space for nonequilibrium states. Motivated by our recent finding that there is a related linear instability, catastrophic cooling instability, that can dominate over TI, here we carry out such a study. We show that Balbus instability criteria for TI can be used to define a critical cooling rate, Λ c , that permits a nonequilibrium analysis of cooling functions through the mapping of TI zones. We furthermore illustrate how thermal conduction modifies the shape of TI zones. Upon applying a Λ c -based stability analysis to coronal loop simulations, we find that loops undergoing periodic episodes of coronal rain formation are linearly unstable to catastrophic cooling instability, while TI is stabilized by thermal conduction.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Radiation GRMHD Models of Accretion onto Stellar-mass Black Holes. I. Survey of Eddington Ratios

We summarize results from a survey of radiation-dominated black hole accretion flows across a wide range of mass accretion rates, as well as two values of black hole spin and initial magnetic field geometry. These models apply an algorithm targeting direct solutions to the radiation transport equation in full general relativity and have been enabled by access to modern exascale computing systems. Super-Eddington accretion flows form geometrically thick radiation-pressure-supported disks that drive powerful equatorial outflows. A narrow funnel-shaped photosphere in the inner region results in very low radiative efficiencies in this regime. The structure of near- and sub-Eddington accretion depends on whether there is net vertical magnetic flux at the midplane of the disk. With net flux, the disk forms a thin, dense layer at the midplane surrounded by a magnetically dominated corona, whereas without net flux, the disk remains magnetically dominated everywhere. Although none of our models achieve the magnetically arrested disk regime, those with net vertical flux and a rapidly spinning black hole still produce powerful relativistic jets. Our calculations adopt simple opacity models (with scalings appropriate to stellar-mass black hole accretion). We discuss the application of our results to observations of X-ray binaries and ultraluminous X-ray sources such as Cyg X-3 and SS433. We also speculate on the application of our super-Eddington models to the interpretation of little red dots recently discovered by JWST.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Radiation GRMHD Models of Accretion onto Stellar-mass Black Holes. II. Super-Eddington Accretion

We present a comprehensive analysis of super-Eddington black hole accretion simulations that solve the GRMHD equations coupled with angle-discretized radiation transport. The simulations span a range of accretion rates, two black hole spins, and two magnetic field topologies, and include resolution studies as well as comparisons with nonradiative models. Super-Eddington accretion flows consistently develop geometrically thick disks supported by radiation pressure, regardless of magnetic field configuration. Radiation generated in the inner disk drives substantial outflows, forming conical funnel regions that limit photon escape and result in very low radiation efficiency. The accretion flows are highly turbulent, with thermal energy transport dominated by radiation advection rather than diffusion. Angular momentum is primarily carried outward by Maxwell stress, with turbulent Reynolds stress playing a subdominant role. Both strong and weak jets are produced. Strong jets arise from sufficient net vertical magnetic flux and rapid black hole spin, and they can effectively evacuate the funnel, enabling radiation to escape through strong geometric beaming. In contrast, weak jets fail to clear the funnel, which becomes obscured by radiation-driven outflows and leads to distinct observational signatures. Spiral structures are observed in the plunging region, behaving like density waves. These super-Eddington models are applicable to a variety of astronomical systems, including ultraluminous X-ray sources, little red dots, and black hole transients.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Magnetic Flux Plays an Important Role during a Black Hole X-Ray Binary Outburst in Radiative Two-temperature General Relativistic Magnetohydrodynamic Simulations

Abstract Black hole (Bh) X-ray binaries cycle through different spectral states of accretion over the course of months to years. Although persistent changes in the Bh mass accretion rate are generally recognized as the most important component of state transitions, it is becoming increasingly evident that magnetic fields play a similarly important role. In this article, we present the first radiative two-temperature general relativistic magnetohydrodynamics simulations in which an accretion disk transitions from a quiescent state at an accretion rate of M ̇ ∼ 10 − 10 M ̇ Edd to a hard-intermediate state at an accretion rate of M ̇ ∼ 10 − 2 M ̇ Edd . This huge parameter space in mass accretion rate is bridged by artificially rescaling the gas density scale of the simulations. We present two jetted BH models with varying degrees of magnetic flux saturation. We demonstrate that in “standard and normal evolution” models, which are unsaturated with magnetic flux, the hot torus collapses into a thin and cold accretion disk when M ̇ ≳ 5 × 10 − 3 M ̇ Edd . On the other hand, in “magnetically arrested disk” models, which are fully saturated with vertical magnetic flux, the plasma remains mostly hot with substructures that condense into cold clumps of gas when M ̇ ≳ 1 × 10 − 2 M ̇ Edd . This suggests that the spectral signatures observed during state transitions are closely tied to the level of magnetic flux saturation.

Astronomy & Astrophysics↗

DOE OSTI2021

Radiation GRMHD simulations of M87: funnel properties and prospects for gap acceleration

Here, we use the public code EBHLIGHT to carry out 3D radiative general relativistic magnetohydrodynamics (GRMHD) simulations of accretion on to the supermassive black hole in M87. The simulations self-consistently evolve a frequency-dependent Monte Carlo description of the radiation field produced by the accretion flow. We explore two limits of accumulated magnetic flux at the black hole (SANE and MAD), each coupled to several subgrid prescriptions for electron heating that are motivated by models of turbulence and magnetic reconnection. We present convergence studies for the radiation field and study its properties. We find that the near-horizon photon energy density is an order of magnitude higher than is predicted by simple isotropic estimates from the observed luminosity. The radially dependent photon momentum distribution is anisotropic and can be modeled by a set of point-sources near the equatorial plane. We draw properties of the radiation and magnetic field from the simulation and feed them into an analytic model of gap acceleration to estimate the very high energy (VHE) γ-ray luminosity from the magnetized jet funnel, assuming that a gap is able to form. We find luminosities of $\rm \sim 10^{41} \, erg \, s^{-1}$ for MAD models and $\rm \sim 2\times 10^{40} \, erg \, s^{-1}$ for SANE models, which are comparable to measurements of M87’s VHE flares. The time-dependence seen in our calculations is insufficient to explain the flaring behaviour. Our results provide a step towards bridging theoretical models of near-horizon properties seen in black hole images with the VHE activity of M87.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Bremsstrahlung in GRMHD Models of Accreting Black Holes

Here, the role of bremsstrahlung in the emission from hot accretion flows around slowly accreting supermassive black holes is not thoroughly understood. In order to appraise the importance of bremsstrahlung relative to other radiative processes, we compute spectral energy distributions (SEDs) of accretion disks around slowly accreting supermassive black holes including synchrotron radiation, inverse Compton scattering, and bremsstrahlung. We compute SEDs for (i) four axisymmetric radiative general relativistic magnetohydrodynamics (RadGRMHD) simulations of 10 8 M ⊙ black holes with accretion rates between 10 -8 $\dot{M}$ Edd and 10 -5 $\dot{M}$ Edd , (ii) four axisymmetric RadGRMHD simulations of M87* with varying dimensionless spin a$_*$ and black hole mass, and (iii) a 3D GRMHD simulation scaled for Sgr A*. At 10 -8 $\dot{M}$ Edd , most of the luminosity is synchrotron radiation, while at 10 -5 $\dot{M}$ Edd the three radiative processes have similar luminosities. In most models, bremsstrahlung dominates the SED near 512 keV. In the M87* models, bremsstrahlung dominates this part of the SED if a$_*$ = 0.5, but inverse Compton scattering dominates if a$_*$ = 0.9375. Since scattering is more variable than bremsstrahlung, this result suggests that 512 keV variability could be a diagnostic of black hole spin. In the appendix, we compare some bremsstrahlung formulæ found in the literature.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

X-ray imaging and radiation transport effects on cylindrical implosions

Magnetization of inertial confinement implosions is a promising means of improving their performance, owing to the potential reduction of energy losses within the target and mitigation of hydrodynamic instabilities. In particular, cylindrical implosions are useful for studying the influence of a magnetic field, thanks to their axial symmetry. In this work, we present experimental results from cylindrical implosions on the OMEGA-60 laser using a 40-beam, 14.5 kJ, 1.5 ns drive and an initial seed magnetic field of B 0 = 30 T along the axes of the targets, compared with reference results without an imposed B-field. Implosions were characterized using time-resolved x-ray imaging from two orthogonal lines of sight. We found that the data agree well with magnetohydrodynamic simulations, once radiation transport within the imploding plasma is considered. We show that for a correct interpretation of the data in these types of experiments, explicit radiation transport must be taken into account.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Neutrino transport in general relativistic neutron star merger simulations

Abstract Numerical simulations of neutron star–neutron star and neutron star–black hole binaries play an important role in our ability to model gravitational-wave and electromagnetic signals powered by these systems. These simulations have to take into account a wide range of physical processes including general relativity, magnetohydrodynamics, and neutrino radiation transport. The latter is particularly important in order to understand the properties of the matter ejected by many mergers, the optical/infrared signals powered by nuclear reactions in the ejecta, and the contribution of that ejecta to astrophysical nucleosynthesis. However, accurate evolutions of the neutrino transport equations that include all relevant physical processes remain beyond our current reach. In this review, I will discuss the current state of neutrino modeling in general relativistic simulations of neutron star mergers and of their post-merger remnants. I will focus on the three main types of algorithms used in simulations so far: leakage, moments, and Monte-Carlo scheme. I will review the advantages and limitations of each scheme, as well as the various neutrino–matter interactions that should be included in simulations. We will see that the quality of the treatment of neutrinos in merger simulations has greatly increased over the last decade, but also that many potentially important interactions remain difficult to take into account in simulations (pair annihilation, oscillations, inelastic scattering).

Foucart, Francois (ORCID:0000000346174738)↗

DOE OSTI2023

ALEGRA: Finite element modeling for shock hydrodynamics and multiphysics

ALEGRA is a multiphysics finite-element shock hydrodynamics code, under development at Sandia National Laboratories since 1990. Fully coupled multiphysics capabilities include transient magnetics, magnetohydrodynamics, electromechanics, and radiation transport. Importantly, ALEGRA is used to study hypervelocity impact, pulsed power devices, and radiation effects. The breadth of physics represented in ALEGRA is outlined here, along with simulated results for a selected hypervelocity impact experiment.

42 ENGINEERING↗

DOE OSTI2022

Formation of Magnetically Truncated Accretion Disks in 3D Radiation-transport Two-temperature GRMHD Simulations

Multiwavelength observations suggest that the accretion disk in the hard and intermediate states of X-ray binaries (XRBs) and active galactic nucleus transitions from a cold, thin disk at large distances into a hot, thick flow close to the black hole (BH). However, the formation, structure, and dynamics of such truncated disks are poorly constrained due to the complexity of the thermodynamic, magnetic, and radiative processes involved. We present the first radiation-transport two-temperature general relativistic magnetohydrodynamic (GRMHD) simulations of truncated disks radiating at ~35% of the Eddington luminosity with and without large-scale poloidal magnetic flux. We demonstrate that when a geometrically thin accretion disk is threaded by large-scale net poloidal magnetic flux, it self-consistently transitions at small radii into a two-phase medium of cold gas clumps floating through a hot, magnetically dominated corona. This transition occurs at a well-defined truncation radius determined by the distance out to which the disk is saturated with magnetic flux. The average ion and electron temperatures in the semiopaque corona reach, respectively, $T_i$ ≳ 10 10 K and $T_e$ ≳ 5 × 10 8 K. The system produces radiation, powerful collimated jets, and broader winds at the total energy efficiency exceeding 90%, the highest ever energy extraction efficiency from a spinning BH by a radiatively efficient flow in a GRMHD simulation. This is consistent with jetted ejections observed during XRB outbursts. The two-phase medium may naturally lead to broadened iron line emission observed in the hard state.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Diagnosing the pedestal magnetic field and magnetohydrodynamics radial structure with pedestal–scrape of layer electron cyclotron emission radiation inversion in H-mode plasma (invited)

Forward modeling is used to interpret inversion patterns of the pedestal–Scrape of Layer (SOL) Electron Cyclotron Emission (ECE) in DIII-D H-mode experiments. The modeling not only significantly improves the ECE data interpretation quality but also leads to the potential measurements of (1) the magnetic field strength |B| at the separatrix, (2) the pedestal |B| evolution during an inter-Edge Localized Mode (ELM) period, and (3) the pedestal Magnetohydrodynamics (MHD) radial structure. The ECE shine-through effect leads to three types of pedestal–SOL radiation inversions that are discussed in this paper. The first type of inversion is the non-monotonic T e,rad profile with respect to the major radius. Using the ECE frequency at the minimum T e,rad , the inversion can be applied to measure the magnetic field |B| at the separatrix and calibrate the mapping of the ECE channels with respect to the separatrix. The second type of inversion refers to the opposite phase between the radiation fluctuations δT e,rad at the pedestal and SOL. This δT e,rad phase inversion is sensitive to density and temperature fluctuations at the pedestal foot and, thus, can be used to qualitatively measure the MHD radial structure. The third type of inversion appears when the pedestal and SOL T e,rad evolve in an opposite trend, which can be used to infer the pedestal |B| field change during an inter-ELM period. Finally, the bandwidth effect on measuring δT e,rad due to pedestal MHD is also investigated in the radiation modeling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Formation and evolution of protostellar accretion discs – II. From 3D simulation to a simple semi-analytic model of Class 0/I discs

Here we use a 3D radiative non-ideal magnetohydrodynamic simulation to investigate the formation and evolution of a young protostellar disc from a magnetized pre-stellar core. The simulation covers the first ${\sim }10\, {\rm kyr}$ after protostar formation and shows a massive, weakly magnetized disc with radius that initially grows and then saturates at ${\sim }30\, {\rm au}$. The disc is gravitationally unstable with prominent large-amplitude spiral arms. We use our simulation results and a series of physical arguments to construct a predictive and quantitative physical picture of Class 0/I protostellar disc evolution from several aspects, including (i) the angular-momentum redistribution in the disc, self-regulated by gravitational instability to make most of the disc marginally unstable; (ii) the thermal profile of the disc, well-approximated by a balance between radiative cooling and accretion heating; and (iii) the magnetic-field strength and magnetic-braking rate inside the disc, regulated by non-ideal magnetic diffusion. Using these physical insights, we build a simple 1D semi-analytic model of disc evolution. We show that this 1D model, when coupled to a computationally inexpensive simulation for the evolution of the surrounding pseudo-disc, can be used reliably to predict disc evolution in the Class 0/I phase. The predicted long-term evolution of disc size, which saturates at ${\sim }30\, {\rm au}$ and eventually shrinks, is consistent with a recent observational survey of Class 0/I discs. Such hierarchical modelling of disc evolution circumvents the computational difficulty of tracing disc evolution through Class 0/I phase with direct, numerically converged simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Measurement of near- and far-field impurity flows during pellet-induced rapid shutdown in DIII-D

Both near-field (<1 m away toroidally from the pellet) and far-field (>1 m away toroidally from the pellet) poloidal and toroidal impurity (carbon ion) flows are measured using visible imaging and fast bolometry during a polypropylene pellet-induced rapid plasma shutdown in the DIII-D tokamak. In the near field, the pellet appears to increase poloidal flow in the ion diamagnetic direction, possibly due to the strong radial temperature gradient caused by the pellet ablation. In the far field, the poloidal impurity flow typically appears slower and in the opposite direction. Toroidal impurity flow appears to be strongly influenced by the plasma initial toroidal rotation, especially in the far field. These results demonstrate that rapid shutdown impurity flows are not necessarily global in structure but can be quite different close to and far from the injected pellet.

Electromagnetic radiation detectors↗

DOE OSTI2026

Collapse of magnetized white dwarfs as site of heavy-element formation and kilonova signal

We present the first end-to-end calculation connecting the accretion-induced collapse (AIC) of a magnetized, rapidly rotating white dwarf to observable kilonova signatures, combining two-dimensional (2D) general-relativistic neutrino-magnetohydrodynamic simulations, followed by radiation hydrodynamics with in-situ nuclear network and 2D Monte Carlo radiative transfer with spatially resolved heating rates. Unlike all previous unmagnetized AIC models – which predicted proton-rich, $^{56}$Ni-dominated ejecta – strong magnetic fields eject ${\approx }\, 0.2\, \mathrm{ M}_\odot$ of neutron-rich material ($\langle Y_e \rangle \sim 0.24$) on dynamical time-scales, before neutrino irradiation can raise the electron fraction, enabling strong r-process nucleosynthesis up to and beyond the third peak. The resulting kilonova is lanthanide-rich ($X_{\rm lan} \approx 8~{{\ \rm per\ cent}}$) and dominated by near-infrared emission. We compute synthetic light curves in the Large Synoptic Survey Telescope and J ames Webb Space Telescope bands and find striking agreement, without parameter tuning, between the observations of AT 2023vfi/GRB 230307A and our broadband light curves for polar viewing angles. These results establish magnetized AIC as a viable channel for heavy r-process element production and a compelling progenitor candidate for long-duration gamma-ray bursts with kilonova signatures.

MHD↗