Entropy Profiles Research Articles

Multiphase condensation in cluster haloes: interplay of cooling, buoyancy, and mixing

ABSTRACT Gas in the central regions of cool-core clusters and other massive haloes has a short cooling time (≲1 Gyr). Theoretical models predict that this gas is susceptible to multiphase condensation, in which cold gas is expected to condense out of the hot phase if the ratio of the thermal instability growth time-scale (tti) to the free-fall time (tff) is tti/tff ≲ 10. The turbulent mixing time tmix is another important time-scale: if tmix is short enough, the fluctuations are mixed before they can cool. In this study, we perform high-resolution (5122 × 768–10242 × 1536 resolution elements) hydrodynamic simulations of turbulence in a stratified medium, including radiative cooling of the gas. We explore the parameter space of tti/tff and tti/tmix relevant to galaxy and cluster haloes. We also study the effect of the steepness of the entropy profile, the strength of turbulent forcing and the nature of turbulent forcing (natural mixture versus compressive modes) on multiphase gas condensation. We find that larger values of tti/tff or tti/tmix generally imply stability against multiphase gas condensation, whereas larger density fluctuations (e.g. due to compressible turbulence) promote multiphase gas condensation. We propose a new criterion min (tti/min (tmix, tff)) ≲ c2 × exp (c1σs) for when the halo becomes multiphase, where σs denotes the amplitude of logarithmic density fluctuations and c1 ≃ 6, c2 ≃ 1.8 from an empirical fit to our results.

Entropy and Energy Profiles of Chemical Reactions.

The description of chemical processes at the molecular level is often facilitated by the use of reaction coordinates or collective variables (CVs). The CV measures the progress of the reaction and allows the construction of profiles that track how specific properties evolve as the reaction progresses. Whereas CVs are routinely used, especially alongside enhanced sampling techniques, the links among reaction profiles, thermodynamic state functions, and reaction rate constants are not rigorously exploited. Here, we report a unified treatment of such reaction profiles. Tractable expressions are derived for the free-energy, internal-energy, and entropy profiles as functions of only the CV. We demonstrate the ability of this treatment to extract quantitative insight from the entropy and internal-energy profiles of various real-world physicochemical processes, including intramolecular organic reactions, ionic transport in superionic electrolytes, and molecular transport in nanoporous materials.

Consistent ramifications of prescribed surface temperature and prescribed heat flux boundary conditions for the slip flow of Walter B fluid in a stretching channel

ABSTRACT The present work delves into the Walter B fluid flow across the channel with the elongating enclosures when enthralled by linear radiation. The magnetic field is contemplated throughout the examination. The fluid suction and injection is permitted through the lower permeable wall. The slip regime is confined at the boundaries of the channel. Heat transfer in the channel is brought to light under two heating processes, namely prescribed surface temperature and prescribed surface heat flux case. The modeled equations are non-dimensionalized and then solved by the Runge-Kutta Fehlberg method in association with shooting scheme. Results deduce that the Reynolds number magnifies the velocity in the channel. Under two different heat boundary conditions, it is recorded that temperature is more pronounced for prescribed surface temperature case than prescribed heat flux. Flow profile for the varying viscoelastic parameter deciphers that at the lower end of the channel, the velocity is augmented and reverse response is recorded at the upper half of channel. Entropy profile magnifies with the augmentation of the magnetic parameter and shows depleting nature for higher Reynolds number. Examining the Walter B fluid flow in the channel enclosed with stretchable walls deliberates the flow of blood in the arterial wall under the exertion of strong magnetic field.

Entropy generation in viscous flow due to generalized exponential wall velocity and temperature

The study of entropy generation in convective transport processes is of current interest. For the better understanding of this phenomenon it is preferred to investigate it for those flows which admit an exact solution. This is the reason that majority of the published literature, concerning entropy generation analysis, has been done for the self-similar flows. Particular to the stretching sheet flows, which do also have important applications in industry, entropy production analysis is of particular importance. In this regard a two dimensional boundary layer flow due to an exponentially stretching wall (following generalized exponential form) has been considered in this study for the analysis of entropy generation. The stretching wall velocity and the wall temperature function have so properly been chosen that an similarity solution is possible. The modeled, equations are converted to ordinary differential equations by employing appropriate similarity transformations. These equations are solved numerically by using bvp-4c implemented in Matlab. To implement this method, differential equations are converted to set of first order equations and are solved. The problem has been analyzed for the heat transfer phenomenon and the entropy generation. The dimensionless form of entropy generation number requires m ≡ n for a similarity solution to exist. The enhancement is observed in the Nusselt number by enhancing the values of m, n, and Pr. Eventually, the entropy generation at the wall is maximum for increasing values of and However, for such a large values of of and the entropy profile reduces rapidly in the boundary layer thus avoiding a farther speed of entropy in the boundary layer. It is also noticed that to minimize the entropy generation across the boundary layer and also to get an enhanced rate of heat transfer some higher values of and must be chosen.

Frequencies of f - and p -oscillation modes in cold and hot compact stars

A large collection of equations of state (EOSs) built within the covariant density functional theory of hadronic matter and allowing for density dependent couplings is employed to study polar $f$- and $p$-oscillations of cold and hot compact stars. Correlations between oscillation frequencies of cold purely nucleonic neutron stars (NSs), their global parameters as well as properties of nuclear matter (NM) are investigated by considering a set of models from Beznogov and Raduta, [Phys. Rev. C 107, 045803 (2023)], where a number of constraints on the saturation properties of NM, pure neutron matter and the lower bound of the maximal NS mass were imposed within a Bayesian framework. The roles of finite temperature and exotic particle degrees of freedom, e.g., hyperons, $\mathrm{\ensuremath{\Delta}}$-resonances, antikaon condensates or a hadron to quark phase transition, are addressed by employing a family of models publicly available on compose and assuming idealized profiles of temperature or entropy per baryon and charge fraction. We find that finite temperature effects reduce the oscillation frequencies of nucleonic stars while the opposite effect is obtained for stars with exotic particle degrees of freedom. When the $\mathrm{\ensuremath{\Gamma}}$-law is employed to build finite temperature EOSs, errors in estimating oscillation modes frequencies are of the order of 10% to 30%, depending on the mass. Throughout this work the Cowling approximation is used.

The Three Hundred Project: the evolution of physical baryon profiles

ABSTRACT The distribution of baryons provides a significant way to understand the formation of galaxy clusters by revealing the details of its internal structure and changes over time. In this paper, we present theoretical studies on the scaled profiles of physical properties associated with the baryonic components, including gas density, temperature, metallicity, pressure and entropy as well as stellar mass, metallicity and satellite galaxy number density in galaxy clusters from z = 4 to z = 0 by tracking their progenitors. These mass-complete simulated galaxy clusters are coming from The Three Hundred with two runs: Gizmo-SIMBA and Gadget-X. Through comparisons between the two simulations, and with observed profiles that are generally available at low redshift, we find that (1) the agreements between the two runs and observations are mostly at outer radii r ≳ 0.3r500, in line with the self-similarity assumption. While Gadget-X shows better agreements with the observed gas profiles in the central regions compared to Gizmo-SIMBA; (2) the evolution trends are generally consistent between the two simulations with slightly better consistency at outer radii. In detail, the gas density profile shows less discrepancy than the temperature and entropy profiles at high redshift. The differences in the cluster centre and gas properties imply different behaviours of the AGN models between Gadget-X and Gizmo-SIMBA, with the latter, maybe too strong for this cluster simulation. The high-redshift difference may be caused by the star formation and feedback models or hydrodynamics treatment, which requires observation constraints and understanding.

Explosion Mechanism of Core-collapse Supernovae: Role of the Si/Si–O Interface

We present a simple criterion to predict the explodability of massive stars based on the density and entropy profiles before collapse. If a pronounced density jump is present near the Si/Si–O interface, the star will likely explode. We develop a quantitative criterion by using ∼1300 1D simulations where ν-driven turbulence is included via time-dependent mixing-length theory. This criterion correctly identifies the outcome of the supernova more than 90% of the time. We also find no difference in how this criterion performs on two different sets of progenitors, evolved using two different stellar evolution codes: FRANEC and KEPLER. The explodability as a function of mass of the two sets of progenitors is very different, showing: (i) that uncertainties in the stellar evolution prescriptions influence the predictions of supernova explosions; (ii) the most important properties of the pre-collapse progenitor that influence the explodability are its density and entropy profiles. We highlight the importance that ν-driven turbulence plays in the explosion by comparing our results to previous works.

Exergy Analysis for Combustible Third-Grade Fluid Flow through a Medium with Variable Electrical Conductivity and Porous Permeability

A mathematical investigation of a thermodynamical system linked with energy management and its impact on the environment, especially climate change, is presented in this study. In this regard, a numerical investigation of the flow and heat transfer of hydromagnetic third-grade liquid through a porous medium. The permeability of the medium and electrical conductivity of the fluid are assumed to be temperature functions. The appropriate mathematical formulations for momentum, energy, and entropy equations are presented in both dimensional and dimensionless forms. We obtained the numerical solutions using the spectral version of the Chebyshev collocation method and compared the result with the shooting Runge–Kutta method. Numerical results for velocity, temperature, entropy, and Bejan profiles are communicated through tables and graphs with adequate physical interpretation. The thermal stability of the thermo-fluid system that guarantees the prevention of spontaneous fluid heating that fuels climate change is also included in the analysis.

Quasi-spiral solution to the mixed intracluster medium and the universal entropy profile of galaxy clusters

ABSTRACT Well-resolved galaxy clusters often show a large-scale quasi-spiral structure in deprojected density ρ and temperature T fields, delineated by a tangential discontinuity known as a cold front, superimposed on a universal radial entropy profile with a linear K(r) ∝ Tρ−2/3 ∝ r adiabat. We show that a spiral structure provides a natural quasi-stationary solution for the mixed intracluster medium (ICM), introducing a modest pressure spiral that confines the locally buoyant or heavy plasma phases. The solution persists in the presence of uniform or differential rotation, and can accommodate both an inflow and an outflow. Hydrodynamic adiabatic simulations with perturbations that deposit angular momentum and mix the plasma thus asymptote to a self-similar spiral structure. We find similar spirals in Eulerian and Lagrangian simulations of 2D and 3D, merger and offset, clusters. The discontinuity surface is given in spherical coordinates {r, θ, ϕ} by ϕ(r, θ) ∝ Φ(r) , where Φ is the gravitational potential, combining a trailing spiral in the equatorial (θ = π/2) plane and semicircles perpendicular to the plane, in resemblance of a snail shell. A local convective instability can develop between spiral windings, driving a modified global instability in sublinear K(r) regions; evolved spirals thus imprint the observed K ∝ r onto the ICM even after they dissipate. The spiral structure brings hot and cold phases to close proximity, suggesting that the observed fast outflows could sustain the structure even in the presence of radiative cooling.

Entropy and Energy Profiles of Chemical Reactions

Entropy and Energy Profiles of Chemical Reactions

EAGLE-like simulation models do not solve the entropy core problem in groups and clusters of galaxies

ABSTRACTRecent high-resolution cosmological hydrodynamic simulations run with a variety of codes systematically predict large amounts of entropy in the intra-cluster medium at low redshift, leading to flat entropy profiles and a suppressed cool-core population. This prediction is at odds with X-ray observations of groups and clusters. We use a new implementation of the EAGLE galaxy formation model to investigate the sensitivity of the central entropy and the shape of the profiles to changes in the sub-grid model applied to a suite of zoom-in cosmological simulations of a group of mass M500 = 8.8 × 1012 M⊙ and a cluster of mass 2.9 × 1014 M⊙. Using our reference model, calibrated to match the stellar mass function of field galaxies, we confirm that our simulated groups and clusters contain hot gas with too high entropy in their cores. Additional simulations run without artificial conduction, metal cooling or active galactic nuclei (AGN) feedback produce lower entropy levels but still fail to reproduce observed profiles. Conversely, the two objects run without supernova feedback show a significant entropy increase which can be attributed to excessive cooling and star formation. Varying the AGN heating temperature does not greatly affect the profile shape, but only the overall normalization. Finally, we compared runs with four AGN heating schemes and obtained similar profiles, with the exception of bipolar AGN heating, which produces a higher and more uniform entropy distribution. Our study leaves open the question of whether the entropy core problem in simulations, and particularly the lack of power-law cool-core profiles, arise from incorrect physical assumptions, missing physical processes, or insufficient numerical resolution.

Entropy Generation for MHD Peristaltic Transport of Non-Newtonian Fluid in a Horizontal Symmetric Divergent Channel

The analysis in view is proposed to investigate the impacts of entropy in the peristaltically flown Ree–Eyring fluid under the stress of a normally imposed uniform magnetic field in a non-uniform symmetric channel of varying thickness. The administering equations of the present flow problem are switched into the non-dimensional form and then reduced by the availing of long wavelengths and creeping flow regime restrictions. The analytical treatment for the developed problem is performed to attain closed-form solutions which are further displayed as graphs of velocity, pressure, temperature, and entropy distribution. The trapping phenomenon has also been an area of our current examination. The role of relevant pronounced parameters such as the Brinkmann number, Hartmann number, and Ree–Eyring parameter for throwing vivid impacts are also concerned. It has been inferred that both the Brinkmann number and Ree–Eyring parameter with rising values inflate temperature and entropy profiles. The velocity profile shows the symmetric nature due to the horizontally assumed symmetric channel of varying thickness. The circulation of streamlines and bolus formations is visibly reduced in response to the increasing Hartmann number.

Modeling and computational framework of radiative hybrid nanofluid configured by a stretching surface subject to entropy generation: Using Keller box scheme

This study examines the characteristics of the velocity, thermal field and entropy profiles for hybrid nanofluid flow passing through a starching sheet with thermal radiation. The carbon nanotube (SWCNT and MWCNT) are used as a nanoparticles with Cattaneo-Christov (CC) heat flux. Ethylene glycol is utilized as a base fluid in this case. To achieve an improved solution, the fluid flow over the geometric properties is designed using highly non-linear PDEs, and the governing equations must be converted into dimensionless non-similar equation systems using the highly efficient well-known Keller-box scheme in computational software MATLAB. The practical feasibility of these solutions is determined by the range of the controlling parameters. The velocity distribution reduces as the magnetic parameter estimate increases, however, the temperature field and entropy production increase as the magnetic parameter fluctuation esclates. As the slip parameter is increased, the velocity field diminish. The thermal field is enhanced for rising the radiation parameter, and the entropy profile is boosted for increasing Brinkman parameter values. The findings of this research might have a significant impact on industries where local cooling and heating via impingement jets are needed in electronic devices, heat sinks, drying technologies, and so on. To the best of the authors' knowledge, this is the first effort to employ a hybrid nanofluid to analyze entropy formation due to magnetohydrodynamics flow over a starching sheet.

Gas clumping in the outskirts of galaxy clusters, an assessment of the sensitivity ofSTAR-X

AbstractIn the outskirts of galaxy clusters, entropy profiles measured from X-ray observations of the hot intracluster medium (ICM) drops off unexpectedly. One possible explanation for this effect is gas clumping, where pockets of cooler and denser structures within the ICM are present. Current observatories are unable to directly detect these hypothetical gas clumps. One of the science drivers of the proposed STAR-X observatory is to resolve these or similar structures. Its high spatial resolution, large effective area, and low instrumental background make STAR-X ideal for directly detecting and characterizing clumps and diffuse emission in cluster outskirts. The aim of this work is to simulate observations of clumping in clusters to determine how well STAR-X will be able to detect clumps, as well as what clumping properties reproduce observed entropy profiles. This is achieved by using yt, pyXSIM, SOXS, and other tools to inject ideally modelled clumps into 3D models derived from actual clusters using their observed profiles from other X-ray missions. Radial temperature and surface brightness profiles are then extracted from mock observations using concentric annuli. We find that in simulated observations for STAR-X, a parameter space of clump properties exists where gas clumps can be successfully identified using wavdetect and masked, and are able to recover the true cluster profiles. This demonstrates that STAR-X could be capable of detecting substructure in the outskirts of nearby clusters and that the properties of both the outskirts and the clumps will be revealed.

Thermal Behavior of the Time-Dependent Radiative Flow of Water-Based CNTs/Au Nanoparticles Past a Riga Plate with Entropy Optimization and Multiple Slip Conditions

This communication deliberates the time-reliant and Darcy-Forchheimer flow of water-based CNTs/gold nanoparticles past a Riga plate. In addition, nonlinear radiation, heat consumption and multiple slip conditions are considered. Entropy generation is computed through various flow parameters. A suitable transformation with symmetry variables is invoked to remodel the governing mathematical flow models into the ODE equations. The homotopy analysis scheme and MATLAB bvp4c method are imposed to solve the reduced ODE equations analytically and numerically. The impact of sundry flow variables on nanofluid velocity, nanofluid temperature, skin friction coefficient, local Nusselt number, entropy profile and Bejan number are computed and analyzed through graphs and tables. It is found that the nanofluid velocity is reduced by greater porosity and slip factors. The thickness of the thermal boundary layer increases with increasing radiation, temperature ratio, and heat consumption/generation parameters. The surface drag force is reduced when there is a higher Forchheimer number, unsteadiness parameter and porosity parameter. The amount of entropy created is proportional to the radiation parameter, porosity parameter and Reynolds number. The Bejan number profile increases with radiation parameter, heat consumption/generation parameter and the Forchheimer number.

Redshift evolution of galaxy group X-ray properties in the Simba simulations

ABSTRACT We examine the evolution of intragroup gas rest-frame X-ray scaling relations for group-sized haloes (M500 = 1012.3–1015 M⊙) in the Simba galaxy formation simulation. X-ray luminosity LX versus M500 shows increasing deviation from self-similarity from z = 3 → 0, with M500 < 1013.5 M⊙ haloes exhibiting a large reduction in LX and slight increase in X-ray luminosity-weighted temperature TX. These shifts are driven by a strong drop in fgas with time for these haloes, and coincides with the onset of Simba’s black hole (BH) jet feedback, occurring when MBH > 107.5 M⊙ and Eddington ratio <0.2, in group haloes at z ∼ 1.5. The connection with BH feedback is corroborated by fBH ≡ MBH/M500 in M500 < 1013.5 M⊙ haloes being strongly anticorrelated with LX and fgas at $z\lesssim 1.5$. This is further reflected in the scatter of LX − TX: haloes with small fBH lie near self-similarity, while those with the highest fBH lie furthest below. Turning off jet feedback results in mostly self-similar behaviour down to z = 0. For the X-ray weighted metallicity ZX, stellar feedback impacts the enrichment of halo gas. Finally, halo profiles show that jet feedback flattens the electron density and entropy profiles, and introduces a core in X-ray surface brightness, particularly at M500 < 1013.5 M⊙. This argues that in Simba, intragroup X-ray evolution is largely driven by jet feedback removing hot gas from the cores of massive groups, and expelling gas altogether in less massive groups.

An entropy analysis in a slip condition flow over a linear stretching sheet

In this study, we present the slip conditions along with entropy generation of 2-D flow induced by a linear stretching surface with thermo-physical characteristics. We used the viscous model for shear flow conduct and calculate the steady flow field with the slip effect near the stretching surface. The concentration and energy equations are analyzed under the effect of thermo-physical properties. In this study, the thermo-physical properties are presumed to be variable. The system of equations occurs with boundary layer technique are transformed into ODEs by new similarity approach. The study is analyzed completely on base flow and entropy profiles. The radial slip coefficient shows reduction in the radial velocity and normal velocity profile creates incrementing in roughness of surface. The entropy function increases due to upper values of Brinkman number and diffusivity parameter. The mass diffusion coefficient and concentration ratio variable creates enhancement in entropy generation. The physical aspects are given through figures. The correlation of mean flow and entropy generation are presented by making the graphical plots. The comparison analysis with already published articles is also reported here.

The flat entropy profile at the outskirts of the Abell 2244 galaxy cluster

ABSTRACT Entropy is an advantageous diagnostics to study the thermodynamic history of the intracluster plasma of galaxy clusters. We present the entropy profile of the Abell 2244 galaxy cluster derived both exclusively using X-ray data from the low-background Swift XRT telescope and using the Planck y data. The entropy profile derivation using X-rays only is robust at least to the virial radius because the cluster brightness is large compared to the X-ray background at low energies, the temperature is strongly bounded by the lack of cluster X-ray photons at energies kT > 3 keV, and the XRT background is low, stable, and understood. In the observed solid angle, about one quadrant, the entropy radial profile deviates from a power law at the virial radius, mainly because of a sharp drop in the cluster temperature. This bending of the entropy profile is confirmed when X-ray spectral information is replaced by the Compton map. Clumping and non-thermal pressure support are insufficient to restore a power-law entropy profile because they are bound to be small by: (i) the agreement between mass estimates from different tracers (gas and galaxies), (ii) the agreement between entropy profile determinations based on combinations of observables with different sensitivities and systematics, and (iii) the low value of clumping as estimated using the azimuthal scatter and the gas fraction. Based on numerical simulations, ion–electron equilibration is also insufficient to restore a linear entropy profile. Therefore, the bending of the entropy profiles seems to be robustly derived and witnesses the theoretically predicted decrease in the inflow through the virial boundary.

Heating of the intracluster medium by buoyant bubbles and sound waves

ABSTRACT Active galactic nuclei (AGN) powered by the central supermassive black holes (SMBHs) play a major role in modifying the thermal properties of the intracluster medium (ICM). In this work, we implement two AGN heating models: (i) by buoyant cavities rising through stratified ICM (effervescent model) and, (ii) by viscous and conductive dissipation of sound waves (acoustic model). Our aim is to determine whether these heating models are consistent with ICM observables and if one is preferred over the other. We assume an initial entropy profile of ICM that is expected from the purely gravitational infall of the gas in the potential of the dark matter halo. We then incorporate heating, radiative cooling, and thermal conduction to study the evolution of ICM over the age of the clusters. Our results are: (i) Both the heating processes can produce comparable thermal profiles of the ICM with some tuning of relevant parameters. (ii) Thermal conduction is crucially important, even at the level of 10 per cent of the Spitzer values, in transferring the injected energy beyond the central regions, and without which the temperature/entropy profiles are unrealistically high. (iii) The required injected AGN power scales with cluster mass as $M_{\rm vir}^{1.5}$ for both models. (iv) The required AGN luminosity is comparable with the observed radio jet power, reinforcing the idea that AGNs are the dominant heating source in clusters. (v) Finally, we estimate that the fraction of the total AGN luminosity available as the AGN mechanical luminosity at 0.02 r500 is less than 0.05 per cent.

MRI-drivenαΩ dynamos in protoneutron stars

Context.Magnetars are highly magnetized neutron stars that can produce a wide diversity of X-ray and soft gamma-ray emissions that are powered by magnetic dissipation. Their magnetic dipole is constrained in the range of 1014–1015G by the measurement of their spin-down. In addition to fast rotation, these strong fields are also invoked to explain extreme stellar explosions, such as hypernovae, which are associated with long gamma-ray bursts and superluminous supernovae. A promising mechanism for explaining magnetar formation is the amplification of the magnetic field by the magnetorotational instability (MRI) in fast-rotating protoneutron stars (PNS). This scenario is supported by recent global incompressible models, which showed that a dipole field with magnetar-like intensity can be generated from small-scale turbulence. However, the impact of important physical ingredients, such as buoyancy and density stratification, on the efficiency of the MRI in generating a dipole field is still unknown.Aims.We assess the impact of the density and entropy profiles on the MRI dynamo in a global model of a fast-rotating PNS. The model focuses on the outer stratified region of the PNS that is stable to convection.Methods.Using the pseudo-spectral code MagIC, we performed 3D Boussinesq and anelastic magnetohydrodynamics simulations in spherical geometry with explicit diffusivities and with differential rotation forced at the outer boundary. The thermodynamic background of the anelastic models was retrieved from the data of 1D core-collapse supernova simulations from the Garching group. We performed a parameter study in which we investigated the influence of different approximations and the effect of the thermal diffusion through the Prandtl number.Results.We obtain a self-sustained turbulent MRI-driven dynamo. This confirms most of our previous incompressible results when they are rescaled for density. The MRI generates a strong turbulent magnetic field and a nondominant equatorial dipole, which represents about 4.3% of the averaged magnetic field strength. Interestingly, an axisymmetric magnetic field at large scales is observed to oscillate with time, which can be described as a mean-fieldαΩ dynamo. By comparing these results with models without buoyancy or density stratification, we find that the key ingredient explaining the appearance of this mean-field behavior is the density gradient. Buoyancy due to the entropy gradient damps turbulence in the equatorial plane, but it has a relatively weak influence in the low Prandtl number regime overall, as expected from neutrino diffusion. However, the buoyancy starts to strongly impact the MRI dynamo for Prandtl numbers close to unity.Conclusions.Our results support the hypothesis that the MRI is able to generate magnetar-like large-scale magnetic fields. The results furthermore predict the presence of aαΩ dynamo in the protoneutron star, which could be important to model in-situ magnetic field amplification in global models of core-collapse supernovae or binary neutron star mergers.