Initial Magnetic Field Research Articles

Exploring the Formation of Resistive Pseudodisks with the GPU Code Astaroth

Pseudodisks are dense structures formed perpendicular to the direction of the magnetic field during the gravitational collapse of a molecular cloud core. Numerical simulations of the formation of pseudodisks are usually computationally expensive with conventional CPU codes. To demonstrate the proof of concept of a fast computing method for this numerically costly problem, we explore the GPU-powered MHD code Astaroth, a sixth-order finite difference method with low adjustable finite resistivity implemented with sink particles. The formation of pseudodisks is physically and numerically robust and can be achieved with a simple and clean setup for this newly adopted numerical approach for science verification. The method’s potential is illustrated by evidencing the dependence on the initial magnetic field strength of specific physical features accompanying the formation of pseudodisks, e.g., the occurrence of infall shocks and the variable behavior of the mass and magnetic flux accreted on the central object. As a performance test, we measure both weak and strong scaling of our implementation to find the most efficient way to use the code on a multi-GPU system. Once suitable physics and problem-specific implementations are realized, the GPU-accelerated code is an efficient option for 3D magnetized collapse problems.

Could the TeV emission of starburst galaxies originate from pulsar wind nebulae?

ABSTRACT While the GeV γ-ray emission of starburst galaxies (SBGs) is commonly thought to arise from hadronic interactions between accelerated cosmic rays and interstellar gas, the origin of the TeV γ-ray emission is more uncertain. One possibility is that a population of pulsar wind nebulae (PWNe) in these galaxies could be responsible for the TeV γ-ray emission. In this work, we first synthesize a PWNe population in the Milky Way and assess their contribution to the γ-ray emission of the Galaxy, using a time-dependent model to calculate the evolution of the PWN population. Such a synthetic PWN population can reproduce the flux distribution of PWNe identified in the Milky Way given a distribution of the initial state of the pulsar population. We then apply it to starburst galaxies and quantitatively calculate the spectral energy distribution of all PWNe in the SBGs NGC 253 and M82. We propose that TeV γ-ray emission in starburst galaxies can be dominated by PWNe for a wide range of parameter space. The energetic argument requires that ηe × vSN > 0.01 yr−1, where ηe is the fraction of spin-down energy going to electrons and vSN is the supernova rate. By requiring the synchrotron emission flux of all PWNe in the galaxy not to exceed the hard X-ray measurement of NGC 253, we constrain the initial magnetic field strength of PWNe to be $\lesssim 400\,\mu{\rm G}$. Future observations at higher energies with the Large High Altitude Air Shower Observatory (LHAASO) or the next-generation neutrino observatory IceCube-Gen2 will help us to understand the origin of the TeV γ-ray emission in SBGs better.

Electromagnetic Shielding of Two-Circuit Overhead Power Lines Magnetic Field

The purpose of the work is to design an electromagnetic shield to reduce the level of the magnetic field generated by double-circuit overhead power lines to increase the shielding efficiency of the initial magnetic field in residential buildings to the level of sanitary standards and reduce the sys-tem's sensitivity to changes in system parameters. To achieve this goal, the structure of the electro-magnetic shield is determined, which consists of a single-circuit active and multi-circuit passive parts and is characterized by an increased efficiency of reducing the magnetic field of industrial frequency. The design of an electromagnetic shield is reduced to solving a minimax vector optimization problem, in which the vector objective function is calculated based on solutions of Maxwell's equations in a quasi-stationary approximation using the COMSOL Multiphysics software package. The solution of the minimax vector optimization problem is calculated on the basis of optimization algorithms by a multiswarm of particles from Pareto-optimal solutions. The most important results are theoretical and experimental studies of the effectiveness of the designed electromagnetic shield of the magnetic field generated by double-circuit overhead power lines. The significance of the results obtained lies in the fact that practical recommendations are given on the reasonable choice of the spatial arrangement of the contours of the multi-circuit passive screen and the shielding winding of the robust system of elec-tromagnetic shielding of the magnetic field generated by double-circuit overhead power lines. The possibility of reducing the induction of the initial magnetic field to the level of sanitary standards has been shown as well.

Evolution of MHD torus and mass outflow around spinning AGNs

ABSTRACT We perform axisymmetric, 2D magnetohydrodynamic simulations to investigate accretion flows around spinning active galactic nuclei. To mimic the space–time geometry of spinning black holes, we consider effective Kerr potential, and the mass of the black holes is 108 M⊙. We initialize the accretion disc with a magnetized torus by adopting the toroidal component of the magnetic vector potential. The initial magnetic field strength is set by using the plasma beta parameter (β0). We observe self-consistent turbulence generated by magneto rotational instability (MRI) in the disc. The MRI turbulence transports angular momentum in the disc, resulting in an angular momentum distribution that approaches a Keplerian distribution. We investigate the effect of the magnetic field on the dynamics of the torus and associated mass outflow from the disc around a maximally spinning black hole (ak = 0.99). For the purpose of our analysis, we investigate the magnetic state of our simulation model. The model β0 = 10 indicates the behaviour similar to the ‘magnetically arrested disc’ state, and all the other low magnetic model remains in the SANE state. We observe that mass outflow rates are significantly enhanced with the increased magnetic field in the disc. We find a positive correlation between the magnetic field and mass outflow rates. We also investigate the effect of black hole spin on the magnetized torus evolution. However, we have not found any significant effect of black hole spin on mass outflows in our model. Finally, we discuss the possible astrophysical applications of our simulation results.

Global well-posedness and large-time behavior of solutions to the 3D inviscid magneto-micropolar equations with damping

We first establish the existence of global strong solutions to the 3D inviscid incompressible magneto-micropolar equations with a velocity damping in Sobolev spaces H K ( K ⩾ 3 ) , where the H 3 norm of initial data is small, but its higher order derivatives could be large. Combining the H ˙ − s norm ( 0 ≤ s < 3 2 ) or B ˙ 2 , ∞ − s norm ( 0 < s ≤ 3 2 ) of the initial magnetic field is finite with some tricky interpolation estimates, we show ‖ ∇ n B ( t ) ‖ L 2 ≤ C 0 ( 1 + t ) − n 2 − 3 2 p + 3 4 and two faster decay rates for the velocity and the micro-rotation field ‖ ∇ n ( U , w ) ( t ) ‖ L 2 ≤ C 0 ( 1 + t ) − n 2 − 3 2 p + 1 4 , which are shown to be the usual L p − L 2 ( 1 ≤ p ≤ 2 ) type of the optimal time decay rates for 3D inviscid incompressible magneto-micropolar equations with damping. We then conclude the damping term contributes to weaken the assumption of initial condition and enhance the decay rate of velocity compared to the classical incompressible viscous magneto-micropolar equations. Meanwhile, for the 3D inviscid compressible magneto-micropolar fluid, the damping term also has the same effect on the decay rate of the velocity.

Splash singularity for the free boundary incompressible viscous MHD

In this paper, we prove the existence of smooth initial data for the two-dimensional free boundary incompressible viscous magnetohydrodynamics (MHD) equations, for which the interface remains regular but collapses into a splash singularity (self-intersects in at least one point) in finite time. The existence of the splash singularities is guaranteed by a local existence theorem, in which we need suitable spaces for the modified magnetic field together with the modification of the velocity and pressure such that the modified initial velocity is zero, and a stability result which allows us to construct a class of initial velocities and domains for an arbitrary initial magnetic field. It turns out that the presence of the magnetic field does not prevent the viscous fluid from forming splash singularities for certain smooth initial data.

Magnetic field effects on nucleosynthesis and kilonovae from neutron star merger remnants

ABSTRACT We investigate the influence of parametric magnetic field configurations of a hypermassive neutron star (HMNS) on the outflow properties, nucleosynthesis yields, and kilonova light curves. We perform three-dimensional dynamical space–time general-relativistic magnetohydrodynamic simulations, including a neutrino leakage scheme, microphysical finite-temperature equation of state, and an initial poloidal magnetic field. We find that varying the magnetic field strength and falloff impacts the formation of magnetized winds or mildly relativistic jetted outflows, which in turn has profound effects on the outflow properties. All of the evolved configurations collapse to a black hole ∼38–40 ms after coalescence, where the ones forming jetted outflows seem more effective at redistributing angular momentum, which result in earlier collapse times. Larger mass ejecta rates and radial velocities of unbound material characterize the systems that form jetted outflows. The bolometric light curves of the kilonovae and r-process yields that are produced by the post-merger remnant system change considerably with different magnetic field parameters. We conclude that the magnetic field strength and falloff have robust effects on the outflow properties and electromagnetic observables. This can be particularly important as the total ejecta mass from our simulations (≃10−3 M⊙) makes the ejecta from HMNS a compelling source to power kilonova through radioactive decay of r-process elements.

First measurement of prompt and non-prompt D⁎+ vector meson spin alignment in pp collisions at [formula omitted] TeV

This letter reports the first measurement of spin alignment, with respect to the helicity axis, for D⁎+ vector mesons and their charge conjugates from charm-quark hadronisation (prompt) and from beauty-meson decays (non-prompt) in hadron collisions. The measurements were performed at midrapidity (|y|<0.8) as a function of transverse momentum (pT) in proton–proton (pp) collisions collected by ALICE at the centre-of-mass energy s=13TeV. The diagonal spin density matrix element ρ00 of D⁎+ mesons was measured from the angular distribution of the D⁎+→D0(→K−π+)π+ decay products, in the D⁎+ rest frame, with respect to the D⁎+ momentum direction in the pp centre of mass frame. The ρ00 value for prompt D⁎+ mesons is consistent with 1/3, which implies no spin alignment. However, for non-prompt D⁎+ mesons an evidence of ρ00 larger than 1/3 is found. The measured value of the spin density element is ρ00=0.455±0.022(stat.)±0.035(syst.) in the 5<pT<20GeV/c interval, which is consistent with a Pythia 8 Monte Carlo simulation coupled with the EvtGen package, which implements the helicity conservation in the decay of D⁎+ meson from beauty mesons. In non-central heavy-ion collisions, the spin of the D⁎+ mesons may be globally aligned with the direction of the initial angular momentum and magnetic field. Based on the results for pp collisions reported in this letter it is shown that alignment of non-prompt D⁎+ mesons due to the helicity conservation coupled to the collective anisotropic expansion may mimic the signal of global spin alignment in heavy-ion collisions.

Secular outflows from 3D MHD hypermassive neutron star accretion disc systems

ABSTRACT Magnetized hypermassive neutron stars (HMNSs) have been proposed as a way for neutron star mergers to produce high electron fraction, high-velocity ejecta, as required by kilonova models to explain the observed light curve of GW170817. The HMNS drives outflows through neutrino energy deposition and mechanical oscillations, and raises the electron fraction of outflows through neutrino interactions before collapsing to a black hole (BH). Here, we perform 3D numerical simulations of HMNS–torus systems in ideal magnetohydrodynamics, using a leakage/absorption scheme for neutrino transport, the nuclear APR equation of state, and Newtonian self-gravity, with a pseudo-Newtonian potential added after BH formation. Due to the uncertainty in the HMNS collapse time, we choose two different parametrized times to induce collapse. We also explore two initial magnetic field geometries in the torus, and evolve the systems until the outflows diminish significantly ($\sim\!\! 1\!\! - \!\!2\ \mathrm{s}$). We find bluer, faster outflows as compared to equivalent BH–torus systems, producing M ∼ 10−3 M⊙ of ejecta with Ye ≥ 0.25 and v ≥ 0.25c by the simulation end. Approximately half the outflows are launched in disc winds at times $t\lesssim 500 \ \mathrm{ms}$, with a broad distribution of electron fractions and velocities, depending on the initial condition. The remaining outflows are thermally driven, characterized by lower velocities and electron fractions. Nucleosynthesis with tracer particles shows patterns resembling solar abundances in all models. Although outflows from our simulations do not match those inferred from two-component modelling of the GW170817 kilonova, self-consistent multidimensional detailed kilonova models are required to determine whether our outflows can power the blue kilonova.

Formation of an observed eruptive flux rope above the torus instability threshold through tether-cutting magnetic reconnection

Context. Erupting magnetic flux ropes (MFRs) are believed to play a crucial role in producing solar flares. However, the formation of erupting MFRs in complex coronal magnetic configurations and the role of their subsequent evolution in the flaring events are not fully understood. Aims. We perform a magnetohydrodynamic (MHD) simulation of active region NOAA 12241 to understand the formation of a rising magnetic flux rope during the onset of an M6.9 flare on 2014 December 18 around 21:41 UT (SOL2014-12- 18T21:41M6.9), which was followed by the appearance of parallel flare ribbons. Methods. The MHD simulation was initialised with an extrapolated non-force-free magnetic field generated from the photospheric vector magnetogram of the active region taken a few minutes before the flare. Results. The initial magnetic field topology displays a pre-existing sheared arcade enveloping the polarity inversion line. The simulated dynamics exhibit the movement of the oppositely directed legs of the sheared arcade field lines towards each other due to the converging Lorentz force, resulting in the onset of tether-cutting magnetic reconnection that produces an underlying flare arcade and flare ribbons. Concurrently, a magnetic flux rope above the flare arcade develops inside the sheared arcade and shows a rising motion. The flux rope is found to be formed in a torus-unstable region, thereby explaining its eruptive nature. Interestingly, the location and rise of the rope are in good agreement with the corresponding observations seen in extreme-ultraviolet channels of the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). Furthermore, the foot points of the simulation’s flare arcade match well with the location of the observed parallel ribbons of the flare. Conclusions. The presented simulation supports the development of the MFR by the tether-cutting magnetic reconnection inside the sheared coronal arcade during flare onset. The MFR is then found to extend along the polarity inversion line (PIL) through slip-running reconnection. The MFR’s eruptive nature is ascribed both to its formation in the torus-unstable region and also to the runaway tether-cutting reconnection.

Formation Mechanism of Laser-driven Magnetized “Pillars of Creation”

The Pillars of Creation, one of the most recognized objects in the sky, are believed to be associated with the formation of young stars. However, so far, the formation and maintenance mechanism of the pillars are still not fully understood due to the complexity of the nonlinear radiation magnetohydrodynamics (RMHD). Here, assuming laboratory laser-driven conditions, we studied the self-consistent dynamics of pillar structures in magnetic fields by means of two-dimensional and three-dimensional (3D) RMHD simulations, and the results support our proposed experimental scheme. We find that only when the magnetic pressure and ablation pressure are comparable, the magnetic field can significantly alter the plasma hydrodynamics. For medium-magnetized cases (β initial ≈ 3.5), the initial magnetic fields undergo compression and amplification. This amplification results in the magnetic pressure inside the pillar becoming large enough to support the sides of the pillar against radial collapse due to pressure from the surrounding hot plasma. This effect is particularly pronounced for the parallel component (B y ), which is consistent with observational results. In contrast, a strong perpendicular (B x , B z ) magnetic field (β initial < 1) almost retains its initial distribution and significantly suppresses the expansion of blown-off gas plasma, leading to the inability to form pillar-like structures. The 3D simulations suggest that the bending at the head of “Column I” in the Pillars of Creation may be due to nonparallel magnetic fields. After similarity scaling transformation, our results can be applied to explain the formation and maintenance mechanism of the pillars, and can also provide useful information for future experimental designs.

The Galactic Population of Pulsar Wind Nebulae and the Contribution of Its Unresolved Component to the Diffuse High-Energy Gamma-ray Emission

In this work, we provide a phenomenological description of the population of galactic TeV pulsar wind nebulae (PWNe) based on suitable assumptions for their space and luminosity distribution. We constrain the general features of this population by assuming that it accounts for the majority of bright sources observed by H.E.S.S. Namely, we determine the maximal luminosity and fading time of PWNe (or, equivalently, the initial period and magnetic field of the pulsar powering the observed emission) by performing a statistical analysis of bright sources in the H.E.S.S. galactic plane survey. This allows us to estimate the total luminosity and flux produced by galactic TeV PWNe. We also evaluate the cumulative emission from PWNe that cannot be resolved by H.E.S.S., showing that this contribution can be as large as ∼40% of the total flux from resolved sources. We argue that also in the GeV domain, a relevant fraction of this population cannot be resolved by Fermi-LAT, providing a non-negligible contribution to the large-scale diffuse emission in the inner galaxy. This additional component could naturally account for a large part of the spectral index variation observed by Fermi-LAT, weakening the evidence of cosmic ray spectral hardening in the inner galaxy. Finally, the same result is obtained for PeV energy, for which the sum of the diffuse component, due to unresolved PWNe, and the truly diffuse emission well saturates the recent Tibet AS-γ data, without the need to introduce a progressive hardening of the cosmic-ray spectrum toward the galactic centre.

Method for control by orbital spacecraft magnetic cleanliness based on multiple magnetic dipole models with consideration of their uncertainty

Aim. Development of method for control by orbital spacecraft magnetic cleanliness based on multiple magnetic dipole models using compensation of the initial magnetic field with consideration of magnetic characteristics uncertainty. Methodology. Orbital spacecraft multiple magnetic dipole models calculated as solution of nonlinear minimax optimization problem based on near field measurements for prediction orbital spacecraft far magnetic field magnitude. Nonlinear objective function calculated as the weighted sum of squared residuals between the measured and predicted magnetic field. Weight matrix calculated as inverse covariance matrix of random errors vector. Values of magnetic moments and coordinates of placement of compensating magnetic dipoles for compensation of the orbital spacecraft initial magnetic field also calculated as solution of nonlinear minimax optimization problem. Both solutions of this nonlinear minimax optimization problems calculated based on particle swarm nonlinear optimization algorithms. Results. Results of prediction spacecraft far magnetic field magnitude based on orbital spacecraft multiple magnetic dipole models using near field measurements and compensation of the initial magnetic field with consideration of orbital spacecraft magnetic characteristics uncertainty for ensuring the orbital spacecraft magnetic cleanliness. Originality. The method for control by orbital spacecraft magnetic cleanliness based on multiple magnetic dipole models using compensation of the initial magnetic field with consideration of magnetic characteristics uncertainty is developed. Practical value. An important practical problem of ensuring orbital spacecraft magnetic cleanliness based on orbital spacecraft multiple magnetic dipole models using near field measurements and compensation of the initial magnetic field with consideration of orbital spacecraft magnetic characteristics uncertainty solved.

Hybrid Active-Passive Shielding of Magnetic Field of Overhead Power Lines with Triangular Phase Conductors Arrangements

The aim of the work is to design a robust hybrid active-passive magnetic field shielding system created by overhead power lines with a triangular arrangement of phase wires, designed to increase the shielding efficiency of the initial magnetic field in residential premises to the level of sanitary standards and reduce the system's sensitivity to changes in system parameters. To achieve this goal, the following tasks were solved: the structure of a hybrid system of active-passive shielding was developed, and the synthesis of a system consisting of a double-circuit active and multi-circuit passive parts was performed. The synthesis of the system is reduced to solving a vector game, in which the vector payoff is calculated based on the solutions of the Maxwell equations in the quasi-stationary approximation using the COMSOL Multiphysics software. The solution of a multicriteria game is found on the basis of algorithms for optimizing a multi-swarm of particles from Pareto optimal solutions, taking into account binary preference relations. The most important results are theoretical and experimental studies of the effectiveness of the synthesized hybrid active-passive shielding system for the magnetic field created by overhead power lines with a triangular arrangement of phase wires in the shielding zone. The significance of the results obtained lies in the fact that in the course of designing a hybrid active and multiloop passive screens, the parameters of passive and active screens were calculated; as well as practical recommendations are given on the reasonable choice of the spatial arrangement of a multi-loop passive shield and two shielding windings of a robust system of hybrid shielding of the magnetic field created by overhead power lines with a triangular arrangement of phase wires.

Simulation of polarized emission from recollimation shocks in relativistic jets

ABSTRACT This paper presents a method for obtaining synthetic images of linearly polarized synchrotron radiation from steady-state numerical simulations of relativistic jets, in which the magnetic field is assumed to be initially either partially or completely disordered. The method is based on the earlier work which characterized the deformation of the fluid using infinitessimal fluid elements that are initially cubic, and which evolve into parallelepipeds. The method is described for a range of models for the initial magnetic field, including ordered components that are axial, helical, and toroidal with a bi-directional axial component. The method is then applied to steady, axisymmetric simulations of initially overpressured jets and the initial results are discussed. Some characteristic patterns and trends in polarization angle are identified. Although the recollimation shocks that form in these jets are not clearly visible in the total intensity images presented here, arcs of strongly polarized emission associated with radial velocity gradients in the vicinity of the shock waves are seen, and might prove to be a useful diagnostic feature of this model.

Derivative analysis of fractional order on reflection of p-waves with electromagnetic, temperature, and initial stress with three-phase-lag

In this paper, the three-phase-lag model of fractional analysis on the reflection of two-dimensional problem of p-waves with initial stress, temperature-dependent, and magnetic field is investigated. The formulation of the problem for an isotropic homogeneous medium based on a three phase-lag theory. The boundary conditions applied on the surface for the stresses and thermal insulation. The numerical solution presented as well as the graphical representation of the impact of analysis considering the external parameters. Also, the modified elastic waves reflected under the action of the magnetic field, initial stress, fractional degree coefficient, and temperature to determine the more exact nature of the reflection of these waves, particularly seismic waves. A comparison has been made between the results obtained and the previous results obtained by others and already published and are in agreement with these, when external parameters considered in the present investigation neglected. The results obtained indicate that the new external parameters have new impact on the waves reflection and applicable in diverse fields as engineering, earthquakes, volcanos, geophysics, acoustics, and astronomy.

Magnetic field and thermal environment effects on sound transmission loss of double-walled cracked piezoelectric cylindrical nanoshells

Based on a non-local strain gradient theory (NSGT), this article analytically studies the sound transmission loss (STL) performance of a special type of double-walled partially cracked piezoelectric nanoshell structures of cylindrical shape undergoing initial electric potential and longitudinal magnetic field. The structure, which includes a specific number of axial and circumferential surface cracks, is struck by a plane wave in a thermal setting. Such cracks have minimal size compared to the nano-shell structure as a whole, minimizing the effects of curvature for this problem. The first-order shear deformation theory (FSDT) is utilized to explain the displacement components, and Hamilton’s concept is applied to obtain the coupled vibroacoustic equations that are used to generate the governing equations of the system for the two crack types, giving us an idea of the resulting structural stiffness in the presence of cracks using coefficients of crack compliance that are derived from the line spring model (LSM). The mechanical and acoustic properties are then checked to see their effect on the system response followed by a series of validation case studies. This evaluation also allows one to optimize a similar structure by selecting appropriate external parameters such as electric voltage, magnetic field intensity, different crack types, nonlocal and strain gradient parameters, variations of temperature, and incident angle of sound waves.

The Effects of Rotation, Metallicity, and Magnetic Field on the Islands of Failed Supernovae

Failed supernovae (FSN) are a possible channel for the formation of heavy stellar-mass black holes (M BH > ∼30 M ⊙). However, the effects of metallicity, rotation, and magnetic field on the islands of explodabilty of massive stars are not clear. Here, we simulate the stellar structure and evolution in the mass range between 6 and 55 M ⊙ with different initial rotational velocities, metallicities, and magnetic fields from zero-age main sequence (ZAMS) to pre-collapse. We find that the rapid rotating stars can remain lower 12C mass fraction at the time of C ignition, which allows the transition, from convective carbon burning to radiative burning, to occur at lower M ZAMS than those from stars without rotation. However, the rapid rotation is unfavorable for FSN occurring but is conducive to long gamma-ray bursts (lGRBs) because it results in the specific angular momentum in the CO core being greater than the last stable orbit at core collapse. The increasing metallicity does not affect FSN islands, but high metallicity inhibits rotational mixing and is unfavorable for producing lGRBs. A magnetic field can constrain the mass-loss rate even for rapid rotating stars, resulting in higher mass at pre-collapse. The magnetic braking triggered by the magnetic field can reduce the rotation velocity for high-metallicity models, which decreases the specific angular momentum in the CO core and is favorable for FSN occurring. We suggest that the heavy-mass black holes detected by LIGO may originate from rapidly rotating massive stars with strong magnetic fields, rather than those with very low metallicity.

Effects of Partial Ionization on Magnetic Flux Emergence in the Sun

We have performed 3D numerical simulations to investigate the effect of partial ionization on the process of magnetic flux emergence. In our study, we have modified the single-fluid MHD equations to include the presence of neutrals and have performed two basic experiments: one that assumes a fully ionized plasma (FI case) and one that assumes a partially ionized plasma (PI case). We find that the PI case brings less dense plasma to and above the solar surface. Furthermore, we find that partial ionization alters the emerging magnetic field structure, leading to a different shape of the polarities in the emerged bipolar regions compared to the FI case. The amount of emerging flux into the solar atmosphere is larger in the PI case, which has the same initial plasma beta as the FI case, but a larger initial magnetic field strength. The expansion of the field above the photosphere occurs relatively earlier in the PI case, and we confirm that the inclusion of partial ionization reduces cooling due to adiabatic expansion. However, it does not appear to work as a heating mechanism for the atmospheric plasma. The performance of these experiments in three dimensions shows that PI does not prevent the formation of unstable magnetic structures, which erupt into the outer solar atmosphere.

Magnetic Effects Promote Supermassive Star Formation in Metal-enriched Atomic-cooling Halos

Intermediate-mass black holes (with ≥105 M ⊙) are promising candidates for the origin of supermassive black holes (with ∼109 M ⊙) in the early universe (redshift z ∼ 6). Chon & Omukai first pointed out direct collapse black hole (DCBH) formation in metal-enriched atomic-cooling halos (ACHs), which relaxes the DCBH formation criterion. On the other hand, Hirano et al. showed that magnetic effects promote DCBH formation in metal-free ACHs. We perform a set of magnetohydrodynamical simulations to investigate star formation in magnetized ACHs with metallicities Z/Z ⊙ = 0, 10−5, and 10−4. Our simulations show that the mass accretion rate onto the protostars becomes lower in metal-enriched ACHs than in metal-free ACHs. However, many protostars form from gravitationally and thermally unstable metal-enriched gas clouds. Under such circumstances, the magnetic field rapidly increases as magnetic field lines wind up due to the spin of protostars. The region with the amplified magnetic field expands outwards due to the orbital motion of protostars and the rotation of the accreting gas. The amplified magnetic field extracts angular momentum from the accreting gas, promotes the coalescence of low-mass protostars, and increases the mass growth rate of the primary protostar. We conclude that the magnetic field amplification is always realized in metal-enriched ACHs regardless of the initial magnetic field strength, which affects the DCBH formation criterion. In addition, we find a qualitatively different trend from the previous unmagnetized simulations in that the mass growth rate is maximal for extremely metal-poor ACHs with Z/Z ⊙ = 10−5.