Equipartition Field Research Articles

Multiwavelength Observations of Sgr A*. II. 2019 July 21 and 26

We report on the final two days of a multiwavelength campaign of Sgr A* observing in the radio, submillimeter, infrared (IR), and X-ray bands in 2019 July. Sgr A* was remarkably active, showing multiple flaring events across the electromagnetic spectrum. We detect a transient ∼35 minute periodicity feature in Spitzer light curves on 2019 July 21. Time-delayed emission was detected in Atacama Large Millimeter/submillimeter Array light curves, suggesting a hotspot within the accretion flow on a stable orbit. On the same night, we observe a decreased flux in the submillimeter light curve following an X-ray flare detected by Chandra, and we model the feature with an adiabatically expanding synchrotron hotspot occulting the accretion flow. The event is produced by a plasma 0.55 R S in radius with an electron spectrum p = 2.84. It is threaded by a ∼130 Gauss magnetic field and expands at 0.6% the speed of light. Finally, we reveal an unambiguous flare in the IR, submillimeter, and radio, demonstrating that the variable emission is intrinsically linked. We jointly fit the radio and submillimeter light curves using an adiabatically expanding synchrotron hotspot and find it is produced by a plasma with an electron spectrum p = 0.59, 187 Gauss magnetic field, and radius 0.47 R S that expands at 0.029c. In both cases, the uncertainty in the appropriate lower and upper electron energy bounds may inflate the derived equipartition field strengths by a factor of 2 or more. Our results confirm that both synchrotron- and adiabatic-cooling processes are involved in the variable emission’s evolution at submillimeter and IR wavelengths.

Radio continuum study of the Large Magellanic Cloud supernova remnant Honeycomb Nebula

We present the first and deepest Australia Telescope Compact Array radio continuum images of the Honeycomb Nebula at 2000 and 5500MHz solely from archival data. The resolutions of these images are 3:6 x 2:8 arcsec2 and 1:3 x 1:2 arcsec2 at 2000 and 5500 MHz. We find an average radio spectral index for the remnant of -0:76?0:07. Polarisation maps at 5500MHz reveal an average fractional polarisation of 25 ? 5% with a maximum value of 95 ? 16. We estimate the equipartition field for Honeycomb Nebula of 48 ? 5 ?G, with an estimated minimum energy of Emin = 3 x 1049 erg. The estimated surface brightness, ?1 GHz, is 30 x 10-20Wm-2 Hz-1 sr-1; applying the ?-D relation suggests this supernova remnant is expanding into a low-density environment. Finally, using Hi data, we can support the idea that the Honeycomb Nebula exploded inside a low-density wind cavity. We suggest that this remnant is likely to be between late free expansion stage and early Sedov phase of evolution and expanding into a low-density medium.

ATCA study of Small Magellanic Cloud supernova remnant 1E 0102.2–7219

ABSTRACT We present new and archival Australia Telescope Compact Array and Atacama Large Millimeter/submillimeter Array data of the Small Magellanic Cloud supernova remnant 1E 0102.2–7219 at 2100, 5500, 9000, and 108 000 MHz; as well as H i data provided by the Australian Square Kilometre Array Pathfinder. The remnant shows a ring-like morphology with a mean radius of 6.2 pc. The 5500 MHz image reveals a bridge-like structure, seen for the first time in a radio image. This structure is also visible in both optical and X-ray images. In the 9000 MHz image, we detect a central feature that has a flux density of 4.3 mJy but rule out a pulsar wind nebula origin, due to the lack of significant polarization towards the central feature with an upper limit of 4 per cent. The mean fractional polarization for 1E 0102.2–7219 is 7 ± 1 and 12 ± 2 per cent for 5500 and 9000 MHz, respectively. The spectral index for the entire remnant is −0.61 ± 0.01. We estimate the line-of-sight magnetic field strength in the direction of 1E 0102.2–7219 of ∼44 µG with an equipartition field of $65\pm 5\, \mu$G. This latter model uses the minimum energy of the sum of the magnetic field and cosmic ray electrons only. We detect an H i cloud towards this remnant at the velocity range of ∼160–180 km s−1 and a cavity-like structure at the velocity of 163.7–167.6 km s−1. We do not detect CO emission towards 1E 0102.2–7219.

Compressible Test-field Method and Its Application to Shear Dynamos

In this study, we present a compressible test-field method (CTFM) for computing α-effect and turbulent magnetic diffusivity tensors, as well as those relevant for the mean ponderomotive force and mass source, applied to the full MHD equations. We describe the theoretical background of the method and compare it to the quasi-kinematic test-field method and to the previously studied variant working in simplified MHD (SMHD). We present several test cases using velocity and magnetic fields of the Roberts geometry and also compare with the imposed-field method. We show that, for moderate imposed-field strengths, the nonlinear CTFM (nCTFM) gives results in agreement with the imposed-field method. A comparison of different flavors of the nCTFM in the shear dynamo case also yields agreement up to equipartition field strengths. Some deviations between the CTFM and SMHD variants exist. As a relevant physical application, we study nonhelically forced shear flows, which exhibit large-scale dynamo action, and present a reanalysis of low-Reynolds-number, moderate shear systems, where we previously ignored the pressure gradient in the momentum equation and found no coherent shear-current effect. Another key difference is that in the earlier study we used magnetic forcing to mimic small-scale dynamo action, while here it is self-consistently driven by purely kinetic forcing. The kinematic CTFM with general validity forms the core of our analysis. We still find no coherent shear-current effect, but do recover strong large-scale dynamo action that, according to our analysis, is driven by incoherent effects.

Are low-frequency quasi-periodic oscillations in accretion flows the disk response to jet instability?

Low-frequency quasi-periodic oscillations, or LFQPOs, are ubiquitous in black hole X-ray binaries and provide strong constraints on the accretion-ejection processes. Although several models have been proposed, none has been proven to reproduce all observational constraints, and no consensus has emerged so far. We make the conjecture that disks in binaries are threaded by a large-scale vertical magnetic field that splits it into two radial zones. In the inner jet-emitting disk (JED), a near equipartition field allows driving powerful self-collimated jets, while beyond a transition radius, the disk magnetization is too low and a standard accretion disk (SAD) is settled. In a series of papers, this hybrid JED-SAD disk configuration has been shown to successfully reproduce most multiwavelength (radio and X-rays) observations, as well as the concurrence with the LFQPOs for the archetypal source GX 339-4. We first analyze the main QPO scenarios provided in the literature: (1) a specific process occurring at the transition radius, (2) the accretion-ejection instability, and (3) the solid-body Lense-Thirring disk precession. We recall their main assumptions and shed light on some severe theoretical issues that question the capability of reproducing LFQPOs. We then argue that none of these models can be operating under JED-SAD physical conditions. We finally propose an alternative scenario according to which LFQPOs are the disk response to an instability triggered in the jets near a magnetic recollimation zone. This situation can account for most of the type C QPO phenomenology and is consistent with the global behavior of black hole binaries. This nondestructive jet instability remains to be calculated, however. If this instability is numerically confirmed, then it might also naturally account for the jet wobbling phenomenology seen in various accreting sources such as compact objets and young forming stars.

FRB 190520B – An FRB in a young supernova remnant?

ABSTRACT FRB 190520B, a repeating FRB near-twin of FRB 121102, has a dispersion measure excess over the intergalactic and Galactic contributions of about 900 pc cm−3, attributable to its host galaxy or near-source environment. This excess varies on a time-scale of $\sim30$ yr and might be explained by a supernova remnant no more than a few decades old. A magnetic field in equipartition with the remnant’s expansion would be $\sim1\, \rm{G}$. I suggest the use of baseband data to measure very large rotation measures.

Parsec‐scale view of CSS/GPS sources at 327 MHz

AbstractGlobal very long baseline interferometry (VLBI) observations at low frequencies are of great importance since they allow us to test the oldest part of the relativistic electron populations in young radio sources. At 327 MHz ( 92 cm), the most compact regions are self‐absorbed, and the number of cores detected is very small. This could provide useful measurements of the magnetic field in the relativistic plasma, to be compared with the equipartition field derived from minimum energy arguments. Partial self‐absorption takes place also in hot‐spots. However, disentangling the hot‐spot emission from that of the lobe turned out to be rather difficult. On the other hand, a clearer and more complete characterization of the volumes occupied by the magnetized relativistic plasma and its total energy content can be obtained at 327 MHz. In turn, an independent estimate of the source age can be inferred, on the basis of simple assumptions on the jet power. Here, we show that the ages derived in this way (between and year) are consistent with the radiative ages determined from the break frequency in the radio spectrum.

The relationship between cross correlations and Green’s functions in ambient noise interferometry with Bayesian constraints

SUMMARYCross correlation of ambient seismic noise has begun to provide detailed images of the Earth that are not possible to attain using earthquake-based or active-source imaging techniques. However, the theoretical justification for the ambient noise correlation or seismic interferometry approach typically relies on an equipartition or diffuse field assumption that is not expected to be satisfied on Earth. Here we demonstrate that a Bayesian inference approach to calculating the expected cross correlation of seismic signals leads to an improved understanding of its relationship with the Green’s function. The Bayesian derivation is found to exactly replicate the equipartition result under a global energy constraint, and is able to accommodate any number of other constraints that typically cannot be utilized in other approaches. With these stronger constraints, the cross correlation is found to deviate more and more strongly from the ‘expected’ Green’s function, but nonetheless a specific prediction can be made regarding the expected cross correlation which can be used as a more reliable point of comparison with observations than the Green’s function. The approach therefore provides a path forward for how to use seismic cross correlation data under more and more realistic conditions and improvements in knowledge, and should eventually help improve the accuracy of resulting images of the Earth.

Magnetic fields in the accretion disks for various inner boundary conditions

Context. The magnetic fields of accretion disks play an important role in studying their evolution. We may assume that its generation is connected to the dynamo mechanism, which is similar with that in the galactic disks. Aims. Here, we propose a model of the magnetic field of the accretion disk that uses the same approaches that have been used for galaxies. It is necessary to obtain the field, which is expected to be less than the equipartition value, and without destroying the disk. To do so, it is necessary to formulate the basic properties of the ionized medium and to estimate the parameters governing the dynamo. Methods. We used the no-z approximation that has been developed for thin disks. We also take different boundary conditions that can change the value of the field significantly. Results. We show that the magnetic field strictly depends on the boundary conditions. Taking zero conditions and the fixed magnetic field condition on the inner boundary, which are connected to the physical properties of the accretion disk, we can avoid solutions that are greater than the equipartition field.

Longitudinal modes in diffusion and localization of light

In this work we include the elastic scattering of longitudinal electromagnetic waves in transport theory using a medium filled with point-like, electric dipoles. The interference between longitudinal and transverse waves creates two new channels among which one allows energy transport. This picture is worked out by extending the independent scattering framework of radiative transfer to include binary dipole-dipole interactions. We calculate the diffusion constant of light in the new transport channel and investigate the role of longitudinal waves in other aspects of light diffusion by considering the density of states, equipartition, and Lorentz local field. In the strongly scattering regime, the different transport mechanisms couple and impose a minimum conductivity of electromagnetic waves, thereby preventing Anderson localization of light in the medium. We extend the self-consistent theory of localization and compare the predictions to extensive numerical simulations.

A distinct magnetic property of the inner penumbral boundary

Context. Analyses of sunspot observations revealed a fundamental magnetic property of the umbral boundary: the invariance of the vertical component of the magnetic field. Aims. We analyse the magnetic properties of the umbra-penumbra boundary in simulated sunspots and thus assess their similarity to observed sunspots. We also aim to investigate the role of the plasma β and the ratio of kinetic to magnetic energy in simulated sunspots in the convective motions because these quantities cannot be reliably determined from observations. Methods. We used a set of non-gray simulation runs of sunspots with the MURaM code. The setups differed in terms of subsurface magnetic field structure and magnetic field boundary imposed at the top of the simulation domain. These data were used to synthesize the Stokes profiles, which were then degraded to the Hinode spectropolarimeter-like observations. Then, the data were treated like real Hinode observations of a sunspot, and magnetic properties at the umbral boundaries were determined. Results. Simulations with potential field extrapolation produce a realistic magnetic field configuration on the umbral boundaries of the sunspots. Two simulations with a potential field upper boundary, but different subsurface magnetic field structures, differ significantly in the extent of their penumbrae. Increasing the penumbra width by forcing more horizontal magnetic fields at the upper boundary results in magnetic properties that are not consistent with observations. This implies that the size of the penumbra is given by the subsurface structure of the magnetic field, that is, by the depth and inclination of the magnetopause, which is shaped by the expansion of the sunspot flux rope with height. None of the sunspot simulations is consistent with the observed properties of the magnetic field and the direction of the Evershed flow at the same time. Strong outward-directed Evershed flows are only found in setups with an artificially enhanced horizontal component of the magnetic field at the top boundary that are not consistent with the observed magnetic field properties at the umbra-penumbra boundary. We stress that the photospheric boundary of simulated sunspots is defined by a magnetic field strength of equipartition field value.

Radio emission from interstellar shocks: Young type Ia supernova remnants and the case of N 103B in the Large Magellanic Cloud

Here we present a radio continuum study based on new and archival data from the Australia Telescope Compact Array towards N 103B, a young (<=1000 yrs) spectroscopically confirmed type Ia SNR in the Large Magellanic Cloud (LMC) and proposed to have originated from a single degenerate progenitor. The radio morphology of this SNR is asymmetrical with two bright regions towards the north-west and south-west of the central location as defined by radio emission. N 103B identified features include: a radio spectral index of -0.75+-0.01 (consistent with other young type Ia SNRs in the Galaxy); a bulk SNR expansion rate as in X-rays; morphology and polarised electrical field vector measurements where we note radial polarisation peak towards the north-west of the remnant at both 5500 and 9000 MHz. The spectrum is concave-up and the most likely reason is the non-linear diffusive shock acceleration effects or presence of two different populations of ultra-relativistic electrons. We also note unpolarized clumps near the south-west region which is in agreement with this above scenario. We derive a typical magnetic field strength for N 103B, of 16.4 microG for an average rotation measurement of 200 rad m^-2. However, we estimate the equipartition field to be of the order of ~235 microG with an estimated minimum energy of Emin=6.3*10^48 erg. The close (~0.5 degree) proximity of N 103B to the LMC mid-plane indicates that an early encounter with dense interstellar medium may have set an important constrain on SNR evolution. Finally, we compare features of N 103B, to six other young type Ia SNRs in the LMC and Galaxy, with a range of proposed degeneracy scenarios to highlight potential differences due to a different models. We suggest that the single degenerate scenario might point to morphologically asymmetric type Ia supernova explosions.

Insights into the physics when modelling cold gas clouds in a hot plasma

ABSTRACT This paper aims at studying the reliability of a few frequently raised, but not proven, arguments for the modelling of cold gas clouds embedded in or moving through a hot plasma and at sensitizing modellers to a more careful consideration of unavoidable acting physical processes and their relevance. At first, by numerical simulations we demonstrate the growing effect of self-gravity on interstellar clouds and, by this, moreover argue against their initial set-up as homogeneous. We apply the adaptive-mesh refinement code flash with extensions to metal-dependent radiative cooling and external heating of the gas, self-gravity, mass diffusion, and semi-analytic dissociation of molecules, and ionization of atoms. We show that the criterion of Jeans mass or Bonnor–Ebert mass, respectively, provides only a sufficient but not a necessary condition for self-gravity to be effective, because even low-mass clouds are affected on reasonable dynamical time-scales. The second part of this paper is dedicated to analytically study the reduction of heat conduction by a magnetic dipole field. We demonstrate that in this configuration, the effective heat flow, i.e. integrated over the cloud surface, is suppressed by only 32 per cent by magnetic fields in energy equipartition and still insignificantly for even higher field strengths.

Detection of Superluminal Motion in the X-Ray Jet of M87

Abstract Chandra HRC observations are investigated for evidence of proper motion and brightness changes in the X-ray jet of the nearby radio galaxy M87. Using images spanning 5 yr, proper motion is measured in the X-ray knot HST-1, with a superluminal apparent speed of 6.3 ± 0.4c, or 24.1 ± 1.6 mas yr−1, and in Knot D, with a speed of 2.4 ± 0.6c. Upper limits are placed on the speeds of the remaining jet features. The X-ray knot speeds are in excellent agreement with existing measurements in the radio, optical, and ultraviolet. Comparing the X-ray results with images from the Hubble Space Telescope indicates that the X-ray and optical/UV emitting regions co-move. The X-ray knots also vary by up to 73% in brightness, whereas there is no evidence of brightness changes in the optical/UV. Using the synchrotron cooling models, we determine lower limits on magnetic field strengths of ∼ 420 μG and ∼ 230 μG for HST-1 and Knot A, respectively, consistent with estimates of the equipartition fields. Together, these results lend strong support to the synchrotron cooling model for Knot HST-1, which requires that its superluminal motion reflects the speed of the relativistic bulk flow in the jet.

Gamma rays from red giant wind bubbles entering the jets of elliptical host blazars

Context. Blazars in elliptical hosts have a population of red giants surrounding their jet. These stars can carry large wind-blown bubbles into the jets, leading to gamma-ray emission through bubble-jet interactions. Aims. We study the interaction dynamics and the gamma-ray emission produced when the bubbles formed by red giant winds penetrate the jet of a blazar in an elliptical galaxy. Methods. First, we characterized the masses and penetration rates of the red giant wind bubbles that enter the jet. Then, the dynamical evolution of these bubbles under the jet impact was analysed analytically and numerically, and the radiation losses of the particles accelerated in the interaction were characterised. Finally, the synchrotron and the inverse Compton contributions above ∼100 MeV were estimated under different jet magnetic fields, powers, and Lorentz factors. Results. We find that an analytical dynamical model is a reasonable approximation for the red giant wind bubble-jet interaction. The radiation produced by these wind bubbles interacting with a jet can have a duty cycle of up to ∼1. For realistic magnetic fields, gamma rays could be detectable from sources within the local universe, preferentially from those with high Lorentz factors (∼10), and this could be a relatively common phenomenon for these sources. For magnetic fields in equipartition with the jet power, and high acceleration rates, synchrotron gamma rays may be detectable even for modest Lorentz factors (∼3), but with a much lower duty cycle. Conclusions. Blazars in elliptical galaxies within the local universe can produce detectable transient or persistent gamma-ray emission from red giant wind bubbles entering their jets.

The magnetic field strength of the Faraday screen surrounding the radio galaxy Coma A

Studying the interaction between AGN jets and lobes and their surrounding environment is important in order to understand how they transfer energy to their environment as well as determining the intrinsic physical properties of the sources themselves. This paper presents broadband VLA polarization and Faraday rotation observations of the radio galaxy Coma A (3C 277.3) from 1 to 4 GHz, including archival VLA observations at 4.9 and 15 GHz. Through broadband polarization model-fitting, we find that an external Faraday screen with a turbulent magnetic field provides an appropriate description to most of the data. By combining the polarization and Faraday rotation results with previous H$\alpha$ observations, we identified the H$\alpha$-emitting gas as the Faraday screen responsible for the observed Faraday depolarization. We were able to derive the magnetic field strength in the H$\alpha$-emitting gas, finding typical field strengths of $\sim1$ $\mu$G, which is consistent with studies of the intra-group medium local to other radio galaxies. However, we find a highly depolarized region of the southern lobe coincident with a H$\alpha$ filament that has a field strength comparable to the equipartition field strength in the radio lobe (i.e. $\gtrsim$36 $\mu$G). This implies that the H$\alpha$ filament is internal to the radio emitting plasma. Such clear examples of internal Faraday depolarization are rare, thus providing another key insight into the evolution of radio galaxies and their ability to provide significant feedback on the local gas that would otherwise cool and form stars.

A small-scale dynamo in feedback-dominated galaxies – II. The saturation phase and the final magnetic configuration

Magnetic fields in galaxies are believed to be the result of dynamo amplification of initially weak seed fields, reaching equipartition strength inside the interstellar medium. The small-scale dynamo appears to be a viable mechanism to explain observations of strong magnetic fields in present-day and high-redshift galaxies, considering the extreme weakness of seed fields predicted by battery mechanisms or primordial fields. Performing high-resolution adaptive mesh magneto-hydrodynamic simulations of a small mass, isolated cooling halo with an initial magnetic seed field strength well below equipartition, we follow the small-scale dynamo amplification from supernova-induced turbulence up to saturation of the field. We find that saturation occurs when the average magnetic pressure reaches only 3 % to 5 % of the turbulent pressure. The magnetic energy growth transitions from exponential to linear, and finally comes to halt. The saturation level increases slightly with grid resolution. These results are in good agreement with theoretical predictions for magnetic Prandtl numbers of order $\mathrm{Pr_M} \sim 1$ and turbulent Mach numbers of order $\mathrm{M} \sim 10$. When we suppress supernova feedback after our simulation has reached saturation, we find that turbulence decays and that the gas falls back onto a thin disk with the magnetic field in local equipartition. We propose a scenario in which galactic magnetic fields are amplified from weak seed fields in the early stages of the Universe to sub-equipartition fields, owing to the turbulent environment of feedback-dominated galaxies at high redshift, and are evolved further in a later stage up to equipartition, as galaxies transformed into more quiescent, large spiral disks.

Exploring shallow sunspot formation by using Implicit Large-eddy simulations

AbstractThe mechanism by which sunspots are generated at the surface of the sun remains unclear. In the current literature two types of explanations can be found. The first one is related to the buoyant emergence of toroidal magnetic fields generated at the tachocline. The second one states that active regions are formed, from initially diffused magnetic flux, by MHD instabilities that develop in the near-surface layers of the Sun. Using the anelastic MHD code EULAG we address the problem of sunspot formation by performing implicit large-eddy simulations of stratified magneto-convection in a domain that resembles the near-surface layers of the Sun. The development of magnetic structures is explored as well as their effect on the convection dynamics. By applying a homogeneous magnetic field over an initially stationary hydrodynamic convective state, we investigate the formation of self-organized magnetic structures in the range of the initial magnetic field strength, 0.01 &lt; B0/Beq &lt; 0.5, where Beq is the characteristic equipartition field strength.

Detection of an ∼20 kpc coherent magnetic field in the outskirt of merging spirals: the Antennae galaxies

We present a study of the magnetic field properties of NGC 4038/9 (the `Antennae' galaxies), the closest example of a late stage merger of two spiral galaxies. Wideband polarimetric observations were performed using the Karl G. Jansky Very Large Array between 2 and 4 GHz. Rotation measure synthesis and Faraday depolarization analysis was performed to probe the magnetic field strength and structure at spatial resolution of $\sim1$ kpc. Highly polarized emission from the southern tidal tail is detected with intrinsic fractional polarization close to the theoretical maximum ($0.62\pm0.18$), estimated by fitting the Faraday depolarization with a volume that is both synchrotron emitting and Faraday rotating containing random magnetic fields. Magnetic fields are well aligned along the tidal tail and the Faraday depths shows large-scale smooth variations preserving its sign. This suggests the field in the plane of the sky to be regular up to $\sim20$ kpc, which is the largest detected regular field structure on galactic scales. The equipartition field strength of $\sim8.5~\mu$G of the regular field in the tidal tail is reached within a few 100 Myr, likely generated by stretching of the galactic disc field by a factor of 4--9 during the tidal interaction. The regular field strength is greater than the turbulent fields in the tidal tail. Our study comprehensively demonstrates, although the magnetic fields within the merging bodies are dominated by strong turbulent magnetic fields of $\sim20~\mu$G in strength, tidal interactions can produce large-scale regular field structure in the outskirts.

Bipolar region formation in stratified two-layer turbulence

This work presents an extensive study of the previously discovered formation of bipolar flux concentrations in a two-layer model. We interpret the formation process in terms of negative effective magnetic pressure instability (NEMPI), which is a possible mechanism to explain the origin of sunspots. In our simulations, we use a Cartesian domain of isothermal stratified gas that is divided into two layers. In the lower layer, turbulence is forced with transverse nonhelical random waves, whereas in the upper layer no flow is induced. A weak uniform magnetic field is imposed in the entire domain at all times. In this study we vary the stratification by changing the gravitational acceleration, magnetic Reynolds number, strength of the imposed magnetic field, and size of the domain to investigate their influence on the formation process. Bipolar magnetic structure formation takes place over a large range of parameters. The magnetic structures become more intense for higher stratification until the density contrast becomes around $100$ across the turbulent layer. For the Reynolds numbers considered, magnetic flux concentrations are generated at magnetic Prandtl number between 0.1 and 1. The magnetic field in bipolar regions increases with higher imposed field strength until the field becomes comparable to the equipartition field strength of the turbulence. A larger horizontal extent enables the flux concentrations to become stronger and more coherent. The size of the bipolar structures turns out to be independent of the domain size. In the case of bipolar region formation, we find an exponential growth of the large-scale magnetic field, which is indicative of a hydromagnetic instability. Additionally, the flux concentrations are correlated with strong large-scale downward and converging flows. These findings imply that NEMPI is responsible for magnetic flux concentrations.