On the possibility of the solar flare energy accumulation in the vicinity of a singular line

The energy of a solar flare can be accumulated as the magnetic energy of the current sheet created in the vicinity of a magnetic field singular line by the focusing of disturbances. Conditions which define the singular line in general were obtained using the properties of a singular line as it focuses disturbances. Numerical simulations and an analytical model show the possibility of the creation of a stable current sheet which becomes unstable after a quasistationary evolution. The nonlinear development of the instability leads to a fast reconstruction of the magnetic field with the release of a substantial part of the magnetic energy. The longitudinal magnetic field in our experiment increases the sheet thickness by at most a factoring of ten.     

Simulation of the current sheet in a flare-active region and comparison to radio data

Numerical three-dimensional MHD simulations demonstrated that a current sheet (CS) was formed over active region AR 0365 before the flare of May 27, 2003, and the energy was accumulated in its magnetic field. Maps of the photospheric magnetic field in its preflare state were used in the simulations to define the boundary conditions instead of the usually applied approximation of the field in an active region by dipoles or magnetic charges. The CS was formed in the vicinity of a singular line as a result of focusing the magnetic field disturbances observed before the flare. The calculated CS position corresponded to the maximum brightness temperature of the flare detected by the Siberian Solar Radio Telescope SSRT (Institute of Solar-Terrestrial Physics, Russian Academy of Sciences, Siberian Branch, Irkutsk). This testifies that the flare could result from the dissipation of energy accumulated in the field of the CS, which arose over the active region.     

Dynamics of charged particles and perpendicular diffusion in turbulent magnetic field

A test particle code is employed to explore the dynamics of charged particles and perpendicular diffusion in turbulent magnetic field, where a three-dimensional (3D) isotropic turbulence model is used in this paper. The obtained perpendicular diffusion at different particle energies is compared with that of the nonlinear guiding center (NLGC) theory. It is found that the NLGC theory is consistent with test particle simulations when the particle energies are small. However, the difference between the NLGC theory and test particle simulations tends to increase when the particle energy is sufficiently large, and the threshold is related to the turbulence bend-over length. In the NLGC theory, the gyrocenter of a charged particle is assumed to follow the magnetic field line. Therefore, when the particle has sufficiently large energy, its gyroradius will be larger than the turbulence bend-over length. Then the particle can cross the magnetic field lines, and the difference between the test particle simulations and NLGC theory occurs.     

The Temperature – Magnetic Field Relation in Observed and Simulated Sunspots

Observations of the relation between continuum intensity and magnetic field strength in sunspots have been made for nearly five decades. This work presents full-Stokes measurements of the full-split (\(g = 3\)) line Fe i 1564.85 nm with a spatial resolution of \(0.5^{\prime\prime}\) obtained with the GREGOR Infrared Spectrograph in three large sunspots. The continuum intensity is corrected for instrumental scattered light, and the brightness temperature is calculated. Magnetic field strength and inclination are derived directly from the line split and the ratio of Stokes components. The continuum intensity (temperature) relations to the field strength are studied separately in the umbra, light bridges, and penumbra. The results are consistent with previous studies, and it was found that the scatter of values in the relations increases with increasing spatial resolution thanks to resolved fine structures. The observed relations show trends common for the umbra, light bridges, and the inner penumbra, while the outer penumbra has a weaker magnetic field than the inner penumbra at equal continuum intensities. This fact can be interpreted in terms of the interlocking comb magnetic structure of the penumbra. A comparison with data obtained from numerical simulations was made. The simulated data generally have a stronger magnetic field and a weaker continuum intensity than the observations, which may be explained by stray light and limited spatial resolution of the observations, and also by photometric inaccuracies of the simulations.     

Line formation in a magnetic field

The effect of noncoherent scattering is examined for an absorption line formed in a uniform magnetic field. It is shown that the Stokes parameters of the line radiation may be computed by using the line source function in the absence of a magnetic field as a first approximation for that in the presence of a magnetic field.     

Spatially intermittent fields in photospheric magnetoconvection

Motivated by recent high-resolution observations of the solar surface, we investigate the problem of non-linear magnetoconvection in a three-dimensional compressible layer. We present results from a set of numerical simulations which model the situation in which there is a weak imposed magnetic field. This weak-field regime is characterized by vigorous granular convection and spatially intermittent magnetic field structures. When the imposed field is very weak, magnetic flux tends to accumulate at the edges of the convective cells, where it forms compact, almost 'point-like' structures which are reminiscent of those observed in the quiet Sun. If the imposed field is slightly stronger, there is a tendency for magnetic flux to become concentrated into 'ribbon-like' structures which are comparable to those observed in solar plages. The dependence of these simulations upon the strength of the imposed magnetic field is analysed in detail, and the concept of the fractal dimension is used to make a further, more quantitative comparison between these simulations and photospheric observations.     

Dynamo saturation in direct simulations of the multi‐phase turbulent interstellar medium

The ordered magnetic field observed via polarised synchrotron emission in nearby disc galaxies can be explained by a mean‐field dynamo operating in the diffuse interstellar medium (ISM). Additionally, vertical‐flux initial conditions are potentially able to influence this dynamo via the occurrence of the magnetorotational instability (MRI). We aim to study the influence of various initial field configurations on the saturated state of the mean‐field dynamo. This is motivated by the observation that different saturation behaviour was previously obtained for different supernova rates. We perform direct numerical simulations (DNS) of three‐dimensional local boxes of the vertically stratified, turbulent interstellar medium, employing shearing‐periodic boundary conditions horizontally. Unlike in our previous work, we also impose a vertical seed magnetic field. We run the simulations until the growth of the magnetic energy becomes negligible. We furthermore perform simulations of equivalent 1D dynamo models, with an algebraic quenching mechanism for the dynamo coefficients. We compare the saturation of the magnetic field in the DNS with the algebraic quenching of a mean‐field dynamo. The final magnetic field strength found in the direct simulation is in excellent agreement with a quenched α) dynamo. For supernova rates representative of the Milky Way, field losses via a Galactic wind are likely responsible for saturation. We conclude that the relative strength of the turbulent and regular magnetic fields in spiral galaxies may depend on the galaxy's star formation rate. We propose that a mean field approach with algebraic quenching may serve as a simple sub‐grid scale model for galaxy evolution simulations including a prescribed feedback from magnetic fields. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical MHD Simulations of Solar Magnetoconvection and Oscillations in Inclined Magnetic Field Regions

The sunspot penumbra is a transition zone between the strong vertical magnetic field area (sunspot umbra) and the quiet Sun. The penumbra has a fine filamentary structure that is characterized by magnetic field lines inclined toward the surface. Numerical simulations of solar convection in inclined magnetic field regions have provided an explanation of the filamentary structure and the Evershed outflow in the penumbra. In this article, we use radiative MHD simulations to investigate the influence of the magnetic field inclination on the power spectrum of vertical velocity oscillations. The results reveal a strong shift of the resonance mode peaks to higher frequencies in the case of a highly inclined magnetic field. The frequency shift for the inclined field is significantly greater than that in vertical-field regions of similar strength. This is consistent with the behavior of fast MHD waves.     

Slip-Running Reconnection in Quasi-Separatrix Layers

Using time dependent MHD simulations, we study the nature of three-dimensional magnetic reconnection in thin quasi-separatrix layers (QSLs), in the absence of null points. This process is believed to take place in the solar atmosphere, in many solar flares and possibly in coronal heating. We consider magnetic field configurations which have previously been weakly stressed by asymmetric line-tied twisting motions and whose potential fields already possessed thin QSLs. When the line-tied driving is suppressed, magnetic reconnection is solely due to the self-pinching and dissipation of narrow current layers previously formed along the QSLs. A generic property of this reconnection process is the continuous slippage of magnetic field lines along each other, while they pass through the current layers. This is contrary to standard null point reconnection, in which field lines clearly reconnect by pair and abruptly exchange their connectivities. For sufficiently thin QSLs and high resistivities, the field line footpoints slip-run at super-Alfvénic speeds along the intersection of the QSLs with the line-tied boundary, even though the plasma velocity and resistivity are there fixed to zero. The slip-running velocities of a given footpoint have a well-defined maximum when the field line crosses the thinnest regions of the QSLs. QSLs can then physically behave as true separatrices on MHD time scales, since magnetic field lines can change their connections on time scales far shorter than the travel-time of Alfvén waves along them. Since particles accelerated in the diffusive regions travel along the field much faster than the Alfvén speed, slip-running reconnection may also naturally account for the fast motion of hard X-ray sources along chromospheric ribbons, as observed during solar flares. Electronic Supplementary Material Supplementary material is available for this article at     

Magnetic fields and the dynamics of spiral galaxies

We investigate the dynamics of magnetic fields in spiral galaxies by performing 3D magnetohydrodynamics simulations of galactic discs subject to a spiral potential using cold gas, warm gas and a two-phase mixture of both. Recent hydrodynamic simulations have demonstrated the formation of interarm spurs as well as spiral arm molecular clouds, provided the interstellar medium model includes a cold H  i phase. We find that the main effect of adding a magnetic field to these calculations is to inhibit the formation of structure in the disc. However, provided a cold phase is included, spurs and spiral arm clumps are still present if β≳ 0.1 in the cold gas. A caveat to the two-phase calculations though is that by assuming a uniform initial distribution, β≳ 10 in the warm gas, emphasizing that models with more consistent initial conditions and thermodynamics are required. Our simulations with only warm gas do not show such structure, irrespective of the magnetic field strength.
Furthermore, we find that the introduction of a cold H  i phase naturally produces the observed degree of disorder in the magnetic field, which is again absent from simulations using only warm gas. Whilst the global magnetic field follows the large-scale gas flow, the magnetic field also contains a substantial random component that is produced by the velocity dispersion induced in the cold gas during the passage through a spiral shock. Without any cold gas, the magnetic field in the warm phase remains relatively well ordered apart from becoming compressed in the spiral shocks. Our results provide a natural explanation for the observed high proportions of disordered magnetic field in spiral galaxies and we thus predict that the relative strengths of the random and ordered components of the magnetic field observed in spiral galaxies will depend on the dynamics of spiral shocks.     

Modelling the Global Solar Corona: Filament Chirality Observations and Surface Simulations

The hemispheric pattern of solar filaments is considered in the context of the global magnetic field of the solar corona. In recent work Mackay and van Ballegooijen have shown how, for a pair of interacting magnetic bipoles, the observed chirality pattern could be explained by the dominant range of bipole tilt angles and helicity in each hemisphere. This study aims to test this earlier result through a direct comparison between theory and observations, using newly developed simulations of the actual surface and 3D coronal magnetic fields over a 6-month period, on a global scale. We consider two key components: (1) observations of filament chirality for the sample of 255 filaments and (2) our new simulations of the large-scale surface magnetic field. Based on a flux-transport model, these will be used as the lower boundary condition for the future 3D coronal simulations. Our technique differs significantly from those of other authors, where the coronal field is either assumed to be purely potential or has to be reset back to potential every 27 days for the photospheric field to remain accurate. In our case we ensure accuracy by the insertion of newly emerging bipolar active regions, based on observed photospheric synoptic magnetograms. The large-scale surface field is shown to remain accurate over the 6-month period, without any resetting. This new technique will enable future simulations to consider the long-term buildup and transport of helicity and shear in the coronal magnetic field over many months or years.     

双重电流片和日冕瞬变

当背景磁场在日冕中存在零磁场线时,反向新磁通量的喷发将会产生双重电流片,包括零场区附近的磁场受到挤压而形成的横向电流片和新喷发场、原背景场之间形成的拱形电流片、本文用一对线偶极子来模拟背景场,用一对线磁荷来模拟反向喷发场,讨论了上述双重电流片的形成和演变过程。在电流片形成过程中,物质将向电流片集中。拱形电流片物质主要来自过渡层和光球层,并通过辐射损失进一步冷却,形成低温日珥环;横向电流片的物质则全部来自日冕,从而形成高温日冕环。以上结果可用来解释1984年4月14日观测到的日冕瞬变。     

Three-dimensional simulations of shear instabilities in magnetized flows

Shear mixing is believed to be the main mechanism to provide extra mixing in stellar interiors. We present results of three-dimensional (3D) simulations of the magnetohydrodynamic Kelvin–Helmholtz instability in a stratified shear layer. The magnetic field is taken to be uniform and parallel to the shear flow. We describe the evolution of the fluid flow and the magnetic field for a range of initial conditions. In particular, we investigate how the mixing rate of the fluid depends on the Richardson number and the magnetic field strength. It is found that the magnetic field can enhance as well as suppress mixing. Moreover, we have performed two-dimensional (2D) simulations and discuss some interesting differences between the 2D and 3D results.     

Magnetograph measurements with temperature-sensitive lines

Certain discrepancies between theoretical and empirical calibrations of magnetograph response are resolved by recognizing the existence of line profile changes in magnetic regions. Many of the photospheric lines commonly used for magnetic field measurements weaken greatly in magnetic regions outside of sunspots. Unless due account is made of the line profile change, the magnetograph measurements underestimate magnetic flux and field strengths.The 5250.2 Å line is especially sensitive to weakening in magnetic regions. Measurements made with this line underestimate the true field by a factor ranging from about two on the linear portion of the profile to five near the line core.Kitt Peak National Observatory Contribution No. 500.Operated by the Association of Universities for Research in Astronomy Inc., under contract with the National Science Foundation.     

The helicity constraint in turbulent dynamos with shear

The evolution of magnetic fields is studied using simulations of forced helical turbulence with strong imposed shear. After some initial exponential growth, the magnetic field develops a large-scale travelling wave pattern. The resulting field structure possesses magnetic helicity, which is conserved in a periodic box by the ideal magnetohydrodynamics equations and can hence only change on a resistive time-scale. This strongly constrains the growth time of the large-scale magnetic field, but less strongly constrains the length of the cycle period. Comparing this with the case without shear, the time-scale for large-scale field amplification is shortened by a factor Q , which depends on the relative importance of shear and helical turbulence, and which also controls the ratio of toroidal to poloidal field. The results of the simulations can be reproduced qualitatively and quantitatively with a mean-field α Ω-dynamo model with alpha-effect and turbulent magnetic diffusivity coefficients that are less strongly quenched than in the corresponding α ²-dynamo.     

Solar Magnetic Carpet III: Coronal Modelling of Synthetic Magnetograms

This article is the third in a series working towards the construction of a realistic, evolving, non-linear force-free coronal-field model for the solar magnetic carpet. Here, we present preliminary results of 3D time-dependent simulations of the small-scale coronal field of the magnetic carpet. Four simulations are considered, each with the same evolving photospheric boundary condition: a 48-hour time series of synthetic magnetograms produced from the model of Meyer et al. (Solar Phys. 272, 29, 2011). Three simulations include a uniform, overlying coronal magnetic field of differing strength, the fourth simulation includes no overlying field. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. In particular, we study their dependence upon the evolution of the photospheric magnetic field and the strength of the overlying coronal field. We also consider where energy is stored and dissipated within the coronal field. The free magnetic energy built up is found to be more than sufficient to power small-scale, transient phenomena such as nanoflares and X-ray bright points, with the bulk of the free energy found to be stored low down, between 0.5?–?0.8 Mm. The energy dissipated is currently found to be too small to account for the heating of the entire quiet-Sun corona. However, the form and location of energy-dissipation regions qualitatively agree with what is observed on small scales on the Sun. Future MHD modelling using the same synthetic magnetograms may lead to a higher energy release.     

Rotational circulation-preserving magnetogeostrophic flows

It has been shown that the only steady, inviscid, magnetogeostrophic rotational circulation-preverving motion whose magnetic field line pattern is that of the irrotational motion is a complex-lamellar motion whose magnetic field magnitude bears a constant value on a magnetic field line.     

Helicity as a Component of Filament Formation

In this paper we seek the origin of the axial component of the magnetic field in filaments by adapting theory to observations. A previous paper (Mackay, Gaizauskas, and van Ballegooijen, 2000) showed that surface flows acting on potential magnetic fields for 27 days – the maximum time between the emergence of magnetic flux and the formation of large filaments between the resulting activity complexes – cannot explain the chirality or inverse polarity nature of the observed filaments. We show that the inclusion of initial helicity, for which there is observational evidence, in the flux transport model results in sufficiently strong dextral fields of inverse polarity to account for the existence and length of an observed filament within the allotted time. The simulations even produce a large length of dextral chirality when just small amounts of helicity are included in the initial configuration. The modeling suggests that the axial field component in filaments can result from a combination of surface (flux transport) and sub-surface (helicity) effects acting together. Here surface effects convert the large-scale helicity emerging in active regions into a smaller-scale magnetic-field component parallel to the polarity inversion line so as to form a magnetic configuration suitable for a filament.