Showing papers on "Dipole model of the Earth's magnetic field published in 2008"

Nonlinear Force-Free Modeling of Coronal Magnetic Fields. II. Modeling a Filament Arcade and Simulated Chromospheric and Photospheric Vector Fields

Abstract: We compare a variety of nonlinear force-free field (NLFFF) extrapolation algorithms, including optimization, magneto-frictional, and Grad – Rubin-like codes, applied to a solar-like reference model. The model used to test the algorithms includes realistic photospheric Lorentz forces and a complex field including a weakly twisted, right helical flux bundle. The codes were applied to both forced “photospheric” and more force-free “chromospheric” vector magnetic field boundary data derived from the model. When applied to the chromospheric boundary data, the codes are able to recover the presence of the flux bundle and the field’s free energy, though some details of the field connectivity are lost. When the codes are applied to the forced photospheric boundary data, the reference model field is not well recovered, indicating that the combination of Lorentz forces and small spatial scale structure at the photosphere severely impact the extrapolation of the field. Preprocessing of the forced photospheric boundary does improve the extrapolations considerably for the layers above the chromosphere, but the extrapolations are sensitive to the details of the numerical codes and neither the field connectivity nor the free magnetic energy in the full volume are well recovered. The magnetic virial theorem gives a rapid measure of the total magnetic energy without extrapolation though, like the NLFFF codes, it is sensitive to the Lorentz forces in the coronal volume. Both the magnetic virial theorem and the Wiegelmann extrapolation, when applied to the preprocessed photospheric boundary, give a magnetic energy which is nearly equivalent to the value derived from the chromospheric boundary, but both underestimate the free energy above the photosphere by at least a factor of two. We discuss the interpretation of the preprocessed field in this context. When applying the NLFFF codes to solar data, the problems associated with Lorentz forces present in the low solar atmosphere must be recognized: the various codes will not necessarily converge to the correct, or even the same, solution.

The magnetic structure of convection-driven numerical dynamos

Abstract: The generation of a magnetic field in numerical simulations of the geodynamo is an intrinsically 3-D and time-dependent phenomenon. The concept of magnetic field lines and the frozen-flux approximation can provide insight into such systems, but a suitable visualization method is required. This paper presents results obtained using the Dynamical Magnetic Field line Imaging (DMFI) technique, which is a representation of magnetic field lines accounting for their local magnetic energy, together with an algorithm for the time evolution of their anchor points. The DMFI illustrations are consistent with previously published dynamo mechanisms, and allow further investigation of spatially and temporally complex systems. We highlight three types of magnetic structures: (i) magnetic cyclones and (ii) magnetic anticyclones are expelled by, but corotate with axial flow vortices; (iii) magnetic upwellings are amplified by stretching and advection within flow upwellings, and show structural similarity with helical plumes found in rotating hydrodynamic experiments. While magnetic anticyclones are responsible for the regeneration of a stable axial dipole, herewe showthat excursions and reversals of the dipole axis are caused by the emergence of magnetic upwellings, which amplify and transport a generally multipolar magnetic field from the inner to the outer boundary of the models. Geomagnetic observations suggest the presence of magnetic structures similar to those found in our models; thus,we discuss howour results may pertain to Earth's core dynamo processes. In order to make DMFI a standard tool for numerical dynamo studies, a public software package is available upon request to the authors (supplementary material is available at: http://www.ipgp.jussieu. fr/∼aubert/DMFI.html).

Rapidly changing flows in the Earth's core

Abstract: Variations in the Earth’s magnetic field over a span of a few months can be resolved despite the potential filtering effects of the electrically conducting mantle, and are indicative of rapid flow in the Earth’s outer core. A large part of the Earth’s magnetic field is generated by fluid motion in the molten outer core1. As a result of continuous satellite measurements since 1999, the core magnetic field and its recent variations can now be described with a high resolution in space and time2. These data have recently been used to investigate small-scale core flow3,4, but no advantage has yet been taken of the improved temporal resolution, partly because the filtering effect of the electrically conducting mantle was assumed to mask short-period magnetic variations5. Here we show that changes in the magnetic field occurring over only a few months, indicative of fluid flow at the top of the core, can in fact be resolved. Using nine years of magnetic field data obtained by satellites as well as Earth-based observatories, we determine the temporal changes in the core magnetic field and flow in the core. We find that the core flow is spatially localized and involves rapid variations over a few months, with surprisingly large local accelerations. Our results suggest that short-term fluctuations of the core magnetic field are robust features of rapid core dynamics and should be considered in the development of future numerical models of the geodynamo.

GRIMM: the GFZ Reference Internal Magnetic Model based on vector satellite and observatory data

Abstract: SUMMARY In this paper the new GFZ Reference Internal Magnetic Model (GRIMM) is presented. The model has been derived from nearly 6 yr of CHAMP satellite data and 5 yr of observatory hourly means. At high latitudes, full vector satellite data are used at all local times which allows a separation between, on one hand, the fields generated by ionosphere and field aligned currents, and, on the other hand, the fields generated in the Earth's core and lithosphere. This selection technique leads to a data set without gaps during the polar summers resulting in a core field model that has an unprecedented time resolution. The modelled static core field, secular variation and lithospheric field are all in good agreement with previously published magnetic field models. Order five B-splines are used to model the variation in time of the core field. The energy in the secular acceleration has, therefore, a smooth behaviour in time and increases continuously from 2003.5. Mapping the field acceleration from 2001.5 to 2005.5 reveals its rapid and complex evolution over this time period at the Earth's surface. Due to the applied regularization technique, the acceleration energy in spherical harmonics 6–11 is significantly larger than for other models and we show that such a spectrum is acceptable.

A fisk-parker hybrid heliospheric magnetic field with a solar-cycle dependence

Abstract: We present a refinement of the Fisk-Parker hybrid field of Burger and Hitge which now includes a region bordering the solar rotational equator where magnetic field footpoint motion occurs only through diffusive reconnection. The hybrid field, therefore, only occurs above a certain latitude in a given hemisphere, and in the equatorial region the field is a pure Parker field. We also propose a simple qualitative model for the solar cycle dependence of the hybrid field, taking into account changes in the tilt angle of the heliospheric current sheet and the latitudinal extend of the polar coronal hole on the photosphere and on the source surface over the course of a solar activity cycle. We find that the amplitude of magnetic field fluctuations for assumed solar minimum parameters would not be observable above the background noise (see Roberts and coworkers). We also show that for these parameters, periodicities associated with differential footpoint motion would be barely distinguishable from rigid rotation at the solar equatorial rate. We point out that the question of periodicities in magnetic field data is perhaps more complicated than previously thought. We confirm the result of Burger and Hitge that a Fisk-type heliospheric magnetic field provides a natural explanation for the observed linear relationship between the amplitude of the recurrent cosmic-ray variations and the global latitude gradient (see Zhang). We show that this relationship holds for helium, protons, and electrons. Moreover, we show that the constant of proportionality is larger when qA > 0 than when qA < 0, as inferred from observations by Richardson and coworkers.

The Global Solar Magnetic Field Through a Full Sunspot Cycle: Observations and Model Results

Abstract: Based on 11 years of SOHO/MDI observations from the cycle minimum in 1997 to the next minimum around 2008, we compare observed and modeled axial dipole moments to better understand the large-scale transport properties of magnetic flux in the solar photosphere. The absolute value of the axial dipole moment in 2008 is less than half that in the corresponding cycle-minimum phase in early 1997, both as measured from synoptic maps and as computed from an assimilation model based only on magnetogram data equatorward of 60° in latitude. This is incompatible with the statistical fluctuations expected from flux-dispersal modeling developed in earlier work at the level of 7 – 10 σ. We show how this decreased axial dipole moment can result from an increased strength of the diverging meridional flow near the Equator, which more effectively separates the two hemispheres for dispersing magnetic flux. Based on the combination of this work with earlier long-term simulations of the solar surface field, we conclude that the flux-transport properties across the solar surface have changed from preceding cycles to the most recent one. A plausible candidate for such a change is an increase of the gradient of the meridional-flow pattern near the Equator so that the two hemispheres are more effectively separated. The required profile as a function of latitude is consistent with helioseismic and cross-correlation measurements made over the past decade.

Constraints on the Magnetic Field Geometry of Magnetars

Abstract: We study the effect of the magnetic field geometry on the oscillation spectra of strongly magnetized stars. We construct a configuration of magnetic field where a toroidal component is added to the standard poloidal one. We consider a star with a type I superconductor core so that both components of the magnetic field are expelled from the core and confined in the crust. Our results show that the toroidal contribution does not influence significantly the torsional oscillations of the crust. On the contrary, the confinement of the magnetic field in the crust drastically affects the torsional oscillation spectrum. A comparison with estimations for the magnetic field strength, from observations, excludes the possibility that magnetars will have a magnetic field solely confined in the crust, that is, our results suggest that the magnetic field in whatever geometry has to permeate the whole star.

Can We Improve the Preprocessing of Photospheric Vector Magnetograms by the Inclusion of Chromospheric Observations

Abstract: The solar magnetic field is key to understanding the physical processes in the solar atmosphere. Nonlinear force-free codes have been shown to be useful in extrapolating the coronal field upward from underlying vector boundary data. However, we can only measure the magnetic field vector routinely with high accuracy in the photosphere, and unfortunately these data do not fulfill the force-free condition. We must therefore apply some transformations to these data before nonlinear force-free extrapolation codes can be self-consistently applied. To this end, we have developed a minimization procedure that yields a more chromosphere-like field, using the measured photospheric field vectors as input. The procedure includes force-free consistency integrals, spatial smoothing, and – newly included in the version presented here – an improved match to the field direction as inferred from fibrils as can be observed in, for example, chromospheric Hα images. We test the procedure using a model active-region field that included buoyancy forces at the photospheric level. The proposed preprocessing method allows us to approximate the chromospheric vector field to within a few degrees and the free energy in the coronal field to within one percent.

A uniform-twist magnetic flux rope in the solar wind

Abstract: We describe magnetic field, proton, electron, and α-particle observations made by WIND on 24–25 October, 1995 of a structure consisting of a magnetic flux rope containing a relatively low beta plasma. While the flux rope structure was inferred from the magnetic field data, the particle behavior corroborates the inference. Minimum variance analysis of the magnetic field data indicates an axis highly inclined to the ecliptic plane and pointing away from the Sun-Earth line. The diameter of the flux rope is estimated as 0.07 AU. Despite a pronounced overpressure, the structure is not expanding but is rather being convected passively with the ambient flow. An intense antisunward field-aligned flow of heat flux electrons indicates that the flux rope is connected at one end to the Sun. The field variation is suggestive of a magnetic flux rope of constant field line twist, and a least-squares fit of this model to the data confirms this to a good approximation. The field line twist per unit length is estimated as ...

The non-dipolar magnetic fields of accreting T Tauri stars

Abstract: Models of magnetospheric accretion on to classical T Tauri stars often assume that stellar magnetic fields are simple dipoles. Recently published surface magnetograms of BP Tau and V2129 Oph have shown, however, that their fields are more complex. The magnetic field of V2129 Oph was found to be predominantly octupolar. For BP Tau, the magnetic energy was shared mainly between the dipole and octupole field components, with the dipole component being almost four times as strong as that of V2129 Oph. From the published surface maps of the photospheric magnetic fields, we extrapolate the coronal fields of both stars, and compare the resulting field structures with that of a dipole. We consider different models where the disc is truncated at, or well within, the Keplerian corotation radius. We find that although the structure of the surface magnetic field is particularly complex for both stars, the geometry of the larger scale field, along which accretion is occurring, is somewhat simpler. However, the larger scale field is distorted close to the star by the stronger field regions, with the net effect being that the fractional open flux through the stellar surface is less than would be expected with a dipole magnetic field model. Finally, we estimate the disc truncation radius, assuming that this occurs where the magnetic torque from the stellar magnetosphere is comparable to the viscous torque in the disc.

An advanced approach to finding magnetometer zero levels in the interplanetary magnetic field

Abstract: For a magnetometer that measures weak interplanetary fields, the in-flight determination of zero levels is a crucial step of the overall calibration procedure. This task is more difficult when a time-varying magnetic field of the spacecraft interferes with the surrounding natural magnetic field or when the spacecraft spends only short periods of time in the interplanetary magnetic field. Thus it is important to examine the algorithms by which these zero levels are determined, and optimize them. We find that the method presented by Davis and Smith (1968 EOS Trans. AGU 49 257) has significant mathematical advantages over that published by Belcher (1973 J. Geophys. Res. 71 5509) as well as over the correlation technique published by Hedgecock (1975 Space Sci. Instrum. 1 83–90). We present an alternative derivation of the Davis–Smith method which illustrates that it is also a correlation technique. It also works with first differences as well as filtered data as input. In contrast to the postulate by Hedgecock (1975 Space Sci. Instrum. 1 83–90), we find that using first differences in general provides no advantage in determining the zero levels. Our new algorithm obtains zero levels by searching for pure rotations of the interplanetary magnetic field, with a set of sophisticated selection criteria. With our algorithm, we require shorter periods (of the order of a few hours, depending on solar wind conditions) of interplanetary data for accurate zero level determination than previously published algorithms.

Paraboloid model of Mercury's magnetosphere

Abstract: [1] A new “Paraboloidal” model of Mercury's magnetospheric magnetic field based upon the earlier terrestrial model and using similar techniques is developed. The model describes the field of Mercury's dipole, which is considered to be offset from the planet's center; the magnetopause currents driven by the solar wind; and the tail current system including the cross-tail currents and their closure currents at the magnetopause. The effect of the interplanetary magnetic field (IMF) is modeled as a partial penetration of the IMF into the magnetosphere. The goals of the present work are (1) to develop an easily usable, yet robust model of Mercury's magnetospheric magnetic field and (2) to produce an improved “unified” determination of Mercury's magnetic dipole moment which fits the measurements taken during both Mariner 10's first and third flybys. This new model of Mercury's magnetosphere is described and used to determine a best Mercury magnetic dipole moment of 192 nT RM3, from the two Mariner 10 flybys, a value which is intermediate between the various estimates produced by previous models. The best fit to the Mariner 10 measurements gives the dipole offset 0.18 RM above the equatorial plane. The new Paraboloidal model is used to predict the configuration of this miniature magnetosphere under average and extreme solar wind conditions.

An Improved Approach to Non-Force-Free Coronal Magnetic Field Extrapolation

Abstract: We develop an approach to deriving the three-dimensional non-force-free coronal magnetic field from vector magnetograms. Based on the principle of minimum dissipation rate, a general non-force-free magnetic field is expressed as the superposition of one potential field and two constant-α (linear) force-free fields. Each is extrapolated from its bottom boundary data, providing the normal component only. The constant-α parameters are distinct and determined by minimizing the deviations between the numerically computed and measured transverse magnetic field at the bottom boundary. The boundary conditions required are at least two layers of vector magnetograms, one at the photospheric level and the other at the chromospheric level, presumably. We apply our approach to a few analytic test cases, especially to two nonlinear force-free cases examined by Schrijver et al. (Solar Phys.235, 161, 2006). We find that for one case with small α parameters, the quantitative measures of the quality of our result are better than the median values of those from a set of nonlinear force-free methods. The reconstructed magnetic-field configuration is valid up to a vertical height of the transverse scale. For the other cases, the results remain valid to a lower vertical height owing to the limitations of the linear force-free-field solver. Because our method is based on the fast-Fourier-transform algorithm, it is much faster and easy to implement. We discuss the potential usefulness of our method and its limitations.

A first step in reconstructing the solar corona self-consistently with a magnetohydrostatic model during solar activity minimum

Abstract: Aims. We compute the distribution of the magnetic field and the plasma in the global corona with a self-consistent magnetohydrostatic (MHS) model. Methods. Because direct measurements of the solar coronal magnetic field and plasma are extremely difficult and inaccurate, we use a modeling approach based on observational quantities, e.g. the measured photospheric magnetic field, to reconstruct the structure of the global solar corona. We take an analytic magnetohydrostatic model to extrapolate the magnetic field in the corona from photospheric magnetic field measurement. In the model, the electric current density can be decomposed into two components: one component is aligned with the magnetic field lines, whereas the other component flows in spherical shells. The second component of the current produces finite Lorentz forces that are balanced by the pressure gradient and the gravity force. We derive the 3D distribution of the magnetic field and plasma self-consistently in one model. The boundary conditions are given by a synoptic magnetogram on the inner boundary and by a source surface model at the outer boundary. Results. The density in the model is higher in the equatorial plane than in the polar region. We compare the magnetic field distribution of our model with potential and force-free field models for the same boundary conditions and find that our model differs noticeably from both. We discuss how to apply the model and how to improve it.

Suppression of the filamentation instability by a flow-aligned magnetic field: testing the analytic threshold with PIC simulations

Abstract: The impact of a flow-aligned and spatially homogeneous magnetic field on the filamentation instability (FI) is examined in a system of two equal counterstreaming non-relativistic cool electron beams. Particle-in-cell simulations that represent the plane perpendicular to the flow velocity vector confirm the reduction of the linear growth rate by the initial magnetic field. The FI is, however, not inhibited by a magnetic field with the critical strength, for which the solution of the linear dispersion relation predicts a full suppression. The saturation of the electromagnetic fields in the plasma involves a balance between the magnetic pressure gradient and the electric field resulting from the charge displacement. The simulations demonstrate that the magnetic energy gain and the field structure upon saturation do not depend on the initial magnetic field strength. This can be explained by the qualitative similarity of the spectrum of unstable wavenumbers, at least for subcritical strengths of the background magnetic field, and by the vanishing of the pressure gradient of a spatially homogeneous magnetic field. Magnetic trapping is apparently not the saturation mechanism for the considered plasma parameters. The spatial power spectrum of the saturated magnetic fields in the simulation plane can be approximated by a power-law function and the magnetic and electric spectra are similar at high wavenumbers. The final electron velocity distributions are comparable for all magnetic field strengths.

Analysis of the magnetic field discontinuity at the potential field source surface and Schatten Current Sheet interface in the Wang–Sheeley–Arge model

Abstract: [1] The Wang–Sheeley–Arge solar wind model makes use of coupled potential field source surface (PFSS) and Schatten Current Sheet (SCS) models to reconstruct the coronal magnetic field on the basis of the observed line-of-sight photospheric magnetic field and a 1D kinematic code to propagate the solar wind to 1 AU. The source surface serves as the outer boundary of the PFSS model and the inner boundary of the SCS model. Known discontinuities arise in the tangential components of the magnetic field across this surface owing to differences in the imposed boundary conditions (Wang et al., 1998). Here we introduce a more flexible coupling between the two models, which considerably reduces the discontinuous behavior of the magnetic field across the model interface surface, to investigate the effects and importance of these kinks on the accuracy of the model's solar wind speed predictions at 1 AU. A detailed analysis of select Carrington rotations shows that removing the kinks can lead to changes in connectivity, creating different source regions for the solar wind. These changes lead to significantly improved predictions of solar wind structures at 1 AU some of the time, but most of the time, the kinks do not affect the predicted solar wind speed. This improvement is born out statistically by increases in the prediction skill scores of both solar wind velocity (1.7%) and interplanetary magnetic field polarity (1.4%) at 1 AU.

A magnetic null geometry reconstructed from Cluster spacecraft observations

Abstract: [1] This paper reports for the first time the identification of a magnetic structure around a magnetic null in a magnetic reconnection region in the magnetotail. Magnetic reconnection is one of the fundamental processes in astrophysical and solar-terrestrial plasmas. Though the concept of reconnection has been studied for many years, the process that really occurs has not been fully revealed by direct measurements. In particular, the lack of a description of three-dimensional (3-D) reconnecting magnetic field from observations makes the task more difficult. The Cluster spacecraft array provide an opportunity to reconstruct the 3-D magnetic reconnection structure based on magnetic field vectors simultaneously measured at four positions. The identification of this structure comes from a new method of analysis of in situ measurements proposed here. Applying a fitting model of 10 spherical harmonic functions and a Harris current sheet function, plus a constant field, we reconstruct a 3-D magnetic field configuration around the magnetic null in an reconnection event observed by Cluster in the geo-magnetotail.

The geomagnetic power spectrum

Abstract: SUMMARY Combining CHAMP satellite magnetic measurements with aeromagnetic and marine magnetic data, the global geomagnetic field has now been modelled to spherical harmonic degree 720. An important tool in field modelling is the geomagnetic power spectrum. It allows the comparison of field models estimated from different data sets and can be used to identify noise levels and systematic errors. A correctly defined geomagnetic power spectrum is flat (white) for an uncorrelated field, such as the Earth's crustal magnetic field at long wavelengths. It can be inferred from global spherical harmonic models as well as from regional grids. Marine and aeromagnetic grids usually represent the anomaly of the total intensity of the magnetic field. Appropriate corrections have to be applied in estimating the geomagnetic power spectrum from such data. The comparison of global and regional spectra using a consistently defined azimuthally averaged geomagnetic power spectrum facilitates quality control in field modelling and should provide new insights in magnetic anomaly interpretation.

Behavior of current sheets at directional magnetic discontinuities in the solar wind at 0.72 AU

Abstract: [1] Venus Express interplanetary magnetic field measurements have been examined for magnetic ‘‘holes,’’ accompanied by magnetic field directional changes. We examine both the thickness of the current sheet and the depth of the magnetic field depression. We find the thickness of the current sheet is not correlated with the depth of the field depression. The depth of the magnetic holes is related to directional angle change. Since total pressure should balance across these discontinuities, there must be enhanced plasma pressure within the magnetic holes. The dependence of the depth of the hole (i.e., size of the plasma pressure enhancement) on the directional changes suggests that the heating of the plasma associated with the hole formation may be provided by annihilation of the magnetic energy in the current sheet, via slow reconnection. Citation: Zhang, T. L., et al. (2008), Behavior of current sheets at directional magnetic discontinuities in the solar wind at 0.72 AU, Geophys. Res. Lett., 35, L24102, doi:10.1029/2008GL036120.

Magnetic source separation in Earth's outer core.

Abstract: We present evidence that the source of Earth's axial dipole field is largely independent from the sources responsible for the rest of the geomagnetic field, the so-called nonaxial dipole (NAD) field. Support for this claim comes from correlations between the structure of the historic field and the behavior of the paleomagnetic field recorded in precisely dated lavas at those times when the axial dipole was especially weak or nearly absent. It is argued that a "stratification" of magnetic sources exists in the fluid core such that the axial dipole is the only observed field component that is nearly immune from the influence exerted by the lowermost mantle. It follows that subsequent work on spherical harmonic-based field descriptions may now incorporate an understanding of a dichotomy of spatial-temporal dynamo processes.

Simulation study of the symmetry-breaking instability and the dipole field reversal in a rotating spherical shell dynamo

Abstract: The reversal mechanism of a dipole magnetic field generated by dynamo action in a rotating spherical shell is investigated by a three-dimensional nonlinear magnetohydrodynamic simulation as well as a linear stability analysis. The emphasis of the study is on understanding the relationship between dipole reversal and the symmetry properties of the dynamo solution. As a result, first, it is found that there is a threshold of the magnetic Prandtl number, below which the dipole field is never reversed, and above which the reversal occurs at irregular intervals like the paleomagnetic evolution of the geodynamo. Second, it is shown that the dynamo process responsible for the generation of a dipole field (called “a-dynamo” in this paper) consists only of the antimirror symmetric magnetic field and the mirror symmetric velocity field with respect to the equatorial plane. Third, it is found that the components of the opposite symmetry to the a-dynamo grow only during the polarity reversal events and quickly decay afterwards. This indicates that the dipole field reversal and the loss of equatorial symmetry are tightly connected. In fact, it is clearly demonstrated by numerical analyses that the a-dynamo process is linearly unstable for the perturbation of opposite symmetry when the magnetic Prandtl number exceeds the threshold for dipole reversal. Mode coupling between the longitudinal Fourier components plays a crucial role in creating the instability. Based on the above results, it is proposed that symmetry-breaking instability could be the mechanism for dipole field reversal in the geodynamo process. The energy conversion between components of different symmetry is also analyzed in the quasistable polarity phase and in the polarity reversal phase, respectively.

Relationship between powerful flares and dynamic evolution of the magnetic field at the solar surface

Abstract: Powerful flares are closely related to the evolution of the complex magnetic field configuration at the solar surface. The strength of the magnetic field and speed of its evolution are two vital parameters in the study of the change of magnetic field in the solar atmosphere. We propose a dynamic and quantitative depiction of the changes in complexity of the active region: E=u×B, where u is the velocity of the footpoint motion of the magnetic field lines and B is the magnetic field. E represents the dynamic evolution of the velocity field and the magnetic field, shows the sweeping motions of magnetic footpoints, exhibits the buildup process of current, and relates to the changes in nonpotentiality of the active region in the photosphere. It is actually the induced electric field in the photosphere. It can be deduced observationally from velocities computed by the local correlation tracking (LCT) technique and vector magnetic fields derived from vector magnetograms. The relationship between E and ten X-class flares of four active regions (NOAA 10720, 10486, 9077, and 8100) has been studied. It is found that (1) the initial brightenings of flare kernels are roughly located near the inversion lines where the intensities of E are very high, (2) the daily averages of the mean densities of E and its normal component (E n) decrease after flares for most cases we studied, whereas those of the tangential component of E (E t) show no obvious regularities before and after flares, and (3) the daily averages of the mean densities of E t are always higher than those of E n, which cannot be naturally deduced by the daily averages of the mean densities of B n and B t.

Effect of flux tubes in the solar wind on the diffusion of energetic particles

Abstract: Current sheets are common structures in the solar wind and possibly the boundaries of individual flux tubes. Observations show that magnetic field directions often change abruptly upon crossing these structures. The presence of these structures introduces a new source of solar wind turbulence intermittency and can affect the transport of energetic particles. Previous studies of energetic-particle transport in the solar wind often assume a uniform large-scale background magnetic field, with a turbulent field superposed. With the existence of flux tubes in the solar wind, this picture needs to be changed. In this Letter, we study the effects of flux tubes on the transport of energetic particles in the solar wind. We construct a model turbulence of the solar wind by including explicitly flux-tube-like structures. In our model, the solar wind is composed of many individual cells with a local uniform mean magnetic field chosen randomly. The turbulence in each cell is modeled by either a slab and/or 2D type. We then calculate numerically the particle diffusion coefficients by following single particle trajectories. Our results show that flux tubes in the solar wind can lead to stronger scatterings of particles in directions both parallel and perpendicular to the large-scale background magnetic field. In particular, a true diffusion in the large-scale perpendicular direction (with respect to B0) is obtained even when the local intrinsic turbulence in individual cells is of pure slab type.

MHD simulations of the global solar corona around the Halloween event in 2003 using the synchronic frame format of the solar photospheric magnetic field

Abstract: [1] We performed two time-relaxation magnetohydrodynamics (MHD) simulations of the solar corona: one uses the boundary map representing the solar surface magnetic field distribution before the Halloween event in 2003, and the other uses map representing the postevent distribution. The aims of this study are to test a new concept of a solar surface magnetic field map capable of representing a particular time of interest and to examine the coronal responses to the solar photospheric magnetic field changes occurring over a few days. We used a new mapping scheme named “synchronic frame” that can include the longitudinal shift caused by the solar differential rotation and the solar surface variations occurring at the time of interest. These two time-relaxation MHD simulations using the two maps are separately performed to numerically obtain the quasi steady states of the solar corona before and after the Halloween event. Comparisons of the simulated coronal magnetic field structures to the SOHO/EIT measurements show that the combinations of our mapping method and simulation model reproduce the changes of the coronal structures well. We also find that the consequences of solar surface variations can be seen in the plasma quantities in the solar corona. These results show the capability and importance of the solar surface magnetic field mapping scheme for better reconstruction of global coronal structures, parts of which are sensitive to the solar surface magnetic field variations.

Comparison of Heliospheric In Situ Data with the Quasi-steady Solar Wind Models

Abstract: The standard theory for the solar-heliospheric magnetic field is the so-called quasi-steady model in which the field is determined by the observed magnetic flux at the photosphere and the balance between magnetic and plasma forces in the corona. In this model, the solar magnetic flux that opens to the heliosphere can increase or decrease as the photospheric flux evolves. The most sophisticated implementation of the quasi-steady theory is the SAIC model, which solves the fully time-dependent 3D MHD equations for the corona and wind until a steady state is achieved. In order to test the quasi-steady theory, we compare the 3D MHD model with observations of the heliospheric flux using multipoint measurements from the VHM instrument on the Ulysses spacecraft from 1991 to 2005 and from magnetic field measurements from various spacecraft at L1 compiled into the OMNI data set from 1976 through 2005. We also compare the observations to the predictions of the potential-field source-surface model, an older and simpler implementation of the quasi-steady theory. During solar maximum, ICMEs significantly disturb the heliospheric magnetic field, making our comparisons difficult. We find that the MHD model compares well with the general trends of the observed heliospheric fluxes. Variations on short timescales, presumably due to local effects, are missed by the model, but the long-term evolution is well matched. The model disagrees with observations most when Ulysses is in slow wind or ICME-related flows. The model underestimates the flux at solar maximum; however, this is to be expected, given the large number of ICMEs in the heliosphere at this time. We discuss the possible sources of discrepancy between the observations and the quasi-steady models.