The effect of the neutron-star crust on the evolution of a core magnetic field

We consider the expulsion of the magnetic field from the super-conducting core of a neutron star and its subsequent decay in the crust. Particular attention is paid to a strong feedback of the distortion of magnetic field lines in the crust on the expulsion of the flux from the core. This causes a considerable delay in the core flux expulsion if the initial field strength is larger than 10¹¹ G. It is shown that the hypothesis on the magnetic field expulsion induced by the neutron-star spin-down is adequate only for a relatively weak initial magnetic field B ≈10¹¹ G. The expulsion time-scale depends not only on the conductivity of the crust, but also on the initial magnetic field strength itself. Our model of the field evolution naturally explains the existence of the residual magnetic field of neutron stars. Its strength is correlated with the impurity concentration in neutron-star crusts and anticorrelated with the initial field strengths.     

On the effect of the martian crustal magnetic field on atmospheric erosion

Without the shielding of a strong intrinsic magnetic field, the martian atmosphere directly interacts with the impacting solar wind. The neutral constituents of the atmospheric corona can be ionized, and then picked up and accelerated by the magnetic field and convection electric field in the solar wind. A significant fraction of pickup ions escape Mars’ gravitational pull and are lost to space. This non-thermal escape process of heavy species is an important mechanism responsible for atmospheric erosion. While there is a perception that the martian magnetic anomalies are significant for the ionospheric density distribution and the bow shock standoff location, little is known about the quantitative influence of the martian crustal magnetic field on the global distribution of escaping pickup ions. In this paper, we apply a newly developed Monte Carlo ion transport model to resolve the crustal field effect on the pickup oxygen ion distribution around Mars. The background magnetic and electric fields, in which test particles are followed, are calculated using an independent three-dimensional multispecies MHD model. The effects of the crustal magnetic field on particle escape are quantified by varying the crustal field orientation in the model setup and comparing the corresponding test particle simulation results. The comparison is made by turning on or off the crustal field or changing the local time of the strongest field from the dayside to the dawnside. It is found that without the protection of the crustal magnetic field, the total amount of atmospheric escape through the tail region would be enhanced by more than a factor of two. It is shown that the crustal magnetic field not only regionally deflects the solar wind around the martian atmosphere, but also has an important global effect on atmospheric erosion and thus on long-term atmospheric evolution.     

On some problems concerning the calculation of the form of the magnetopause and the electric field on the magnetopause in the framework of the continuum medium model

In order to understand the reason of the existence of the electric field in the magnetosphere, and for the theoretical evaluation of its value, it is necessary to find the solution of the problem of determination of the magnetosphere boundary form in the frameworks of the continuum medium model which takes into account part of the magnetospheric plasma movement in supporting the magnetospheric boundary equilibrium. A number of problems for finding the distribution of the pressure, the density, the magnetic field and the electric field on the particular tangential discontinuity is considered in the case when the form of discontinuity is set (the direct problem) and a number of problems for finding the form of the discontinuity and the distribution of the above-mentioned physical quantities on the discontinuity is considered when the law of the change of the external pressure along the boundary is set (for example, with the help of the approximate Newton equation). The problem which is considered here, which deals with the calculation of the boundary form and with the calculation of the distribution of the corresponding physical quantities on the discontinuity of the 1st kind for the compressible fluid with the magnetic field with field lines which are perpendicular to the plane of the flow in question, concerns the last sort of problems. The comparison of the results of the calculation with the data in the equatorial cross-section of the magnetosphere demonstrates that the calculated form of the boundary, the value of the velocity of the return flow and the value of the electric field on the magnetopause, agree satisfactorily with the observational data.     

Magnetic fields and the structure of the solar corona

Several different mathematical methods are described which use the observed line-of-sight component of the photospheric magnetic field to determine the magnetic field of the solar corona in the current-free (or potential-field) approximation. Discussed are (1) a monopole method, (2) a Legendre polynomial expansion assuming knowledge of the radial photospheric magnetic field, (3) a Legendre polynomial expansion obtained from the line-of-sight photospheric field by a least-meansquare technique, (4) solar wind simulation by zero-potential surfaces in the corona, (5) corrections for the missing flux due to magnetograph saturation. We conclude (1) that the field obtained from the monopole method is not consistent with the given magnetic data because of non-local effects produced by monopoles on a curved surface, (2) that the field given by a Legendre polynomial (which is fitted to the measured line-of-sight magnetic field) is a rigorous and self-consistent solution with respect to the available data, (3) that it is necessary to correct for the saturation of the magnetograph (at about 80 G) because fields exceeding 80 G provide significant flux to the coronal field, and (4) that a zero-potential surface at 2.5 solar radii can simulate the effect of the solar wind on the coronal magnetic field.     

Dependence of the amount of open magnetic flux on the direction of the interplanetary magnetic field

The power generated by the solar wind—magnetosphere dynamo is proportional to the amount of the open magnetic flux Φ. It is difficult to use this fact in determining observationally the dependence of Φ on the orientation of the interplanetary magnetic field vector. It is shown that, for a simple vacuum superposition of the earth's dipole field and a uniform magnetic field, Φ is very closely proportional to sin θ/2) for a wide range of the intensity of the uniform field, where θ denotes the polar angle of the interplanetary magnetic field vector in the Y-Z plane of solar-magnetospheric coordinates.     

Effects of the interplanetary magnetic field on the magnetotail structure: Large-scale changes of the plasma sheet during magnetospheric substorms

The effects of the orientation of the interplanetary magnetic field (IMF) on the structure of the distant magnetotail are studied by superposing a uniform magnetic field on a magnetospheric model. It is shown that a southward component of the IMF alone can reduce the closed field region in the magnetotail, while a northward turning of the IMF can produce a new closed field region. It is suggested that these two effects can explain thinning and thickening, respectively, of the plasma sheet during magnetospheric substorms without invoking internal instabilities.     

On the divergence of the ionospheric electric field around the westward travelling surge

The pattern of the ionospheric electric field around the westward travelling surge (WTS) is theoretically studied. This is obtained by solving the current continuity equation at the ionospheric altitude for temporal and spatial development of the field-aligned current density modelled as the WTS phenomenon. The results show that the divergence of the ionospheric electric field is significantly changed depending on the dawn-to-dusk convection electric field E₀ because of non-uniformity in the ionospheric conductivity: the ionospheric electric field diverges in the upward current region (around the head of the WTS) when a westward electric field E₀ of 10 mV m⁻¹ is uniformly applied. On the other hand, the ionospheric electric field converges without E₀. From the observational inference that the ionospheric electric field converges around the head of the WTS, it is suggested that the WTS phenomenon may not be accounted for by the discharging process in the presence of the enhanced dawn-to-dusk convection electric field and non-uniform conductivity as was studied by previous authors.     

Possible relations between the rotational axis of the Earth's inner core and the magnetic dipole axis

The geomagnetic field is maintained by amagnetohydrodynamic dynamo process within the liquid outer core. The distribution of the associated electric currents is modified if the outer core is bounded by electrically conducting material. Then, eddy currents and the related magnetic fields are generated within these regions. In particular, the relative rigid rotation of the inner core produces a secondary magnetic field, which is superimposed on the dynamo field. The angle between the dipole axis of the total field and the rotational axis of the inner core is an important quantity needed for the theory of polar motion of the Earth. This angle is investigated for a broad spectrum of angular velocities of the inner core. To simplify the mathematical procedure, we model the dynamo field using an axisymmetric field generated by a system of electric currents within the outer core. The conductivity of the mantle is neglected. We find that the position of the dipole axis depends on the angular velocity of the inner core as well as on the distribution of the current system within the outer core. Coincidence of both axes can be reached if the angular velocity is high enough and if the current system is concentrated within a thin sheet near the outer core-inner core boundary.     

An axisymmetric magnetohydrodynamic model for the interaction of the solar wind with the local interstellar medium

We numerically analyze a magnetohydrodynamic, steady-state model for the interaction of a spherically symmetric solar wind with a three-component local interstellar medium (LISM), which is composed of plasma, hydrogen atoms, and a magnetic field. The magnetic field is assumed to be parallel to the velocity in the LISM. In this case, the model is axisymmetric. We study the effects of magnetic field on the plasma-flow geometry and on the distribution of hydrogen-atom parameters. In particular, we show that the presence of hydrogen atoms does not affect the qualitative change in the shape of the bow shock, the heliopause, and the solar-wind shock with increasing strength of the interstellar magnetic field. The presence of a magnetic field in the LISM can strongly affect the parameters of the energetic hydrogen atoms originated in the solar wind, although its effect on the “hydrogen wall” observed with the GHRS instrument onboard the HST spacecraft (Linsky and Wood 1996) is marginal.     

磁重联电流片的参数变化对电子加速的影响

通过采用试验粒子的方法,研究了在有引导磁场Bz存在的磁重联电流片中,电子被super-Dreicer电场Ez加速后的运动特征.首先,考虑了引导磁场恒定且与电场有不同方向时对粒子加速的影响.在这种情况下,Bz方向的改变直接改变了电子的运动轨迹,使其沿着不同的路径离开电流片.在Bz和Ez同向时,高能电子的pitch-angle接近于180°.然而,当2者反向时,高能电子的pitch-angle接近0°.引导磁场的取向只是使电场有选择地对不同区域的电子进行加速,不会最终影响电子的能量分布,最终得到的能谱是普遍的幂率谱E-γ.在典型的日冕条件下, γ大约等于2.9.进一步的研究表明γ的大小依赖于引导磁场及磁重联电场的强弱,以及电流片的尺度.随后,也研究了包含多个X-点和O-点电流片中被加速粒子的运动特征.结果表明X-点和O-点的存在使得粒子被束缚在加速区并获得最大的加速,而且最终的能谱具有多幂率谱的特征.     

Configuration of the auroral oval and the interplanetary magnetic field

The poleward boundary of the auroral oval, whose footline forms the periphery of the polar cap, is calculated, based on a model in which the geomagnetic field is interpermeated with the interplanetary field. It is shown that the calculated auroral oval size varies with the strength and direction of the interplanetary magnetic field, in agreement with recent observations of the location of large-scale nightside auroras.     

Unified theory of the interplanetary magnetic field

A simple model is used to present a unified picture of the polarity pattern of the interplanetary magnetic field observed during the solar cycle. Emphasis in this paper is on the field near solar maximum. The heliographic latitude dependence of the dominant polarity of the interplanetary magnetic field is explained in terms of weak poloidal (dipolar) field sources in the sun's photosphere. Unlike the Babcock theory, the author hypothesizes that the dipolar field exists at equatorial latitudes (0–20°), too, (as well as in polar regions) and that the major source of the interplanetary magnetic field observed near the ecliptic plane is the dipolar field from equatorial latitudes. The polarity of the interplanetary field data taken in 1968 and in the first half of 1969 near solar maximum may possibly be explained in terms of a depression of the dipolar field boundary in space. The effect on the solar wind of the greater activity in the northern hemisphere of the sun that existed in 1968 and in the first half of 1969 is believed responsible for this hypothesized depression, especially near solar maximum, of the plane separating the + and - dipolar polarity below the solar equatorial plane in space. Predictions are made concerning the interplanetary field to be observed near the ecliptic plane in each portion of the next solar cycle.     

Stability of the solar tachocline with magnetic fields

The stability of magnetic fields in the solar tachocline is investigated. We present stability limits for higher azimuthal wave numbers and results on the dependence of the stability on the location of toroidal magnetic fields in latitude. While the dependence of the wave number with the largest growth rate on the magnetic field strength and the magnetic Prandtl number is small, the dependence on the magnetic Reynolds number Rm indicates that lowest azimuthal modes are excited for very high Rm. Upon varying the latitudinal position of the magnetic field belts, we find slightly lower stability limits for high latitudes, and very large stability limits at latitudes below 10°, with little dependence on latitude in between. An increase of the maximum possible field was achieved by adding a poloidal field. The upper limit for the toroidal field which can be stored in the radiative tachocline is then 1000 G, compared to about 100 G for a purely toroidal field as was found in an earlier work. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dependence of the solar wind speed on the coronal magnetic field in cycle 23

The dependence of the position of the solar wind sonic point on the magnetic field in the solar corona during cycle 23 is studied. This dependence is shown to be rather strong in the rising phase and at the cycle maximum. As the coronal magnetic field grows, the distance to the sonic point decreases. Since the distance to the sonic point has been shown previously to anticorrelate with the solar wind speed, the result obtained suggests a strong positive correlation between the later and the coronal magnetic field. The situation changed dramatically two years after the calendar date of the cycle maximum. Beginning in 2004 the solar wind speed ceased to depend on the magnetic field up until the cycle minimum in December 2008. In 2009 a strong dependence of the wind speed on the coronal magnetic field was restored. It is hypothesized that this effect is associated with two different coronal heating mechanisms whose relative efficiency, in turn, depends on the contribution from magnetic fields of different scales.     

On the formation of coronal cavities

We present a theoretical study of the formation of a coronal cavity and its relation to a quiescent prominence. We argue that the formation of a coronal cavity is initiated by the condensation of plasma which is trapped by the coronal magnetic field in a closed streamer and which then flows down to the chromosphere along the field lines due to lack of stable magnetic support against gravity. The existence of a coronal cavity depends on the coronal magnetic field strength; with low strength, the plasma density is not high enough for condensation to occur. Furthermore, we suggest that prominence and cavity material is supplied from the chromospheric level. Whether a coronal cavity and a prominence coexist depends on the magnetic field configuration; a prominence requires stable magnetic support.We initiate the study by considering the stability of condensation modes of a plasma in the coronal streamer model obtained by Steinolfson et al. (1982) using a 2-D, time dependent, ideal MHD computer simulation; they calculated the dynamic interaction between outward flowing solar wind plasma and a global coronal magnetic field. In the final steady state, they found a density enhancement in the closed field region with the enhancement increasing with increasing strength of the magnetic field. Our stability calculation shows that if the density enhancement is higher than a critical value, the plasma is unstable to condensation modes. We describe how, depending on the magnetic field configuration, the condensation may produce a coronal cavity and/or initiate the formation of a prominence.NRC Research Associate.     

Skinning process stability of the magnetic field in the solar active regions

Skinning process stability of the magnetic field in homogeneous plasma is studied. A set of magnetohydrodynamic equations is used. Dependence of electrical conductivity on the plasma parameters and radiation intensity in grey-body approximation are taken into account. The investigation is carried out on the model problems in linear approximation and by means of numerical solution of MHD equations. Threshold of stability and critical gradient of magnetic field in skin-layer are obtained. The model of the phenomenon proposed in the paper indicates on overheating instability of plasma with electric current in large gradient magnetic field zones as a possible trigger mechanism of solar flare origin.     

A Numerical Study of the Response of the Coronal Magnetic Field to Flux Emergence

Large-scale solar eruptions, known as coronal mass ejections (CMEs), are regarded as the main drivers of space weather. The exact trigger mechanism of these violent events is still not completely clear; however, the solar magnetic field indisputably plays a crucial role in the onset of CMEs. The strength and morphology of the solar magnetic field are expected to have a decisive effect on CME properties, such as size and speed. This study aims to investigate the evolution of a magnetic configuration when driven by the emergence of new magnetic flux in order to get a better insight into the onset of CMEs and their magnetic structure. The three-dimensional, time-dependent equations for ideal magnetohydrodynamics are numerically solved on a spherical mesh. New flux emergence in a bipolar active region causes destabilisation of the initial stationary structure, finally resulting in an eruption. The initial magnetic topology is suitable for the ??breakout?? CME scenario to work. Although no magnetic flux rope structure is present in the initial condition, highly twisted magnetic field lines are formed during the evolution of the system as a result of internal reconnection due to the interaction of the active region magnetic field with the ambient field. The magnetic energy built up in the system and the final speed of the CME depend on the strength of the overlying magnetic field, the flux emergence rate, and the total amount of emerged flux. The interaction with the global coronal field makes the eruption a large-scale event, involving distant parts of the solar surface.     

Criticism of reconnection models of the magnetosphere

Reconnection involves singular lines called X-lines on the day and night sides of the magnetosphere, and the reconnection rate is proportional to the component of the electric field along the X-line. Although there is some indirect support for this model, nevertheless direct support is totally lacking. However, there are two distinct pieces of clearly contradictory observational evidence on the dayside. First is the failure to account for the implied energy dissipation by the magnetopause current, over 10¹¹ W, which should be easily observable as heating or enhanced flow of the plasma near the magnetopause. In marked contrast to this prediction, HEOS-2 satellite data reveal a plasma with decreased energy density and reduced flow. Second, the boundary of closed magnetic field lines is in the wrong location. In the reconnection process the plasma outflow would cut across open field lines toward higher latitudes; there should be a band of open field lines equatorward of the cleft. Observations of trapped energetic particles indicate closed field lines within the entry layer and cleft. Either one of these pieces of evidence is sufficient by itself to require drastic revision, even rejection, of the reconnection model. There is also contradictory evidence on the night side. The last closed field line capable of trapping energetic particles is poleward of auroral arcs. The implication is that the X-line is at the distant magnetopause, and not in the plasma sheet. Consequently, even if the reconnection process were operative at the nightside X-line, it would be isolated from steady state plasma sheet and auroral processes. On the other hand, substorm phenomena, in which stored magnetic energy is converted into particle kinetic energy, necessarily involve an induced electric field; that is excluded in theories of the reconnection process in which it is assumed that curl E = 0. Nevertheless, the observed easy access of energetic solar flare particles to the polar caps, and especially the preservation of interplanetary anisotropies as differences between the two polar caps, argues strongly for an open magnetosphere, with interconnection between geomagnetic and inter-planetary magnetic field lines. It is suggested that the resolution of this apparent paradox involves electric fields parallel to the magnetic field lines somewhere on the dawn and dusk sides of the magnetosphere, with an equipotential dayside magnetopause.     

On the Shape of Force-Free Field Lines in the Solar Corona

This paper studies the shape parameters of looped field lines in a linear force-free magnetic field. Loop structures with a sufficient amount of kinking are generally seen to form S or inverse S (Z) shapes in the corona (as viewed in projection). For a single field line, we can ask how much the field line is kinked (as measured by the writhe), and how much neighbouring flux twists about the line (as measured by the twist number). The magnetic helicity of a flux element surrounding the field line can be decomposed into these two quantities. We find that the twist helicity contribution dominates the writhe helicity contribution, for field lines of significant aspect ratio, even when their structure is highly kinked. These calculations shed light on some popular assumptions of the field. First, we show that the writhe of field lines of significant aspect ratio (the apex height divided by the footpoint width) can sometimes be of opposite sign to the helicity. Secondly, we demonstrate the possibility of field line structures which could be interpreted as Z-shaped, but which have a helicity value sign expected of an S-shaped structure. These results suggest that caution should be exercised in using two-dimensional images to draw conclusions on the helicity value of field lines and flux tubes.     

The separation of field and fluid in the Sun

The magnetic field at the surface of the Sun is confined to widely separated small, intense magnetic flux bundles or fibrils with most of the gas in a relatively field free state in the interstices. There is evidently a systematic field and fluid separation effect in operation, overriding the tendency for turbulent mixing of the two phases. It is well known that a constantly rotating volume of fluid soon excludes any exterior magnetic field. To take the next theoretical step, this paper examines the exclusion of magnetic field from a circular cylinder with oscillating angular velocity. The result is that the field is effectively excluded from any oscillating or tumbling body of fluid that maintains coherence over a sufficiently long time. However, there is no expectation of such long term coherence in turbulent convection in the Sun, suggesting that the observed separation of field and fluid does not come about by the exclusion of field from convective cells. This leads to the conclusion that the separation of fluid and field is a consequence of extraction of fluid from the field through buoyancy and reconnection.