Current-driven plasma turbulence in a magnetic flux tube

The behaviour of a multi-component anisotropic plasma in a magnetic flux tube is studied in the presence of current-driven electrostatic ion-cyclotron turbulence. The plasma transport is considered in both parallel and perpendicular directions with respect to the given tube. As one of the sources of the parallel electric field, the anomalous resistivityof the plasma caused by the turbulence is taken into account. The acceleration and heating processes of the plasma are simulated numerically. It is found that at the upper boundary of the nightside auroral ionosphere, the resonant wave-particle interactions are most effective in the case of upward field-aligned currents with densities of a few 10^—6 A/m². The occurring anomalous resistivity maycause differences of the electric potential along the magnetic field lines of some kV. Further it is shown that the thickness of the magnetic flux tube and the intensity of the convection strongly influence the turbulent plasma heating.     

Oscillations of flux tube bundles and the structure of sunspot magnetic fields

Observational aspects of the previously found quasi-hourly oscillations of magnetic fragments in sunspot polar coordinates are investigated. The orientation of the oscillations is shown to be azimuthally anisotropic, with their amplitude reaching a maximum in penumbra at a distance of ～0.8 sunspot radius (the maximum amplitude is estimated to be 3700 km). Based on the detected deviations of the oscillations from the radial direction, we numerically simulate the horizontal configuration of field lines in the region of the major spots in bipolar groups.     

Magnetostatic configuration of a confined magnetic flux tube

In this paper an isolated magnetic flux tube confined in stratified atmosphere is studied for slender and axisymmetric model. The functions of the pressure, density, and temperature are expanded as a Taylor series of magnetic surface function . Several models of an isolated magnetic flux tube confined in a stratified atmosphere are constructed, and the external pressure of the stratified atmosphere decreases reasonably with increasing height. The distribution of thermal dynamic quantities and the magnetic pressure in the flux tube are also obtained.     

Small-scale magnetic flux tube diagnostics in a solar flare

I ±V profiles of the Fei 5247 and 5250 lines in the 2B flare of June 16, 1989 have been analyzed. A bright knot of the flare outside the sunspot where the central intensity of H reached a peak value of 1.4 (relative to the continuum) has been explored. The Fei 5250/Fei 5247 magnetic line ratio based on the StokesV peak separations of these lines at five evolutionary phases of the flare (including the start of the flare, the flash phase, the peak and 16 min after the peak) has been analyzed. It was found that the StokesV peak separation for the Fei 5250 line was systematically larger than that of the Fei 5247 line. This is evidence for the presence in the flare of small-scale flux tubes with kG fields. The flux tube magnetic field strength was about 1.1 kG at the start of the flare and during the flash phase, 1.55 kG during the peak, and 1.38 kG 16 min after the peak. The filling factor,, appears to decrease monotonically during the flare.     

Magnetic flux tube in a stratified atmosphere under the influence of the vertical magnetic field

The magnetohydrostatic equilibrium of a magnetic flux tube in a homogeneous gravitational and vertical magnetic field is studied. Gas pressure and density are presented explicitly as a function of the external magnetic field. The influence of the external magnetic field on the magnetic and thermodynamic structures is illustrated by two exact solutions. The possible applications to sunspot and facular modeling are discussed.Work done at the Space Environment Laboratory, NOAA/ERL, Boulder, CO 80303, U.S.A.     

What is a flux tube? On the magnetic field topology of buoyant flux structures

We study the topology of field lines threading buoyant magnetic flux structures. The magnetic structures, visually resembling idealized magnetic flux tubes, are generated self-consistently by numerical simulation of the interaction of magnetic buoyancy and a localized velocity shear in a stably stratified atmosphere. Depending on the parameters, the system exhibits varying degrees of symmetry. By integrating along magnetic field lines and constructing return maps, we show that, depending on the type of underlying behaviour, the stages of the evolution, and therefore the degree of symmetry, the resulting magnetic structures can have field lines with one of three distinct topologies. When the x -translational and y -reflectional symmetries remain intact, magnetic field lines lie on surfaces but individual lines do not cover the surface. When the y symmetry is broken, magnetic field lines lie on surfaces and individual lines do cover the surface. When both x and y symmetries are broken, magnetic field lines wander chaotically over a large volume of the magnetically active region. We discuss how these results impact our simple ideas of a magnetic flux tube as an object with an inside and an outside, and introduce the concept of 'leaky' tubes.     

The stability of a magnetic flux element in a horizontally stratified compressible plasma

The configuration of a magnetic flux element in a static, compressible, gravitationally stratified plasma is considered. Under isothermal conditions an exact force-free solution is given for a two-dimensional cartesian flux sheath but for an axi-symmetric element, i.e. a flux tube, approximate solutions, applicable only to thin flux tubes, are obtained.When the isothermal condition is relaxed within the flux tube, non-force-free solutions are obtained exhibiting either a temperature excess or deficit on the axis of the flux tube. Using these solutions, the total potential energy of such a tube and its surroundings may be calculated. By comparing this with the total energy of an equivalent system ofn flux tubes the temperature excess or deficit in these tubes corresponding to the adiabatic subdivision of the single tube is determined.It is shown that under non-adiabatic conditions the subdivision process must be endothermic (i.e., external energy is required) if the temperature within the original tube is significantly less than its surroundings but exothermic if the temperatures are comparable. Thus it is conjectured that magnetic structures are less susceptible to subdivision if they are significantly cooler than their surroundings.     

To the description of long-term variations in the solar magnetic flux: The sunspot area index

We show that the Wolf sunspot numbers W and the group sunspot numbers GSN are physically different indices of solar activity and that it is improper to compare them. Based on the approach of the so-called “primary” indices from the observational series of W(t) and GSN(t), we suggest series of yearly mean sunspot areas beginning in 1610 and monthly mean sunspot areas beginning in 1749.     

Equilibrium of a thin,isolated, axisymmetric force-free magnetic flux tube in a stratified atmosphere

We show that up to second order in the thinness parameter, the equations of equilibrium of a thin, isolated, axisymmetric, force-free magnetic flux tube in a stratified atmosphere and the other essential constraints form a mathematically closed system. Auxiliary assumptions about temperature of the tube plasma are neither needed nor possible.     

3-D non-linear evolution of a magnetic flux tube in a spherical shell: The isentropic case

We present recent 3-D MHD numerical simulations of the non-linear dynamical evolution of magnetic flux tubes in an adiabatically stratified convection zone in spherical geometry, using the anelastic spherical harmonic (ASH) code.We seek to understand the mechanism of emergence of strong toroidal fields from the base of the solar convection zone to the solar surface as active regions. We confirm the results obtained in cartesian geometry that flux tubes that are not twisted split into two counter vortices before reaching the top of the convection zone. Moreover, we find that twisted tubes undergo the poleward-slip instability due to an unbalanced magnetic curvature force which gives the tube a poleward motion both in the non-rotating and in the rotating case. This poleward drift is found to be more pronounced on tubes originally located at high latitudes. Finally, rotation is found to decrease the rise velocity of the flux tubes through the convection zone, especially when the tube is introduced at low latitudes. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on the values of the vertical gradient of the magnetic field in the return flux sunspot model

The Return Flux (RF) sunspot model (Osherovich, 1982) imposes a restriction on the value of the vertical gradient of the magnetic field, dB/dz, analogous to a restriction implied by the self-similar sunspot model of Schlüter and Temesvary (ST). The maximum value of the gradient, (dB/dz)_max, is shown to be 10% smaller in the RF model than in the ST model. The dependence of (dB/dz)_max on the sunspot radius is predicted.     

Configuration of the chromospheric magnetic field in a unipolar sunspot region

A set of H chromospheric magnetograms at various wavelengths near the line center, chromospheric Dopplergrams, and photospheric vector magnetograms of a unipolar sunspot region near the solar limb were obtained with the vector video magnetograph at the Huairou Solar Observing Station. The superpenumbral chromospheric magnetic field is almost parallel to the surface at the outside of the sunspot penumbra, where the magnetic lines of force are mainly concentrated in the superpenumbral filaments. In the gaps between the filaments the chromospheric horizontal field is weak.     

Large-scale flow and transport of magnetic flux in the solar convection zone

Horizontal large-scale velocity field describes horizontal displacement of the photospheric magnetic flux in zonal and meridian directions. The flow systems of solar plasma, constructed according to the velocity field, create the large-scale cellular-like patterns with up-flow in the center and the down-flow on the boundaries. Distribution of the largescale horizontal eddies (with characteristic scale length from 350 to 490 Mm) was found in the broad equatorial zone, limited by 60‡ latitude circles on both hemispheres. The zonal averages of the zonal and meridian velocities, and the total horizontal velocity for each Carrington rotation during the activity cycles no. 21 and 22 varies during the 11-yr activity cycle. Plot of RMS values of total horizontal velocity is shifted about 1.6 years before the similarly shaped variation of the magnetic flux.     

Studies of grand minima in sunspot cycles by using a flux transport solar dynamo model

We propose that grand minima in solar activity are caused by simultane- ous fluctuations in the meridional circulation and the Babcock-Leighton mechanism for the poloidal field generation in the flux transport dynamo model. We present the following results： （a） fluctuations in the meridional circulation are more effective in producing grand minima; （b） both sudden and gradual initiations of grand minima are possible; （c） distributions of durations and waiting times between grand minima seem to be exponential; （d） the coherence time of the meridional circulation has an effect on the number and the average duration of grand minima, with a coherence time of about 30 yr being consistent with observational data. We also study the occurrence of grand maxima and find that the distributions of durations and waiting times between grand maxima are also exponential, like the grand minima. Finally we address the question of whether the Babcock-Leighton mechanism can be operative during grand minima when there are no sunspots. We show that an a-effect restricted to the upper portions of the convection zone can pull the dynamo out of the grand minima and can match various observational requirements if the amplitude of this a-effect is suitably fine-tuned.     

The use of abnormal quiet days in Sq(H) for predicting the magnitude of sunspot maximum at the time of preceding sunspot minimum

The previously established connection between the occurence of AQDs (“abnormal quiet days” when the phase of the solar diurnal variation of horizontal magnetic field, Sq(H), at a mid-latitude northern hemisphere station is anomalous) at sunspot minimum and the magnitude of the following sunspot maximum is examined in the light of our recent improved understanding of the nature and cause of AQDs. A small contribution to the relationship is found to arise from variations from cycle to cycle in the additional northward field which is characteristic of AQDs and leads to a reduced Sq(H) amplitude at stations poleward of the Sq focus. However, the main factor which determines the connection is a variation from one sunspot minimum to another of the amplitude of the small southward bay-like field perturbations which constitute the AQD events, and evidence is presented which suggests that this parameter may be quantitatively related to the extent of southward swing of the B_z component of the interplanetary magnetic field which determines the energy transfer from the solar wind into the magnetospheric tail. It thus appears that the magnitude of southward swing in B_z might be another solar parameter which anticipates the size of a forthcoming sunspot cycle during its build-up over the declining phase of the previous cycle and at the minimum.     

Effect of magnetic flux advection on the dynamics of shock in accretion flow around a rotating black hole

We investigate the dynamical behavior of a magnetized, dissipative accretion flow around a rapidly rotating black hole. We solve the magnetohydrodynamic equations and calculate the transonic accretion solutions which may contain discontinuous shock transitions. We investigate the effect of ζ-parameter(parametrizing the radial variation of the toroidal magnetic flux advection rate) on the dynamical behavior of shocks. For a rapidly rotating black hole and for fixed injection parameters at the outer edge, we show that stationary shocks are sustained in the global magnetized accretion solutions for a wide range of ζ and accretion rate( ˙m). To investigate the observational implications, we consider dissipative shocks and estimate the maximum accessible energy from the post-shock corona(PSC) for nine stellar mass black hole candidates. We compare this with the observed radio jet kinetic power reported in the literature, whenever available. We find close agreement between the estimated values from our model and those reported in the literature.     

Observations of the longitudinal magnetic field in the transition region and photosphere of a sunspot

The Ultraviolet Spectrometer and Polarimeter on the Solar Maximum Mission spacecraft has observed for the first time the longitudinal component of the magnetic field by means of the Zeeman effect in the transition region above a sunspot. The data presented here were obtained on three days in one sunspot, have spatial resolutions of 10 arc sec and 3 arc sec, and yield maximum field strengths greater than 1000 G above the umbrae in the spot. The method of analysis, including a line-width calibration feature used during some of the observations, is described in some detail in an appendix; the line width is required for the determination of the longitudinal magnetic field from the observed circular polarization.The transition region data for one day are compared with photospheric magnetograms from the Marshall Space Flight Center. Vertical gradients of the magnetic field are computed from the two sets of data; the maximum gradients of 0.41 to 0.62 G km^–1 occur above the umbra and agree with or are smaller than values observed previously in the photosphere and low chromosphere.     

Detection of opposite polarities in a sunspot light bridge: evidence of low-altitude magnetic reconnection

A multiwavelength photometric analysis was performed in order to study the sub-structure of a sunspot light bridge in the photosphere and the chromosphere. Active region NOAA 8350 was observed on 1998 October 8. The data consist of a 100 min time series of 2D spectral scans of the lines Fe  i 5576 Å, Hα 6563 Å, Fe  i 6302.5 Å, and continuum images at 5571 Å. We recorded line-of-sight magnetograms in 6302.5 Å. The observations were taken at the Dunn Solar Telescope at US National Solar Observatory, Sacramento Peak. We find evidence for plasma ejection from a light bridge followed by Ellerman bombs. Magnetograms of the same region reveal opposite polarity in light bridge with respect to the umbra. These facts support the notion that low-altitude magnetic reconnection can result in the magnetic cancellation as observed in the photosphere.     

The latitude of filament bands at the sunspot minimum and the activity level in the two following 11-year solar cycles

The zonal structure of the distribution of filaments is considered. The mean latitudes of two filament bands are calculated in each solar hemisphere at the minima of the sunspot cycle in the period 1924–1986: middle latitude _{2, m} and low latitude _{1, m} . It is shown that the mean latitude of the filament band _{2, m} at the minimum -m of the cycle correlates, with = 0.94, with the maximum - M sunspot area S(M) and maximum Wolf number W(M) in the succeeding solar cycle M. It is shown that the mean latitude of the low-latitude filament band _{1, m} is linearly dependent on the mean latitude filament band _{2, m + 1} at the succeeding minimum. We found a correlation of the latitude of the low-latitude filament band _{1, m} with the maximum sunspot area in the M + 1 cycle. This enables us to predict the power of two succeeding 11-year solar cycles on the basis of the latitude of filament bands at the minimum of activity, 1985–1986: W(22) - 205 ± 10, W(23) - 210 ± 10. The importance of the relationships found for theory and applied aspects is emphasized. An attempt is made to interpret the relationships physically.     

String cosmological model in the presence of a magnetic flux

A Bianchi type I string cosmological model in the presence of a magnetic flux is investigated. A few plausible assumptions regarding the parametrization of the cosmic string and magneto-fluid are introduced and some exact analytical solutions are presented.